url
stringlengths 14
1.76k
| text
stringlengths 100
1.02M
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|
https://archive.softwareheritage.org/browse/content/sha1_git:71f0dcd362c07934208b45ce3f47caf7e4e5cff1/?branch=refs/tags/R-2.9.1&origin_url=https://github.com/cran/FSelector&path=dae20ad128f7a6c25ad0b5549aeb61d89e08c315/man/cfs.Rd
|
We are hiring ! See our job offers.
##### https://github.com/cran/FSelector
Tip revision: 893e2d9
cfs.Rd
\name{cfs}
\alias{cfs}
\title{ CFS filter }
\description{
The algorithm finds attribute subset using correlation and entropy measures for continous and discrete data.
}
\usage{
cfs(formula, data)
}
\arguments{
\item{formula}{ a symbolic description of a model }
\item{data}{ data to process }}
\details{
The alorithm makes use of \code{\link{best.first.search}} for searching the attribute subset space.
}
}
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2047247290611267, "perplexity": 22276.26355057883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572870.85/warc/CC-MAIN-20220817062258-20220817092258-00394.warc.gz"}
|
https://www.scielo.br/j/rarv/a/fgNkWhxBR9KRYdPKCnH7QXG/?lang=en
|
# ABSTRACT
Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. Creep may change the purely elastic parameters determined in wood characterization initial tests, as its behavior depends on the rheology of the material, even under a constant stress level. Mathematically, creep can be characterized by models in which the immediate elastic deformation is increased by a viscous deformation, resulting in a temporal function. For this reason, the calculation of the natural frequency of vibration and the stability verification of a slender column should include the reducing effects of stiffness both of axial force and creep. The first one can be considered through the geometrical portion and the second one by the introduction, in the conventional portion, of a variable elasticity modulus over time, obtained in relation to the adopted rheological model. A numerical simulation was performed to evaluate the aspects above, considering a bar compressed by a force at the free end equivalent to 10% of the Euler critical force, plus its own weight, adopting a rheological model with three parameters for the variation of the elasticity modulus. The results show differences of 60% and 50% for the frequency and elasticity modulus, besides defining the exact instant of column collapse in the case of its non-observance.
Keywords:
Three-parameter model; Vibration; Stability
# RESUMO
Palavras-chave:
Modelo de três parâmetros; Vibração; Estabilidade
# 1. INTRODUCTION
The slow increase of deformation under constant stress over time is called creep. Mathematically, creep can be represented by a time-dependent function associated with viscoelastic rheological models capable of describing the phenomenon, according to Findley; Lai; Onaran (1989)FINDLEY, W.N.; LAI, J.S.; ONARAN, K. Creep and relaxation of nonlinear viscoelastic materials, whit an introduction to linear viscoelasticity. New York: Dover Publications, 1989.. The slow deformation, or creep, in wooden structures, is a time-dependent phenomenon, which is also related to loads and deformations, defined as the increase of deformation under the action of loads, or permanent stresses, over time. Creep produces residual deformation and can change the characteristics of the materials and their mechanical properties, and it is even able to produce the failure of a structure, as reported by Gottron; Harries; Xu (2014)GOTTRON, J.; HARRIES, K.A.; XU, Q. Creep behaviour of bamboo. Construction and Building Materials, v.66, p.79-88, 2014.. When wooden structures are used as horizontal components and loaded, they undergo long-term deformation and, in different humidity conditions, the wood has a tendency to increase its deformation due to creep, which can lead to operational problems due to excessive deformation, or may cause safety problems due to loss of resistance, which can decrease the load capacity and, in the case of columns, reach the buckling stress, emphasize Epmeier; Johansson; Kliger; Westin (2007)EPMEIER, H.; JOHANSSON, M.; KLIGER, R.; WESTIN, M., Bending creep performance of modified timber. Holz als Roh- und Werkstoff, v.65, p.343-351, 2007..
In general, two types of criteria are used to represent the creep within the structural design. The first one is related to a deformation limit value, restricting it to validity intervals, and the second one, less common, takes into account a monotonic growth of deformation. From a practical point of view, the technical standards take into account the creep phenomenon in the design of structures by two considerations: by proposing a coefficient of increase or decrease of stiffness, or proposing a coefficient of increase or decrease in resistance as the loading acting time and humidity class, according to Celia-Silva; Calil Junior (1992)CELIA-SILVA, A.H.; CALIL JÚNIOR, C. Fluência da madeira. In: ENCONTRO BRASILEIRO EM MADEIRAS E EM ESTRUTURAS DE MADEIRA, 1992, São Carlos. Anais... São Carlos: Lamem/Eesc-Usp, EESC - Escola de Engenharia de São Carlos, 1992.. The decrease in stiffness is related to the fact that the axial force is responsible for this effect and can lead to loss of stability of a column. In this sense, Gambhir (2004)GAMBHIR, M.L. Stability analysis and design of structures. Berlin: Heidelberg, Springer, 2004. refers to the influence of the compressive force highlighting that once there is a reduction in the structural stiffness, the effect of the loads on the structure increases, which also increases the forces on the elements, so the structure resistance capacity decreases. For this reason, in the case of compressed columns, a premature analysis can produce undesirable consequences, and any failure causes catastrophic effects since it involves the balance of structures, Timoshenko (1992)TIMOSHENKO, G. Mecânica dos sólidos. 2.ed. Rio de Janeiro: Livros Técnicos e Científicos, 1992..
Regarding the study of wood mechanical properties, it is a typically elastic or elastoplastic material, depending on the level to which it is subjected. Its behavior, concerning the elasticity, is considered as anisotropic, i.e., a material whose elastic properties vary with the considered direction, differently from an isotropic material, which keeps its properties constant regardless of direction. During tree growth, the internal structure of the solid material which consists of wood becomes highly oriented; for this reason, it is an anisotropic material. On a macroscopic level, the arrangement of the wood structure results from both length and diametral growth processes. Therefore, wood structure is usually referred to two privileged axes: the longitudinal direction (L) along the fiber and on the radial direction (R) in relation to the annual growth rings. The direction (T) is tangential to the annual growth rings. The three orthogonal planes (RT), (RL) and (LT) are then three planes of symmetry to the internal structure of wood, as explained by Oudjehane; Raclin (1995)OUDJEHANE, A.; RACLIN, J. On the influence of orientation upon the mechanical behavior of oakwood in a general state of stress. Wood Science and Technology, v.29, p.1-10, 1995.. Wood anisotropy also results from its cell structure, which is most composed of fibrous material, which will influence its apparent mechanical properties. The anisotropy changes the vibrational properties of viscoelastic materials, i.e., it modifies the structural dynamics since it depends on the elastic or Young's modulus (E0) and shear (G0), changing the standard of modes and vibration frequencies, said by Brémaud; Gril; Thibaut (2011)BRÉMAUD I.; GRIL, J.; THIBAUT, B. Anisotropy of wood vibrational properties: dependence on grain angle and review of literature data. Wood Science Technology, v.45, p.735-754, 2011..
Wood anisotropy is well represented by the mentioned orthotropic model, which takes the longitudinal, radial and tangential directions, with elastic parameters for each of them. That means there is a modulus of elasticity and poison coefficient for each of these directions, making impossible to operate the known linear elastic relationship, specific to isotropic material, between these parameters to determine the transversal elasticity modulus. Accordingly, creep, given the considerations presented in this study, is characterized by specific deformation analyzed in the longitudinal direction of the column, which varies with time, and whose elastic reference is the elasticity modulus parallel to fibers. In line with this approach, Schniewind; Barrett (1972)SCHNIEWIND, A.P.; BARRETT, J.D. Wood as a linear orthotropic viscoelastic material. Wood Science and Technology, v.6, p.43-57, 1972. state that wood can be considered as an orthotropic viscoelastic material. They observed that for certain purposes and under certain conditions, the analysis of stress on wood can be considered as linear elastic and viscoelastic and that the region of viscoelastic behavior is large and has considerable practical importance. A mathematical approach on creep which includes the three directions of wood orthotropy was developed in the sixties of the twentieth century (BHATNAGAI; GUPTA, 1967BHATNAGAI, N.S.; GUPTA, R.P. "On the constitutive equations of the orthotropic theory of creep". Wood Science and Technology, v.1, p.142-148, 1967.).
Because of its plastic behavior, even with a constant level of tension, the deformations in structural elements of wood tend to increase with time, i.e. after the initial elastic deformations, additional deformations occur, which can be reversible or not, but never complete. The slow creep is partially reversible. For an unloading, after elastic recovery, there is a later recovery, which is called slow recoverable deformation, slow reversible deformation, or delayed elastic deformation, and only a remaining portion of the deformation is residual or irreversible, being this portion of deformation called creep, Leohard; Mong (1977)LEOHARD, F.; MONG, E. Construções de concreto - princípios básicos do dimensionamento de estruturas de concreto armado. Rio de Janeiro: Interciência, 1977. v.1..
Commonly, the representation of creep is based on rheological models, which associate deformations deferred at the time. These models, according to Gomes et al (2007)GOMES, E.A.S.; DANTAS NETO, A.A.; BARROS NETO, E.L.B.; LIMA, F.M.; SOARES, R.G.F.; NASCIMENTO, R.E.S., Aplicação de modelos reológicos em sistemas: Parafina/Solvente/Tensoativo, 4º PDPETRO, 3.1.0197 - 1. Campinas: 2007., allow to simulate the response of the material to forces and tensions applied to it. The inclusion of these rheological models can be made both in static analysis and dynamic of the structures. In the case of dynamic analysis, the structure stiffness must be composed of two terms; the first one corresponding to the portion of conventional stiffness and the second to the portion of geometric stiffness, according to Clough; Penzien (1993)CLOUGH, R.W.; PENZIEN, J. Dynamic of structures. 2.ed. Taiwan: McGraw Hill International, 1993.. Thus, it is possible to adapt the first portion of stiffness by introducing a variable elasticity modulus over time, making possible to monitor the increase of deformations, according to the adopted rheological model, keeping a constant stress level. Therefore, the total stiffness assumes the form introduced by the first portion, via elasticity modulus, in the rheological model intended to represent the creep; and the second portion is geometrical, which is a function of normal operating force, which includes the own weight of the structural element.
A numerical simulation was performed to evaluate the creep in natural frequency and in the stability of a slender wood column, taking into account a three-parameter model to represent its viscoelastic behavior. The formulation developed to calculate the column natural frequency of vibration was based on the method of virtual works and allowed the evaluation of the buckling critical load and loss of system instability, besides calculating the frequency of the first mode. The results indicated significant differences in the fundamental frequency and elastic modulus, considering values obtained by a purely elastic analysis and those non-linear with the creep, in relation to the material, and geometric value considering the geometric stiffness. It was also possible to define the exact moment of the column collapse in the case of non-observance of creep, considering a force of 10% of the critical load of Euler concentrated at the free end of the structural element. Comparison with design criteria and verification for parts in flexo-compression and stability of the NBR 7190 - Wooden Structures Design (1996)ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT - NBR 7190/1996. Projeto de Estruturas de Madeira. Rio de Janeiro: 1996. were adopted for this level of loading, as well as the definition of the limit percentage of the Euler critical load, which leads the system to the collapse, using these same criteria and mathematical tools developed in the present study.
# 2. MATERIAL AND METHODS
## 2.1 Mathematical simulation support
The rheological models used to represent the viscoelastic behavior of fluids and solids are usually based on the association of springs and dampers that predict total deformations and try to describe more appropriately the behavior of each material or group of materials, as presented in Figure 1. The model of Group I (Figure 1a), for example, represents bodies that have an initial elastic deformation and viscous deformation that occurs over time, so this model is more suitable for the description of certain solids. The model of Group II (Figure 1b) describes the behavior of liquids simulating an initial viscous outflow and a slow elastic deformation over time. The model of Group III (Figure 1c) shows an instantaneous elastic response followed by a viscous response with a slow deformation as well. The model of Group IV (Figure 1d) simultaneously presents two slow viscous deformations over time. These models can be used alone or in associations, forming chains, in an attempt to obtain the best representation for each situation.
Figura 1
Viscoelastic rheological models.
Figura 1
Modelo reológicos viscoelásticos.
One of the models more used to represent the creep in several materials is the three-parameter model, in which an elastic parameter E0 is associated with a viscoelastic model of parameters E1 and η1 called Kelvin-Voigt model, which is a simplification of the Burgers model of Group type I (Figure 1a). According to Keramat; Shirazi (2014)KERAMAT, A.; SHIRAZI, K.H. Finite element based dynamic analysis of viscoelastic solids using the approximation of Volterra integrals. Finite Elements in Analysis and Design, v.86, p.89-100, 2014., a single model of the Kelvin-Voigt is enough to describe the viscoelastic nature of many solid. Based on this consideration an adaptation of the Burgers model was used by Kränkel; Lowke; Gehlen (2015)KRÄNKEL, T.; LOWKE, D.; GEHLEN, C. Prediction of the creep behaviour of bonded anchors until failure - A rheological approach. Construction and Building Materials, v.75, p.458-464, 2015. to analyze the non-linear viscoelastic deformation in bonded anchors. In relation to the wood, Mukudai (1983)MUKUDAI, J. Evaluation of linear and non-linear viscoelastic bending loads of wood as a function of prescribed deflections. Wood Science Technology, v.17, p.203-216, 1983. mentions that the functional form represented by the Voigt and Maxwell models is very efficient since they can be conveniently applied to assess the viscoelastic behavior of that material through mathematical models. In this sense Hering; Niemz (2012)HERING, S.; NIEMZ, P. Moisture-dependent, viscoelastic creep of European beech wood in longitudinal direction. European Journal Wood Production, v.70, p.667-670, 2012. have used the Kelvin-Voigt model, together with experimental activity to descript the creep in bended pieces. A Burger chain of four elements was used by Gao; Wang; Shao (2016)GAO, H.; WANG, F.; SHAO, Z. Study on the rheological model of Xuan paper, Wood Science Technology, v.50, p.427-440, 2016. to study the behavior of Xuan paper, making possible to description convenientily the elastic, viscoelastic and plastic deformations presented by the material.
The adoption of Kelvin-Voigt model has repeatedly been made to study phenomena in various science fields. Hackney; Aifantis; Tangtrakarn; Shrivastava (2012)HACKNEY, S.A.; AIFANTIS, K.E.; TANGTRAKARN, A.; SHRIVASTAVA, S. Using the Kelvin-Voigt model for nanoindentation creep in Sn-C/PVDF nanocomposites. Materials Science and Technology, v.28, n.9-10, p.1161-1166, 2012. used this model to examine the creep behavior of nanostructures of composites. In the context of the finite element method, Chung; Tamma; Namburu (2000)CHUNG, P.W.; TAMMA, K.K.; NAMBURU, R.R. A finite element thermo-viscoelastic creep approach for heterogeneous structures with dissipative correctors. Finite Elements in Analysis and Design, v.36, p.279-313, 2000. used the Kelvin-Voigt model to represent the primary creep to investigated the thermo-viscoelastic of composite structures. Puertas; Gallego (2014)PUERTAS, E.; GALLEGO, R. Función de Green para el problema elastodinámico armónico en un semiespacio con amortiguamiento histerético. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.4, p.247-255, 2014. used the same model, together with the boundary element method, to consider the viscoelasticity in the solution of the three-dimensional dynamic problems.
Mathematically, the total deformation of the Kelvin-Voigt model is given by equation (1),
(1) $ε = ε e + ε v ,$
where ee is the deformation in the elastic model and ev is the deformation in the plastic model. Take into account its derivative relative to time, the total deformation of the model is found by equation (2), which is the constitutive equation of the Kelvin-Voigt model.
(2) $ε = ε ˙ e + ε ˙ v ,$
The equation (3), for this specific case, is obtained by assuming E0 = E1 = Ec0ef ,
(3) $σ = E c 0 ef ε e and σ = E c 0 ef ε v + η 1 ε v .$
From the previous equations, it is obtained the differential equation (4) for the Kelvin-Voigt model, with t representing the moment of load application.
(4) $σ ˙ + E c 0 ef + E c 0 ef η 1 σ = E c 0 ef ε ˙ + E c 0 ef E c 0 ef η 1 ε , where σ = 0 , for t < 0 σ 0 , for ⪖ 0$
As the stress is constant, the derivative of stress relative to time is null. By applying the above stress conditions, the equation (4) is reduced to equation (5), which is an ordinary differential equation,
(5) $E c 0 ef ε ˙ + E c 0 ef E c 0 ef η 1 ε = σ 0 ,$
whose general solution, for t > 0, with the initial condition $ε(0)=σ0Ec0ef$ is given by equation (6).
(6) $ε ( t ) = σ 0 1 E c 0 ef + 1 E c 0 ef 1 − e − E c 0 ef η 1 t .$
Obviously, if the stress level remains constant, the elasticity modulus must simultaneously reduce to as the deformation increases, then:
(7) $E ( t ) = 1 1 E c 0 ef + 1 E c 0 ef 1 − e − E c 0 ef η 1 t$
After finding the variable elasticity modulus over time, it is necessary to establish the conditions for an analysis of vibrations that, from the point of view of structural dynamics, make possible the obtainment of the temporal variation of the system natural frequency. One of the classic methods is the Modal Analysis. This method allows the obtainment of information about the behavior of a structural system and therefore reveals important aspects related to its dynamics, such as frequencies and natural modes of vibration, according to Carrion; Mesquita; Ansoni (2014)CARRION, R.; MESQUITA, E.; ANSONI, J.L. "Dynamic response of a frame-foundation-soil system: a coupled BEM-FEM procedure and a GPU implementation". Journal of the Brazilian Society of Mechanical Sciences and Engineering, v.37, n.4, p.1055-1063, 2014.. In addition, it is possible to verify the stability of a structural system and the moment of its collapse, based on the nullability conditions of the fundamental frequency and, consequently, its stiffness.
The formulation developed in this simulation to consider the creep in the vibration of a column is based on the principle of virtual works associated with the Rayleigh technique, which suggests that for a system containing infinite degrees of freedom can be associated with another system with a single degree of freedom to bring its frequency closer, as described by Leissa (2004)LEISSA, A.W. The historical bases of the Rayleigh and Ritz methods. Journal of Sound and Vibration, v.287, n.4-5, p.961-978, 2004.. The process takes into account the suitable choice of the generalized coordinate that describes the structure deformation, considering the first vibration mode. In the end, the equation of motion appears regarding the generalized system properties such as stiffness and mass, which are necessary to calculate the frequency. It is important to note that the technique developed by Rayleigh aimed to calculate the fundamental frequency of vibration of elastic systems, and the precision obtained by this method depends directly on the function chosen to represent this vibration mode, as also said by Leissa (2004)LEISSA, A.W. The historical bases of the Rayleigh and Ritz methods. Journal of Sound and Vibration, v.287, n.4-5, p.961-978, 2004..
The basic concept of the method is the principle of conservation of energy, and can, therefore, apply to linear structures (or not), according to Clough; Penzien (1993)CLOUGH, R.W.; PENZIEN, J. Dynamic of structures. 2.ed. Taiwan: McGraw Hill International, 1993.. Temple; Bickley (1933)TEMPLE, G.; BICKLEY, W.G. Rayleigh´s principle and its applications to engineering. London: Oxford University Press, 1933. consider that the Rayleigh technique is applied both to systems with infinite degrees of freedom and continuous systems, and serves both to determine the fundamental period of vibration and to verify the stability of mechanical systems, but it is not limited to these purposes. As seen in studies carried out by Villasenor; Farfán; Guzmánb; Romero; Castellanos; Sesma (2014)VILLASENOR, E.O.; FARFÁN, J.N.; GUZMÁNB, N.F.; ROMERO, M.C.; CASTELLANOS, A.R.; SESMA, F.J.S. Propagación de ondas de Rayleigh en medios con grietas. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.1, p.35-41, 2014., the Rayleigh technique was used in the detection of subsurface cracks in solids. Pena (2015)PENA, F. Modelo simplificado para el estudio del balanceo asimétrico de cuerpos rígidos esbeltos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.31, n.1, p.1-7, 2015. studied the asymmetric vibration of rigid bodies, considering the damping of Rayleigh in the context of small rotations, allowing the mathematical simplification of the problem. Cámara and Astiz (2014)CÁMARA, A.; ASTIZ, M.Á. "Aplicabilidad de las diversas estrategias de análisis sísmico en puentes atirantados en rango elástico". Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.1, p.42-50, 2014. used the form function technique as recommended by Rayleigh in the dynamic modal analysis of cable-stayed bridges, within the region of elastic deformation of the material.
It is considered the model of the bar in Figure 2, of length L, in a free motion non-damping free motion, with the generalized coordinate q(t) defined on the upper end of the element. The function v(x,t) provides the horizontal displacements for each x position along the height, in relation to a function φ(x) that describes the form of the vibration and meets the boundary conditions of the problem. It is assumed this system is composed of a prismatic bar, made of a viscoelastic material, clamped on its the base, supporting, in addition to its own weight m, a mass m0 at the free end, representative of bodies fixed to its top. N(x) is the normal generalized force and e(t) is the vertical displacement of the bar.
Figure 2
Mathematical model.
Figura 2
Modelo matemático.
It is also considered that the system motion does not change the direction of the normal force. Thus, the represented structure is a bar in bending, so that the virtual work of internal forces δWI is performed by the bending moment M(x,t), acting on the deflection of the virtual bar. It is assumed that the section remains flat after deformation. The Principle of Virtual Works requires that the virtual work of external forces is equal to the virtual work of the internal forces. The virtual work of the external forces is obtained by equation (8),
(8) $δ W E = − ∫ 0 L f 1 ( x ) δ v ( x ) dx + N ( x ) δ e ,$
in which the is fI(x) = m1(x) v(x,t) the inertial force. In turn, the virtual work of the internal forces is given by equation (9).
(9) $δ W I = ∫ 0 L M ( x , t ) δ v ″ ( x ) dx , com δ v ″ ( x ) = δ ∂ 2 v ( x ) ∂ x 2 .$
An infinitesimal element ds of the curved bar is required to find the axial displacement e(t). The shortening of the axis due to the axial displacement is given by equation (10).
(10) $ds − dx = dx 2 − dv 2 − dx = dx 1 + dv dx 2 − dx .$
From the binomial development, considering that the higher order terms are smaller compared to the first order term, the initial series can be reduced, as observed in equation (11).
(11) $1 + dv dx 2 1 2 = 1 + dv dx 2 2 − dv dx 4 8 + dv dx 6 16 − ... ⇒ 1 + dv dx 2 1 2 = 1 + dv dx 2 2 ,$
The reduction of the series by the binomial development allows rewriting equation (10) into a more compact form, as shown in equation (12).
(12) $ds − dx = dx 1 + 1 2 dv dx 2 − dx = 1 2 dv dx 2 .$
The total displacement e(t) throughout the column comes from the integration of equation (12), as indicated in equation (13) in which the first derivative of that function is represented by an upper row to the right.
(13) $e ( t ) = 1 2 ∫ 0 L v ′ ( x , t ) 2 dx .$
The real and virtual displacements and their derivatives, with the same notation established in equation (13), which are expressed in function of the generalized coordinate and the chosen shape function to represent the considered vibration mode, are calculated by equation (14).
(14) $v ( x , t ) = φ ( x ) q ( t ); v ¨ ( x , t ) = φ ( x ) q ¨ ( t ); δ v ′ ( x , t ) = φ ( x ) ′ q ( t ); v ′ ( x , t ) = φ ′ ( x ) q ( t ); v ″ ( x , t ) = φ ″ ( x ) q ˙ ( t ); δ v ″ ( x , t ) = φ ( x ) ″ δ q ( t ); v ″ ( x , t ) = φ ″ ( x ) q ( t ); δ v ( x , t ) = φ ( x ) δ q ( t ); δ e = ∫ 0 L v ′ ( x , t ) δ v ′ ( x ) dx .$
Appropriately substituting the equations (13) and (14) in the equations (8) and (9), the equations (15) and (16) are obtained.
(15) $δ W E = − q ¨ ( t ) ∫ 0 L m 1 ( x )( φ ( x )) 2 dx + q ( t ) ∫ 0 L N ( x )( φ ′ ( x )) 2 dx δ q e$
(16) $δ W I = q ( t ) ∫ 0 L E ( t ) I φ ″ ( x ) 2 dx δ q .$
By equating the expressions (15) and (16) and adjusting the terms, the equation of the free undamped motion appears regarding the generalized coordinate q(t), as equation (17),
(17) $M q ¨ ( t ) + K 0 ( t ) q ( t ) − K g q ( t ) = 0 ,$
in which M, K0 and Kg are the generalized mass and the generalized conventional and geometric stiffness, described from the chosen form function $φ(x)=1−cosπx2L$. By assuming the trigonometric function to describe the vibratory motion, the generalized conventional stiffness is given by equation (18),
(18) $K 0 ( t ) = ∫ 0 L E ( t ) I d 2 φ ( x ) dx 2 2 dx ,$
where E(t) is the variable modulus of elasticity with time, as shown in equation (7), and I is the inertia of the section in relation to the considered motion. The generalized geometric stiffness is calculated by equation (19),
(19) $K g = ∫ 0 L N ( x ) d φ ( x ) dx 2 dx ,$
in which N(x) = [m0 +m (L - x)]g is the normal force function, which includes the own weight of the column and the force concentrated at the free end. The generalized mass is obtained by equation (20),
(20) $M = m 0 + m , with m = ∫ 0 L m ¯ ( φ ( x )) 2 dx ,$
where m0 is the mass concentrated at the top of the bar and m is the mass per unit length obtained by multiplying the section area by the density of the material. As the natural frequency depends directly on the total stiffness and inversely on the mass, it should be calculated by equation (21).
(21) $ω ( t ) = K ( t ) M ( in r d / s ), with K ( t ) = K 0 ( t ) − K g .$
Therefore, the equation of the frequency of the first mode of vibration, in Hertz, which includes the geometric effect and creep, is finally provided by equation (22),
(22) $f ( t ) = 1 2 π 1 32 π 4 L 3 E ( t ) I − 1 16 π 2 g 2 m 0 + mL ¯ L + 1 4 mg ¯ m 0 + 1 2 mL ¯ 3 π − 8 π 1 2 ( in HZ ),$
in which L is the length of the column, g is the gravity acceleration and E(t) the temporal elastic modulus as found in equation (7). In equation (22), it can be observed the conventional portion of the stiffness of the column to the left of the negative sign in the numerator, in which is included the variable elasticity modulus due to creep, and the stiffness geometric portion to the right of the same sign, in which it is considered the force concentrated at the free end of the column by mass m0 in addition to its own weight by the parameter m, which is the mass distributed per unit length, both multiplied by the gravity acceleration. In the denominator is the generalized mass of the system, where there is a factor of 0.227 multiplying the product mL. This fact induces which buckling critical load of the column is seen decreased from this value, when the own weight of the structural element is introduced, which is in line with Timoshenko (1992)TIMOSHENKO, G. Mecânica dos sólidos. 2.ed. Rio de Janeiro: Livros Técnicos e Científicos, 1992. who predicted, in static analysis, that this factor would be of the order 1/3.
By applying the equation (22), it is performed, using a single mathematical operation and at once, a non-linear material analysis, with the creep, and a geometric non-linear analysis, with the effect of the normal force, dispensing the use of computational tools or iterative calculations. It is worth mentioning that the equation (22) was comparatively evaluated by experimental activity, in physical laboratory, and by modeling using the finite element method - FEM, by Wahrhaftig; Brasil; Balthazar (2013)WAHRHAFTIG, A.M.; BRASIL, R.M.L.R.F., BALTHAZAR, J.M., The first frequency of cantilever bars with geometric effect: a mathematical and experimental evaluation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, v.35, n.4, p.457-467, 2013., and again using the FEM by Wahrhaftig and Brasil (2016)WAHRHAFTIG, A.M.; BRASIL, R.M.L.R.F. Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast. Journal of the Brazilian Society of Mechanical Sciences and Engineering. (2016), studying the frequency of a real structure, considering for both studies, linear and isotropic elastic material, presenting excellent convergence of results in both cases.
## 2.2 Evaluated model problem
For this simulation, a composite section wooden column was idealized, with the parameters of interest shown in Table 1. The adopted gravity acceleration g was 9.81 m/s2. The characteristic parallel resistance to fibers (fc0k) and the elastic modulus (Eco) were adopted considering class wood C-60. The effective elastic modulus and calculating the resistance of the material were defined according to the recommendations of NBR 7190/1996 - Wood Structural Design (1996)ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT - NBR 7190/1996. Projeto de Estruturas de Madeira. Rio de Janeiro: 1996., according to equation (23). The used weighting and modification coefficients were: Kmod1 = 0.7, Kmod2 = 1.0, Kmod3 = 0.8 and γwc= 1.4, then:
(23) $K mod = K mod 1 · K mod 2 · K mod 3 = 0 . 7 · 1 . 0 · 0 . 8 = 0 . 56 ∴ E c 0 ef = K mod E c 0 = 0 . 56 · 24500 = 13720 MPa and f cod = K mod f cok γ wc = 0 . 56 60 1 . 4 = 24 MPa .$
Table 1
Data of numerical simulation
Tabela 1
Dados da simulação numérica.
The numerical simulation was performed based on a column of height L and cross section as represented in Figure 3. The arrangement of the composite section was defined within a design reality typical of wooden structures and in function of the commercial limitations of laminated and glued wood, which had already been adopted in a design carried out by Wahrhaftig and Carvalho (2016)WAHRHAFTIG, A.M.; CARVALHO, R. Design and construction of wooden structure to replace collapsed steel structure, practice periodical on structural design and construction. Practice Periodical on Structural Design and Construction, v.21, n.3, Aug. 2016.. It is important to mention that the viscous parameter was adjusted so that the deformations stabilized at 90 days, as shown in Figure 4(a), as indicated by Almeida (1990)ALMEIDA, P.A.O. "Estruturas de Grande Porte de Madeira". Tese (Doutorado em Engenharia Civil) - São Paulo: EPUSP, 1990., Celia-Silva; Calil Júnior (1992)CELIA-SILVA, A.H.; CALIL JÚNIOR, C. Fluência da madeira. In: ENCONTRO BRASILEIRO EM MADEIRAS E EM ESTRUTURAS DE MADEIRA, 1992, São Carlos. Anais... São Carlos: Lamem/Eesc-Usp, EESC - Escola de Engenharia de São Carlos, 1992. and Kataoka; Bittencourt (2014)KATAOKA, L.T.; BITTENCOURT, T.N. Análise numérica e experimental da transferência de carga do concreto para a armadura em pilares. Revista IBRACON de Estruturas e Materiais, v.7, n.5, p.747-774, 2014.. Thus, the variation of the elastic modulus E(t) was obtained, represented by Figure 4 (b).
Figure 3
Model of the structure.
Figura 3
Modelo da estrutura.
Figure 4
Results obtained by the numerical simulation.
Figura 4
Resultados obtidos na simulação numérica.
It is emphasized the need to reduce the section inertia moment by multiplying it by a reduction factor of 0.7, since it is a composite section, constructed with screws, which is an important procedure to provide protection against plastic accommodation, specific of wooden connections, which was studied by Kharouf; Mcclure; Smith (2003)KHAROUF, N.; MCCLURE, G.; SMITH, I. Elasto-plastic modeling of wood bolted connections. Computers and Structures, v.81, p.747-754, 2003. and Wilkinson; Rowland; Cooks (1981)WILKINSON, T.L; ROWLAND, R.E.; COOKS, R.D. An incremental finite-element determination of stresses around loaded holes in wood plates. Computers and Structures, v.14, n.I-2, p.123-128, 1981..
# 3. RESULTS
The column section was verified in relation to the flexocompression and stability according to the criteria of NBR 7190/1996 - Wooden Structures Design (1996)ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT - NBR 7190/1996. Projeto de Estruturas de Madeira. Rio de Janeiro: 1996., proving to be able, as the results presented in equation (24), in which KM = 0.5, and equation (25), respectively.
(24) $σ Ncd f c 0 d + σ Md f c 0 d + K M σ Md f c 0 d ≤ 1 , σ Ncd = N cd A = 173 . 504 N 0 . 18 m 2 = 0 . 964 MPa , σ Md = M d y I = 4851 . 07 Nm · 0 . 45 m 0 . 002 m 4 = 0 . 684 MPa ∴ 0 . 964 24 + 0 . 684 24 + 0 . 5 0 . 684 24 = 0 . 07 .$
(25) $σ Md f c 0 d + σ Md f c 0 d ≤ 1 , 0 . 964 24 + 0 . 684 24 = 0 . 06 .$
In equations (24) and (25), σNd, σMd and fc0d are the calculation stresses due to the normal stress and bending moment, and calculation resistance to parallel compression to the fibers, obtained according to equations (26), with the results shown as MPa (106 Pa; Pa = N/m2). The force concentrated at the free end of the bar, which induces the stresses σNcd and σMd was established to represent one-tenth of the Euler force (FE) expected in equation (26)(c) where φ = 0.8, ψ1 = 0.6 and ψ2 = 0.4 are the creep coefficients appropriate to the case under study.
In equation (26) subindices c for N, E and γ mean compression; E in F is the buckling critical force of Euler; for e, the subindice i means initial, a accidental, c creep; for w in g means weighting. Regarding the stress conditions in the design g and q in N, they indicate variable and permanent actions; k means characteristic, d for the design and ef effective value, calculated with the modification coefficients, shown in section 2.2.
(26) $M d = N cd e d = 4851 . 07 Nm , with N cd = N ck γ wc = 173504 . 051 N , N ck = m 0 g = 123931 . 46 N , γ wc = 1 . 4 , e d = e 1 ef F E F E − N cd = 2 . 796 cm , with F E = π 2 E c 0 ef I x L b 2 = 1239314 . 65 N , e 1 ef = e i + e a + e c , with e i = M k N ck = 0 , e a = L 300 = 2 . 2 cm , and e c = e ig + e a exp φ N gk + ψ 1 + ψ 2 N qk F E − N gk + ψ 1 + ψ 2 N qk − 1 = 2 . 405 cm .$
# 4. DISCUSSION
The frequency of the column was then numerically calculated at the instants zero and 90 by equation (22), as shown in Figure 4(c) and Figure 4(d). In the first case, the frequency variation was obtained by considering the original height of the column, adopted to obtain the limit slenderness established by the NBR 7190/1996 - Wooden Structures Design (1996)ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT - NBR 7190/1996. Projeto de Estruturas de Madeira. Rio de Janeiro: 1996.. In the second case, the height of the column was designed to initiate its collapse at 90 days, defining thus the limit height it can have when the creep is introduced in the frequency calculation. In the first condition, the column is stable, whereas in the second case, the creep effect leads to loss of stability at the considered instant (90 days). Any height of the structure which is defined between the stability limit at 90 days (second condition) and the limit established without creep, i.e., stability at instant zero (first condition), puts at risk the system equilibrium, which can be observed in Figure 4(e). For a height of 8 m, for example, the collapse would occur on the 16th day.
# 5. CONCLUSION
The elasticity modulus of 6865.265 MPa calculated by equation (7), at 90 days, represents a 50% decrease compared to the initial value of 13720 MPa. The structure frequency calculated at the initial time of loading is 0.262 Hz, and at 90 days is 0.106 Hz, representing a decrease of 60%. The column reaches its stability limit at the height of 7.35 m (slenderness of 156.19), collapsing at 90 days. Without considering the creep effect, the height limit is 10.37 m, at instant zero (slenderness of 220.41); a height of 29.14% higher than the previous one. This aspect is of great importance because, since if the height of the structure had been defined between the limit established without the creep and the limit determined considering the creep, the structure would collapse even before completing 90 days in service. For a height of 8 m (slenderness of 169.99), e.g., the collapse would occur close to the 16th day.
It can be concluded that the slenderness limit of 140, established by the Brazilian Standard, keeps the structure in safety condition regarding the loss of stability, considering a force 10% of the Euler force concentrated at the free end of the column. Additionally, it can be added that the safety limit condition is established by equation (24) for a critical load of 44.41% of the Euler Force at the end of the structure when it is simultaneously evaluated by equation (22).
# 6. REFERENCES
• ALMEIDA, P.A.O. "Estruturas de Grande Porte de Madeira". Tese (Doutorado em Engenharia Civil) - São Paulo: EPUSP, 1990.
• ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS - ABNT - NBR 7190/1996. Projeto de Estruturas de Madeira Rio de Janeiro: 1996.
• BHATNAGAI, N.S.; GUPTA, R.P. "On the constitutive equations of the orthotropic theory of creep". Wood Science and Technology, v.1, p.142-148, 1967.
• BRÉMAUD I.; GRIL, J.; THIBAUT, B. Anisotropy of wood vibrational properties: dependence on grain angle and review of literature data. Wood Science Technology, v.45, p.735-754, 2011.
• CÁMARA, A.; ASTIZ, M.Á. "Aplicabilidad de las diversas estrategias de análisis sísmico en puentes atirantados en rango elástico". Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.1, p.42-50, 2014.
• CARRION, R.; MESQUITA, E.; ANSONI, J.L. "Dynamic response of a frame-foundation-soil system: a coupled BEM-FEM procedure and a GPU implementation". Journal of the Brazilian Society of Mechanical Sciences and Engineering, v.37, n.4, p.1055-1063, 2014.
• CELIA-SILVA, A.H.; CALIL JÚNIOR, C. Fluência da madeira. In: ENCONTRO BRASILEIRO EM MADEIRAS E EM ESTRUTURAS DE MADEIRA, 1992, São Carlos. Anais.. São Carlos: Lamem/Eesc-Usp, EESC - Escola de Engenharia de São Carlos, 1992.
• CHUNG, P.W.; TAMMA, K.K.; NAMBURU, R.R. A finite element thermo-viscoelastic creep approach for heterogeneous structures with dissipative correctors. Finite Elements in Analysis and Design, v.36, p.279-313, 2000.
• CLOUGH, R.W.; PENZIEN, J. Dynamic of structures 2.ed. Taiwan: McGraw Hill International, 1993.
• EPMEIER, H.; JOHANSSON, M.; KLIGER, R.; WESTIN, M., Bending creep performance of modified timber. Holz als Roh- und Werkstoff, v.65, p.343-351, 2007.
• FINDLEY, W.N.; LAI, J.S.; ONARAN, K. Creep and relaxation of nonlinear viscoelastic materials, whit an introduction to linear viscoelasticity New York: Dover Publications, 1989.
• GAMBHIR, M.L. Stability analysis and design of structures Berlin: Heidelberg, Springer, 2004.
• GAO, H.; WANG, F.; SHAO, Z. Study on the rheological model of Xuan paper, Wood Science Technology, v.50, p.427-440, 2016.
• GEORGE, B.; SIMON, C.; PROPERZI, M.; PIZZI, A. Comparative creep characteristics of structural glulam wood adhesives. Holz als Roh- und Werkstoff, v.61, 79-80, 2003.
• GOMES, E.A.S.; DANTAS NETO, A.A.; BARROS NETO, E.L.B.; LIMA, F.M.; SOARES, R.G.F.; NASCIMENTO, R.E.S., Aplicação de modelos reológicos em sistemas: Parafina/Solvente/Tensoativo, 4º PDPETRO, 3.1.0197 - 1. Campinas: 2007.
• GOTTRON, J.; HARRIES, K.A.; XU, Q. Creep behaviour of bamboo. Construction and Building Materials, v.66, p.79-88, 2014.
• HACKNEY, S.A.; AIFANTIS, K.E.; TANGTRAKARN, A.; SHRIVASTAVA, S. Using the Kelvin-Voigt model for nanoindentation creep in Sn-C/PVDF nanocomposites. Materials Science and Technology, v.28, n.9-10, p.1161-1166, 2012.
• HERING, S.; NIEMZ, P. Moisture-dependent, viscoelastic creep of European beech wood in longitudinal direction. European Journal Wood Production, v.70, p.667-670, 2012.
• HONFI, D.; MARTENSSON, A.; THELANDERSSON, S.; KLIGER, R. Modelling of bending creep of low- and hightemperature-dried spruce timber. Wood Science Technology, v.48, p.23-36, 2014.
• KATAOKA, L.T.; BITTENCOURT, T.N. Análise numérica e experimental da transferência de carga do concreto para a armadura em pilares. Revista IBRACON de Estruturas e Materiais, v.7, n.5, p.747-774, 2014.
• KERAMAT, A.; SHIRAZI, K.H. Finite element based dynamic analysis of viscoelastic solids using the approximation of Volterra integrals. Finite Elements in Analysis and Design, v.86, p.89-100, 2014.
• KHAROUF, N.; MCCLURE, G.; SMITH, I. Elasto-plastic modeling of wood bolted connections. Computers and Structures, v.81, p.747-754, 2003.
• KRÄNKEL, T.; LOWKE, D.; GEHLEN, C. Prediction of the creep behaviour of bonded anchors until failure - A rheological approach. Construction and Building Materials, v.75, p.458-464, 2015.
• LEISSA, A.W. The historical bases of the Rayleigh and Ritz methods. Journal of Sound and Vibration, v.287, n.4-5, p.961-978, 2004.
• LEOHARD, F.; MONG, E. Construções de concreto - princípios básicos do dimensionamento de estruturas de concreto armado. Rio de Janeiro: Interciência, 1977. v.1.
• MUKUDAI, J. Evaluation of linear and non-linear viscoelastic bending loads of wood as a function of prescribed deflections. Wood Science Technology, v.17, p.203-216, 1983.
• OUDJEHANE, A.; RACLIN, J. On the influence of orientation upon the mechanical behavior of oakwood in a general state of stress. Wood Science and Technology, v.29, p.1-10, 1995.
• PENA, F. Modelo simplificado para el estudio del balanceo asimétrico de cuerpos rígidos esbeltos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.31, n.1, p.1-7, 2015.
• PUERTAS, E.; GALLEGO, R. Función de Green para el problema elastodinámico armónico en un semiespacio con amortiguamiento histerético. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.4, p.247-255, 2014.
• REYNOLDS, T.; HARRIS, R.; CHANG, W-S. Viscoelastic embedment behaviour of dowels and screws in timber under in-service vibration. European Journal Wood Production, v.71, p.623-634, 2013.
• SAIFOUNI, O.; DESTREBECQ, J.F.; FROIDEVAUX, J.; NAVI, P. Experimental study of the mechanosorptive behaviour of softwood in relaxation. Wood Science Technology, v.50, p.789-805, 2016.
• SCHNIEWIND, A.P.; BARRETT, J.D. Wood as a linear orthotropic viscoelastic material. Wood Science and Technology, v.6, p.43-57, 1972.
• SHARAPOV, E.; MAHNERT, K.C.; MILITZ, H. Residual strength of thermally modified Scots pine after fatigue testing in flexure. European Journal of Wood and Wood Products, (2016).
• TEMPLE, G.; BICKLEY, W.G. Rayleigh´s principle and its applications to engineering London: Oxford University Press, 1933.
• TIMOSHENKO, G. Mecânica dos sólidos 2.ed. Rio de Janeiro: Livros Técnicos e Científicos, 1992.
• VILLASENOR, E.O.; FARFÁN, J.N.; GUZMÁNB, N.F.; ROMERO, M.C.; CASTELLANOS, A.R.; SESMA, F.J.S. Propagación de ondas de Rayleigh en medios con grietas. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, v.30, n.1, p.35-41, 2014.
• WAHRHAFTIG, A.M.; BRASIL, R.M.L.R.F. Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast. Journal of the Brazilian Society of Mechanical Sciences and Engineering (2016)
• WAHRHAFTIG, A.M.; BRASIL, R.M.L.R.F., BALTHAZAR, J.M., The first frequency of cantilever bars with geometric effect: a mathematical and experimental evaluation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, v.35, n.4, p.457-467, 2013.
• WAHRHAFTIG, A.M.; CARVALHO, R. Design and construction of wooden structure to replace collapsed steel structure, practice periodical on structural design and construction. Practice Periodical on Structural Design and Construction, v.21, n.3, Aug. 2016.
• WANG, J.B.; FOSCHI, R.O.; LAM, F. Duration-of-load and creep effects in strand-based wood composite: a creep-rupture model. Wood Science Technology, v.46, p.375-391, 2012a.
• WANG, J.B.; LAM, F.; FOSCHI, R.O. Duration-of-load and creep effects in strand-based wood composite: experimental research. Wood Science Technology, v.46, p.361-373, 2012a.
• WILKINSON, T.L; ROWLAND, R.E.; COOKS, R.D. An incremental finite-element determination of stresses around loaded holes in wood plates. Computers and Structures, v.14, n.I-2, p.123-128, 1981.
# Publication Dates
• Publication in this collection
Nov-Dec 2016
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 54, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7148800492286682, "perplexity": 4486.658517366279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711376.47/warc/CC-MAIN-20221209011720-20221209041720-00285.warc.gz"}
|
https://socratic.org/questions/the-larger-of-two-numbers-is-23-less-than-twice-the-smaller-if-the-sum-of-the-tw
|
Algebra
Topics
# The larger of two numbers is 23 less than twice the smaller. If the sum of the two numbers is 70, how do you find the two numbers?
39, 31
#### Explanation:
Let $L$ & $S$ be the larger & smaller numbers respectively then
First condition:
$L = 2 S - 23$
$L - 2 S = - 23 \setminus \ldots \ldots \ldots . \left(1\right)$
Second condition:
$L + S = 70 \setminus \ldots \ldots . . \left(2\right)$
Subtracting (1) from (2), we get
$L + S - \left(L - 2 S\right) = 70 - \left(- 23\right)$
$3 S = 93$
$S = 31$
setting $S = 31$ in (1), we get
$L = 2 \left(31\right) - 23 = 39$
Hence, the larger number is $39$ & smaller number is $31$
##### Impact of this question
578 views around the world
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8575744032859802, "perplexity": 875.5438631491808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251694176.67/warc/CC-MAIN-20200127020458-20200127050458-00165.warc.gz"}
|
https://krntneja.github.io/posts/2018/attention-based-models-2
|
# Tutorial on Attention-based Models (Part 2)
Published:
In part one of this series, I introduced the fundamentals of sequence-to-sequence models and attention-based models. I briefly mentioned two sequence-to-sequence models that don't use attention and then introduced soft-alignment based models. In this post, I’m going to discuss about various monotonic attention mechanisms.
### 3.2. Monotonic Alignments
Monotonic alignments are motivated by the limitations of soft alignments i.e. the quadratic-time complexity and no option for online decoding. The mechanisms discussed achieve quadratic-time training but linear-time decoding and the facility of online decoding as well.
3.2.1. Hard Monotonic Mechanism [paper]
Hard monotonic alignments attend to exactly one vector in memory $h_j$ at output time step $i$ i.e. $c_i = h_j$, unlike soft alignments which use expectation over complete memory to calculate the context vector.
If model attends to the input time step $t_{i-1}$ at the output time step $i-1$, we calculate the energy of $h_j$ where $j \in \{t_{i-1}, t_{i-1}+1, \ldots, T\}$ i.e. starting from the memory previously used. We pass each energy output through the logistic sigmoid function to produce 'selection probability' $p_{i, j}$ and sample $z_{i, j}$ from $Bernoulli(p_{i, j})$.
&&e_{i, j} = MonotonicEnergy(s_{i-1},h_j)&&
&&p_{i,j} = \sigma(e_{i,j})&&
&&z_{i,j} = Bernoulli(p_{i,j})&&
As soon as we see $z_{i, t_i} = 1$, we stop and use $h_{t_i}$ as our context vector and repeat the above process starting from input time step $t_i$ at output time step $i$. If $z_{i, j} = 0~\forall~j\in\{t_{i-1}, t_{i-1}+1, \ldots, T\}$, we set $c_i = \mathbf{0}$.
Here is an example of output time step of hard monotonic mecchanism. Here $t_{i-1} = 3$ is the index of memory vector selected at previous step. Model, therefore, starts from $h_3$ and moves forward until it finds $z_{i,7}=1$. Hence, $h_7$ is selected as $c_i$ and we say that $t_i=7$.
Note that the above model only needs $h_k, k\in\{1, 2, \ldots,j\}$ to compute $h_j$. If we use a unidirectional RNN as the encoder, we can perform online decoding where the time complexity will be $\mathcal{O}(\max\{T, U\})$. Also note that, because of sampling, we cannot train this model using back-propagation. We, therefore, use the expectation of $h_j$ during training (inspired from soft alignments) and try to induce discreteness into $p_{i,j}$ to later decode monotonically. The $\alpha_{i,j}$ defines the probability that input time step $j$ is attended at output time step $i$. We go through a simple, worded derivation below for the calculation of $\alpha_{i,j}$. (You can skip it in the first pass of reading.)
&&\alpha_{i, j} = \mathbb{P}_i(h_j\text{ used}) = \mathbb{P}_i(h_j\text{ used}|h_j\text{ checked})\mathbb{P}_i(h_j\text{ checked})&&
&&\mathbb{P}_i(h_j\text{ used}|h_j\text{ checked}) = p_{i,j}&&
&&\mathbb{P}_i(h_j\text{ checked}) = \mathbb{P}_i(h_{j-1}\text{ not used}, h_{j-1}\text{ checked}) + \mathbb{P}_{i-1}(h_j\text{ used}|j\text{ checked})&&
Two possible cases are depicted when $h_j$ is a candidate for context vector. First case on left: $h_j$ is candidate because $h_{j-1}$ was rejected i.e. $z_{i,j-1}=0$. Second case on right: model starts from $h_j$ itself as it was the last used context vector i.e. $c_{i-1}=h_j$ or $t_{i-1} = j$.
The last relation can be reasoned out by noting that $h_j$ will be a candidate for context vector either when $h_{j-1}$ is rejected or $h_j$ itself was selected as context vector in previous output time step $i-1$. Using above relations for memory vector $h_{j-1}$, we get the relations
&&\mathbb{P}_i(j-1\text{ checked}) = \frac{\alpha_{i,j-1}}{p_{i,j-1}}&& &&\mathbb{P}_i(j-1\text{ not used}|j-1\text{ checked}) = 1-p_{i,j-1}&&
Finally putting all relations together, we get
&&\alpha_{i,j} = p_{i,j} \Big((1-p_{i,j-1})\frac{\alpha_{i,j-1}}{p_{i,j-1}} + \alpha_{i-1,j}\Big)&&
which can also be written as following, allowing us to compute this parallelly by writing it in terms of cumulative products and cumulative sums.
&&q_{i,j} = \frac{\alpha_{i,j}}{p_{i,j}} = (1-p_{i,j-1})q_{i,j-1} + \alpha_{i-1,j}&&
A tricky way to promote discreteness, a zero-mean unit-variance Gaussian noise is added to logistic sigmoid activation. This forces the model to learn to produce $p_{i,j}$ close to zero or one, effectively making it binary.
Energy function used for hard monotonic alignments is as follows:
&&\text{MonotonicEnergy}(s_{i-1},h_j) = g\frac{v^T}{||v||}\tanh(W_s s_{i-w}+W_h h_j+b)+r&&
It is very similar to Bahdanau energy function but a little different because sigmoid function applied on monotonic energy is not shift-invariant like the softmax function. Therefore, for giving in more control on values of energy, the vector $v$ in Bahdanau energy is replaced by a normalized vector $\frac{v}{||v||}$ and then scaled with a scalar $g$ and offset with a scalar $r$. As you might guess, $g$ and $r$ are also learned parameters.
3.2.2. Monotonic Chunkwise Mechanism [paper]
Hard monotonic alignments which I just described are just too hard in their conditions! Using only one vector $h_{t_i}$ as context vector $c_i$ is a little too much constraint and this is reflected in its poor performance on some tasks. A novel solution to this problem is Monotonic Chunkwise Mechanism.
We use a middle path between soft alignments and hard monotonic alignments by allowing the model to use soft attention over fixed-size chunks (say, size $w$) of memory ending at input time step $t_i$ for each output time step $i$. Therefore, model uses a context vector derived from memory elements ${h_{v}, h_{v+1}, \ldots h_{t_i}}$ where $v= t_i-w+1$. The memory index $t_i$ is derived in the same way as in the hard monotonic mechanism. The energy of each memory element is given by the following equation.
&&u_{i,k} = \text{ChunkEnergy}(s_{i-1}, h_k) = v^T \tanh(W_{s}s_{i-1} + W_{h}h_j + b)&&
A diagram showing the flow of monotonic chunkwise mechanism. Notice that a soft alignment over a chunk of size $w=4$ is applied in addition to monotonic attention. First, using mechanism explained in an earlier figure, $h_7$ is selected. Then a soft alignment is used over a chunk ending at $h_7$.
The context vector is given by a weighted sum of $w$ memory elements ending at $t_i$. This is exactly applying soft-alignment over small chunks!
&&c_i = \sum_{k=v}^{t_i}\frac{\exp(u_{i,k})}{\sum_{l=v}^{t_i}\exp(u_{i,l})}h_k&&
Similar to the training in the hard monotonic mechanism, we need to take expected value of context vector by using the induced probability distribution. We use the $\alpha_{i,j}$ derived for the hard monotonic mechanism. Given below is (another!) worded derivation of $\beta_{i,j}$ which is the probability of using $h_j$ as context vector for output time step $i$.
&&\beta_{i,j}=\mathbb{P}_i(h_j\text{ used}) = \sum_{k=j}^{j+w-1}\mathbb{P}_i(h_j\text{ used}|t_i = k)\mathbb{P}(t_i = k)&&
&&\mathbb{P}_i(h_j\text{ used}|t_i = k) = \frac{\exp(u_{i,k})}{\sum_{l=v}^{t_i}(u_{i,l})}&&
&&\mathbb{P}(t_i = k) = \alpha_{i,k}&&
&&\beta_{i,j}=\sum_{k=j}^{j+w-1} \frac{\exp(u_{i,k})}{\sum_{l=v}^{t_i}\exp(u_{i,l})}\alpha_{i,k}&&
The equation derived for $\beta_{i,j}$ can be parallelized using moving sum and computation, therefore, is very efficient. Note that number of parameters have increased (and therefore computations as well) as monotonic chunkwise mechanism is using both $\text{MonotonicEnergy}(s_{i-1}, h_j)$ and $\text{ChunkEnergy}(s_{i-1}, h_j)$. This increase is very marginal, about $1\%$, but the performance of model increases significantly, reaching almost at par with soft alignments for some tasks.
3.2.3. Limitations of Monotonic Alignments
There are two major limitations of the hard monotonic mechanism. First, the one we discussed as a motivation for the chunkwise monotonic mechanism, is that there is not enough context in the context vector as we force the model to capture complex dependencies only using a single memory vector. This concern is almost resolved by using chunks of memory summed over a soft distribution.
The second limitation is the assumption of strict monotonicity in input and output alignments. For example, in translation task, we can expect a degraded performance when translation is performed on languages with different sentence structure i.e. a different order of subject, verb and object, though this assumption can be almost true for structurally similar languages.
We note here that soft alignments, though computationally expensive and unsuited for online decoding, are robust to input-output alignment relations and use a much wider context for producing outputs as compared to monotonic alignments.
## References
Online and Linear-Time Attention by Enforcing Monotonic Alignments
Colin Raffel, Minh-Thang Luong, Peter J. Liu, Ron J. Weiss, Douglas Eck
Proceedings of the 34th International Conference on Machine Learning, 2017
Monotonic Chunkwise Attention
Chung-Cheng Chiu, Colin Raffel
International Conference on Learning Representations, 2018
Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation
Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, Yoshua Bengio
Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)
Sequence to Sequence Learning with Neural Networks
Ilya Sutskever, Oriol Vinyals, Quoc V. Le
Proceedings of the 27th International Conference on Neural Information Processing Systems (NIPS 2014)
Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks
Alex Graves, Santiago Feránandez, Faustino Gomez, Jürgen Schmidhuber
Proceedings of the 23rd International Machine Learning Conference, 2006
Neural Machine Translation by Jointly Learning to Align and Translate
Dzmitry Bahdanau, Kyunghyun Cho, Yoshua Bengio
International Conference on Learning Representations, 2015
Effective Approaches to Attention-based Neural Machine Translation
Minh-Thang Luong, Hieu Pham, Christopher D. Manning Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing
Structured Attention Networks
Yoon Kim, Carl Denton, Luong Hoang, Alexander M. Rush
5th International Conference on Learning Representations, 2017
Listen, Attend and Spell
William Chan, Navdeep Jaitly, Quoc V. Le, Oriol Vinyals
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Attention-Based Models for Speech Recognition
Jan Chorowski, Dzmitry Bahdanau, Dmitriy Serdyuk, Kyunghyun Cho, Yoshua Bengio
Proceedings of the 28th International Conference on Neural Information Processing Systems (NIPS 2015)
Attention Is All You Need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, Illia Polosukhin
31st Conference on Neural Information Processing Systems (NIPS 2017)
State-of-the-art Speech Recognition With Sequence-to-Sequence Models
Chung-Cheng Chiu, Tara N. Sainath, Yonghui Wu, Rohit Prabhavalkar, Patrick Nguyen, Zhifeng Chen, Anjuli Kannan, Ron J. Weiss, Kanishka Rao, Ekaterina Gonina, Navdeep Jaitly, Bo Li, Jan Chorowski, Michiel Bacchiani
arXiv:1712.01769
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8162844777107239, "perplexity": 3047.766429151195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107918164.98/warc/CC-MAIN-20201031121940-20201031151940-00309.warc.gz"}
|
https://www.physicsforums.com/threads/solubility-problem.263495/
|
# Solubility Problem
1. Oct 11, 2008
### cncbmb
1. The Problem
The Following Steps Occur in Order:
a. Aqueous silver nitrate is added to a sodium bromide solution to form a white precipitate.
b. Aqeuous ammonia is added to the above. The contents of the container change color slightly and there is still a precipitate.
c. After step b, sodium thiosulfate is added and all of the precipitate disappears.
Part 1: Explain why the precipitate disappears in step c.
Part 2: Find the reaction that occurs in part c.
2. Relevant equations
none
3. Attempt to Solve the Problem
After step a, we have silver bromide, which is the initial precipitate.
After step b, I thought that we had $Ag(NH_3)_2^{+}$ and some bromide and nitrate anions, so I predicted that there wouldn't be a precipitate. My prediction was wrong and I realized that I made an error in tracing the reactions.
I. Why is there still a precipitate at the end of part b?
II. Why does the addition of sodium thiosulfate make the precipitates disappear?
Last edited: Oct 12, 2008
2. Oct 12, 2008
### Staff: Mentor
It all depends on the equilibrium between precipitate and the complexing agent. Ammonia complex is not stable enough to dissolve AgBr (although it is stable enough to dissolve AgCl).
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9325079917907715, "perplexity": 3385.439036602104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698544097.11/warc/CC-MAIN-20161202170904-00432-ip-10-31-129-80.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/a-question-about-operators.147267/
|
1. Dec 8, 2006
Let be the Kelin-gordon equation (m=0) with a potential so:
$$(-\frac{\partial ^{2}}{\partial t^{2}}+V(x) )\Phi=0$$
my question is if you consider the wave function above as an operator..is the K-G operator of the form:
$$<0|T(\Phi(x)\Phi(x')|0>$$ T=time ordered
I think that in both cases..we use the same wave function but once is an scalar (or an spinor for electrons) and the other is an escalar...:shy: :shy:
2. Dec 9, 2006
### dextercioby
1.I don't know who Kelin was. Maybe you could supply some reference.
2. Your equation, misses a laplacian.
3. You depicted the Feynman Green function, which is a Green function for the operator written with a Laplacian.
All of course, if you mean "Klein-Gordon"
Daniel.
3. Dec 9, 2006
I apologize "DSextercioby"... i missed the keyboard.. yes i was referring Klein-Gordon equation with rest mass m=0 so:
$$(-\frac{\partial ^{2}}{\partial t^{2}}+\nabla +V(x))\Phi=0$$
then if you define the Green function by $$G(x,x')=<0|T(\Phi(x)\Phi(x'))0>$$
then my question were if the "Phi" wave function defined in both G and K-G equation is the same ,but in one case is an operator and in the other is an scalar with T=time ordered product.
- By the way i looked at the paper by Scwinger ..taking the Dirac equation with Electromagnetism:
$$(i\gamma_{\mu}\partial _{\mu}-eA_{\mu}+m)\Psi =0$$
he got the Green function (i don't know how he did it..:grumpy: ), he got the functional equation:
$$\partial _{\mu}-eA_{\mu}+m+\frac{\delta}{\delta J_{\mu}}G(x,x')=\delta(x-x')$$
4. Dec 9, 2006
### dextercioby
In the field eqn, the $\varphi (x)$ is not a wavefunction, it is a classical field.
In the VEV of the time-ordered product, it is an operator acting on a Fock space. It still keeps the scalar behavior wrt restricted Poincare' transformations.
As for the second part of your post, please supply the reference to Schwinger's paper.
Daniel.
5. Dec 9, 2006
A brief resume..can be found at:
http://www.pnas.org/cgi/content/full/102/22/7783
with the Dirac equation + magnetic field+ scalar potential V(x) and the functional approach to the Green function involving functional derivatives.
Similar Discussions: A question about operators
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.959384560585022, "perplexity": 1742.9847051989575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118950.30/warc/CC-MAIN-20170423031158-00087-ip-10-145-167-34.ec2.internal.warc.gz"}
|
https://www.math.uni-bielefeld.de/~beyn/AG_Numerik/html/de/preprints/sfb_11_31.html
|
# Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3
## Numerische Analyse äquivarianter Evolutionsgleichungen
11-031 Raphael Kruse.
Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler-Maruyama method. In both cases we obtain optimal error estimates. The proofs are based on sharp integral versions of well-known error estimates for the corresponding deterministic linear homogeneous equation together with optimal regularity results for the mild solution of the SPDE. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin approximations.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.862159013748169, "perplexity": 684.6909052187915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738653.47/warc/CC-MAIN-20200810072511-20200810102511-00228.warc.gz"}
|
https://www.physicsforums.com/threads/solution-of-equation-for-decaying-real-scalar-field.812578/
|
# Solution of equation for decaying real scalar field
1. May 6, 2015
### karlzr
Suppose there is a real scalar field $\phi$ with some decay width $\Gamma$ to some fermion. The quantum equation of motion after one-loop correction takes the form
$\ddot{\phi}+(m^2+im\Gamma)\phi=0$
where $m$ is the renormalized mass.
The solution can be obtained as $\phi=\phi_0 e^{imt}e^{-\Gamma t/2}$. So how do we use this complex solution? since the solution we need for application must be real. Usually we can take the real part when we have a complex solution. But In this case the real part of this solution does not solve the full quantum equation of motion due to the imaginary component.
2. May 8, 2015
### Brage
Surely the equation $\ddot{\phi}+(m^2+im\Gamma)\phi=0$ has the solution
$$\phi=Ae^{-im^2t}e^{\Gamma m t/2}+Be^{im^2t}e^{-\Gamma m t/2}$$, where A and B are complex constants to be determined from initial and boundary conditions. Unless I've missed something fundamental here?
3. May 8, 2015
### karlzr
But $\phi$ starts as a real field, how can it have complex solution?
In quantum mechanics, an imaginary part in Hamiltonian of some system indicates decaying amplitude. But isn't the total Hamiltonian of the whole system always real in order to obey unitarity? I don't know how to draw an analogy in this case.
4. May 8, 2015
### bhobba
Some solutions to equations are not necessarily physically sensible eg the requirement for the solution to be real will put constraints on A and B if you expand things out.
Thanks
Bill
Last edited: May 8, 2015
5. May 8, 2015
### karlzr
When $\Gamma << m$, the full solution is $\phi(t)= A e^{imt-\Gamma t/2}+B e^{-imt+\Gamma t/2}$. It doesn't seem to be possible to make it real by constraining the two constant coefficients $A$ and $B$.
Actually, this question is from Phys.Lett. B117 (1982) 29
6. May 8, 2015
### bhobba
Well that simply means it has no real solution. So?
Thanks
Bill
7. May 8, 2015
### karlzr
I need to find the evolution of its energy density $\rho=\dot{\phi}^2/2+m^2\phi^2/2$. With complex solution for $\phi$, I get complex energy density which doesn't make sense.
8. May 8, 2015
### bhobba
Maybe the answer is to apply Noethers theorem to get the stress energy tensor:
http://www.itp.phys.ethz.ch/research/qftstrings/archive/12HSQFT1/Chapter04.pdf [Broken]
Notice the Lagrangian in 4.1 while containing a complex field is real.
Thanks
Bill
Last edited by a moderator: May 7, 2017
9. May 8, 2015
### Brage
Well the real part of $\phi(t)= A e^{imt-\Gamma t/2}+B e^{-imt+\Gamma t/2}$ would be $$Re(\phi(t))[Re(A)cos(mt)-Im(A)sin(mt)]e^{-\Gamma t/2}+[Re(B)cos(mt)+Im(B)sin(mt)]e^{\Gamma t/2}$$ just by use of Euler's formula and taking the resulting real part.
10. May 8, 2015
### karlzr
But the real part doesn't solve the equation.
11. May 8, 2015
### bhobba
It has no real solution.
If you want to find the Hamiltonian use the methods in the link I gave and apply Noether. I am pretty sure a simple modification of the Lagrangian in 4.1 of my link will give your equation.
The problem as you stated it at the start is inconsistent - there is no real scalar field that is the solution to that equation. I am pretty sure its Lagrangian contains a complex field so its obvious why that's so. However when you work out the Hamilitonian it will give real values of energy - as it must.
Thanks
Bill
12. May 8, 2015
### karlzr
My equation is indeed from the quantum action. A fermion loop ($m_f<m_\phi/2$) will contribute a complex term to the effective potential, which means the free scalar particle is not the eigenstate of Hamiltonian. It will decay. I believe the Hamiltonian is also complex just like in quantum mechanics.
When I say the scalar field is real, I mean there is only one degree of freedom. I don't know whether it is inconsistent for such a real scalar field to have a complex solution. But my problem is to find the evolution of energy density from my solution to the equation and I expect it to be real. Actually I expect the solution to oscillate as in free field theory and also the energy density to decrease since the decay channel is open in our case.
13. May 8, 2015
### bhobba
A complex field is simply a tricky way of elegantly writing the equation of two real fields. You cant have a single real field that is complex. It makes no sense.
What I think you should do is post the full details of what you are trying to do. We have some quite high powered theorists that post here (I an not one - my knowledge of QFT is not as good as I would like) and hopeful they can sort it out.
Thanks
Bill
14. May 9, 2015
### karlzr
Thanks.
This question is from Phys.Lett. B117 (1982) 29
This is a 5-page paper and my question is from page two. The scalar is the inflaton which reheats the universe at the end of inflation by perturbative decaying. We can assume the potential energy of inflaton has only quadratic term. That's pretty much all the background of my question.
15. May 9, 2015
### bhobba
16. May 9, 2015
### fzero
If we look back at the equation of motion, we've replaced the mass by a complex number. As you've found, the solutions have a complex energy and are no longer real. Sometimes in the literature, these solutions are called Gamow states. The rationalization is that these states represent a resonance that decays after a short time. Usually, the solution of an equation of motion represents an equilibrium configuration (stationary state), but we've cooked up our system in such a way that it does not have equilibrium solutions but quasistationary ones.
As you can see from the paper in question, there is a physical interpretation of the solutions that has a predictive value for certain problems so the utility of the method is evident. But you will not be able to demand that you find a real solution to an equation that has been analytically continued to complex parameters.
17. May 10, 2015
### karlzr
Thanks. Since we are on this paper, I have a related question.
I am a little confused about how energy goes from inflaton to fermions. So during reheating, this paper says we can find the amplitude of fermion production from $<f_i,\bar{f}_i|\phi \bar{\psi}_i\psi_i|0>$. Here $\phi$ is purely classical field which should be replaced by the complex solution of its equation, right? It seems this amplitude depends only on the value of $\phi$ and has nothing to do with the energy density which doesn't make sense to me. Also, in my opinion, a classical field $\phi$ in this case serves only to give a oscillating mass to the fermion (preheating, non-perturbative decay), and I don't know why we can get information of its perturbative decay. Is it the inflaton field or inflaton particle that decays to fermion?
18. May 10, 2015
### fzero
As you say, we have a classical value of $\phi$ so we are talking about the field and not a particle state. The physical situation is that we start with the scalar somewhere away from the minimum of its potential, as it would be at high temperature. This is modeled by putting in a source term that is suddenly turned off at $t=0$. The field will naturally settle into a minimum of the potential, but the energy that was stored in the field has to go somewhere. The paper considers the case where all of this energy goes to fermions via the Yukawa-type coupling.
Given an amplitude $\mathcal{A}_{fi}$ from some initial state $i$ to a final state $j$, Fermi's Golden rule:
$$\Gamma_{i\rightarrow f} \sim | \mathcal{A}_{fi} |^2$$
gives the probability per unit time to create the final state $f$. I think you can convert this into an energy released per unit time by considering the expression for the Hamiltonian evaluated on the classical solution for $\psi$. When you integrate that over time, you will find the energy density of the fermions.
Last edited: May 10, 2015
Similar Discussions: Solution of equation for decaying real scalar field
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8983660340309143, "perplexity": 320.8941654352422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948530841.24/warc/CC-MAIN-20171213201654-20171213221654-00346.warc.gz"}
|
https://groupprops.subwiki.org/wiki/Divisible_nilpotent_group
|
Divisible nilpotent group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: divisible group and nilpotent group
View other group property conjunctions OR view all group properties
Definition
A group $G$ is termed a divisible nilpotent group if it satisfies the following equivalent conditions:
1. $G$ is a divisible group.
2. The abelianization of $G$ is a divisible abelian group.
3. For every positive integer $i$, the quotient group $\gamma_i(G)/\gamma_{i+1}(G)$ of successive members of the lower central series is a divisible abelian group.
4. For any two positive integers $i < j$, if $\gamma_i(G),\gamma_j(G)$ denote respectively the $i^{th}$ and $j^{th}$ members of the lower central series of $G$, then the quotient group $\gamma_i(G)/\gamma_j(G)$ is a divisible group.
Relation with other properties
Stronger properties
Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9087700843811035, "perplexity": 465.61679581904644}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540507109.28/warc/CC-MAIN-20191208072107-20191208100107-00124.warc.gz"}
|
http://sciforum.net/conference/ecas2016/Section-A
|
### The platform for open scholarly exchange and collaboration.
Home » ECAS 2016 » Section A: Atmospheric Physics
# A: Atmospheric Physics
List of presentations (7)
List of Accepted Abstracts (2)
Inversion of nighttime PM2.5 mass concentration in Beijing based on the VIIRS Day-Night Band
Research on the methods and experiments of rainfall intensity inversion using a microwave link based on linear regression theory and support vector machine
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8008934259414673, "perplexity": 15312.36774001291}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560284429.99/warc/CC-MAIN-20170116095124-00037-ip-10-171-10-70.ec2.internal.warc.gz"}
|
http://physics.stackexchange.com/questions/60072/is-the-diffusion-coefficient-for-a-macromolecule-sensitive-to-mass
|
Is the diffusion coefficient for a macromolecule sensitive to mass?
Suppose I have two neutrally-buoyant macromolecules diffusing in water. They have the same radius of gyration (i.e. same root-mean-square distance from their center of mass), but one of them is compact (its mass is roughly the cube of its size) and the other is extended (its mass is roughly the square of its size).
Since these molecules are the same size, do they have roughly the same diffusion coefficient?
Alternatively, their root-mean-square velocities should be different since they have different mass. Does this lead to substantially different diffusion coefficients?
-
The mass will play the role in the relaxation time to go from a ballistic regime in the Langevin equation to an overdamped regime where only diffusion matters.
The bigger the mass, the higher the inertia and therefore the longer the time it takes to reach the overdamped regime.
Once the overdamped regime is reached or, to phrase it differently, if your time window allows you to only see the overdamped regime in both cases then you will see no difference between the two.
-
This is what I thought, thanks. – Mark Eichenlaub Apr 5 '13 at 18:07
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8762748837471008, "perplexity": 459.1117409572097}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894250.40/warc/CC-MAIN-20140722025814-00190-ip-10-33-131-23.ec2.internal.warc.gz"}
|
http://www.ams.org/joursearch/servlet/DoSearch?f1=msc&v1=76M99&jrnl=one&onejrnl=tran
|
# American Mathematical Society
Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS
You are here: Home > Publications
AMS eContent Search Results
Matches for: msc=(76M99) AND publication=(tran) Sort order: Date Format: Standard display
Results: 1 to 3 of 3 found Go to page: 1
[1] Athanassios S. Fokas and Laihan Luo. On the asymptotic linearization of acoustic waves. Trans. Amer. Math. Soc. 360 (2008) 6403-6445. MR 2434293. Abstract, references, and article information View Article: PDF This article is available free of charge [2] E. J. Wilczynski. An application of group theory to hydrodynamics . Trans. Amer. Math. Soc. 1 (1900) 339-352. MR 1500542. Abstract, references, and article information View Article: PDF This article is available free of charge [3] E. J. Wilczynski. Errata: An application of group theory to hydrodynamics'' [Trans.\ Amer.\ Math.\ Soc. {\bf 1} (1900), no. 3, 339--352; 1500542] . Trans. Amer. Math. Soc. 1 (1900) 509. MR 1500435. Abstract, references, and article information View Article: PDF This article is available free of charge
Results: 1 to 3 of 3 found Go to page: 1
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6262395977973938, "perplexity": 3772.5404456334045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657110730.89/warc/CC-MAIN-20140914011150-00161-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
|
http://math.stackexchange.com/questions/399368/how-to-prove-the-inequality-between-mathematical-expectations/414701
|
# How to prove the inequality between mathematical expectations?
Let $X$ and $Y$ be independent random variables having the same distribution and the finite mathematical expectation. How to prove the inequality $$E(|X-Y|) \le E(|X+Y|)?$$
-
Sorry, I missed the moduli. It has been fixed. – user64494 May 22 '13 at 16:38
What do you mean by "same distribution"? are they IID? – Calvin Lin May 24 '13 at 20:04
@ Calvin Lin : It means that their distribution functions are identical. Could you explain what you mean by IID? – user64494 Jun 3 '13 at 4:19
@user64494 IID is shorthand for “independent, identically distributed” – Ewan Delanoy Jun 6 '13 at 7:55
@user64494: could you tell us where you have found this inequality? – Siméon Oct 2 '13 at 11:01
After a little inspection, we see that $$E(|X+Y|-|X-Y|) = 2E[Z(1_{XY\geq 0}-1_{XY<0})]$$ where $Z = \min(|X|,|Y|)$.
Remember that for any non-negative random variable $T$, $$E(T) = \int_0^\infty P(T>t)\,dt.$$
We apply this with $T=Z\,1_{X \geq 0, Y\geq 0}$, $T=Z\,1_{X < 0, Y< 0}$ and $T=Z\,1_{X \geq 0, Y< 0}$. Since $\{Z > t\} = \{|X| > t\}\cap\{|Y| > t\}$, we obtain
$$E(Z \,1_{X \geq 0,Y\geq 0}) = \int_0^\infty P(X > t)P(Y > t)\,dt = \int_0^\infty P(X > t)^2\,dt$$
$$E(Z\, 1_{X < 0, Y < 0}) = \int_0^\infty P(X < -t)P(Y < - t)\,dt = \int_0^\infty P(X < -t)^2\,dt$$
$$E(Z\,1_{X \geq 0, Y< 0}) = E(Z\,1_{\{X < 0, Y \geq 0\}}) = \int_0^\infty P(X > t)P(X < -t)\,dt$$
So finally, $$E(|X+Y|-|X-Y|) = 2\int_0^\infty (P(X>t)-P(X<-t))^2\,dt \geq 0$$
Remark 1. The inequality is an equality if and only if the distribution of $X$ is symetric, that is $P(X > t) = P(X < -t)$ for any $t \geq 0$.
Remark 2. When $|X|=1$ a.s. the inequality is nothing but the semi-trivial fact that if $X$ and $Y$ are independent with same distribution, then $P(XY \geq 0) \geq \dfrac{1}{2}$.
Remark 3. It is worthwile to mention a nice corollary : $E(|X+Y|) \geq E(|X|)$. The function $x \mapsto |x|$ is convex hence $|X| \leq \frac{1}{2}(|X+Y|+|X-Y|)$. Taking expectations we find $$\Bbb E(|X+Y|-|X|) \geq \frac{1}{2}\Bbb E(|X+Y|-|X-Y|) \geq 0.$$ Furthermore, there is an equality if and only if $X=0$ a.s.
-
Nice! I'm perfectly satisfied with this answer, I’ll wait before awarding the bounty to it, just in case someone comes up with an even better proof. – Ewan Delanoy Jun 8 '13 at 15:01
I am ok with that. Notice that I added some remarks in my answer. – Siméon Jun 9 '13 at 11:06
It's really nice! +1. – 23rd Jun 9 '13 at 11:19
Edit: Question has changed. Will give answer when time permits.
By the linearity of expectation, the inequality $E(X-Y)\le E(X+Y)$ is equivalent to $-E(Y)\le E(Y)$, which in general is false. It is true precisely if $E(Y)\ge 0$.
Independence is not needed for the argument. Neither is the hypothesis that the random variables have the same distribution.
-
Sorry, I missed the moduli. It has been fixed. – user64494 May 22 '13 at 16:03
Below is a set of remarks that’s too long to be put in a comment.
Conjecture. The inequality becomes an equality iff $-X$ has the same distribution as $X$.
Remark 1. The “if” part of the conjecture is easy : if $X$ and $-X$ have the same distribution, then by the independence hypothesis $(X,Y)$ and $(X,-Y)$ have the same joint distribution, therefore $|X+Y|$ and $|X-Y|$ share the same distribution, so they will certainly share the same expectation.
Remark 2. Let $\phi_n(t)=t$ if $|t| \leq n$ and $0$ otherwise. If the inequality holds for any $(\phi_n(X),\phi_n(Y))$ for any $n$, then it will hold for $(X,Y)$ also, by a dominated convergence argument. So we may assume without loss of generality that the support of $X$ is bounded.
-
Thank you. It is helpful. It would be interesting to answer the question in the partial case of absolutely continuous distributions. – user64494 May 31 '13 at 6:52
Let's consider the question of when $E[f(X,Y)] \geq 0$ in the generality of real-valued functions of arbitrary i.i.d. random variables on probability spaces. With no loss of generality take $f$ to be symmetric in $X$ and $Y$, because $E[f]$ is the same as $E$ of the symmetrization of $f$.
There is a simple, and greatly clarifying, reduction to the case of random variables with at most two values. The general case is a mixture of such distributions, by representing the selection of $(X,Y)$ as first choosing an unordered pair according to the induced distribution on those, and then the ordered pair conditional on the unordered one (the conditional distribution is the $1$ or $2$-valued distribution, and the weights in the mixture are the probability distribution on the de-ordered pair). One then sees, after some more or less mechanical analysis of the 2-valued case, that the key property is:
$f(x,y)=|x+y| - |x-y|$, the symmetric function for which we want to prove $E[f(X,Y)] \geq 0$, is diagonally dominant. That is, $f(x,x)$ and $f(y,y)$ both are larger than or equal to $|f(x,y)|$. By symmetry we really need only to check one of those conditions, $\forall x,y \hskip4pt f(x,x) \geq |f(x,y)|$.
A function satisfying these conditions, now on a general probability space, has non-negative expectation in the 2-valued case, because for $p+q=1$ (the probability distribution), $$E[f] = p^2 f(a,a) + q^2 f(b,b) + 2pq f(a,b) \geq (p-q)^2|f(a,b)| \geq 0$$
The equality cases when expectation is zero are when $p=q$ and $f(a,b) = -f(a,a) = -f(b,b)$. For 1-valued random variables, equality holds at values where $f(p,p)=0$. Due to diagonal dominance these are null points, with $f(p,x)=0$ for all $x$.
This allows a generalization and proof of Ewan Delanoy's observation, in the general situation: if the support of the random variable has an involution $\sigma$ such that $\sigma(p)=p$ for null points and for non-null points $b=\sigma(a)$ is the unique solution of $f(a,a)=f(b,b)=-f(a,b)$, then the expectation is zero (when finite) if and only if the distribution is $\sigma$-invariant. That is because the expectation zero case must be a mixture of the $1$ and $2$-atom distributions with zero expectation, and all of those assign probability in a $\sigma$-invariant way to the atoms.
Returning to the original problem, for $f(x,y)=|x+y| - |x-y|$ with the absolute value interpreted as any norm on any vector space, diagonal dominance follows from the triangle inequality, $0$ is a unique null point, and the involution pairing every non-null $x$ with the unique solution of $f(x,y)=-f(x,x)=-f(y,y)$ is $x \to -x$. This recovers the characterization that the distribution is symmetric in the critical case, for any $f$ derived from a norm.
Note (*). In passing between ordered and unordered pairs, there might be some issue of "measurable choice" on general measure spaces, or not, and it is an interesting matter what exactly is true about that and whether any condition is needed on the measure space. In the original problem one has a selection function $(\min(X,Y),\max(X,Y))$, if needed to avoid any complications, and the same would be true in any concrete case by using order statistics on coordinates.
-
Note that mixtures of diagonally dominant 2x2 matrices are diagonal dominant in the linear algebra sense, so the terminology is consistent, and one can quote the theorem on positive-semidefinite nature of such matrices as another argument. – zyx Jun 9 '13 at 16:49
Beautiful and unexpected. All that you say here, I had already guessed more or less intuitively, but I could not find a formal proof. So this proof is like my dream come true. – Ewan Delanoy Jun 9 '13 at 16:53
I am not sure I understand fully your reduction to the two-valued case. How do you choose the unordered pair and how do you manage the case $X=Y$? – Siméon Oct 2 '13 at 6:56
I apologize for my poor English, but I cannot understand what you said in the second paragraph. Did you mean that you had proved the following statement? If $X$ and $Y$ are i.i.d. and if $f(x,y)$ satisfies that $f(x,y)=f(y,x)$ and $f(x,x)\ge |f(x,y)|$ for any $(x,y)$, then $E[f(X,Y)]\ge 0$. However, the statement is clearly false in general. @Ju'x: What is you opinion about my comment? – 23rd Oct 4 '13 at 15:25
@Landscape, it is a few months since I wrote the above, so I do not remember exactly what I meant, but I think that is for the $2$-element case and the statement of diagonal dominance needed in the general case is for mixtures (weighted averages) of $\leq 2$-element cases, $f(x,x) \geq \int_y |f(x,y)|$. If you write it in this "global" form one can write the proof without any reduction to the $2$-element case. However, if the reduction is correct then we do not need to think about globalizing the condition and can reason about $2$-element situations. – zyx Oct 4 '13 at 15:58
let $F(x) = P(X < x)$. I assume that $F$ is differentiable so there is no atom and $F'$ is the cdf of $X$ (and $Y$).
$E(|X+Y|) - E(|X-Y|) = E(|X+Y|-|X-Y|) \\ = 2E(X \; 1_{Y \ge |X|} + Y \; 1_{X \ge |Y|} - X \; 1_{-Y\ge |X|} - Y \; 1_{-X \ge |Y|}) \\ = 4E(X (1_{Y \ge |X|} - 1_{-Y \ge |X|})) \\ = 4E(X(1-F(-X)-F(X))) \\ = 4 \int_\Bbb R x(1-F(-x)-F(x))F'(x)dx \\ = 4 \int_\Bbb R (-x)(1-F(x)-F(-x))F'(-x)dx \\ = 2 \int_\Bbb R x(1-F(x)-F(-x))(F'(x)-F'(-x))dx \\ = \int_\Bbb R (1-F(x)-F(-x))^2dx - [x(1-F(x)-F(-x))^2]_\Bbb R \\ = \int_\Bbb R (1-F(x)-F(-x))^2dx \ge 0$
I am not entirely sure about the last step. $G(x) = 1-F(x)-F(-x)$ does converge to $0$ at both ends, and $G$ has finite variation. But still I am not convinced we can't carefully pick $F$ such that the bracket doesn't vanish.
However this is valid if $X$ has compact support or if $G(x)$ vanishes quickly enough (like the normal distribution for example). In this case it also proves Ewan's conjecture : the difference is $0$ if and only if the distribution is symmetrical with respect to $0$.
-
E[x] is a linear operator.
This means E[X + Y] = E[X] + E[Y]
Also, E[X - Y] = E[X] - E[Y]
The statement will be true when $E[Y] \ge 0$
-
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9606378674507141, "perplexity": 247.278253256815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500826025.8/warc/CC-MAIN-20140820021346-00368-ip-10-180-136-8.ec2.internal.warc.gz"}
|
http://mathoverflow.net/questions/123624/nearby-homomorphisms-from-compact-lie-groups-are-conjugate
|
Nearby homomorphisms from compact Lie groups are conjugate
I'm looking for a proof (that I can understand) of the following fact: If $K$ and $G$ are Lie groups, and $K$ is compact, then nearby homomorphisms $K\to G$ are conjugate.
That is, if $\mathrm{Hom}(K,G)$ is the set of Lie group homomorphisms, endowed with a suitable topology (I'd like to say compact-open), then the orbits of the conjugation-by-$G$ action on it are open. (Note that there are obvious conterexamples if $K$ is not compact.)
This is referred to in The space of Lie group homomorphisms. A reference is given there to Connor-Floyd, Differentiable Periodic Maps, Ch. VIII, Lemma 38.1.
Following the reference, we see that Connor and Floyd derive this as an easy consequence of a theorem from Montgomery-Zippin, Topological Transformation Groups, p. 216. That is, by thinking about the graph $K\to K\times G$, of a homomorphism, the statement can be deduced from the following:
• If $K\subseteq G$ is a compact subgroup, then there exists a neighborhood $U$ of $K$ in $G$ such that for any subgroup $H\subset U$, there exists $g\in G$ such that $gHg^{-1}\subseteq K$. (I.e., all subgroups "close" to a compact subgroup are conjugate to a subgroup of it.)
Montgomery-Zippin's proof is an exercise involving geodesics in symmetric spaces, which is opaque to me and will probably always remain so. (They have statements such as: "there exists a neighborhood $U$ of $x$ such that for any geodesic in $U$, for any points $a,b,c$ in that order along the geodesic, $d(x,b)< \mathrm{max}(d(x,a),d(x,c))$" (quoting from memory, don't take it literally). I'm just a simple algebraic topologist, and sort of thing goes right over my head.)
Can anyone describe a more modern proof, or give a reference? I'm imagining such a proof will be an exercise involving the exponential map. (In fact, it seems easy to prove that any subgroup "close" to the identity is trivial in just this way.)
-
You could derive this from the fixed point property for affine actions of compact groups, a la the proof of Property T. The point is that lack of local rigidity for representations of a compact group means that $H^1$ of $K$ with coefficients in Lie algebra is nonzero, which is impossible. Note also that geodesic property you are referring to is just the fact that the distance function on a totally normal neighborhood in Riemannian mld is convex. – Misha Mar 5 '13 at 16:11
Check out the short survey staff.science.uu.nl/~Schat001/survey_Lie_algebras.pdf I think it might go in the direction you want. – Claudio Gorodski Mar 5 '13 at 16:11
Claudio: it goes in a nice direction, but I don't see that it gets there. The claim is true for $\mathrm{Hom}(U(1),U(1))$, but false for $\mathrm{Hom}(\mathbb{R}, U(1))$, so I don't see how I can prove it purely from Lie algebra considerations. As Misha suggests, I probably need to know something about $H^1(K,\mathfrak{g})$, not just $H^1(\mathfrak{k},\mathfrak{g})$. What I'm missing is probably really easy. – Charles Rezk Mar 5 '13 at 19:47
That $H^1(K,\mathgfrak{g})$ is easy: indeed a continuous 1-cocycle induces an affine continuous action of $K$ on the finite-dimensional vector space $\mathfrak{g}$, which has a fixed point iff the 1-cocycle is a 1-coboundary. Now for $K$ compact there is a fixed point (integrate along an orbit, or fix a $K$-invariant Euclidean metric and take the circumcenter of an orbit). – YCor Mar 5 '13 at 21:47
It looks like you need the vanishing of a kind of nonabelian continuous cohomology: If $K$ acts continuously on $G$ then any continuous 1-cocycle $K\to G$ (crossed homomorphism, $f(xy)=f(x)^yf(y)$) that is close enough to the trivial one is a coboundary, i.e. is determined by an element $a\in G$ ($f(x)=a^xa^{−1}$). – Tom Goodwillie Mar 6 '13 at 2:52
Here is a sketch of the proof expanding on my comment.
Suppose that there exists a sequence of continuous homomorphisms $\rho_i: K\to G$ which converges (uniformly) to a representation $\rho: K\to G$. Repeating the arguments from A.Weil "Remarks on cohomology of groups", Annals of Math. (1964), you obtain a cocycle $\zeta\in Z^1(K, {\mathfrak g}_{Ad\circ \rho})$. (Think of rescaling the group $G$, so that in the limit it becomes its Lie algebra ${\mathfrak g}$ and the homomorphism condition for $\rho_i$'s becomes a cocycle condition for $\zeta$.)
Note they Weyl's arguments deal with finitely-generated groups, while your group $K$ is compact and infinitely generated, so you have to work a bit more and use uniformity of convergence to guarantee that the cocycle $\zeta$ is continuous. Now, if you have a continuous $V$-valued cocycle $\zeta$ of a topological group $K$ (where $V$ is a topological vector space), it gives you a continuous affine action of $K$ on $V$ by the formula $g\cdot v= L(g)v + \zeta(g)$, where $L(g)$ is the linear action of $g$ on $V$. In your case, $V$ is the Lie algebra ${\mathfrak g}$ of $G$ and the linear action of $K$ on $V$ is via composition of $Ad$ and $\rho$. Since $K$ is compact, the action on the finite-dimensional space $V$ in question will be isometric for some choice of an inner product, thus, by taking the center of a $K$-orbit on $V$ (with respect to the invariant Euclidean metric), we conclude that the affine action of $K$ has a fixed point. In other words, the cocycle $\zeta$ is a coboundary.
Now, the space of continuous coboundaries $B^1_{c}(K, V)$ is tangent to the orbit of $\rho$ under the group $G$ acting on representations $K\to G$ via conjugation (see Weil's paper). If, again, $K$ were finitely-generated, the space of cocycles would be finite-dimensional and you could take a complementary subspace ${\mathcal H}^1(K, V)\subset Z^1(K, V)$ to $B^1(K, V)$ and postcompose the representations $\rho_i$ with the action of $G$ by conjugation, so that the sequence $\rho_i$ converges to $\rho$ in a conical neighborhood of ${\mathcal H}^1(K, V)$. This would ensure that the cocycle $\zeta$ cannot be a coboundary, thereby giving you a contradiction. In your setting, you maye have to do some analysis to make sure that this argument works (again, using uniformity of convergence).
One possible simplification would be to take a finitely-generated dense subgroup $F$ in $K$ (it always exists: The proof goes back to Hausdorff-Banach-Tarsky paradox) for the last part of the argument and argue with the restriction of the cocycle $\zeta$ and representations $\rho_i$ to $F$, thereby reducing the problem to finite-dimensional one.
-
This is very helpful! Though I'm a little confused by the penultimate paragraph, since it seems that by this point we've shown that $Z^1=B^1$. Looking at Weil's paper, it seems that the deformation theory already tells us that $\mathrm{Hom}(K,G)$ is a manifold (assuming $K$ finitely generated), and so we are done once we have $H^1=0$. – Charles Rezk Mar 7 '13 at 14:22
Charles: Yes, you are absolutely right. I lost track of the fact that in your setting $Hom(K, G)$ is a real-analytic variety (as a homomorphism for connected $K$ is determined by the homomorphism of Lie algebras), so things are easier than I thought. Thus, everything reduces to the fact that $H^1_{cont}(K, {\mathfrak g})=0$, as in Weil's paper. There is one issue you need to check though: Uniform convergence of representations implies $C^1$-convergence (in order to use Lie algebras). But, if you use the topology of $C^1$-convergence, this will not be a problem. – Misha Mar 7 '13 at 23:01
Here is a proof sketch using cohomological ideas. The argument is in four main steps:
I. General theory of families of Lie algebra homomorphisms.
II. The case of a semisimple $G$.
III. The case of a torus (here is a major gap in my argument)
IV. combining both cases.
A preliminary observation: if $H$ is the full linear group of a complex vector space, then the result is well-known, because up to conjugacy, a homomorphism $G \to H$ is given by its character; and the set of characters is a discrete subspace of the space of all smooth maps $G \to \mathbb{C}$.
I. For arbitrary Lie algebras, $Hom_{Lie -alg} (\mathfrak{g},\mathfrak{h})$ is a real algebraic variety and thus it is locally path- connected. Therefore, nearby homomorphisms can be connected by smooth families of homomorphisms (I am not entirely sure whether this is true, but it seems so).
Now consider a smooth family $f_t$, $t \in \mathbb{R}$, of Lie algebra homomorphisms. We study the problem of finding $h: \mathbb{R} \to H$ such that $f_t (X) = Ad (h(t)) f_0 (X)$ holds for all $t$ and $X \in \mathfrak{g}$. If $f_t$ is the derivative of a smooth family of group homomorphisms $\phi_t$, then $h(t)$ conjugates $\phi_0$ to $\phi_t$ and thus solves the original problem.
Let $F_t$ be the derivative of $f_t$ with respect to $t$. Differentiating the equation $[f_t X,f_t Y]=f_t [X,Y]$ shows that $F_t\in Hom (\mathfrak{g},\mathfrak{h})$ satisfies $F_t ([X,Y])= [F_t (X);Y]-[F_t (Y);X]$. This means that $F_t$ is a $1$-cocycle in the Chevalley-Eilenberg complex for $H^{\ast}(\mathfrak{g};f_t)$. By the cohomology I mean cohomology of $\mathfrak{g}$ with coefficients in $\mathfrak{h}$, viewed as a $\mathfrak{g}$-module via $f_t$.
We can consider the collection of all Chevalley-Eilenberg complexes $C^{\ast} (\mathfrak{g},f_t)$ as a complex of vector bundles on the real line; denote the vector bundles by $C^{\ast}(\mathfrak{g},f)$. The derivatives $F_t$ are a smooth family of $1$-cocycles and $[F_t]$ is a family of cohomology classes, smooth in a certain sense. I say that $[F_t]$ is uniformly trivial if there is a smooth family $H_t$ of $0$-cochains such that $[f_t (X);H_t]=F_t (X)$ for all $t$ and all $X \in \mathfrak{g}$ (this means that $d H_t =F_t$, but in a ''uniform way'').
Suppose that the cohomology class $[F_t]$ is uniformly trivial. Then
$$f_t (X) = \int_{0}^{t} F_s (X) ds = - \int_{0}^{1}[H_s;f_s (X)] ds;$$
in other words $f_t (X)$ solves the ODE $\frac{d}{dt} f_t (X) = - [H_t;f_t(X)]$ with initial value $f_0$. Another solution of the same ODE is $Ad (h(t)) f_0(X)$, where $h(t) \in H$ solves $\frac{d}{dt} h(t)= H_t$. So $f_t$ is conjugate to $f_0$. Vice versa, if $Ad (h(t)) f_0(X)$, then $[F_t]$ is uniformly trivial.
If $f_t$ is the derivative of a group homomorphism $G \to H$ and $G$ is compact, then pointwise triviality ($[F_t]=0$ for each $t$) implies uniform triviality. This is by the preliminary observation, which implies that $d_0:C^0 (\mathfrak{g},f) \to C^1 (\mathfrak{g},f)$ has constant rank and so its image is a vector bundle (pass to the complexification of $\mathfrak{h}$, which is unproblematic as we are only interested in the dimension of the invariant subspace). Thus we can pick a smooth $r: im (d_0) \to C^0 (\mathfrak{g},f)$ with $d_0 r = id$. Choosing $H_t:= r (F_t)$ solves the problem. Thus we arrive at
THEOREM: ''If $f_t: \mathfrak{g} \to \mathfrak{h}$ is a family of homomorphisms of Lie algebras and $H$ a Lie group with Lie algebra $\mathfrak{h}$, then there is a smooth map $h: \mathbb{R} \to H$ with $f_t = Ad (h(t))f_0$ if and only if the obstruction cocycle $[F_t]$ is uniformly trivial.''
ADDENDUM: ''If $G$ is a compact Lie group with Lie algebra $\mathfrak{g}$ and if $f_t$ is the derivative of a smooth family of homomorphisms $G \to H$, then pointwise triviality of $[F_t]$ implies uiform triviality.''
II.
Assume $G$ is semisimple. For each representation $V$ of $\mathfrak{g}$, we have an isomorphism $H^{\ast} (\mathfrak{g};V) \cong H^{\ast} (\mathfrak{g};V^{\mathfrak{g}})$, because of the compactness of $G$. But $H^1 (\mathfrak{g})=0$ since $G$ is semisimple, and so the cohomology class $[F_t]$ is zero, and by the addendum, it is uniformly trivial. Thus by the theorem, nearby homomorphisms are conjugate if $G$ is semisimple.
III.
Assume $G=T$ is a torus (sketch). Let $V$ be the universal cover (equal to $\mathfrak{t}$) and $\Gamma \subset V$ be the kernel; this is a lattice. Smooth families $f_t:\mathfrak{t} \to \mathfrak{h}$ are in bijection with smooth families $\psi_t: V \to H$ and induce families of group homomorphisms $g_t: \Gamma \to H$. As Misha indicates, there is a parallel obstruction theory for such families; with an obstruction in $H^{1}_{group}(\Gamma;\mathfrak{h})$. Consult Weil's paper quoted in Mishas answer.
There is the Van Est isomorphism $H_{Lie}^{\ast} (\mathfrak{t},\mathfrak{h}) \cong H_{smooth} (V,\mathfrak{h})$ to smooth group cohomology and furthermore a restriction $H_{smooth} (V,\mathfrak{h}) \to H^{\ast}_{group}(\Gamma; \mathfrak{h})$; this latter map is an isomorphism. This isomorphism should map the corresponding obstructions onto each other (this is the part of the argument where I do not know the details).
So a family of group homomorphisms $V \to H$ is constant up to conjugacy iff the restriction to the lattice $\Gamma$ is constant up to conjugacy. If the family $V \to H$ is the universal cover of a family $T \to H$, then the restriction to $\Gamma$ is constant; thus $T \to H$ is constant up to conjugacy.
IV.
Consider an arbitrary compact $G$. Without loss of generality, we can pass to a finite cover and thus assume $G=T \times K$, $T$ a torus and $K$ semisimple. Consider a family of group homomorphisms $\phi_t:G \to H$, with Lie algebra maps $f_t$ and obstruction cocycle $F_t$ as above. By the solution of the problem for $T$, the restriction $F_t|_{\mathfrak{t}}$ is uniformly trivial. But by the Künneth formula, the restriction $H^1 (\mathfrak{g} ) \cong H^1 (\mathfrak{k})\oplus H^1 (\mathfrak{t})\to H^1 (\mathfrak{t})$ is an isomorphism. Therefore, $[F_t]$ is trivial and thus uniformly trivial, again by the addendum.
Afterthought: It is probably better to study the whole question in the context of smooth cohomology. A family $\phi_t:G \to H$ should give an obstruction class in $H^{1}_{smooth} (G; \mathfrak{h})$. If $G$ is compact, this space is trivial by invariant integration.
-
How's this for another sketch? I don't know if it's "modern". It's a homemade attempt by another simple algebraic topologist.
Let $f:K\to G$ and $f_1:K\to G$ be continuous homomorphisms, where $K$ is a compact group and $G$ is a Lie group. There is a continuous action of $K$ on $G$ given by $f$, which we denote by writing $g^x=f(x)^{-1}gf(x)$. Define $h:K\to G$ by $f_1(x)=f(x)h(x)$. The fact that $f_1$ is another homomorphism means that $$h(xy)=h(x)^yh(y).$$ Call $h$ a crossed homomorphism if it satisfies this equation. Assume that $f_1$ is close to $f$. This means that $h$ is close to the constant function taking all of $K$ to the identity in $G$. We want $a\in G$ such that $f_1(x)=a^{-1}f(x)a$. This is equivalent to $$h(x)=a^xa^{-1}.$$ So forget about $f$; the problem is to show that if $K$ acts continuously on $G$ by homomorphisms then any small crossed homomorphism $h:K\to G$ can be expressed in this way for some $a$.
Actually $G$ acts on the set of crossed homomorphisms $h$ as follows: given $a\in G$ and $h$, let $h'(x)=(a^x)^{-1}h(x)a$. So the problem is to show that if $h$ is small then some $a$ takes it to the trivial map.
First look at the case where $G$ is abelian. Switching to additive notation, we have $G$ acting linearly on a finite-dimensional vector space and the problem is to show that if $h$ is such that $$h(xy)=h(x)^y+h(y)$$ then there exists $a$ such that $$h(x)=a^x-a.$$ Let $-a$ be the average $Av_x h(x)$. Then $$-a=Av_x h(xy)=Av_x (h(x)^y + h(y))=-a^y+h(y).$$ Thus $h(x)=a^x-a$.
Now for the general case: use linear coordinates in $G$ near the identity, writing the group multiplication as $x\ast y=x+y+Q(x,y)$ where $|Q(x,y)|\le |x||y|$ if $|x|$ and $|y|$ are small enough. So we have $K$ acting on a neighborhood of $0$ so as to preserve the multiplication $\ast$, and we have a small $h$ such that $$h(xy)=h(x)^y\ast h(y)$$ and we want to be able to modify $h$ into $$h'(x)=(a^x)^{-1}\ast h(x)\ast a$$ so as to make it $0$. Do it in steps. First, again let $a$ be the average of $h$. Now, modulo second-order terms, averaging $h(xy)=h(x)^y\ast h(y)$ over $x$ again we have $a=a^y+h(y)$. That is, if we modify $h$ by this $a$ then the $h'$ that we get is zero modulo second-order terms. If $h$ is small enough, $|h(x)|\le \epsilon$, then $|h'(x)|\le \epsilon ^2$.
Repeating this infinitely often and taking a limit, surely this gives $0$ as the result of acting on the original $h$ by some $a\in G$, the infinite product of smaller and smaller elements..
-
I'm worried about averaging $h(x)=h(x)^y*h(y)$ over $x$. In the local coordinates, $x\mapsto x^y$ isn't linear, and a non-linear transformation might not play well with the integral. – Charles Rezk Mar 8 '13 at 15:24
That is the worrisome part, isn't it? But I believe that the error should just give more second-order terms. – Tom Goodwillie Mar 8 '13 at 16:47
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9731285572052002, "perplexity": 125.79480317160396}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927863.72/warc/CC-MAIN-20150521113207-00244-ip-10-180-206-219.ec2.internal.warc.gz"}
|
http://darrenirvine.blogspot.ca/
|
## Wednesday, December 20, 2017
### Equation of Circle in 3D and Snap Tangent
For a time I was on a bit of an AutoCAD like calculation kick and went through some interesting calculations like snap tangent, snap perpendicular, and intersection of a line with a plane. I wanted to take the next step on snap tangent and consider snap tangent to a sphere.
Snap tangent means, start with some point and try to find a point on the destination object (circle, sphere, ellipse, anything) that causes the line segment between the first point and the second point to be tangent to the object selected. My post about snap tangent, showed the result for a circle and worked in 2D. If you get the concept in 2D and are ready to take the concept to 3D for a sphere, you probably recognize without proof that the set of possible points on the sphere which will result in a tangential point, forms a circle. You can pretty much mentally extrapolate from the following picture which a repeat from the previous post.
Fig. 1 - Can you imagine the snap tangent circle on this if we allow the figure to represent a sphere? The snap tangent circle has center $$E$$ and radius $$a$$.
I will not repeat the method of calculation from the previous post but will simply observe that we can produce the values $$E$$ and $$a$$, which are the center and radius of the snap tangent circle. We add to this the normal of this circle, $$N = A - C$$, and then normalize $$N$$.
So, now we need a way to describe this circle which is not too onerous. A parametric vector equation is the simplest expression of it. We take our inspiration from the classic representation of circles in parametric form, which is
$p(\theta) = (x(\theta), y(\theta))$ $x(\theta) = r \cos{\theta}$ $y(\theta) = r \sin{\theta}.$
We have a normal from which to work from, but we need to have an entire coordinate system to work with. The classic parametric equations have everything in a neat coordinate system, but to describe a circle that's oriented any which way, we need to cook up a coordinate system to describe it with. Observe a change to the foregoing presentation that we can make:
$p(\theta) = r \cos{\theta} (1, 0) + r \sin{\theta} (0, 1) = r \cos{\theta} \vec{x} + r \sin{\theta} \vec{y}$
The normal vector we have is basically the z-axis of the impromptu coordinate system we require, but we don't have a natural x-axis or y-axis. The trouble is there are an infinite number of x-axes that we could choose, we just need something perpendicular to $$N = (n_x, n_y, n_z).$$ So, let's just pick one. If I take the cross product between $$N$$ and any other vector that isn't parallel to $$N$$, I will obtain a value which is perpendicular to $$N$$ and it can serve as my impromptu x-axis. To ensure I don't have a vector which is close to the direction of $$N$$, I will grab the basis vector, which is the most "out of line" with the direction of $$N$$. So, for example (F# style),
let b = if abs(normal.[0]) <= abs(normal.[1]) then
if abs(normal.[0]) <= abs(normal.[2]) then
DenseVector([| 1.0; 0.0; 0.0 |])
else
DenseVector([| 0.0; 0.0; 1.0 |])
else
if abs(normal.[1]) <= abs(normal.[2]) then
DenseVector([| 0.0; 1.0; 0.0 |])
else
DenseVector([| 0.0; 0.0; 1.0 |])
In this case, I have
$\vec{x} = b \times N$ $\vec{y} = N \times \vec{x}.$
Using this impromptu coordinate system, I can express an arbitrary circle in parametric form, having center $$C$$ and radius $$r$$ as
$p(\theta) = C + \vec{x} r \cos{\theta} + \vec{y} r \sin{\theta}.$
Thus, our snap tangent circle is given from above as
$p(\theta) = E + \vec{x} a \cos{\theta} + \vec{y} a \sin{\theta},$
where we would use $$N = A - C$$ (normalized) to be the beginning of our coordinate system.
## Saturday, October 21, 2017
### Remembering Gravity
I was recently testing out my vertical and was disappointed in the results. I was also mindful of my current endeavour to slim down a bit. And the thought came to mind, If I lost 20lbs, what would the impact be on my vertical jump? My intuition at that moment was that it should easily be possible to calculate an estimate. But as I thought about it some more, I realized I had oversimplified the matter and I remembered how gravity works.
There are two main pieces to the puzzle:
1. Determine the effect on take off velocity.
2. Determine the impact of that change in velocity to vertical jump (the easy part).
### Introduction to the Easy Part
The classic equations of kinetics will help us with 2, in particular the equation that describes the relationship between displacement and time under constant acceleration. Earth's gravity exerts an amount of force on all bodies in proximity to it which results in the same downward acceleration (in the absence of other forces). The force isn't constant for all objects, but the acceleration is. If you start from a constant acceleration of $$g = -9.81 m/s^2$$ and you know the initial vertical velocity of your take off, you can arrive at the classic velocity and displacement formulas:
$$v(t) = v_0 + g t$$
$$d(t) = d_0 + v_0 t + \frac{1}{2} g t^2,$$
where $$d_0$$ is initial displacement and $$v_0$$ is the initial (vertical) velocity. I was too lazy to look that up, so I just derived it. Note that I have put the minus on the gravity and not in the formulas. We can simplify this down to the variables we care about based on the fact that the velocity at peak (time $$t_p$$) is 0:
$$d(t_p) - d_0 = -\frac{v_0^2}{2 g}.$$
You'll notice that it doesn't matter how much you weigh for this part of the discussion. It matters how fast you are moving vertically at the moment your feet leave the ground. Now, in order to measure your vertical for the purposes of determining your initial velocity, you need to have a starting reach and a final reach. Your starting reach $$d_0$$ will be taken on your tiptoes, because your foot extension is still imparting force to the ground. (I don't enough about this topic to say how critical this phase is, but I did a little self experimentation and my limited self-awareness suggests I'm using foot extension as a part of my jump.) You're going to need your peak reach on the tape as well. My displacement under this manner of measurement is 17" = 0.43m (but for the record my standard reach vertical is 20"). My initial velocity is about $$2.91m/s$$. Does this help with determining my vertical if I lost 20lbs? Not really. But it's a cool number to know.
### 1. The Hard Part
The math we will do here is not difficult, but the justification is a little hazy. We need some kind of a model that explains the relationship between my weight and my initial velocity in a vertical jump. I'm going to model the process of jumping as having near constant acceleration. This is probably bogus, but I want a number. Let's put all the cards on the table:
1. Near constant vertical acceleration.
2. The force production of the legs is the same for the heavy me and the light me.
All of these assumptions are the basic ingredients of a creamy fudge. Assumption 2 is probably okay for small enough changes in weight, but note that large changes in weight would invalidate it. You can convince yourself of the limited applicability of assumption 2 by attempting to do shot put with a softball and a 12 lb shot. You'll be underwhelmed by the distance the softball goes if you haven't already intuited it.
Measuring the distance of the vertical acceleration is a bit of a problem. Consider that your feet are not accelerating for the first part of the movement, but your head is. We're going to need to know the distance that the center of gravity is moved through the movement. There is some research that has gone into the question of the center of gravity of a human body in different positions. Here's a quick and easy to follow presentation of the topic from Ozkaya and Nordin of Simon Fraser University. What's missing is the magic numbers I want.
Physiopedia says the CoG of a person in the anatomical position (like you're dead on a board) "lies approximately anterior to the second sacral vertebra." Another resource (from Peter Vint, hosted on Arizona State University website) indicates that this is located at about 53-56% of standing height in females and 54-57% of standing height in males. I'm going to need to tweak with this to get my take off CoG. I also need my bottom CoG height. I'm going to be a little more vague about coming up with that number. I'm going to eyeball it with a tape measure and reference some google pictures.
55.5% of my height would be about 39". Add to that the height of going on tiptoes (3") to get 42" height of CoG at take off. I estimate my initial CoG at the bottom of my crouch as 27". So, I have 15" = 0.38m within which to accelerate. We need to bring some equations together here:
$$v_f = a t$$
$$d = \frac{1}{2} a t^2,$$
where $$d$$ is the displacement of my CoG from crouch to take off, $$a$$ is my net acceleration and $$v_f$$ is my velocity at the end of the jumping phase (take off). This is the same number as my initial velocity (earlier called $$v_0$$). Solving for $$a$$ yields
$$a = \frac{v_f^2}{2 d} = 11.1 m/s^2.$$
The net force acting on me includes force of gravity $$F_g$$ and the floor pushing me up $$N$$ in response to gravity and the force I am applying to the floor to initiate the jump.
$$F_{NET} = N + F_g$$
The force of the floor pushing me up is in response to the force I am applying and the force of gravity. So, $$N = -F_g - F_a$$. The result is that the net force on my CoG is the force I am applying (in the opposite direction; I am pushing my feet down on the floor but the net force is upward).
(When it comes to the mass involved there is a bit of a conundrum. I am currently about 225 lbs. But the force I generate as part of the jump is not acting to directly accelerate all 225 lbs. Certainly the floor is pushing back on all 225lbs of me though. From the perspective of the force I am applying, I could probably exclude the lower leg. I found an estimate for men of about 4.5% per lower leg. So, knock off 20 lbs. Then the mass I am accelerating is about 205 lbs. However, we started down this path talking about the CoG and we included the lower leg in this. Also, we are thinking in terms of external forces in our basic force equation. If we want to get super detailed, we will need to think of internal forces and that can get complicated. In the end, the calculation appears only to be affected by fractions of an inch. I'm hunting for elephants so I will not make a careful search of the short grass.)
Using my full weight in kg, let's see what my acceleration would be if I lost 10kg. I'm currently about 102kg. Then the projected acceleration can be calculated from
$$F_a = m_i a_i = m_f * a_f$$
$$a_f = \frac{m_i a_i}{m_f} = \frac{102 kg \cdot 11.1 m/s^2}{92 kg} = 12.3 m/s^2$$
Now we can get my new take off velocity:
$$v_f = \sqrt{2 d a} = \sqrt{2 \cdot 0.38 m \cdot 12.3 m/s^2} = 3.06 m/s$$
### 2. The Easy Part
My new vertical, D, is an easy calculation with our new take off velocity.
$$D = -\frac{v_f^2}{2 g} = -\frac{(3.06 m/s)^2}{-9.81 m/s^2} = 0.477m = 18.8"$$
So, if I lose about 22lbs, I will have almost a 2" higher vertical without developing any further explosiveness in my legs.
I believe I will invest in other strategies as well.
## Saturday, September 9, 2017
There are lots of times in life where shortcuts lead to efficiency. Efficiency is great, provided it is actually effective at achieving your goals (or the goals you should have). On the other hand, you can sometimes efficiently achieve a short term goal only to find yourself at a dead end later on.
If you're in a maze, not every step closer to straight-line proximity with the cheese is necessarily actually getting you closer to eating the cheese. In a maze, you can be right beside the cheese with just a single wall between you and the cheese and you might be as far away as possible from being able to eat the cheese. Sometimes you need to head in a direction that seems to take you further from your goal, in order to be closer to achieving it. Do you want to have a really strong smell of cheese or do you want to actually eat cheese?
Take weight lifting as an example. Improving your technique often takes you back to lighter weight. Your goal is to lift lots, right? Well, lighter weight seems like the wrong direction if you're thinking naively. But improved technique will take you further along a path that can actually lead to "having cheese" rather than just "smelling cheese", both because you will be less prone to injuries which will set you back and because you will be training your muscles to work along a more efficient path. So, suck it up!—and reduce the weight if you have to.
What follows is a series of common math shortcuts and suggestions for avoiding the pitfalls of the shortcuts (like, avoiding the shortcuts 😜). Some of these are statements that arise from students who hear a teacher express a proper truth the first time. But, when asked to recall the statement, the student expresses an abbreviated version of the statement that differs in a way that makes it not true anymore. Sometimes the student really did understand, but was experiencing a "verbally non-fluent moment" or just didn't want to expend the energy to explain. The teacher, trying to be positive, accepts this as a token of the student paying attention and then gets lazy themselves and doesn't add a constructive clarification.
In any event, the quest for simplicity and clarity has pitfalls. Merely making something appear simple is not a sure path to understanding. Go deeper.
### Two Negatives Make a Positive
Why it's bad: It is a false statement. If I stub my toe and later hit my thumb with a hammer it is not a good thing, it is cumulatively bad.
How it happens: Quick summary (not intended to be fully accurate) and humor. Unfortunately, the quick summary can supplant the real thing if students are not reminded consistently about the full version of the statement (below).
Better: A negative number multiplied by a negative number, produces a positive number.
Expansion: Negative numbers are a way of expressing a change in direction, as in, (sometimes figuratively) a 180° change in direction. $10 is something you want to see coming your way. -$10 can go to someone else.
With this in mind you can explain that subtraction is equivalent to adding a negative number. A negative number is equivalent to multiplying the corresponding positive number by -1. The negative on the front of the number means you move to the "left" on the number line (a metaphor I think is sound). To put it a little differently, if you pick a random number on the number line and multiply it by -1 it is like mirroring it about zero (0). Also, multiplying by -1 is equivalent to taking its difference with zero. That is,
$$0-z=-1 z = -z,$$ which are more or less a part of the definition and development of negative numbers in a technical sense.
Displacement is one of the easiest illustrations to use. Suppose I am standing on a track that has chalk lines marked from -50 m to 50 m. I am standing at the 0 m mark facing the end with positive numbers. Instructions show up on a board which are in a few different forms:
2. Go back 10 m.
3. Move 10 m.
4. Move -10 m.
It is easy enough to see that 1 is equivalent to 3 and 2 to 4. Following a list of such instructions will result in a predictable finishing position which can be worked out one step at a time in order or can be put into a single mathematical expression. Commutativity and associativity can be explored by comparing differences in order applied to the mathematical expression as well as the list of expressions. I can reorder the sequence of instructions and produce a new expression that gives the same result or I can tweak the expression an spit out revised instructions that parallel the revised expression and produce the same result. Arithmetic is intended to express very practical things and so if something you do with your math expression causes a disconnect with the real life example, you are guilty of bad math. The problem will not be with commutativity or associativity, but with the implementation of it. It is worth investing a good deal of time on this, but it will probably have to be brought up again and again when you move on to other things because, I think, students sometimes get slack on their efforts at understanding when something appears too easy.
The next step is to understand that reversing direction twice puts you back on your original direction. We can see how this works on the track by working with the displacement formula:
$$d = p_f - p_i,$$ where $$p_f$$ is final position and $$p_i$$ is initial position. It is easy to illustrate on a chalk/white board that if I start at the -20 m mark and travel to the 50 m mark I will have traveled 70 m, not 30 m. Using the formula to get there will require combining the negative signs in a multiplication sense.
I would love to have a simple example that involves two negative non-unity numbers, but while I've done this arithmetic step countless times in the solving of physical and geometrical problems, I have trouble isolating a step like this from a detailed discussion of some particular problem and still retaining something that will lead to clearer understanding than the displacement example.
### Heat Rises
Why it's bad: It is a false statement.
How it happens: Unreasonable laziness.
Better: Hot air rises (due to buoyancy effects).
Expansion: The general way that heat transfer works is not related to elevation change. A more accurate but still cute, snappy saying to summarize how heat moves is "heat moves from hot to cold" or, my favorite, "heat moves from where it is to where it isn't" (relatively speaking).
So, why does hot air rise? The cause is density differences. Denser gasses will fall below less dense gasses and "buoy up" or displace the less dense gasses. Density is affected by both atomic weight and configuration of particles. Configuration is affected by temperature. The warmer the temperature the faster the particles move and bang into each other and tend to maintain a sparser configuration making them less dense (collectively).
It might be better to think of the more dense gas displacing the less dense gas. The gravitational effect on the more dense gas pulls it down more strongly than it does the less dense gas and the more dense gas pushes its weight around so that the less dense gas has to get out of the way. "Out of the way" is up. (A bit of a fanciful description, but a good deal better than "heat rises".)
Bottom line, if you want a shortcut, "hot air rises" is better than "heat rises". It's a small difference, but it is still the difference between true and false.
### Cross Multiply and Divide
Why it's bad: It does not require the student to understand what they are doing. For some students, this is all they remember about how to solve equations. Any equation. And they don't do it correctly because they don't have a robust understanding of what the statement is intended to convey.
How it happens: Proportions are one the critical components of a mathematics education that are invaluable in any interesting career from baking, to agriculture, to trades, to finance, to engineering, to medicine (or how about grocery shopping). Teachers are rightly concerned to turn out students who can at least function at this. It breaks down when it is disconnected from a broader understanding of equations. Students may look at the easy case of proportions as a possible key to unlocking other equations, which has a degree of truth to it. However, it is important to emphasize the reason why cross multiply and divide works (below). Without understanding, there is little reason to expect the simple case to spillover to help in the hard cases.
Better: Always do the same thing to both sides of an equation. If both sides are equal, then they are equal to the same number (for a given set of input values for the variables). If I do the same thing to the same number twice, I should get the same result. The result might be expressed differently, but it should still be equivalent.
For simple equations, often the best operation to do (to both sides, as always) is the "opposite" of one of the operations shown on one or both sides of the equation. Cross multiply and divide is a specialization of this principle that is only applicable in certain equations which must be recognized. The ability to recognize them comes from having good training on the handling of mathematical expressions (see remarks on BDMAS).
Expansion: Provided "do" means "perform an operation", the above is pretty valid. The other type of thing you can "do" is rearrange or re-express one or both sides of an equation such that the sides are still equivalent expressions. Rearrangement does not have to be done to both sides of the equation because it does not change its "value". When operations are performed, they must be applied to each side in its entirety as if each entire side was a single number (or thing). Sometimes parentheses are used around each side of the equation so that you can convey that distributivity applies across the "=" sign, but from there, distributivity (or lack thereof) needs to be determined based on the contents of each side of the equation.
### Most Acronyms (but Especially FOIL and BDMAS)
Why they're bad: My objection is qualified here (but not for FOIL). An acronym can sometimes summarize effectively, but it is not an explanation and does not lead to understanding. In rare cases, understanding may not be critical for long term proficiency, maybe. But an acronym is a shoddy foundation to build on. If you're trying to make good robots, use acronyms exclusively.
How it happens: Acronyms can make early work go easier and faster. This makes the initial teaching appear successful—like a fresh coat of paint on rotten wood. Teacher and student are happy until sometime later when the paint starts to peel. Sometimes after the student has sufficient understanding they may continue to use certain acronyms because of an efficiency gain they get from it, which may lead to perpetuating an emphasis on acronyms.
Better: Teach students to understand first. Give the student the acronym as a way for them test if they are on the right track when you're not around. Very sparingly use as a means of prompting them to work a problem out for themselves. (My ideal would be never, but realistically, they need to be reminded of their back up strategy when they get stuck.) Never, ever take the risk of appearing to "prove" the validity of operations you or others have performed by an appeal to an acronym (unless it is a postulate or theorem reference)—that's not just bad math, it is illogical.
Expansion: Certain acronyms, if you stoop to use them, can possibly be viewed as training wheels. Maybe BDMAS qualifies. But is there a strategy for losing the training wheels or are the students who use the acronym doomed to a life of having nothing else but training wheels to keep from falling over?
So, BDMAS is a basic grammar summary. But you need to become fluent in the use of the language. A good way to get beyond the acronym is to have clear, practical examples of things you might want to calculate that involve several operations. Calculating how much paint you need is a good way to help convey how orders of operations work. Before you calculate the amount of paint you need, you get the surface area, $$s$$. The total surface area is a sum of the surface areas of all surfaces I want to paint. If I have the dimensions of a rectangular room, I can get the area of each wall and add them together. To make the example more interesting, we will omit to paint one of the long walls. Because of order of operations giving precedence to multiplication over addition, I have a simple expression for a simple thing:
$$s = lh + wh + wh = lh + 2wh = h(l + 2w).$$ If you explain how to arrive directly at each expression without using algebra (with reference to simple diagrams), the meaning of each expression can be understood at an intuitive level. Understanding the geometry of the situation gets tied to understanding of the sentences you are making in the language of math. To get the number of cans of paint $$N$$, you need coverage, $$c$$ in area per can. Then $$N = s/c$$. And now, if you didn't already demonstrate how parentheses support the act of substitution in the surface area development, now is a good time, because now you can use substitution for one of the ungainlier expressions for the surface area and get:
$$N=(lh + 2wh)/c.$$ If you also walk through how to do the calculation in multiple simple steps you can draw the parallels with the steps you would take in calculating using the above formula. I realize substitution showed up much later in the curriculum I received than order of operations but I believe this is a mistake. Even if the student is not expected to use substitution in grade 5, why not let them have an early preview so it doesn't seem like it's from outer space when they need it?
Oh, yes, and FOIL. Don't use FOIL outside the kitchen. Better to teach how distributivity applies to multiterm factors which will again be something like a grammar lesson and can incorporate some substitution (e.g., replace $$x + y$$ with $$a$$ in one of the factors) or "sentence" diagramming, which is beyond the scope of this post.
### Using Keywords to Solve Word Problems
Why it's bad: It does not require the student to understand what they are reading which masks long-term learning problems, and leads to long-term frustration for the student.
How it happens: Students normally want something to do to help them get unstuck. Telling them they have to understand what they are reading isn't the most helpful and giving a bunch of examples of similar expressions and finding ones they already understand seems like a lot of work to go through. Keywords are fast and easy to tell students and are often enough to get stronger students started.
Better: Find analogous expressions that are already understandable to the student. If you can find statements that the student already understands at an intuitive level, you may be able to point out the similarity between the statement they are having trouble with and the statements they already can relate to.
Expansion: I am not aware of a standard treatment of this issue that meets my full approbation. We use language everyday and we don't use keywords to figure out what people mean by what they are saying. We shouldn't use language any differently with a word problem. It's the same language!
The words used in grade 6 word problems are all everyday words. What is needed is the ability to understand and use the same words in some new contexts. Providing a lot of examples is probably the way forward with this. Being able to restate facts in other equivalent ways may be a good indication of understanding and accordingly a good exercise.
It's important to recognize that language is complex and takes time to learn. Not everyone will learn it at the same rate and having a breadth and variety of examples with varied complexity is probably necessary for students who struggle more with it. Unfortunately, school doesn't support this kind of custom treatment very well (Cf. "growth" as per Franklin, Real World of Technology).
### Conclusion
Explanations, examples, and exercises that lead to genuine understanding are much needed by math students at all levels. I do not believe in the inherent value of making students suffer, figuring everything out for themselves by not giving them the best possible chance of understanding the material with good instruction. But undue opportunities to opt out of understanding are a disservice to them. Training wheels have their place, but we should make every effort to avoid seeming to point to training wheels as any student's long term plan for achieving competency in a subject area.
## Monday, August 7, 2017
### A Novice XC Rider Discovering the Trails of Brandon
There are some good trails near Brandon at Brandon Hills that I have been enjoying starting last summer and continuing into this summer. I probably am not cycling regularly enough to achieve significant adaptation to the stress of cycling, but I am enjoying it just the same. (Most weeks I only cycle once and don't do a lot of endurance activity otherwise.)
I am not setting any world records, but it is an interesting skill to develop.
Above is my most recent ride up at Brandon Hills where I decided that since the route I was taking only took at most 51 min, I might as well skip the rest stops and just go. I am slowly learning how the bike handles on the trail and how to manage turns and the ups and downs a little more fluidly. I felt like I was getting pretty good. But, reality has come along today to rectify my delusion.
I was reminded later that day about a trail on the North Hill in Brandon (Hanbury Bike & Hike Trail / North Hill Loop). It was posted as a trail on trailforks and I thought I should try it out. It is marked as Green/Easy. I did not find it so.
I do believe I will have to practice harder to be able to handle this course. I have just today learned the value of a helmet by personal experience. I was misled onto a faux path that led to a bridge to nowhere and my front wheel caught fast in a rut that was deep enough and terminated abruptly enough that the wheel did not bump over the edge. The front wheel decided it would no longer make forward progress and my momentum pulled the bike into rotational motion around the ridge of dirt that stopped the bike from moving forward. I went over the handle bars and ended up with the seat of the bike landing on my helmeted head. Pretty soft landing, considering.
I went down the tobogganing hill and didn't fall there, but did catch some air. When I landed, my handle bars did a bit of a jerky left turn which I reflexively turned back straight. Maintaining pedal contact was a bit sketchy too. Certainly a highlight for me.
The other tumble was a bit more complicated, but suffice to say that after some failed maneuvering about some rocks I lost control of the bike and tried every trick in the book to avoid a fall but ultimately lay on the ground somewhat removed from my bike but nevertheless unharmed. More of a side dismount, I believe.
Later on I got to the smiley face that is visible from 18th Street. I had to do some walking to get there.
"Come See Again." ...I'll think about it.
There is plenty of interesting terrain on this course and I hope to try again some day. I will likely still have to walk through portions of the trail, but I would like to have a proper completion of the trail without any missed sections. I may want to do a confidence builder or two before I go back.
## Tuesday, January 3, 2017
### Trimming the Split Ends of Waveforms
In a recent post about making sounds in F# (using Pulse Code Modulation, PCM) I noted that my sound production method was creating popping sounds at the ends of each section of sound. I suggested this was due to sudden changes in phase, which I am persuaded is at least involved. Whether or not it is the fundamental cause, it may be a relevant observation about instrumental sound production.
One way to make the consecutive wave forms not have pops between them might well be to carry the phase from one note to the next as it would lessen the sudden change in the sound. Another way, probably simpler, and the method I pursue in this post is to "back off" from the tail—the "split end" of the wave form—and only output full cycles of waves with silence filling in the left over part of a requested duration. My experimentation with it suggests that this approach still results in a percussive sound at the end of notes when played on the speakers. (I suppose that electronic keyboards execute dampening1 when the keyboardist releases a key to avoid this percussive sound.)
The wave forms I was previously producing can be illustrated by Fig. 1. We can reduce the popping by avoiding partial oscillations (Fig. 2.). However, even on the final wave form of a sequence wave forms, there is an apparent percussive sound suggesting that this percussive effect is not (fully) attributable to the sudden start of the next sound. Eliminating this percussive effect would probably involve dampening. Either the dampening would need to be a tail added to the sound beyond the requested duration or a dampening period would need to be built in to the duration requested.
Fig. 1. A partial oscillation is dropped and a new wave form starts at a phase of 0.0. The "jog" is audible as a "pop".
Fig. 2. "Silent partials" means we don't output any pulse signal for a partial oscillation. The feature is perceivable by the human ear as a slight percussive sound.
It's worth thinking a bit about how typical "physical" sound production has mechanisms in it which "naturally" prevent the popping that we have to carefully avoid in "artificial" sound production.
• In a wind instrument, you can't have a sudden enough change in air pressure or sudden enough change in the vibration of the reed or instrument body to create pops.
• In a stringed instrument, alteration of the frequency of the vibration of the string will maintain the phase of the vibration from one frequency to the next.
• The wave form is not "interrupted" by anything you can do to the string. There are no truly "sudden" changes you can make to the vibration of the string.
• Any dampening you can do is gradual in hearing terms.
• A "hammer-on" a guitar string does not suddenly move the position of the string with respect to its vibration period—phase is maintained.
• In a piano, dampening does not create sufficiently sudden changes in the wave form to create a pop.
In short, (non-digital) instrumental sound production avoids "pops" by physical constraints that produce the effects of dampening and/or phase continuity. Digital sound production is not inherently constrained by mechanisms that enforce these effects.
I have altered the sinewave function to fill the last section of the sound with silence, following the pattern suggested by Fig. 2. This does leave an apparent percussive effect, but is a slight improvement in sound.
Something this experiment does not deal with is whether we are hearing an effect of the wave form, per se, or whether we are hearing the behavior of the speakers that are outputting the sound. A sudden stop of something physical within the speaker might generate an actual percussive sound. Also still outstanding is whether the human ear can perceive phase discontinuity in the absence of an amplitude discontinuity.
1 Dampening is a (progressive) reduction in amplitude over several consecutive oscillations of a wave.
## Friday, December 30, 2016
### Packing Spheres into a Cube
In this post I compare three different alignment strategies for putting spheres into a cube. Our main variable will be $$n$$, the ratio of cube side to sphere diameter. The question is, how many spheres can we get into the cube? We denote the number of spheres as $$S$$.
### Matrix Alignment
The simplest alignment of spheres to think about is a matrix alignment, or row, column, layer. If $$n=10$$, then we can fit 1000 spheres into the cube this way. Or, in general, $$S=n^3$$.
Fig. 1. Matrix alignment.
One way to summarize this alignment is that each sphere belongs to its own circumscribing cube and none of these circumscribing cubes overlap each other. For small values of $$n$$, this arrangement is optimal.
### Square Base Pyramid Alignment
An improvement to $$S$$, for larger values of $$n$$ is had by making the alignment of subsequent layers offset. Start with a layer in a square arrangement ($$n$$ by $$n$$). If you look down on this first layer, it's awfully tempting to nestle the next layer of spheres in the depressions between the spheres. We will make better use of the interior space, although we won't make as good a use of the space near the edges. But if we can get enough extra layers in to make up for the losses near the outside, that would carry the day.
Fig. 2. A few red dots show where we're thinking of putting the next layer of spheres. We won't fit as many on this layer, but the second layer isn't as far removed from the first.
In the matrix alignment, consecutive layers were all a distance of 1 unit between layers (center to center). With this current alignment, we need to know the distance between layers. We need to consider a group of four spheres as a base and another sphere nestled on top and find the vertical distance from the center of the four base spheres to the center of the top sphere. (Implicitly, the flat surface the four base spheres are resting on constitute horizontal. Vertical is perpendicular to that.)
Fig. 3. Top view of a square base pyramid packing arrangement.
We can see from Fig. 3., that line segment ab is of length $$\sqrt{2}$$. We take a section parallel to this line segment, shown in Fig. 4.
Fig. 4. We recognize a 45°-45°-90° triangle, abc.
We can calculate the vertical distance between layers, line segment cd, as $$\sqrt{2}/2 \approx 0.7071\dots$$. Note that the spheres in this second layer are in basically the same configuration as the bottom layer. We can see this will be the case because the top sphere in Fig. 3., has its outer circumference pass across the point where the lower spheres meet. So adjacent spheres in the second layer will be in contact. And, further, second layer spheres will follow the rectangular pattern of depressions in the bottom layer which are spaced apart the same as the centers of the spheres in the bottom layer. So we will end up with the same organization of spheres in the second layer as the bottom layer, just one fewer row and one fewer column.
We can now calculate the number of spheres that will fit in a cube using this alignment as
$$S = n^2 \lambda_1 + (n-1)^2 \lambda_2,$$
where $$\lambda_1$$ is the number of full layers and $$\lambda_2$$ is the number of "nestled" layers. (The third layer, which is indeed "nestled" into the second layer is also returned to the configuration of the first layer and so I refer to it as a full layer instead. The cycle repeats.) To find $$\lambda_1$$ and $$\lambda_2$$, we first find the total layers, $$\lambda$$ as
$$\lambda = \left \lfloor{\frac{n-1}{\sqrt{2}/2}}\right \rfloor+1$$
The rationale for this formula is: find how many spaces between layers there are and compensate for the difference between layers and spaces. Imagine a layer at the very bottom and a layer at the very top (regardless of configuration). The layer at the bottom, we get for free and is the 1 term in the formula. (The top layer may or may not be tight with the top when we're done but hold it up there for now.) The distance from the center of the bottom layer to the center of the top layer is $$n-1$$. The number of times we can fit our spacing interval into this number (completely), is the number of additional layers we can fit in. (Additional to the bottom layer, the top layer is the last of the layers we just found room for in the $$n-1$$, or, technically, $$n-1/2$$, er, whatever, do some examples.)
The break down between $$\lambda_1$$ and $$\lambda_2$$ will not be exactly even, with $$\lambda_1$$ having one more if $$\lambda$$ is odd. We can show this neatly using the ceiling operator
$$\lambda_1 = \left \lceil{\lambda/2}\right \rceil$$
$$\lambda_2 = \lambda - \lambda_1$$
As early as $$n=4$$ we get $$S=66$$, which is better than the matrix arrangement by 2 spheres. I modeled this to make sure I didn't let an off by one error sneak into my formula (see Fig. 5.).
Fig. 5. Somewhat surprisingly, rearrangement of spheres (relative to matrix alignment) produces gains in volume coverage even at $$n=4$$.
Here it is in Maxima:
### Tetrahedral Alignment
Another rearrangement is similar to a honeycomb. A honeycomb is an arrangement of hexagons that meet perfectly at their edges. Pictures of this are readily available online. This Wikipedia article suffices. Imagine putting a circle or a sphere in each of these honeycomb cells. The will produce a single layer which is more compact, although it will push the distance between layers apart.
So, what do we need to know to make a formula for this one?
1. Find the distance between successive layers.
2. Formula for the number of layers.
3. Formula for the number of spheres in each layer.
1. This depends on knowing the range of layer configurations (we will only have two different layer configurations).
4. Some assembly required.
This is the same procedure we followed already for the square based pyramid alignment, but we are being more explicit about the steps.
Fig. 6. We need to find the distance of line segment ad.
We recognize we have an equilateral triangle and so we can identify a 30°-60°-90° triangle on each half of altitude ab. We have drawn all of the angle bisectors for this triangle which meet at a common point (commonly known property for triangles). We can recognize/calculate the length of bd as $$\frac{1}{2\sqrt{3}}$$. We can then calculate the length of ad as $$\frac{\sqrt{3}}{2} - \frac{1}{2\sqrt{3}} = 1/\sqrt{3}$$. From the Pythagorean theorem, we have a length for cd of $$\sqrt{2/3}$$.
The number of spheres in the first layer will require us to use the distance for ab. We now need to find the number of rows in the bottom layer. We have
$$L_1=n \rho_1 + (n-1) \rho_2,$$
where $$\rho_1$$ and $$\rho_2$$ are the number of each kind of row in the layer and $$L_1$$ is the number of spheres in the first layer. Since rows are spaced by $$\sqrt{3}/2$$, we have a number of rows, $$\rho$$, of
$$\rho = \left \lfloor{\frac{n-1}{\sqrt{3}/2}}\right \rfloor+1$$
and $$\rho_1$$ and $$\rho_2$$ can be broken out similar to our $$\lambda$$'s earlier.
$$\rho_1 = \left \lceil{\frac{\rho}{2}}\right \rceil$$
$$\rho_2 = \rho - \rho_1.$$
Fig. 7. We're looking for the distance of line segment cd which can be found using ac and ad.
Now, there is a little matter of how nicely (or not) the second layer will behave for us. It is noteworthy that we are not able to put a sphere into every depression. We skip entire rows of depressions. (The Wikipedia article on sphere packing referred to these locations as the "sixth sphere".) These skipped locations may play mind games on you as you imagine going to the third layer. Nevertheless, the third layer can be made identical to the first, which is what I do here.
Fig. 8. The first layer is blue. The second layer is red. Are we going to have trouble with you Mr. Hedral?
There's a couple of things that happen on the second layer. First, instead of starting with a row of size $$n$$, we start with a row of size $$n-1$$. The second issue is that we may not get as many total rows in. We could do the same formula for rows again but now accounting for the fact that we have lost an additional $$\frac{1}{2\sqrt{3}}$$ before we start. However, we can reduce this to a question of "do we lose a row or not?" The total distance covered by the rows, $$R$$, for the bottom layer is
$$R = (\rho-1) \frac{\sqrt{3}}{2} + 1$$
If $$n-R\ge\frac{1}{2\sqrt{3}}$$, then we have the same number of total rows. Otherwise, we have one less row. We let $$r_L$$ represent the number of rows lost in the second layer, which will either be 0 or 1. Noting that the order of the rows is now $$n-1$$ followed by $$n$$, we can give an expression for the number of spheres, $$L_2$$, in our second layer now.
$$L_2 = (n-1)(\rho_1 - r_L) + n\rho_2$$
We have a very similar formula for the total number of spheres in the box.
$$S = L_1\lambda_1 + L_2\lambda_2,$$
where
$$\lambda_1 = \left \lceil{\frac{\lambda}{2}}\right \rceil$$
$$\lambda_2 = \lambda - \lambda_1,$$
where
$$\lambda = \left \lfloor{\frac{n-1}{\sqrt{2/3}}}\right \rfloor+1.$$
My Maxima function for this is
### Comparison Between Methods
It isn't too hard to tell that one of the two second approaches is going to produce better results than the first after some value of $$n$$ (Fig. 9.). What is more surprising is that our latter two alignments stay neck and neck up into very high values of $$n$$. If we divide them by the volume of the containing cube, both appear to be a round about way to arrive at the square root of 2! (Fig. 10.)
Fig. 9. Both of the latter approaches give much better packing densities than the matrix alignment.
Fig. 10. Square base packing in blue, tetrahedral packing in red, both divided by total volume (# of spheres/unit volume). Unclear if there is a distinct winner and we seem to be getting closer to $$\sqrt{2}$$.
Let's see which one wins more often for positive integer values of $$n$$ in Maxima.
So, there's no run away winner, but if you're a betting man, bet on square base pyramid packing out of the available choices in this post. Regardless, it appears that both of these packing arrangements approach optimal packing (see Sphere packing). My density calculation (allowing the $$\sqrt{2}$$ conjecture) for volume coverage comes out to
Gauss, old boy, seems to have approved of this number.
## Tuesday, December 27, 2016
### Sounds Like F#
Last time, I thought that I was going to have to do some special research to account for multiple sources of sound. Reading this short physics snippet I can see that multiple sources is really as simplistic as my initial thinking was inclined to. You can ignore all of the decibel stuff and focus on the statements about amplitude, because, of course, I am already working in terms of amplitude. What can I say, I let the mass of voices on the internet trouble my certainty unduly? Sort of.
There's two important issues to consider:
1. Offsetting of the signals.
2. Psychological issues regarding the perception of sound.
Regarding number 2, here's a quick hit I found: http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/loud.html. It seems credible, but I'm not sufficiently interested to pursue it further. And so, my dear Perception, I salute you in passing, Good day, Sir!
Offsetting of the signals is something that is implicitly accounted for by naively adding the amplitudes, but there is a question of what the sineChord() function is trying to achieve. Do I want:
1. The result of the signals beginning at exactly the same time (the piano player hits all his notes exactly[?] at the same time—lucky dog, guitar player not as much[?]. Hmm...)?
2. The average case of sounds which may or may not be in phase?
Regarding case 2, Loring Chien suggests in a comment on Quora that the average case would be a 41% increase in volume for identical sounds not necessarily in phase. At first glance, I'm inclined to think it is a plausible statement. Seeming to confirm this suggestion is the summary about Adding amplitudes (and levels) found here, which also explains where the the 41% increase comes from, namely, from $$\sqrt{2}\approx 1.414\dots$$. Good enough for me.
All such being said, I will pass it by as I am approaching this from a mechanical perspective. I'm neither interested in the psychological side of things, nor am I interested in getting average case volumes. I prefer the waves to interact freely. If would be neat, for example, to be able to manipulate the offset on purpose and get different volumes. The naive approach is little more subject to experimentation.
I would like to go at least one step further though and produce a sequence of notes and chords and play them without concern of fuzz or pops caused by cutting the tops of the amplitudes off. We need two pieces: a) a limiter and b) a means of producing sequences of sounds in a musically helpful way.
A limiter is pretty straight-forward and is the stuff of basic queries. I have the advantage of being able to determine the greatest amplitude prior to playing any of the sound. The function limiter() finds the largest absolute amplitude and scales the sound to fit.
Here is an example usage:
One concern here is that we may make some sounds that we care about too quiet by this approach. To address such concerns we would need a compressor that affects sounds from the bottom and raises them as well. The general idea of a sound compressor is to take sounds within a certain amplitude range and compress them into a smaller range. So, sounds outside your range (above or below) get eliminated and sounds within your range get squeezed into a tighter dynamic (volume) range. This might be worth exploring later, but I do not intend to go there in this post.
Last post I had a function called sineChord(), which I realize could be generalized. Any instrument (or group of identical instruments) could be combined using a single chord function that would take as a parameter a function that converts a frequency into a specific instrument sound. This would apply to any instruments where we are considering the notes of the chord as starting at exactly the same time (guitar would need to be handled differently). So, instead of sineChord(), let's define instrumentChord():
Next we will create a simple class to put a sequence of notes/chords and durations into which we can then play our sounds from.
### Reference Chords and Values
Here are a few reference chord shapes and duration values. I define the chord shape and the caller supplies the root sound to get an actual chord. The durations are relative to the whole note and the chord shapes are semi-tone counts for several guitar chord shapes. The root of the shapes is set to 0 so that by adding the midi-note value to all items you end up with a chord using that midi note as the root. This is the job of chord().
Next, InstrumentSequence is an accumulator object that knows how to output a wave form and play it. For simplicity, it is limited to the classic equal temperment western scale. Note that it takes a function has the task of turning a frequency into a wave form, which means that by creating a new function to generate more interesting wave forms, we can have them played by the same accumulator. If we only want it to produce the wave form and aggregate the wave forms into some other composition, we can access the wave form through the routine WaveForm.
A sample use of the class which follows a very basic E, A, B chord progression follows:
To get the same progression with minors, use the EmShape, etc., values. But, at the end of the day, we've still got sine waves, lots of them. And, it's mostly true that,
boring + boring = boring.
I will not attempt the proof. You can make some more examples to see if you can generate a counter-example.
There is also some unpleasant popping that I would like to understand a bit better—for now I'm going to guess it relates to sudden changes in the phases of the waves at the terminations of each section of sound. Not sure what the solution is but I'll guess that some kind of dampening of the amplitude at the end of a wave would help reduce this.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.674198567867279, "perplexity": 572.3129464556716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814290.11/warc/CC-MAIN-20180222200259-20180222220259-00363.warc.gz"}
|
https://www.electro-tech-online.com/threads/where-to-buy-infrared-detector-cards.96651/
|
# Where to buy Infrared detector cards?
Status
Not open for further replies.
#### Mr RB
##### Well-Known Member
Hi, does anyone know if you can still buy the infrared detector cards (like a little business card sized thingy) that have an area of infrared fluorescent material?
Of if the infrared fluorescent tape is still available and where to buy either?
Iv'e been working with infrared sensors a lot lately and it's annoying having to use my digital camer to look at the IR spread and what the IR is hitting at the reflection distance etc. Much easier to hold a little card there and see the actual IR dot. Thanks!
#### Hero999
##### Banned
I suppose the card has advantages over electronic solutions: it doesn't require batteries, will show you the beam angle and give you an indication of the intensity.
#### espain13
##### New Member
Digital Camera IR Detection.
If I were to use a Digital Camera for IR detection, would I need a direct shot at the source or would it pick up a side shot of the beam passing through the space before the lens. I'm looking at IR detection for the purpose of detecting IR transmitters used for concealed communication. I would want to cover as wide a scanning area as possible. If you can help, thank you!
Also if anyone had advice on a particularly IR sensitive camera that would be great as well. Thanks!
#### Mr RB
##### Well-Known Member
You may need an older camera as most of the new ones have IR filters over the camera. Sometimes you can remove the IR filter, there are a zillion "IR camera hack" blogs out there.
My old camera works great, it can see the IR from a remote control or an IR LED no problems from across the room.
If you are trying to pick up covert IR comms you could try a high gain AC amplifier connected to a IR photo sensor, as most comms would be modulated you could put a couple of switchable bandpass filters on it and an output meter and see the meter go off scale anytime they are transmitting. If they are using an analogue modulation AM or FM etc you could even listen in.
Status
Not open for further replies.
Replies
6
Views
1K
Replies
4
Views
2K
Replies
3
Views
1K
Replies
7
Views
2K
Replies
1
Views
724
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15986812114715576, "perplexity": 2016.9176868259153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358233.7/warc/CC-MAIN-20211127193525-20211127223525-00179.warc.gz"}
|
https://findscholars.unh.edu/display/publication46665
|
# Distribution of energetic oxygen and hydrogen in the near-Earth plasma sheet
### Abstract
• The spatial distributions of different ion species are useful indicators for plasma sheet dynamics. In this statistical study based on 7 years of Cluster observations, we establish the spatial distributions of oxygen ions and protons at energies from 274 to 955 keV, depending on geomagnetic and solar wind (SW) conditions. Compared with protons, the distribution of energetic oxygen has stronger dawn-dusk asymmetry in response to changes in the geomagnetic activity. When the interplanetary magnetic field (IMF) is directed southward, the oxygen ions show significant acceleration in the tail plasma sheet. Changes in the SW dynamic pressure (\$\mathit{P}_{dyn}\$) affect the oxygen and proton intensities in the same way. The energetic protons show significant intensity increases at the near-Earth duskside during disturbed geomagnetic conditions, enhanced SW \$\mathit{P}_{dyn}\$, and southward IMF, implying there location of effective inductive acceleration mechanisms and a strong duskward drift due to the increase of the magnetic field gradient in the near-Earth tail. Higher losses of energetic ions are observed in the dayside plasma sheet under disturbed geomagnetic conditions and enhanced SW \$\mathit{P}_{dyn}\$. These observations are in agreement with theoretical models.
• ### Authors
• Kronberg, EA
• Grigorenko, EE
• Haaland, SE
• Daly, PW
• Delcourt, DC
• Luo, H
• Kistler, Lynn
• Dandouras, I
• May 2015
### Keywords
• physics.space-ph
• 3415
• 3431
• 120
• 5
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9553418159484863, "perplexity": 8427.927038137332}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540487789.39/warc/CC-MAIN-20191206095914-20191206123914-00068.warc.gz"}
|
https://puzzling.stackexchange.com/questions/2373/what-is-the-number-4-9292683/2374
|
# What is the number 4.9292683…?
Guess the next digits of this number. Where does it came from?
4.9292683
• "Floating point" is actually a computing term, describing how a number is represented and stored. In that sense, this isn't a floating point number; it's a string representing a real number. – TheRubberDuck Nov 24 '14 at 16:53
It's $\pi e \gamma$
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3746623694896698, "perplexity": 1033.4126649759694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488534413.81/warc/CC-MAIN-20210623042426-20210623072426-00409.warc.gz"}
|
http://mathoverflow.net/users/297/david-speyer
|
# David Speyer
less info
reputation
5155354
bio website math.lsa.umich.edu/~speyer location Ann Arbor age 34 member for 5 years, 1 month seen 1 hour ago profile views 30,899
Associate Professor of Mathematics at the University of Michigan. My research interests are in combinatorial algebraic geometry, particularly Schubert calculus, matroids and cluster algebras. I also enjoy thinking about number theory and computational mathematics.
112 Most memorable titles 91 Why do primes dislike dividing the sum of all the preceding primes? 74 Invertible matrices of natural numbers are permutations… why? 61 $\prod_{n=1}^{\infty} n^{\mu(n)}=\frac{1}{4 \pi ^2}$ 54 Irreducibility of polynomials in two variables
# 71,460 Reputation
+10 Hirzebruch's motivation of the Todd class +65 Can all $L^2$ holomorphic functions on a domain vanish at a particular point? +10 Generating a finite group from elements in each conjugacy class +10 What does the generating function $x/(1 - e^{-x})$ count?
# 71 Questions
47 Is there a “Basic Number Theory” for elliptic curves? 43 What is Lagrange Inversion good for? 27 Can assignment solve stable marriage? 24 What is known about this plethysm? 24 Is there software to compute the cohomology of an affine variety?
# 401 Tags
1k ag.algebraic-geometry × 268 341 linear-algebra × 50 1k nt.number-theory × 167 318 gr.group-theory × 57 609 co.combinatorics × 117 293 polynomials × 34 456 ac.commutative-algebra × 69 272 prime-numbers × 19 345 rt.representation-theory × 68 257 at.algebraic-topology × 40
# 17 Accounts
MathOverflow 71,460 rep 5155354 Mathematics 29,242 rep 170132 Mathematics Educators 1,128 rep 113 Mathematica 1,002 rep 715 Academia 432 rep 23
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.529955267906189, "perplexity": 3924.276002276784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400380866.29/warc/CC-MAIN-20141119123300-00170-ip-10-235-23-156.ec2.internal.warc.gz"}
|
http://physics.stackexchange.com/questions/4395/asymptotic-curvature-of-the-universe-and-correlation-with-local-curvature
|
# asymptotic curvature of the universe and correlation with local curvature
There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions regarding this:
1) Does the fact that a manifold with a) asymptotic (space) curvature zero and b) local inhomogeneities with positive (space) curvature imply that there will be regions with negative (space) curvature?
2) a Region of negative (space) curvature implies dark energy in that region?
3) assuming answer to both 1) and 2) are true: does this represent an independent confirmation of dark energy? or there is somehow an geometric relationship relating asymptotic flatness to accelerated expansion (the traditional reason to introduce dark energy in the first place)?
EDITED: to reflect distinction between space and space-time curvatures.
-
You have to be careful to distinguish between curvature of space and curvature of spacetime. When we say that the Universe is flat on large scales, we're talking about space -- that is, about a slice through spacetime at constant cosmic time. With respect to spatial curvature, statement 1 is correct: we do have zero curvature on average, and positive curvature in some regions, which implies negative curvature in other regions.
But statement 2 doesn't follow from statement 1, because in this case we want to talk about spacetime curvature. To be specific, ordinary matter produces positive spacetime curvature (i.e. a positive Ricci scalar), and dark energy produces negative spacetime curvature. But spatial curvature and spacetime curvature are different things.
-
great answer. thanks i didn't realise that the paper was relevant only to space curvature – lurscher Feb 1 '11 at 21:54
Ted, you said: "positive curvature in some regions, which implies negative curvature in other regions".. Are you implying that the density of dark energy is larger in certain regions? – dbrane Feb 1 '11 at 22:16
@dbrane -- No. Once again: the statements about dark energy are about spacetime curvature, while the statements about positive and negative curvature are about spatial curvature. And anyway, the fact that curvature varies from place to place doesn't imply that the density of dark energy varies from place to place -- at most, it implies that the total density varies from place to place. DE could be uniform, with the variations caused by the other stuff. – Ted Bunn Feb 1 '11 at 22:18
@dbrane, the first question doesn't mention dark energy at all, 1st question is entirely about geometry – lurscher Feb 1 '11 at 22:31
The universe is flat spatially, but the space is being stretched with time on the Hubble frame. This means how the space is embedded in spacetime is such that there is curvature, such as a “time-time” Ricci curvature $R^{tt}$. This solution to the Einstein field equations is such that the pressure is equal to the negative of the energy density of the vacuum. So dark energy, which is associated with this pressure is due to a positive energy density. The Hamiltonian for this is $H~=~\Lambda x^2/6$, which is similar to the spring potential. However, the force acts in the same direction as the displacement.
-
thanks. Please, can you rephrase your question as answers to each specific subquestion? – lurscher Feb 1 '11 at 21:42
My main comment is on how dark energy is not due to negative energy. That is clearly not the case. – Lawrence B. Crowell Feb 1 '11 at 21:54
and why negative energy is relevant to the question? are you saying that negative energy is required on regions with negative (space-time) curvature/Ricci scalar? – lurscher Feb 1 '11 at 22:08
Negative energy suffers from a range of problems, where here I am thinking of $T^{00}$. Dark energy is not a case of negative energy. That is the main thrust of what I wrote. – Lawrence B. Crowell Feb 1 '11 at 22:34
thats correct. But i never mentioned negative energy in the question, that is why i asked why you implied that it was relevant – lurscher Feb 1 '11 at 22:41
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9097267389297485, "perplexity": 467.58192496234403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042985140.15/warc/CC-MAIN-20150728002305-00099-ip-10-236-191-2.ec2.internal.warc.gz"}
|
http://mathhelpforum.com/math-topics/65444-volume-metal-block.html
|
# Thread: Volume of Metal Block
1. ## Volume of Metal Block
How do i solve this:
A rectangular block of metal with a square cross-section has a total surface area of 625cm2. Find the maximum volume of the block of metal?
Help!!
2. Let the rectangular block have dimensions x, x and y. (2 x's because the cross section is a square).
So the surface area is given be $2x^2$ (each end face) $+ 4xy$ (each length face).
$2x^2 + 4xy = 625$
$y = \frac{625 - 2x^2}{4x}$
Now,
Volume = 'area of cross section' times 'length' = $x^2y$.
$= x^2 \times \frac{625 - 2x^2}{4x}$
$= x \times \frac{625 - 2x^2}{4}$
$= \frac{1}{4} \left({625x - 2x^3}\right)$
$\frac{dV}{dx} = \frac{1}{4} (625 - 6x^2) = 0$ (for max)
$6x^2 = 625$
$x = \sqrt{\frac{625}{6}}$
Once you have calculated this value, substitute into the equation for y. Use the Volume = $x^2y$ formula to find the max volume.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.853148877620697, "perplexity": 1324.8706858439548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542687.37/warc/CC-MAIN-20161202170902-00114-ip-10-31-129-80.ec2.internal.warc.gz"}
|
http://mathhelpforum.com/calculus/45527-solved-complex-factors-polynomials.html
|
Thread: [SOLVED] Complex factors of polynomials
1. [SOLVED] Complex factors of polynomials
Question:
Find real values for k for which (z - ki) is a factor of the polynomial equation: $z^4-2z^3+7z^2-4z+10=0$
What I did:
I tried splitting them up into two different quadratic equations to use the Qudaratic formula to find the complex roots. But I ended up with a mess of unknowns and it just seemed to complicated and messy to be the right direction.
Any hints as to how I should tackle these questions?
2. Originally Posted by Evales
Question:
Find real values for k for which (z - ki) is a factor of the polynomial equation: $z^4-2z^3+7z^2-4z+10=0$
What I did:
I tried splitting them up into two different quadratic equations to use the Qudaratic formula to find the complex roots. But I ended up with a mess of unknowns and it just seemed to complicated and messy to be the right direction.
Any hints as to how I should tackle these questions?
Let $p(z) = z^4-2z^3+7z^2-4z+10$. You require p(ki) = 0:
$(ki)^4-2(ki)^3+7(ki)^2-4(ki)+10 = k^4 + 2k^3 i - 7k^2 - 4ki + 10 = (k^4 - 7k^2 + 10) + i (2k^3 - 4k)$.
Therefore you require values of k that simultaneously satisfy:
$k^4 - 7k^2 + 10 = 0$ .... (1)
$2 k^3 - 4k = 0 \Rightarrow k^3 - 2k = 0$ .... (2)
Solutions to (2) are $k = 0, \, k = \sqrt{2}, \, k = -\sqrt{2}$.
Keep the value(s) of k that satisfy (1) .....
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.69804447889328, "perplexity": 508.4619650543958}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689806.55/warc/CC-MAIN-20170923231842-20170924011842-00388.warc.gz"}
|
https://worldwidescience.org/topicpages/a/accelerated+testing+evaluation.html
|
#### Sample records for accelerated testing evaluation
1. Evaluation of an Accelerated ELDRS Test Using Molecular Hydrogen
Science.gov (United States)
Pease, Ronald L.; Adell, Philippe C.; Rax, Bernard; McClure, Steven; Barnaby, Hugh J.; Kruckmeyer, Kirby; Triggs, B.
2011-01-01
An accelerated total ionizing dose (TID) hardness assurance test for enhanced low dose rate sensitive (ELDRS) bipolar linear circuits, using high dose rate tests on parts that have been exposed to molecular hydrogen, has been proposed and demonstrated on several ELDRS part types. In this study several radiation-hardened "ELDRS-free" part types have been tested using this same approach to see if the test is overly conservative.
2. Experimental evaluation of the Battelle accelerated test design for the solar array at Mead, Nebraska
Energy Technology Data Exchange (ETDEWEB)
Frickland, P.O.; Repar, J.
1982-04-06
A previously developed test design for accelerated aging of photovoltaic modules was experimentally evaluated. The studies included a review of relevant field experience, environmental chamber cycling of full-size modules, and electrical and physical evaluation of the effects of accelerated aging during and after the tests. The test results indicated that thermally induced fatigue of the interconnects was the primary mode of module failure as measured by normalized power output. No chemical change in the silicone encapsulant was detectable after 360 test cycles.
3. Evaluation of accelerated deterioration in NAPTF flexible test pavements
Institute of Scientific and Technical Information of China (English)
Kasthurirangan GOPALAKRISHNAN
2008-01-01
Previous research studies have successfully demonstrated the use of artificial neural network(ANN)models for predicting critical structural responses and layer moduli of highway flexible pavements.The primary objective of this study was to develop an ANN-based approach for backcalculation of pavement moduli based on heavy weight deflectometer(HWD)test data,especially in the analysis of airport flexible pavements subjected to new generation aircraft(NGA).Two medium-strength subgrade flexible test sections,at the National Airport Pavement Test Facility(NAPTF),were modeled using a finite element(FE) based pavement analysis program,which can consider the non-linear stress-dependent behavior of pavement geomaterials.A multi-layer,feed-forward network which uses an error-backpropagation algorithm was trained to approximate the HWD backcalculation function using the FE program generated synthetic database.At the NAPTF,test sections were subjected to Boeing 777 (B777)trafficking on one lane and Boeing 747(B747)trafficking on the other lane using a test machine.To monitor the effect of traffic and climatic variations on pavement structural responses.HWD tests were conducted on the traffieked lanes and on the untraffieked centerline of test sections as trafficking progressed.The trained ANN models were successfully applied on the actual HWD test data acquired at the NAPTF to predict the asphalt concrete moduli and non-1inear subgrade moduli of the medium-strength subgrade flexible test sections.
4. Ageing evaluation of low voltage cables and insulators with gamma ray irradiation and thermal accelerated ageing tests
International Nuclear Information System (INIS)
To optimize lifetime prediction method of cables and to understand cable ageing mechanism, ageing evaluation of low voltage cables and insulators with gamma ray irradiation and thermal accelerated ageing tests were conducted. Insulators had no indication of the ageing after 1000 hours of the accelerated ageing tests. (author)
5. Evaluation of Dynamic Mechanical Loading as an Accelerated Test Method for Ribbon Fatigue: Preprint
Energy Technology Data Exchange (ETDEWEB)
Bosco, N.; Silverman, T. J.; Wohlgemuth, J.; Kurtz, S.; Inoue, M.; Sakurai, K.; Shinoda, T.; Zenkoh, H.; Hirota, K.; Miyashita, M.; Tadanori, T.; Suzuki, S.
2015-04-07
Dynamic Mechanical Loading (DML) of photovoltaic modules is explored as a route to quickly fatigue copper interconnect ribbons. Results indicate that most of the interconnect ribbons may be strained through module mechanical loading to a level that will result in failure in a few hundred to thousands of cycles. Considering the speed at which DML may be applied, this translates into a few hours o testing. To evaluate the equivalence of DML to thermal cycling, parallel tests were conducted with thermal cycling. Preliminary analysis suggests that one +/-1 kPa DML cycle is roughly equivalent to one standard accelerated thermal cycle and approximately 175 of these cycles are equivalent to a 25-year exposure in Golden Colorado for the mechanism of module ribbon fatigue.
6. Accelerated cyclic corrosion tests
OpenAIRE
Prošek T.
2016-01-01
Accelerated corrosion testing is indispensable for material selection, quality control and both initial and residual life time prediction for bare and painted metallic, polymeric, adhesive and other materials in atmospheric exposure conditions. The best known Neutral Salt Spray (NSS) test provides unrealistic conditions and poor correlation to exposures in atmosphere. Modern cyclic accelerated corrosion tests include intermittent salt spray, wet and dry phases and eventually other technical p...
7. Radiation resistance of polymer materials. Degradation evaluation by accelerated testing for application condition
International Nuclear Information System (INIS)
This paper presents re-evaluated radiation resistance property data of polymer materials, which had been tested in past times in TAKASAKI Quantum Beam Science Directorate, for the future study of ageing evaluation of low voltage electric cable insulation materials used in light-water nuclear reactors. The radiation resistance of 25 types of plastics and rubbers materials applied in practical environments was evaluated by the accelerated testing of gamma-ray irradiation under oxygen pressure, and was compared with the radiation resistance determined from the traditional testing by irradiation with a high dose rate in air. The polymer materials were formulated to be similar or equivalent to practical materials, and the most of formulation (chemical compounds and quantities) were described. For all materials, the tensile properties (elongation at break, ultimate strength, 100% or 200% modulus), electric resistivity, gel-fraction, and density were measured after irradiation in oxidation conditions and irradiation in air with a high dose rate (non-oxidation conditions). The data of relations between each properties and total dose at various conditions were compiled, and the relations among the changes of mechanical properties, electrical properties, and radiation induced chemical reactions were discussed. (author)
8. Evaluation of oxidative behavior of polyolefin geosynthetics utilizing accelerated aging tests based on temperature and pressure
Science.gov (United States)
Li, Mengjia
Polyolefin geosynthetics are susceptible to oxidation, which eventually leads to the reduction in their engineering properties. In the application of polyolefin geosynthetics, a major issue is an estimate of the materials durability (i.e. service lifetime) under various aging conditions. Antioxidant packages are added to the polyolefin products to extend the induction time, during which antioxidants are gradually depleted and polymer oxidation reactions are prevented. In this PhD study, an improved laboratory accelerating aging method under elevated and high pressure environments was applied to evaluate the combined effect of temperature and pressure on the depletion of the antioxidants and the oxidation of polymers. Four types of commercial polyolefn geosynthetic materials selected for aging tests included HDPE geogrid, polypropylene woven and nonwoven geotextiles. A total of 33 different temperature/pressure aging conditions were used, with the incubation duration up to 24 months. The applied oven temperature ranged from 35°C to 105°C and the partial oxygen pressure ranged from 0.005 MPa to 6.3 MPa. Using the Oxidative Induction Time (OIT) test, the antioxidant depletion, which is correlated to the decrease of the OIT value, was found to follow apparent first-order decay. The OIT data also showed that, the antioxidant depletion rate increased with temperature according to the Arrhenius equation, while under constant temperatures, the rate increased exponentially with the partial pressure of oxygen. A modified Arrhenius model was developed to fit the antioxidant depletion rate as a function of temperature and pressure and to predict the antioxidant lifetime under various field conditions. This study has developed new temperature/pressure incubation aging test method with lifetime prediction models. Using this new technique, the antioxidant lifetime prediction results are close to regular temperature aging data while the aging duration can be reduced considerably
9. CESR Test Accelerator
CERN Document Server
Rubin, David L
2013-01-01
The Cornell Electron Storage Ring (CESR) was reconfigured in 2008 as a test accelerator to investigate the physics of ultra-low emittance damping rings. During the approximately 40 days/year available for dedicated operation as a test accelerator, specialized instrumentation is used to measure growth and mitigation of the electron cloud, emittance growth due to electron cloud, intra-beam scattering, and ions, and single and multi-bunch instabilities generated by collective effects. The flexibility of the CESR guide field optics and the integration of accelerator modeling codes with the control system have made possible an extraordinary range of experiments. Findings at CesrTA with respect to electron cloud effects, emittance tuning techniques, and beam instrumentation for measuring electron cloud, beam sizes, and beam positions are the basis for much of the design of the ILC damping rings as documented in the ILC-Technical Design Report. The program has allowed the Cornell group to cultivate the kind of talen...
10. Testing Gravity on Accelerators
CERN Document Server
Kalaydzhyan, Tigran
2016-01-01
Weak equivalence principle (WEP) is one of the cornerstones of the modern theories of gravity, stating that the trajectory of a freely falling test body is independent of its internal structure and composition. Even though WEP is known to be valid for the normal matter with a high precision, it has never been experimentally confirmed for relativistic matter and antimatter. We make an attempt to constrain possible deviations from WEP utilizing the modern accelerator technologies. We analyze the (absence of) vacuum Cherenkov radiation, photon decay, anomalous synchrotron losses and the Compton spectra to put limits on the isotropic Lorentz violation and further convert them to the constraints on the difference between the gravitational and inertial masses of the relativistic electrons/positrons. Our main result is the 0.1% limit on the mentioned difference.
11. Solid oxide materials research accelerated electrochemical testing
Energy Technology Data Exchange (ETDEWEB)
Windisch, C.; Arey, B.
1995-08-01
The objectives of this work were to develop methods for accelerated testing of cathode materials for solid oxide fuel cells under selected operating conditions. The methods would be used to evaluate the performance of LSM cathode material.
12. In vitro evaluation of the bonding durability of self-adhesive resin cement to titanium using highly accelerated life test.
Science.gov (United States)
Lin, Jie; Shinya, Akikazu; Gomi, Harunori; Matinlinna, Jukka Pekka; Shinya, Akiyoshi
2011-01-01
The purpose of this in vitro study was to evaluate the bonding durability of three self-adhesive resin cements to titanium using the Highly Accelerated Life Test (HALT). The following self-adhesive resin cements were used to bond pairs of titanium blocks together according to manufacturers' instructions: RelyX Unicem, Breeze, and Clearfil SA Luting. After storage in water at 37°C for 24 h, bonded specimens (n=15) immersed in 37°C water were subjected to cyclic shear load testing regimes of 20, 30, or 40 kg using a fatigue testing machine. Cyclic loading continued until failure occurred, and the number of cycles taken to reach failure was recorded. The bonding durability of a self-adhesive resin cement to titanium was largely influenced by the weight of impact load. HALT showed that Clearfil SA Luting, which contained MDP monomer, yielded the highest median bonding lifetime to titanium. PMID:22123007
13. Evaluation of solder joint reliability in flip-chip packages during accelerated testing
Science.gov (United States)
Kim, Jong-Woong; Kim, Dae-Gon; Hong, Won Sik; Jung, Seung-Boo
2005-12-01
The microstructural investigation and thermomechanical reliability evaluation of the Sn-3.0Ag-0.5Cu solder bumped flip-chip package were carried out during the thermal shock test of the package. In the initial reaction, the reaction product between the solder and Cu mini bump of chip side was Cu6Sn5 intermetallic compound (IMC) layer, while the two phases which were (Cu,Ni)6Sn5 and (Ni,Cu)3Sn4 were formed between the solder and electroless Ni-P layer of the package side. The cracks occurred at the corner solder joints after the thermal shocks of 400 cycles. The primary failure mechanism of the solder joints in this type of package was confirmed to be thermally-activated solder fatigue failure. The premature brittle interfacial failure sometimes occurred in the package side, but nearly all of the failed packages showed the occurrence of the typical fatigue cracks. The finite-element analyses were conducted to interpret the failure mechanisms of the packages, and revealed that the cracks were induced by the accumulation of the plastic work and viscoplastic shear strains.
14. The Brookhaven Accelerator Test Facility
International Nuclear Information System (INIS)
The Accelerator Test Facility (ATF), presently under construction at Brookhaven National laboratory, is described. It consists of a 50-MeV electron beam synchronizable to a high-peak power CO2 laser. The interaction of electrons with the laser field will be probed, with some emphasis on exploring laser-based acceleration techniques. 5 refs., 2 figs
15. Advanced Superconducting Test Accelerator (ASTA)
Data.gov (United States)
Federal Laboratory Consortium — The Advanced Superconducting Test Accelerator (ASTA) facility will be based on upgrades to the existing NML pulsed SRF facility. ASTA is envisioned to contain 3 to...
16. Application of the accelerated test Rancimat to evaluate oxidative stability of dried microencapsulated oils
Directory of Open Access Journals (Sweden)
Márquez-Ruiz, G.
2000-08-01
Full Text Available The objective of this work was to apply the oxidative test Rancimat to dried microencapsulated oils (DMO, with special emphasis on assessing the efficacy of natural antioxidants. DMO were prepared by freeze-drying emulsions containing sodium caseinate, lactose and fish or sunflower oils, with and without added the antioxidant mixture ALT (ascorbic acid, lecithin and tocopherol. Under the Rancimat working conditions selected for testing DMO (5 g sample, 100ºC and 20 L air/h, excellent repeatability was obtained. The antioxidant effect of ALT was much higher in bulk fish oil than in its counterpart DMO, either in Rancimat or at 30ºC in the dark. Further experiments using Rancimat showed that the moderate increase in stability of DMO added ALT was only attributable to tocopherol while the synergistic actions of lecithin and ascorbic acid were not observed, their action probably depending on their location and orientation in these complex lipid systems. This test enabled to compare monophasic (bulk oils and DMO-extracted oils and heterophasic lipidic systems (DMO and DMO devoid of the accessible, free oil fraction, thus offering a rapid means to examine the influence of oil distribution and partitioning of antioxidants on oxidative stability.El objetivo de este trabajo es la aplicación del test Rancimat a aceites microencapsulados, con especial interés en el estudio de la eficacia de antioxidantes naturales. Los aceites microencapsulados en matriz seca (DMO se prepararon mediante liofilización de emulsiones constituidas por caseinato sódico, lactosa y aceite de pescado o girasol, con o sin la mezcla antioxidante ALT (ácido ascórbico, lecitina y tocoferol. En las condiciones seleccionadas en Rancimat (5 g de muestra, 100ºC y 20 L/h aire se obtuvo excelente repetitividad. La mezcla ALT fue mucho más efectiva en el aceite de pescado que en su correspondiente DMO, tanto en Rancimat como a 30ºC en la oscuridad. Otros experimentos en
17. Accelerated Testing Validation
Energy Technology Data Exchange (ETDEWEB)
Mukundan, Rangachary; James, Greg; Davey, John; Langlois, David; Torraco, Dennis; Yoon, Wonseok; Weber, Adam Z; Borup, Rodney L.
2011-07-01
The DOE Fuel Cell technical team recommended ASTs were performed on 2 different MEAs (designated P5 and HD6) from Ballard Power Systems. These MEAs were also incorporated into stacks and operated in fuel cell bus modules that were either operated in the field (three P5 buses) in Hamburg, or on an Orange county transit authority drive cycle in the laboratory (HD6 bus module). Qualitative agreement was found in the degradation mechanisms and rates observed in the AST and in the field. The HD6 based MEAs exhibited lower voltage degradation rates (due to catalyst corrosion) and slower membrane degradation rates in the field as reflected by their superior performance in the high potential hold and open-circuit potential AST tests. The quantitative correlation of the degradation rates will have to take into account the various stressors in the field including temperature, relative humidity, start/stops and voltage cycles.
18. Accelerated tests of coil coatings
Directory of Open Access Journals (Sweden)
Rosales, B. M.
2003-12-01
Full Text Available Accelerated laboratory tests on 12 materials in study in the Subgroup 6 of the PATINA Network (CYTED, are discussed for different exposition periods in salt spray, SO2 and Prohesion chambers. International standards used to evaluate failures caused by the different aggressive agents of these laboratory tests are the same as those applied for outdoor expositions. The results exposed contribute to a better understanding of the mechanisms occurred in the diverse natural environments, being mentioned the main analogies and differences respect to factors affecting natural tests. They also allowed to evidence the advantages and limitations in the application of these tests during several days, as compared to the years required to attain similar failure magnitudes through outdoor tests.
En este trabajo se discuten los ensayos de laboratorio acelerados, realizados sobre 12 materiales de estudio en el Subgrupo 6 de la Red PATINA (CYTED, a diferentes periodos de exposición en cámaras de niebla salina, SO2 y Prohesion. Se utilizaron las normas internacionales para evaluar los fallos causados por los diferentes agentes agresivos de estos ensayos de laboratorio, las cuales se aplican también para los ensayos de exposición a la intemperie. Los resultados expuestos contribuyen a una mejor comprensión de los mecanismos ocurridos en los diversos ambientes naturales, mencionándose las principales analogías y diferencias respecto de los factores que afectan los ensayos naturales. También permitieron evidenciar las ventajas y limitaciones en la aplicación de estos ensayos durante varios días, en comparación con los años requeridos para alcanzar magnitudes de fallos similares por medio de ensayos a intemperie.
19. Performance Evaluation of Graphics Accelerator
OpenAIRE
Vanek, Juraj
2010-01-01
This paper deals with possibilities and functions of modern graphic accelerators and with measuring performance under OpenGL interface. Widespread algorithms to render scene in real-time are used. It focuses on how to test every part of accelerator's graphic pipeline as well as measure performance in rendering of advanced effects and theoretical speed at general purpose calculations through graphic processor. This testing is realized by implementing multiple test series and their further eval...
20. Test accelerator for linear collider
International Nuclear Information System (INIS)
KEK has proposed to build Test Accelerator Facility (TAF) capable of producing a 2.5 GeV electron beam for the purpose of stimulating R ampersand D for linear collider in TeV region. The TAF consists of a 1.5 GeV S-band linear accelerator, 1.5 GeV damping ring and 1.0 GeV X-band linear accelerator. The TAF project will be carried forward in three phases. Through Phase-I and Phase-II, the S-band and X-band linacs will be constructed, and in Phase-III, the damping ring will be completed. The construction of TAF Phase-I has started, and the 0.2 GeV S-band injector linac has been almost completed. The Phase-I linac is composed of a 240 keV electron gun, subharmonic bunchers, prebunchers and traveling buncher followed by high-gradient accelerating structures. The SLAC 5045 klystrons are driven at 450 kV in order to obtain the rf-power of 100 MW in a 1 μs pulse duration. The rf-power from a pair of klystrons are combined into an accelerating structure. The accelerating gradient up to 100 MeV/m will be obtained in a 0.6 m long structure. 5 refs., 3 figs., 2 tabs
1. Accelerated degradation testing of a photovoltaic module
Science.gov (United States)
Charki, Abdérafi; Laronde, Rémi; Bigaud, David
2013-01-01
There are a great many photovoltaic (PV) modules installed around the world. Despite this, not enough is known about the reliability of these modules. Their electrical power output decreases with time mainly as a result of the effects of corrosion, encapsulation discoloration, and solder bond failure. The failure of a PV module is defined as the point where the electrical power degradation reaches a given threshold value. Accelerated life tests (ALTs) are commonly used to assess the reliability of a PV module. However, ALTs provide limited data on the failure of a module and these tests are expensive to carry out. One possible solution is to conduct accelerated degradation tests. The Wiener process in conjunction with the accelerated failure time model makes it possible to carry out numerous simulations and thus to determine the failure time distribution based on the aforementioned threshold value. By this means, the failure time distribution and the lifetime (mean and uncertainty) can be evaluated.
2. Evaluation of life of insulator materials for electric wires by accelerated deterioration test due to radiation and heat
International Nuclear Information System (INIS)
From the viewpoint of the safe operation and the extension of life of nuclear power stations, the secular deterioration of the machinery and equipment which compose nuclear reactors has become the problem. Also electric wires and cables are the important components of nuclear reactors, and organic materials are used as the insulator materials, the secular deterioration is an unavoidable subject to be investigated. In electric wires and cables, the kinds of insulator and sheath materials are many, and the compositions are diversified, therefore it is very difficult to estimate their life from the past data. In this study, as for the polymer materials which have been widely used for electric wires, the accelerated test by applying radiation and heat to them was carried out, and the method for estimating the secular deterioration was investigated. The testing method and the results are reported. The materials put to the test were ethylene propylene rubber and polyethylene chlorosulfonate, and the samples were the sheets of 1 mm thickness. The tests by the simultaneous application of radiation and heat and the successive application were carried out. The rate of lowering of fracture elongation increased in proportion to the magnification of acceleration. (K.I.)
3. Stability of CIGS Solar Cells and Component Materials Evaluated by a Step-Stress Accelerated Degradation Test Method: Preprint
Energy Technology Data Exchange (ETDEWEB)
Pern, F. J.; Noufi, R.
2012-10-01
4. Test Stand for Linear Induction Accelerator Optimization
International Nuclear Information System (INIS)
Lawrence Livermore National Laboratory has designed and constructed a test stand to improve the voltage regulation in our Flash X-Ray (FXR) accelerator cell. The goal is to create a more mono-energetic electron beam that will create an x-ray source with a smaller spot size. Studying the interaction of the beam and pulse-power system with the accelerator cell will improve the design of high-current accelerators at Livermore and elsewhere. On the test stand, a standard FXR cell is driven by a flexible pulse-power system and the beam current is simulated with a switched center conductor. The test stand is fully instrumented with high-speed digitizers to document the effect of impedance mismatches when the cell is operated under various full-voltage conditions. A time-domain reflectometry technique was also developed to characterize the beam and cell interactions by measuring the impedance of the accelerator and pulse-power component. Computer models are being developed in parallel with the testing program to validate the measurements and evaluate different design changes. Both 3D transient electromagnetic and circuit models are being used
5. Accelerated Leach Test(s) Program: Annual report
International Nuclear Information System (INIS)
A computerized data base of LLW leaching data has been developed. Long-term tests on portland cement, bitumen and vinyl ester-styrene (VES) polymer waste forms containing simulated wastes are underway which are designed to identify and evaluate factors that accelerate leaching without changing the mechanisms
6. Accelerated Leach Test(s) Program: Annual report
Energy Technology Data Exchange (ETDEWEB)
Dougherty, D.R.; Pietrzak, R.F.; Fuhrmann, M.; Colombo, P.
1986-09-01
A computerized data base of LLW leaching data has been developed. Long-term tests on portland cement, bitumen and vinyl ester-styrene (VES) polymer waste forms containing simulated wastes are underway which are designed to identify and evaluate factors that accelerate leaching without changing the mechanisms.
7. The Brookhaven National Laboratory Accelerator Test Facility
International Nuclear Information System (INIS)
The Brookhaven National Laboratory Accelerator Test Facility comprises a 50 MeV traveling wave electron linear accelerator utilizing a high gradient, photo-excited, raidofrequency electron gun as an injector and an experimental area for study of new acceleration methods or advanced radiation sources using free electron lasers. Early operation of the linear accelerator system including calculated and measured beam parameters are presented together with the experimental program for accelerator physics and free electron laser studies
8. Accelerators for Fusion Materials Testing
Science.gov (United States)
Knaster, Juan; Okumura, Yoshikazu
Fusion materials research is a worldwide endeavor as old as the parallel one working toward the long term stable confinement of ignited plasma. In a fusion reactor, the preservation of the required minimum thermomechanical properties of the in-vessel components exposed to the severe irradiation and heat flux conditions is an indispensable factor for safe operation; it is also an essential goal for the economic viability of fusion. Energy from fusion power will be extracted from the 14 MeV neutron freed as a product of the deuterium-tritium fusion reactions; thus, this kinetic energy must be absorbed and efficiently evacuated and electricity eventually generated by the conventional methods of a thermal power plant. Worldwide technological efforts to understand the degradation of materials exposed to 14 MeV neutron fluxes >1018 m-2s-1, as expected in future fusion power plants, have been intense over the last four decades. Existing neutron sources can reach suitable dpa (“displacement-per-atom”, the figure of merit to assess materials degradation from being exposed to neutron irradiation), but the differences in the neutron spectrum of fission reactors and spallation sources do not allow one to unravel the physics and to anticipate the degradation of materials exposed to fusion neutrons. Fusion irradiation conditions can be achieved through Li (d, xn) nuclear reactions with suitable deuteron beam current and energy, and an adequate flowing lithium screen. This idea triggered in the late 1970s at Los Alamos National Laboratory (LANL) a campaign working toward the feasibility of continuous wave (CW) high current linacs framed by the Fusion Materials Irradiation Test (FMIT) project. These efforts continued with the Low Energy Demonstrating Accelerator (LEDA) (a validating prototype of the canceled Accelerator Production of Tritium (APT) project), which was proposed in 2002 to the fusion community as a 6.7MeV, 100mA CW beam injector for a Li (d, xn) source to bridge
9. Accelerated Test Method for Corrosion Protective Coatings Project
Science.gov (United States)
Falker, John; Zeitlin, Nancy; Calle, Luz
2015-01-01
This project seeks to develop a new accelerated corrosion test method that predicts the long-term corrosion protection performance of spaceport structure coatings as accurately and reliably as current long-term atmospheric exposure tests. This new accelerated test method will shorten the time needed to evaluate the corrosion protection performance of coatings for NASA's critical ground support structures. Lifetime prediction for spaceport structure coatings has a 5-year qualification cycle using atmospheric exposure. Current accelerated corrosion tests often provide false positives and negatives for coating performance, do not correlate to atmospheric corrosion exposure results, and do not correlate with atmospheric exposure timescales for lifetime prediction.
10. New Accelerating Modules RF Test at TTF
CERN Document Server
Kostin, D
2004-01-01
Five new accelerating modules were installed into the TTF tunnel as a part of the VUV FEL Linac. They are tested prior to the linac operation. The RF test includes processing of the superconducting cavities, as well as maximum module performance tests. The test procedure and the achieved performance together with the test statistical analysis are presented.
11. RHIC sextant test: Accelerator systems and performance
International Nuclear Information System (INIS)
One sextant of the RHIC Collider was commissioned in early 1997 with beam. We describe here the performance of the accelerator systems, instrumentation subsystems and application software. We also describe a ramping test without beam that took place after the commissioning with beam. Finally, we analyze the implications of accelerator systems performance and their impact on the planning for RHIC installation and commissioning
12. National Fuel Cell Bus Program: Accelerated Testing Evaluation Report and Appendices, Alameda-Contra Costa Transit District (AC Transit)
Energy Technology Data Exchange (ETDEWEB)
Chandler, K.; Eudy, L.
2009-01-01
This is an evaluation of hydrogen fuel cell transit buses operating at AC Transit in revenue service since March 20, 2006 compared to similar diesel buses operating from the same depot. This evaluation report includes results from November 2007 through October 2008. Evaluation results include implementation experience, fueling station operation, fuel cell bus operations at Golden Gate Transit, and evaluation results at AC Transit (bus usage, availability, fuel economy, maintenance costs, and roadcalls).
13. Timescale Correlation between Marine Atmospheric Exposure and Accelerated Corrosion Testing
Science.gov (United States)
Montgomery, Eliza L.; Calle, Luz Marina; Curran, Jerone C.; Kolody, Mark R.
2011-01-01
Evaluation of metal-based structures has long relied on atmospheric exposure test sites to determine corrosion resistance in marine environments. Traditional accelerated corrosion testing relies on mimicking the exposure conditions, often incorporating salt spray and ultraviolet (UV) radiation, and exposing the metal to continuous or cyclic conditions of the corrosive environment. Their success for correlation to atmospheric exposure is often a concern when determining the timescale to which the accelerated tests can be related. Accelerated laboratory testing, which often focuses on the electrochemical reactions that occur during corrosion conditions, has yet to be universally accepted as a useful tool in predicting the long term service life of a metal despite its ability to rapidly induce corrosion. Although visual and mass loss methods of evaluating corrosion are the standard and their use is imperative, a method that correlates timescales from atmospheric exposure to accelerated testing would be very valuable. This work uses surface chemistry to interpret the chemical changes occurring on low carbon steel during atmospheric and accelerated corrosion conditions with the objective of finding a correlation between its accelerated and long-term corrosion performance. The current results of correlating data from marine atmospheric exposure conditions at the Kennedy Space Center beachside corrosion test site, alternating seawater spray, and immersion in typical electrochemical laboratory conditions, will be presented. Key words: atmospheric exposure, accelerated corrosion testing, alternating seawater spray, marine, correlation, seawater, carbon steel, long-term corrosion performance prediction, X-ray photoelectron spectroscopy.
14. Flame Acceleration Tests with Hydrogen Combustions
International Nuclear Information System (INIS)
According to the domestic and foreign regulations, a detonation or DDT (deflagration to detonation transition) by a hydrogen combustion should be prohibited to occur in a containment of a nuclear power plant. A hydrogen control in the IRWST(Incontainment Refueling Water Storage Tank) under a severe accident still remains a debatable issue to be solved in APR1400. The characteristics of the hydrogen flame in the IRWST expected during the station black-out (SBO) and total loss of feed water (LOFW) accidents have been evaluated based on a sigma-lambda criteria from the simulation results by the numerical codes such as GASFLOW. And it was found that hydrogen mixture was non-flammable most of the accident time when the non-condensed steam was released into the free volume of the IRWST, but there existed a small period of time with a high possibility of a flame acceleration during the SBO accident because most of the steam discharged from sparger was well condensed. Therefore, detail analysis and experiment of the hydrogen flame should be required to fix a DDT possibility by the hydrogen combustion in the IRWST of the APR1400. Most experiments on the hydrogen combustion have been limited only to straight pipes or channels. However, the hydrogen flame acceleration phenomena in the IRWST with a closed annular path may be different from those in the straight path in respect to a centrifugal force and degree of freedom in flame propagation etc. So, an experiment of hydrogen combustion in a closed annular chamber is needed to find out the geometrical effect on the flame propagation and to validate the numerical results. KAERI has been performing the experiments of the hydrogen combustion in the IRWST. As the fist stage, flame acceleration tests with the hydrogen combustions are studied preliminarily for a circular straight pipe to confirm the characteristics hydrogen flame propagation, and to evaluate flame detection systems
15. Testing general relativity on accelerators
Directory of Open Access Journals (Sweden)
Tigran Kalaydzhyan
2015-11-01
Full Text Available Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable – maximal energy of the scattered photons – would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC.
16. Testing general relativity on accelerators
Science.gov (United States)
Kalaydzhyan, Tigran
2015-11-01
Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable - maximal energy of the scattered photons - would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC.
17. Testing general relativity on accelerators
CERN Document Server
Kalaydzhyan, Tigran
2015-01-01
Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyse experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable -- maximal energy of the scattered photons -- would experience a significant shift in the Earth's gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of res...
18. The electron test accelerator beam injector
International Nuclear Information System (INIS)
A beam chopper and buncher system has been designed to improve the capture efficiency and reduce the beam spill in the Electron Test Accelerator. The buncher increases the dc beam capture from 30 to 70%. 100% beam transmission through the accelerator structures is obtained with the chopper. This report describes results of experimental tests with the beam injector. Results from computer modeling and from measurements with prototypes that have led to the design of the beam chopper and buncher system are discussed
19. National Fuel Cell Bus Program: Accelerated Testing Evaluation Report #2, Alameda-Contra Costa Transit District (AC Transit) and Appendices
Energy Technology Data Exchange (ETDEWEB)
Eudy, L.; Chandler, K.
2010-06-01
This is an evaluation of hydrogen fuel cell transit buses operating at AC Transit in revenue service since March 20, 2006, comparing similar diesel buses operating from the same depot. It covers November 2007 through February 2010. Results include implementation experience, fueling station operation, evaluation results at AC Transit (bus usage, availability, fuel economy, maintenance costs, and road calls), and a summary of achievements and challenges encountered during the demonstration.
20. A Comprehensive Review of Accelerated Life Test
Institute of Scientific and Technical Information of China (English)
ZHANG Chun-hua; WANG Ya-shun; CHEN Xun; WEN Xi-sen
2005-01-01
Accelerated life test (ALT) is an important branch of reliability test and is a focus of research both for statisticians and reliability engineers. The paper outlines the four topics of study embodied in ALT: statistical analysis of constant-stress test, step-stress test and progressive stress test, and optimal design of ALT. It gives a general review of engineering applications of ALT, and points out some possible directions in ALT, gives some suggestions for further study.
1. Teste de frio e envelhecimento acelerado na avaliação de vigor de sementes de feijão-frade Evaluation of the cowpea seeds vigour through of the coldtest and accelerated aging test
Directory of Open Access Journals (Sweden)
Josiane Marlle Guiscem
2010-12-01
2. Next linear collider test accelerator injector upgrade
Energy Technology Data Exchange (ETDEWEB)
Yeremian, A.D.; Miller, R.H. [Stanford Linear Accelerator Center, CA (United States)
1995-12-31
The Next Linear Collider Test Accelerator (NLCTA) is being constructed at SLAC to demonstrate multibunch beam loading compensation, suppression of higher order deflecting modes and measure transverse components of the accelerating fields in X-band accelerating structures. Currently a simple injector which provides the average current necessary for the beam loading compensations studies is under construction. An injector upgrade is planned to produce bunch trains similar to that of the NLC with microbunch intensity, separation and energy spread, identical to that of NLC. We discuss the design of the NLCTA injector upgrade.
3. Reliability evaluation of a photovoltaic module using accelerated degradation model
Science.gov (United States)
Laronde, Rémi; Charki, Abdérafi; Bigaud, David; Excoffier, Philippe
2011-09-01
Many photovoltaic modules are installed all around the world. However, the reliability of this product is not enough really known. The electrical power decreases in time due mainly to corrosion, encapsulation discoloration and solder bond failure. The failure of a photovoltaic module is obtained when the electrical power degradation reaches a threshold value. Accelerated life tests are commonly used to estimate the reliability of the photovoltaic module. However, using accelerated life tests, few data on the failure of this product are obtained and the realization of this kind of tests is expensive. As a solution, an accelerated degradation test can be carried out using only one stress if parameters of the acceleration model are known. The Wiener process associated with the accelerated failure time model permits to carry out many simulations and to determine the failure time distribution when the threshold value is reached. So, the failure time distribution and the lifetime (mean and uncertainty) can be evaluated.
4. A Statistical Perspective on Highly Accelerated Testing.
Energy Technology Data Exchange (ETDEWEB)
Thomas, Edward V.
2015-02-01
Highly accelerated life testing has been heavily promoted at Sandia (and elsewhere) as a means to rapidly identify product weaknesses caused by flaws in the product's design or manufacturing process. During product development, a small number of units are forced to fail at high stress. The failed units are then examined to determine the root causes of failure. The identification of the root causes of product failures exposed by highly accelerated life testing can instigate changes to the product's design and/or manufacturing process that result in a product with increased reliability. It is widely viewed that this qualitative use of highly accelerated life testing (often associated with the acronym HALT) can be useful. However, highly accelerated life testing has also been proposed as a quantitative means for "demonstrating" the reliability of a product where unreliability is associated with loss of margin via an identified and dominating failure mechanism. It is assumed that the dominant failure mechanism can be accelerated by changing the level of a stress factor that is assumed to be related to the dominant failure mode. In extreme cases, a minimal number of units (often from a pre-production lot) are subjected to a single highly accelerated stress relative to normal use. If no (or, sufficiently few) units fail at this high stress level, some might claim that a certain level of reliability has been demonstrated (relative to normal use conditions). Underlying this claim are assumptions regarding the level of knowledge associated with the relationship between the stress level and the probability of failure. The primary purpose of this document is to discuss (from a statistical perspective) the efficacy of using accelerated life testing protocols (and, in particular, "highly accelerated" protocols) to make quantitative inferences concerning the performance of a product (e.g., reliability) when in fact there is lack-of-knowledge and uncertainty concerning
5. RHIC Sextant Test - Accelerator Systems and Performance
Science.gov (United States)
Pilat, F.; Ahrens, L.; Brown, K.; Connolly, R.; dell, G. F.; Fischer, W.; Kewisch, J.; Mackay, W.; Mane, V.; Peggs, S.; Satogata, T.; Tepikian, S.; Thompson, P.; Trbojevic, D.; Tsoupas, N.; Wei, J.
1997-05-01
One sextant of the RHIC collider and the full AtR (AGS to RHIC) transfer line have been commissioned in early 1997 with beam. We describe here the design and performance of the accelerator systems during the test, such as the magnet and power supply systems, instrumentation subsystems and application software. After reviewing the main milestones of the commissioning we describe a ramping test without beam that took place after the commissioning with beam. Finally, we analyze the implications of accelerator systems preformance and their impact on the plannig for RHIC installation and commissioning.
6. Effective acceptance evaluation of linear resonance accelerator
International Nuclear Information System (INIS)
One of the most important challenges for accelerators is to match an accelerating beam with an accelerator acceptance. It allows one reduce a particle loss. Effective acceptance evaluation of linear resonance accelerator with RF focusing is carried out with no taking into account a beam space charge; a model taking into account non-coherent bunch particle oscillations is considered with the use of an averaging technique over rapid oscillations. Analytical results obtained are verified. Computer simulations of self-consistent low-energy ion beam dynamics are performed.
7. Seismic response evaluation for piping systems with support structures. Effect of input acceleration amplitude on resonance frequency and response reduction in the elastic vibration test
International Nuclear Information System (INIS)
larger than the design damping factor of 0.5% for all of the input accelerations. These results demonstrated that considering the input acceleration dependencies of damping factor is needed to evaluate the seismic response accurately of piping systems vibrating with large displacement of pipes during large scale earthquakes. (author)
8. The BNL Accelerator Test Facility control system
International Nuclear Information System (INIS)
Described is the VAX/CAMAC-based control system for Brookhaven National Laboratory's Accelerator Test Facility, a laser/linac research complex. Details of hardware and software configurations are presented along with experiences of using Vsystem, a commercial control system package
9. Electrical performance characteristics of the SSC Accelerator System String Test
International Nuclear Information System (INIS)
The intent of the Accelerator System String Test (ASST) is to obtain data for model verification and information on the magnitudes of pressures and voltages encountered in an accelerator environment. The ASST milestone run was achieved during July and August, 1992 and consisted of demonstrating the accelerator components could be configured together as a system operating at full current. Following the milestone run, the string was warmed to counteract some design flaws that impeded the operational range. The string was again cooled to cryogenic temperatures in October, and a comprehensive power testing program was conducted through the end of January, 1993. This paper describes how the collider arc components operate in an accelerator environment during quenches induced by firing both strip heaters and spot heaters. Evaluation of the data illustrates how variations in the design parameters on magnets used in a string environment can impact system performance
10. Electrical performance characteristics of the SSC accelerator system string test
International Nuclear Information System (INIS)
The intent of the Accelerator System String Test (ASST) is to obtain data for model verification and information on the magnitudes of pressures and voltages encountered in an accelerator environment. The ASST milestone run was achieved during July and August, 1992 and consisted of demonstrating that the accelerator components could be configured together as a system operating at full current. Following the milestone run, the string was warmed to counteract some design flaws that impeded the operational range. The string was again cooled to cryogenic temperatures in October, and a comprehensive power testing program was conducted through the end of January, 1993. This paper describes how the collider arc components operate in an accelerator environment during quenches induced by firing both strip heaters and spot heaters. Evaluation of the data illustrates how variations in the design parameters on magnets used in a string environment can impact system performance
11. 导弹加速寿命试验及可靠性评估%Accelerated Life Test and Reliability Evaluation of Missile
Institute of Scientific and Technical Information of China (English)
宋贵宝; 崔加鑫
2016-01-01
相对于导弹的常规贮存寿命试验，加速寿命试验可以提高试验效率，节省试验成本，具有很好的军事和经济效益。论文针对导弹部组件多、结构复杂，加速寿命试验难度大的问题，提出了通过对薄弱环节进行加速寿命试验推出导弹贮存寿命的方法，给出了加速寿命试验的基本流程和设计方案，并介绍了基于极大似然估计法的导弹可靠性评估方法。最后以弹上某电子部件为例，开展了加速寿命试验，并对试验数据进行评估，得出了导弹的贮存寿命。%Relative to conventional storage life test of missile ,accelerated life test can improve the test efficiency and save test cost ,has the very good military and economic benefits .In this paper ,aiming at the problem that missile has many units ,complex structure ,accelerated life test is difficult ,a method for accelerating the storage life of a missile is presented , which is based on the accelerated life test of the weak links .The basic processes and design of the accelerated life test are giv‐en ,and the method of missile reliability assessment based on the method of maximum likelihood estimation is introduced .Fi‐nally the paper takes an example of an electronic component on the missile ,and conducts accelerated life test ,and assess the test data ,obtains the storage life of the missile .
12. The Accelerated Test of Chloride Permeability of Concrete
Institute of Scientific and Technical Information of China (English)
TAN Ke-feng; ODD E Gjφrv
2003-01-01
The availability of accelerated chloride permeability test and the effect of w/c ratio, incorporation of silica fume, maximum aggregate size and aggregate type on the chloride permeability were studied. The mathematic analysis certifies that there is a linear relationship between accelerated test and natural diffusion. Test results show that the chloride permeability of concrete increases as w/c ratio increases whilst a limited amount of replacement of cement with silica fume, the chloride permeability decreases dramatically. The maximum aggregate size in the range of 8 to 25 mm seems also affect chloride permeability but with a much less significant level. The chloride permeability of silica fume lightweight aggregate concrete is very low, especially the concrete made with dry lightweight concrete. The chloride permeability can be evaluated by this accelerated test method.
13. Test Particles with Acceleration-Dependent Lagrangian
CERN Document Server
Toller, M
2006-01-01
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and we study its trajectory in the principal fibre bundle of all the Lorentz frames. We discuss in this framework the general form of the Lagrange equations and the connection between symmetries and conservation laws (Noether theorem). We apply these results to a model, already discussed by other authors, which implies an upper bound to the proper acceleration and to another new model in which a similar quantity, called pseudo-acceleration'', is bounded. With some simple choices of the fields, we illustrate some other interesting properties of the models and we show that unwanted features may appear, as instable run-away solutions and unphysical values of the energy-momentum or of the velocity.
14. Manufacturing and Testing of Accelerator Superconducting Magnets
CERN Document Server
Rossi, L
2014-01-01
Manufacturing of superconducting magnet for accelerators is a quite complex process that is not yet fully industrialized. In this paper, after a short history of the evolution of the magnet design and construction, we review the main characteristics of the accelerator magnets having an impact on the construction technology. We put in evidence how the design and component quality impact on construction and why the final product calls for a total-quality approach. LHC experience is widely discussed and main lessons are spelled out. Then the new Nb3Sn technology, under development for the next generation magnet construction, is outlined. Finally, we briefly review the testing procedure of accelerator superconducting magnets, underlining the close connection with the design validation and with the manufacturing process.
15. Tests of compressed geometry acceleration tubes in the Oak Ridge 25URC tandem accelerator
International Nuclear Information System (INIS)
In an effort to further improve voltage performance of the Oak Ridge 25URC accelerator, the original acceleration tubes will be replaced with NEC compressed geometry acceleration tubes. In this paper, we report on tests in the 25URC accelerator of two prototype compressed geometry acceleration tube designs. One of the designs utilizes a novel aperture which provides enhanced electron and ion trapping
16. Test Particles with Acceleration-Dependent Lagrangian
OpenAIRE
Toller, M.
2005-01-01
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and we study its trajectory in the principal fibre bundle of all the Lorentz frames. We discuss in this framework the general form of the Lagrange equations and the connection between symmetries and conservation laws (Noether theorem). We apply these results to...
17. BNL ACCELERATOR TEST FACILITY CONTROL SYSTEM UPGRADE.
Energy Technology Data Exchange (ETDEWEB)
MALONE,R.; BEN-ZVI,I.; WANG,X.; YAKIMENKO,V.
2001-06-18
Brookhaven National Laboratory's Accelerator Test Facility (ATF) has embarked on a complete upgrade of its decade old computer system. The planned improvements affect every major component: processors (Intel Pentium replaces VAXes), operating system (Linux/Real-Time Linux supplants OpenVMS), and data acquisition equipment (fast Ethernet equipment replaces CAMAC serial highway.) This paper summarizes the strategies and progress of the upgrade along with plans for future expansion.
18. Vacuum system for Advanced Test Accelerator
Energy Technology Data Exchange (ETDEWEB)
Denhoy, B.S.
1981-09-03
The Advanced Test Accelerator (ATA) is a pulsed linear electron beam accelerator designed to study charged particle beam propagation. ATA is designed to produce a 10,000 amp 50 MeV, 70 ns electron beam. The electron beam acceleration is accomplished in ferrite loaded cells. Each cell is capable of maintaining a 70 ns 250 kV voltage pulse across a 1 inch gap. The electron beam is contained in a 5 inch diameter, 300 foot long tube. Cryopumps turbomolecular pumps, and mechanical pumps are used to maintain a base pressure of 2 x 10/sup -6/ torr in the beam tube. The accelerator will be installed in an underground tunnel. Due to the radiation environment in the tunnel, the controlling and monitoring of the vacuum equipment, pressures and temperatures will be done from the control room through a computer interface. This paper describes the vacuum system design, the type of vacuum pumps specified, the reasons behind the selection of the pumps and the techniques used for computer interfacing.
19. Vacuum system for Advanced Test Accelerator
International Nuclear Information System (INIS)
The Advanced Test Accelerator (ATA) is a pulsed linear electron beam accelerator designed to study charged particle beam propagation. ATA is designed to produce a 10,000 amp 50 MeV, 70 ns electron beam. The electron beam acceleration is accomplished in ferrite loaded cells. Each cell is capable of maintaining a 70 ns 250 kV voltage pulse across a 1 inch gap. The electron beam is contained in a 5 inch diameter, 300 foot long tube. Cryopumps turbomolecular pumps, and mechanical pumps are used to maintain a base pressure of 2 x 10-6 torr in the beam tube. The accelerator will be installed in an underground tunnel. Due to the radiation environment in the tunnel, the controlling and monitoring of the vacuum equipment, pressures and temperatures will be done from the control room through a computer interface. This paper describes the vacuum system design, the type of vacuum pumps specified, the reasons behind the selection of the pumps and the techniques used for computer interfacing
20. Accelerated aging tests of liners for uranium mill tailings disposal
Energy Technology Data Exchange (ETDEWEB)
Barnes, S.M.; Buelt, J.L.; Hale, V.Q.
1981-11-01
This document describes the results of accelerated aging tests to determine the long-term effectiveness of selected impoundment liner materials in a uranium mill tailings environment. The study was sponsored by the US Department of Energy under the Uranium Mill Tailings Remedial Action Project. The study was designed to evaluate the need for, and the performance of, several candidate liners for isolating mill tailings leachate in conformance with proposed Environmental Protection Agency and Nuclear Regulatory Commission requirements. The liners were subjected to conditions known to accelerate the degradation mechanisms of the various liners. Also, a test environment was maintained that modeled the expected conditions at a mill tailings impoundment, including ground subsidence and the weight loading of tailings on the liners. A comparison of installation costs was also performed for the candidate liners. The laboratory testing and cost information prompted the selection of a catalytic airblown asphalt membrane and a sodium bentonite-amended soil for fiscal year 1981 field testing.
1. Accelerated aging tests of liners for uranium mill tailings disposal
International Nuclear Information System (INIS)
This document describes the results of accelerated aging tests to determine the long-term effectiveness of selected impoundment liner materials in a uranium mill tailings environment. The study was sponsored by the US Department of Energy under the Uranium Mill Tailings Remedial Action Project. The study was designed to evaluate the need for, and the performance of, several candidate liners for isolating mill tailings leachate in conformance with proposed Environmental Protection Agency and Nuclear Regulatory Commission requirements. The liners were subjected to conditions known to accelerate the degradation mechanisms of the various liners. Also, a test environment was maintained that modeled the expected conditions at a mill tailings impoundment, including ground subsidence and the weight loading of tailings on the liners. A comparison of installation costs was also performed for the candidate liners. The laboratory testing and cost information prompted the selection of a catalytic airblown asphalt membrane and a sodium bentonite-amended soil for fiscal year 1981 field testing
2. Stripline kicker for integrable optics test accelerator
OpenAIRE
Antipov, Sergey A.; Didenko, Alexander; Lebedev, Valeri; Valishev, Alexander
2016-01-01
We present a design of a stripline kicker for Integrable Optics Test Accelerator (IOTA). For its experimental program IOTA needs two full-aperture kickers, capable to create an arbitrary controllable kick in 2D. For that reason their strengths are variable in a wide range of amplitudes up to 16 mrad, and the pulse length 100 ns is less than a revolution period for electrons. In addition, the kicker should have a physical aperture of 40 mm for a proposed operation with proton beam, and an oute...
3. Laboratory Test of Newton's Second Law for Small Accelerations
International Nuclear Information System (INIS)
We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5x10-14 m/s2
4. Induction accelerator test module for HIF
International Nuclear Information System (INIS)
An induction linac test module suitable for investigating the drive requirements and the longitudinal coupling impedance of a high-power ion induction linac has been constructed by the Heavy Ion Fusion (HIF) group at LBL. The induction linac heavy ion driver for inertial confinement fusion (ICF) as presently envisioned uses multiple parallel beams which are transported in separate focusing channels but accelerated together in the induction modules. The resulting induction modules consequently have large beam apertures-1--2 meters in diameter- and correspondingly large outside diameters. The module geometry is related to a low-frequency ''gap capacity'' and high-frequency structural resonances, which are affected by the magnetic core loading and the module pulser impedance. A description of the test module and preliminary results are presented. 3 figs
5. Experimental evaluation of 350 MHz RF accelerator windows for the low energy demonstration accelerator
Energy Technology Data Exchange (ETDEWEB)
Cummings, K.; Rees, D.; Roybal, W. [and others
1997-09-01
Radio frequency (RF) windows are historically a point where failure occurs in input power couplers for accelerators. To obtain a reliable, high-power, 350 MHz RF window for the Low Energy Demonstration Accelerator (LEDA) project of the Accelerator Production of Tritium program, RF windows prototypes from different vendors were tested. Experiments were performed to evaluate the RF windows by the vendors to select a window for the LEDA project. The Communications and Power, Inc. (CPI) windows were conditioned to 445 kW in roughly 15 hours. At 445 kW a window failed, and the cause of the failure will be presented. The English Electronic Valve, Inc. (EEV) windows were conditioned to 944 kW in 26 hours and then tested at 944 kW for 4 hours with no indication of problems.
6. Accelerated Strength Testing of Thermoplastic Composites
Science.gov (United States)
Reeder, J. R.; Allen, D. H.; Bradley, W. L.
1998-01-01
Constant ramp strength tests on unidirectional thermoplastic composite specimens oriented in the 90 deg. direction were conducted at constant temperatures ranging from 149 C to 232 C. Ramp rates spanning 5 orders of magnitude were tested so that failures occurred in the range from 0.5 sec. to 24 hrs. (0.5 to 100,000 MPa/sec). Below 204 C, time-temperature superposition held allowing strength at longer times to be estimated from strength tests at shorter times but higher temperatures. The data indicated that a 50% drop in strength might be expected for this material when the test time is increased by 9 orders of magnitude. The shift factors derived from compliance data applied well to the strength results. To explain the link between compliance and strength, a viscoelastic fracture model was investigated. The model, which used compliance as input, was found to fit the strength data only if the critical fracture energy was allowed to vary with temperature reduced stress rate. This variation in the critical parameter severely limits its use in developing a robust time-dependent strength model. The significance of this research is therefore seen as providing both the indication that a more versatile acceleration method for strength can be developed and the evidence that such a method is needed.
7. Hurricane Isabel gives accelerators a severe test
International Nuclear Information System (INIS)
Hurricane Isabel was at category five--the most violent on the Saffir-Simpson scale of hurricane strength--when it began threatening the central Atlantic seaboard of the US. Over the course of several days, precautions against the extreme weather conditions were taken across the Jefferson Lab site in south-east Virginia. On 18 September 2003, when Isabel struck North Carolina's Outer Banks and moved northward, directly across the region around the laboratory, the storm was still quite destructive, albeit considerably reduced in strength. The flood surge and trees felled by wind substantially damaged or even devastated buildings and homes, including many belonging to Jefferson Lab staff members. For the laboratory itself, Isabel delivered an unplanned and severe challenge in another form: a power outage that lasted nearly three-and-a-half days, and which severely tested the robustness of Jefferson Lab's two superconducting machines, the Continuous Electron Beam Accelerator Facility (CEBAF) and the superconducting radiofrequency ''driver'' accelerator of the laboratory's free-electron laser. Robustness matters greatly for science at a time when microwave superconducting linear accelerators (linacs) are not only being considered, but in some cases already being built for projects such as neutron sources, rare-isotope accelerators, innovative light sources and TeV-scale electron-positron linear colliders. Hurricane Isabel interrupted a several-week-long maintenance shutdown of CEBAF, which serves nuclear and particle physics and represents the world's pioneering large-scale implementation of superconducting radiofrequency (SRF) technology. The racetrack-shaped machine is actually a pair of 500-600 MeV SRF linacs interconnected by recirculation arc beamlines. CEBAF delivers simultaneous beams at up to 6 GeV to three experimental halls. An imminent upgrade will double the energy to 12 GeV and add an extra hall for ''quark confinement'' studies. On a smaller scale
8. Planck scale gravity test with accelerators
Energy Technology Data Exchange (ETDEWEB)
Gharibyan, Vahagn
2012-07-15
Quantum or torsion gravity models predict unusual properties of space-time at very short distances. In particular, near the Planck length, around 10{sup -35} m, empty space may behave as a crystal, singly or doubly refractive. However, this hypothesis remains uncheckable for any direct measurement since the smallest distance accessible in experiment is about 10{sup -19} m at the LHC. Here I propose a laboratory test to measure the space refractivity and birefringence induced by gravity. A sensitivity from 10{sup -31} m down to the Planck length could be reached at existent GeV and future TeV energy lepton accelerators using laser Compton scattering. There are already experimental hints for gravity signature at distances approaching the Planck length by 5-7 orders of magnitude, derived from SLC and HERA data.
9. Stripline kicker for integrable optics test accelerator
Energy Technology Data Exchange (ETDEWEB)
Antipov, Sergey A.; Didenko, Alexander; Lebedev, Valeri; Valishev, Alexander
2016-06-30
We present a design of a stripline kicker for Integrable Optics Test Accelerator (IOTA). For its experimental program IOTA needs two full-aperture kickers, capable to create an arbitrary controllable kick in 2D. For that reason their strengths are variable in a wide range of amplitudes up to 16 mrad, and the pulse length 100 ns is less than a revolution period for electrons. In addition, the kicker should have a physical aperture of 40 mm for a proposed operation with proton beam, and an outer size of 70 mm to fit inside existing quadrupole magnets to save space in the ring. Computer simulations using CST Microwave Studio show high field uniformity and wave impedance close to 50 {\\Omega}.
10. Planck scale gravity test with accelerators
International Nuclear Information System (INIS)
Quantum or torsion gravity models predict unusual properties of space-time at very short distances. In particular, near the Planck length, around 10-35 m, empty space may behave as a crystal, singly or doubly refractive. However, this hypothesis remains uncheckable for any direct measurement since the smallest distance accessible in experiment is about 10-19 m at the LHC. Here I propose a laboratory test to measure the space refractivity and birefringence induced by gravity. A sensitivity from 10-31 m down to the Planck length could be reached at existent GeV and future TeV energy lepton accelerators using laser Compton scattering. There are already experimental hints for gravity signature at distances approaching the Planck length by 5-7 orders of magnitude, derived from SLC and HERA data.
11. Stripline kicker for integrable optics test accelerator
CERN Document Server
Antipov, Sergey A; Lebedev, Valeri; Valishev, Alexander
2016-01-01
We present a design of a stripline kicker for Integrable Optics Test Accelerator (IOTA). For its experimental program IOTA needs two full-aperture kickers, capable to create an arbitrary controllable kick in 2D. For that reason their strengths are variable in a wide range of amplitudes up to 16 mrad, and the pulse length 100 ns is less than a revolution period for electrons. In addition, the kicker should have a physical aperture of 40 mm for a proposed operation with proton beam, and an outer size of 70 mm to fit inside existing quadrupole magnets to save space in the ring. Computer simulations using CST Microwave Studio show high field uniformity and wave impedance close to 50 {\\Omega}.
12. Klystron pulse modulator of linear electron accelerator: test results
Directory of Open Access Journals (Sweden)
Z. Zimek
2009-12-01
Full Text Available Purpose: The purpose of the paper is to describe Klystron pulse modulator of linear electron accelerator.Design/methodology/approach: TH-2158 klystron modulator experimental model is based on semiconductor switch HTS 181-160 FI (acceptable current load 1600 A, and voltage up to 18 kV. The results of test measurements carried out during modulator starting up period are presented in this work. TH-2158 klystron was used as a load. The klystron was connected to the second winding of the pulse HV transformer with 1:10 windings turn ratio. The examined modulator is equipped with safety shutdown circuitry for protection against current overload that may appear at IGBT switch in the case of short-circuiting happened in klystron and waveguide system.Findings: Linear electron accelerator type LAE 10/15 with electron energy 10 MeV and beam power up to 15 kW was designed and completed at Institute of Nuclear Chemistry and Technology. This accelerator was installed in facility for radiation sterilization single use medical devices, implants and tissue grafts. The standing wave accelerating section was selected. Microwave energy used for accelerating process is provided by klystron type TH-2158 working at frequency 2856 MHz.Practical implications: Described HV pulse modulator which designed and constructed for klystron TH-2158 was preliminary tested to evaluate the quality of the klystron HV and load current pulses and optimized selected component parameters. Obtained experimental results are better than those which were predicted by computer simulation method.Originality/value: Description of Klystron pulse modulator of linear electron accelerator.
13. Accelerated testing statistical models, test plans, and data analysis
CERN Document Server
Nelson, Wayne B
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "". . . a goldmine of knowledge on accelerated life testing principles and practices . . . one of the very few capable of advancing the science of reliability. It definitely belongs in every bookshelf on engineering.""-Dev G.
14. High Efficiency Water Heating Technology Development Final Report. Part I, Lab/Field Performance Evaluation and Accelerated Life Testing of a Hybrid Electric Heat Pump Water Heater (HPWH)
Energy Technology Data Exchange (ETDEWEB)
Baxter, Van D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Murphy, Richard W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Rice, C. Keith [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Linkous, Randall Lee [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-04-01
DOE has supported efforts for many years with the objective of getting a water heater that uses heat pump technology (aka a heat pump water heater or HPWH) successfully on the residential equipment market. The most recent previous effort (1999-2002) produced a product that performed very well in ORNL-led accelerated durability and field tests. The commercial partner for this effort, Enviromaster International (EMI), introduced the product to the market under the trade name Watter$aver in 2002 but ceased production in 2005 due to low sales. A combination of high sales price and lack of any significant infrastructure for service after the sale were the principal reasons for the failure of this effort. What was needed for market success was a commercial partner with the manufacturing and market distribution capability necessary to allow economies of scale to lead to a viable unit price together with a strong customer service infrastructure. General Electric certainly meets these requirements, and knowing of ORNL s expertise in this area, approached ORNL with the proposal to partner in a CRADA to produce a high efficiency electric water heater. A CRADA with GE was initiated early in Fiscal Year, 2008. GE initially named its product the Hybrid Electric Water Heater (HEWH). 15. Beam Physics of Integrable Optics Test Accelerator at Fermilab OpenAIRE Nagaitsev, S.; Valishev, A.; Danilov, V. V.; Shatilov, D. N. 2013-01-01 Fermilab's Integrable Optics Test Accelerator is an electron storage ring designed for testing advanced accelerator physics concepts, including implementation of nonlinear integrable beam optics and experiments on optical stochastic cooling. The machine is currently under construction at the Advanced Superconducting Test Accelerator facility. In this report we present the goals and the current status of the project, and describe the details of machine design. In particular, we concentrate on ... 16. Operation of the Brookhaven National Laboratory Accelerator Test Facility International Nuclear Information System (INIS) Early operation of the 50 MeV high brightness electron linac of the Accelerator Test Facility is described along with experimental data. This facility is designed to study new linear acceleration techniques and new radiation sources based on linacs in combination with free electron lasers. The accelerator utilizes a photo-excited, metal cathode, radio frequency electron gun followed by two travelling wave accelerating sections and an Experimental Hall for the study program 17. Operation of the Brookhaven national laboratory accelerator test facility International Nuclear Information System (INIS) Early operation of the 50 MeV high brightness electron linac of the Accelerator Test Facility is described along with experimental data. This facility is designed to study new linear acceleration techniques and new radiation sources based on linacs in combination with free electron lasers. The accelerator utilizes a photo-excited, metal cathode, radio frequency electron gun followed by two travelling wave accelerating sections and an Experimental Hall for the study program. (Author) 5 refs., 4 figs., tab 18. Evaluation and Tests Science.gov (United States) ... of these tests is to assess your neurological function, including your muscle strength, how your autonomic nerves are functioning, and ... causes for neuropathy. These include tests for: Vitamin B12 and folate levels Thyroid, liver and ... evaluation Oral glucose tolerance test Antibodies to ... 19. Virtual accelerator concept, implementation and preliminary test International Nuclear Information System (INIS) A virtual accelerator is the coupling of a simulation code with the control system of a real machine. 3 operating modes are considered. First, the monitoring mode in which any action on the control system has an impact on both real and virtual machines. This mode allows a direct comparison between simulation results and the real behaviour of the accelerator. Secondly, the flight simulation mode, this mode allows the accelerator operators to simulate the effect of any change in the parameters of the control system before transferring them to the real machine. The main advantage of this mode is to allow the assessment of operating procedures before implementing them on the real machine. The third mode is the automatic steering mode in which the simulation code assumes the reins of the control system of the real machine. This mode allows the making of complex and time-consuming adjustment procedures in an automatic way. TraceWin is a simulation code dedicated to the behaviour of charged-particle beams in a linear accelerator. TraceWin is consistent with the EPICS technology on which the control system of most accelerators is based. A virtual accelerator composed of the SILHI injector combined to the TraceWin code via the EPICS environment has showed its efficiency in the automatic steering mode. (A.C.) 20. Accelerated lifetime testing of energy storage capacitors used in particle accelerators power converters CERN Document Server AUTHOR|(SzGeCERN)679542; Genton, Charles-Mathieu 2015-01-01 Energy storage capacitors are used in large quantities in high power converters for particle accelerators. In this application capacitors see neither a DC nor an AC voltage but a combination of the two. The paper presents a new power converter explicitly designed to perform accelerated testing on these capacitors and the results of the tests. 1. Analysis of Transmitted Optical Spectrum Enabling Accelerated Testing of CPV Designs: Preprint Energy Technology Data Exchange (ETDEWEB) Miller, D. C.; Kempe, M. D.; Kennedy, C. E.; Kurtz, S. R. 2009-07-01 Reliability of CPV systems' materials is not well known; methods for accelerated UV testing have not been developed. UV and IR spectra transmitted through representative optical systems are evaluated. 2. AREAL test facility for advanced accelerator and radiation source concepts Science.gov (United States) Tsakanov, V. M.; Amatuni, G. A.; Amirkhanyan, Z. G.; Aslyan, L. V.; Avagyan, V. Sh.; Danielyan, V. A.; Davtyan, H. D.; Dekhtiarov, V. S.; Gevorgyan, K. L.; Ghazaryan, N. G.; Grigoryan, B. A.; Grigoryan, A. H.; Hakobyan, L. S.; Haroutiunian, S. G.; Ivanyan, M. I.; Khachatryan, V. G.; Laziev, E. M.; Manukyan, P. S.; Margaryan, I. N.; Markosyan, T. M.; Martirosyan, N. V.; Mehrabyan, Sh. A.; Mkrtchyan, T. H.; Muradyan, L. Kh.; Nikogosyan, G. H.; Petrosyan, V. H.; Sahakyan, V. V.; Sargsyan, A. A.; Simonyan, A. S.; Toneyan, H. A.; Tsakanian, A. V.; Vardanyan, T. L.; Vardanyan, A. S.; Yeremyan, A. S.; Zakaryan, S. V.; Zanyan, G. S. 2016-09-01 Advanced Research Electron Accelerator Laboratory (AREAL) is a 50 MeV electron linear accelerator project with a laser driven RF gun being constructed at the CANDLE Synchrotron Research Institute. In addition to applications in life and materials sciences, the project aims as a test facility for advanced accelerator and radiation source concepts. In this paper, the AREAL RF photoinjector performance, the facility design considerations and its highlights in the fields of free electron laser, the study of new high frequency accelerating structures, the beam microbunching and wakefield acceleration concepts are presented. 3. Terrestrial Photovoltaic Module Accelerated Test-To-Failure Protocol Energy Technology Data Exchange (ETDEWEB) Osterwald, C. R. 2008-03-01 This technical report documents a test-to-failure protocol that may be used to obtain quantitative information about the reliability of photovoltaic modules using accelerated testing in environmental temperature-humidity chambers. 4. Accelerators for Society - TIARA 2012 Test Infrastructure and Accelerator Research Area (in Polish) OpenAIRE Romaniuk, R S 2013-01-01 TIARA (Test Infrastructure and Accelerator Research Area - Preparatory Phae) is an European Collaboration of Accelerator Technology, which by running research projects, technical, networks and infrastructural has a duty to integrate the research and technical communities and infrastructures in the global scale of Europe. The Collaboration gathers all research centers with large accelerator infrastructures. Other ones, like universities, are affiliated as associate members. TIARA-PP (preparato... 5. The electron test accelerator safety in design and operation International Nuclear Information System (INIS) The Electron Test Accelerator is being designed as an experiment in accelerator physics and technology. With an electron beam power of up to 200 kW the operation of the accelerator presents a severe radiation hazard as well as rf and electrical hazards. The design of the safety system provides fail-safe protection while permitting flexibility in the mode of operation and minimizing administrative controls. (auth) 6. Beam acceleration test of the HIMAC injector International Nuclear Information System (INIS) A heavy-ion synchrotron dedicated to medical use is under construction at National Institute of Radiological Sciences. The injector system, comprising a PIG source, an ECR source, an RFQ linac, and an Alvarez linac of 100MHz, accelerates heavy ions with a charge-to-mass ratio as small as 1/7, up to 6 MeV/u. First operation of the injector system has shown satisfactory performance. (author) 7. Accelerators for Society - TIARA 2012 Test Infrastructure and Accelerator Research Area (in Polish) CERN Document Server Romaniuk, R S 2013-01-01 TIARA (Test Infrastructure and Accelerator Research Area - Preparatory Phae) is an European Collaboration of Accelerator Technology, which by running research projects, technical, networks and infrastructural has a duty to integrate the research and technical communities and infrastructures in the global scale of Europe. The Collaboration gathers all research centers with large accelerator infrastructures. Other ones, like universities, are affiliated as associate members. TIARA-PP (preparatory phase) is an European infrastructural project run by this Consortium and realized inside EU-FP7. The paper presents a general overview of TIARA activities, with an introduction containing a portrait of contemporary accelerator technology and a digest of its applications in modern society. 8. An Accelerated Stress Test Method for Electrostatically Driven MEMS Devices OpenAIRE Ruan, Jinyu Jason; Monnereau, Nicolas; Trémouilles, David; Mauran, Nicolas; Coccetti, Fabio; Nolhier, Nicolas; Plana, Robert 2012-01-01 This paper addresses an innovative solution to develop a circuit to perform accelerated stress tests of capacitive microelectromechanical-system (MEMS) switches and shows the use of instruments and equipment to monitor physical aging phenomena. A dedicated test circuit was designed and fabricated in order to meet the need for accelerated techniques for those structures. It integrated an in-house miniaturized circuit connected to additional test equipment (e.g., oscilloscopes and capacitance m... 9. Preliminary power test on C-band accelerator International Nuclear Information System (INIS) A C-band 2 MeV standing wave accelerator is under development for engineering research on accelerator miniaturization. At present, significant progress has been achieved. The accelerating tube has been fully sealed, and the hot test platform for the accelerator has been built. At the repetition rate of 50 Hz, preliminary power test has been performed. It used the ionization chamber dose monitor to test the dose rate of X-rays at 1 m before the target, and the steel absorption method to test the energy of the electron beam. The preliminary test results show that, the beam energy is about 2.5 MeV, and the dose rate can be over 330 mGy/(min · m). (authors) 10. Scientists confirm delay in testing new CERN particle accelerator CERN Multimedia 2007-01-01 "Scientists seeking to uncover the secrets of the universe will have to wait a little longer after the CERN laboratory inswitzerland on Monday confirmed a delay in tests of a massive new particle accelerator." (1 page) 11. Development of a new accelerated salt crystallization test NARCIS (Netherlands) Wijffels, T.J.; Lubelli, B.A. 2006-01-01 TNO Built Environment and Geosciences has developed, in cooperation with other institutes in the European project Compass1, a new accelerated salt crystallization test. In this paper the design process leading to the definition of this test is described. Preliminary tests studying the influence of t 12. Testing of high-vacuum pumps for charged particle accelerators International Nuclear Information System (INIS) To study a possibility of employing different types of pumps in charged-particle accelerators the following pumps have been tested: electric-arc, turbomolecular and cryogenic. The research has been carried out on a test bench which made it possible to determine the pumping-out rate for different gases (constant-volume methods), measure their limiting pressure and study the spectra of different gases by using mass spectrometers. It was possible also to warm up the pumps and pumped-out volumes. From these tests it was concluded that: (1) the electric-arc pump does not meet the accelerator pumping-out requirements; (2) the turbomolecular pump with a nitrogen-sorption trap can be recommended for pumping-out accelerators but requires modification of the supply unit; (3) the cryogenic pump can be recommended for pumpimg-out of accelerators but requires modification of the automatic system for replenishment of the cryogenic fluid 13. Recent progress of the advanced test accelerator Energy Technology Data Exchange (ETDEWEB) Prono, D.S. 1985-05-13 Attempts to further improve the beam brightness from field emission cathodes are currently centered on the issue of how beam optics and phase mixing within the injector transport tend to ''average down'' the beam brightness. Particle simulation work indicates that beam brightness can be significantly improved by simply reducing the injector transport magnetic field and losing peak transport current, i.e., only transporting that high brightness portion of the total current. The simulation results shown in Figure 8 suggest that beam brightness can be increased perhaps a factor of 5 or more simply by ''tuning for brightness'' rather than tuning for peak transported current. If this can indeed be experimentally realized and the resulting beam matched onto accelerator transport (magnetic and/or laser guided) without emittance degradation then simple field emission cathodes would, at least in the immediately near term, saisfy the needs for 10 micron FEL experiments. 8 refs., 8 figs. 14. Acceleration of the LHC commissioning tests CERN Multimedia 2008-01-01 The quadrupole and main dipole circuits have been powered up to 10,200 amps in Sector 4-5. Sector 5-6 is currently being cooled and will be the next to undergo electrical tests, which will be stepped up over the next few weeks. 15. A Study on the Storage Reliability of LSINS Based on Step-stress Accelerated Life Test Directory of Open Access Journals (Sweden) Teng Fei 2015-01-01 Full Text Available Based on the step-stress accelerated life test and the laser strap-down inertial navigation system, this paper studies the accelerated life model and the test method, provides the likelihood function, the likelihood equation and the two-order derivative when the stress level is k, evaluates the effectiveness of the method with the simulation test model established by MATLAB, applies the research findings in the storage reliability study of the XX laser strap-down inertial navigation system, and puts forward an effective evaluation method of the storage life of the inertial navigation system. 16. Accelerated development and flight evaluation of active controls concepts for subsonic transport aircraft. Volume 1: Load alleviation/extended span development and flight tests Science.gov (United States) Johnston, J. F. 1979-01-01 Active wing load alleviation to extend the wing span by 5.8 percent, giving a 3 percent reduction in cruise drag is covered. The active wing load alleviation used symmetric motions of the outboard ailerons for maneuver load control (MLC) and elastic mode suppression (EMS), and stabilizer motions for gust load alleviation (GLA). Slow maneuvers verified the MLC, and open and closed-loop flight frequency response tests verified the aircraft dynamic response to symmetric aileron and stabilizer drives as well as the active system performance. Flight tests in turbulence verified the effectiveness of the active controls in reducing gust-induced wing loads. It is concluded that active wing load alleviation/extended span is proven in the L-1011 and is ready for application to airline service; it is a very practical way to obtain the increased efficiency of a higher aspect ratio wing with minimum structural impact. 17. The Next Linear Collider test accelerator: Status and results International Nuclear Information System (INIS) At SLAC, the authors are pursuing the design of a Next Linear Collider (NLC) which would begin with a center-of-mass energy of 0.5 TeV, and would be upgradable to 1.0 TeV and beyond. To achieve this high energy, for the past several years they have been working on the development of a high-gradient 11.4-GHz (X-band) linear accelerator for the main linac of the collider. In this paper, they present the status and initial results from the ''Next Linear Collider Test Accelerator'' (NLCTA). The goal of the NLCTA is to model the high gradient linac of the NLC. It incorporates the new technologies of X-band accelerator structures, rf pulse compression systems and high-power klystrons into a 0.5 to 1.0 GeV linac which is a test bed for beam dynamics issues related to high-gradient acceleration 18. A comparative study of accelerated tests to simulate atmospheric corrosion International Nuclear Information System (INIS) In this study, specimens coated with five organic coating systems were exposed to accelerated tests for periods up to 2000 hours, and also to weathering for two years and six months. The accelerated tests consisted of the salt spray test, according to ASTM B-117; Prohesion (ASTM G 85-98 annex 5A); Prohesion combined with cyclic exposure to UV-A radiation and condensation; 'Prohchuva' a test described by ASTM G 85-98 using a salt spray with composition that simulated the acid rain of Sao Paulo, but one thousand times more concentrated, and 'Prohchuva' combined with cyclic exposure to UV-A radiation and condensation. The coated specimens were exposed with and without incision to expose the substrate. The onset and progress of corrosion at and of the exposed metallic surface, besides coating degradation, were followed by visual observation, and photographs were taken. The coating systems were classified according to the extent of corrosion protection given to the substrate, using a method based on ASTM standards D-610, D-714, D-1654 and D-3359. The rankings of the coatings obtained from accelerated tests and weathering were compared and contrasted with classification of the same systems obtained from literature, for specimens exposed to an industrial atmosphere. Coating degradation was strongly dependent on the test, and could be attributed to differences in test conditions. The best correlation between accelerated test and weathering was found for the test Prohesion alternated with cycles of exposure to UV-A radiation and condensation. (author) 19. The Advanced Superconducting Test Accelerator at Fermilab: Science Program Energy Technology Data Exchange (ETDEWEB) Piot, Philippe [Fermilab; Harms, Elvin [Fermilab; Henderson, Stuart [Fermilab; Leibfritz, Jerry [Fermilab; Nagaitsev, Sergei [Fermilab; Shiltsev, Vladimir [Fermilab; Valishev, Alexander [Fermilab 2014-07-01 The Advanced Superconducting Test Accelerator (ASTA) currently in commissioning phase at Fermilab is foreseen to support a broad range of beam-based experiments to study fundamental limitations to beam intensity and to develop novel approaches to particle-beam generation, acceleration and manipulation. ASTA incorporates a superconducting radiofrequency (SCRF) linac coupled to a flexible high-brightness photoinjector. The facility also includes a small-circumference storage ring capable of storing electrons or protons. This report summarizes the facility capabilities, and provide an overview of the accelerator-science researches to be enabled. 20. Testing General Relativity With Laser Accelerated Electron Beams OpenAIRE Gergely, L. Á.; Harko, T. 2012-01-01 Electron accelerations of the order of$10^{21} g$obtained by laser fields open up the possibility of experimentally testing one of the cornerstones of general relativity, the weak equivalence principle, which states that the local effects of a gravitational field are indistinguishable from those sensed by a properly accelerated observer in flat space-time. We illustrate how this can be done by solving the Einstein equations in vacuum and integrating the geodesic equations of motion for a un... 1. Nuclear-waste-package materials degradation modes and accelerated testing International Nuclear Information System (INIS) This report reviews the materials degradation modes that may affect the long-term behavior of waste packages for the containment of nuclear waste. It recommends an approach to accelerated testing that can lead to the qualification of waste package materials in specific repository environments in times that are short relative to the time period over which the waste package is expected to provide containment. This report is not a testing plan but rather discusses the direction for research that might be considered in developing plans for accelerated testing of waste package materials and waste forms 2. Acceleration test of heavy-ion with TIT RFQ linac International Nuclear Information System (INIS) A heavy-ion acceleration system with the TIT-RFQ has been developed. The TIT-RFQ was designed to accelerate particles with a charge to mass ratio ε ≥ 1/16, as it was, the kind of particles was limited because of the insufficient withstanding voltage of the beam injection equipment. In order to solve this problem, the development of the new system was planed, and the work has been carried out since last year. By using this system, the first acceleration of N+ beam was observed in January this year; however, the beam intensity was insufficient. Some problems were pointed out, and the synchronous circuit of a RF pulse was constructed up to now. By using this circuit, the increase of the beam intensity was observed in the second acceleration test in this summer. (author) 3. Automatic testing of medium-frequency acceleration transducers International Nuclear Information System (INIS) An automatic test bench for medium-frequency acceleration transducers employing a method of comparison is described. The following points are discussed: the measurement possibilities of this bench in the frequency range 10Hz-10kHz and for applied acceleration levels of 1000m.s-2 or below; the transducer parameters checked; the uncertainties on the measurement of these parameters. The test procedure is described in detail and illustrated by a concrete case showing the particular form of presentation of the results 4. Mechanical stability study for Integrable Optics Test Accelerator at Fermilab OpenAIRE McGee, M. W.; Andrews, R; Carlson, K.; Leibfritz, J.; Nobrega, L.; Valishev, A. 2016-01-01 The Integrable Optics Test Accelerator (IOTA) is proposed for operation at Fermilab. The goal of IOTA is to create practical nonlinear accelerator focusing systems with a large frequency spread and stable particle motion. The IOTA is a 40 m circumference, 150 MeV (e-), 2.5 MeV (p+) diagnostic test ring. A heavy low frequency steel floor girder is proposed as the primary tier for IOTA device component support. Two design lengths; (8) 3.96 m and (2) 3.1 m long girders with identical cross secti... 5. High current electron linacs (advanced test accelerator/experimental test accelerator) International Nuclear Information System (INIS) The high current induction accelerator development at the Lawrence Livermore National Laboratory is described. The ATA facility is designed for 10 kA peak currents, 50 nsec pulse lengths and 50 MeV energies. At this time, half of the design current has been accelerated through the entire machine to particle energies of about 45 MeV. Current problem areas and operational experience to date will be discussed. Several key technical areas required development for the ATA machine; this report will survey these developments. The control of transverse beam instabilities required an accelerating cavity design with very low Q. Electron sources capable of 10 kA operation at high rep rates were developed using a plasma sparkboard approach. The pulse power systems on ATA, using the same type of spark gap switches as ETA, have exhibited excellent operational reliability 6. An accelerated test method for efflorescence in clay bricks International Nuclear Information System (INIS) An investigation into the creation of accelerated efflorescence in clay bricks was undertaken with a view to creating a viable test procedure for determining efflorescence potential. The testing programme incorporated ambient conditions similar to those which promote efflorescence growth in bricks in use. Theoretical investigations into the physical mechanism underlying the creation of efflorescence directed the attempts to accelerate the process. It was found that calcium sulphate efflorescence could not be sufficiently accelerated such that a useful efflorescence test procedure could be proposed. The inability to produce accelerated efflorescence in brick samples was attributed to limitations associated with time dependent salt diffusion in the efflorescence mechanism. The preliminary testing that was undertaken into the creation of efflorescence prompted the use of acid assisted methods to accelerate efflorescence. The acid assisted method that was adopted to provide a possible indication of efflorescence potential relies upon the transformation of low solubility calcium to a more soluble form. The movement of the transformed salt is then induced by cyclic temperature exposure at temperatures similar to those experienced in Spring. The appearance of the transformed calcium salt on the surface of the brick specimen provides an indication of the efflorescence potential. Brick piers constructed on an exposed site and monitored over a 12 month period provided information on the validity of the acid assisted test method. The efflorescence observed on the piers correlated well with that predicted by the acid assisted test, suggesting that the new test has the potential to accurately predict the efflorescence potential of clay bricks Relationships between other properties such as air permeability, sorptivity and tensile strength were investigated such that an alternative method of predicting efflorescence could be achieved. It was found that (within the bounds of the 7. Quick setup of test unit for accelerator control system International Nuclear Information System (INIS) Testing a single hardware unit of an accelerator control system often requires the setup of a program with graphical user interface. Developing a dedicated application for a specific hardware unit test could be time consuming and the application may become obsolete after the unit tests. This paper documents a methodology for quick design and setup of an interface focused on performing unit tests of accelerator equipment with minimum programming work. The method has three components. The first is a generic accelerator device object (ADO) manager which can be used to setup, store, and log testing controls parameters for any unit testing system. The second involves the design of a TAPE (Tool for Automated Procedure Execution) sequence file that specifies and implements all te testing and control logic. The sting third is the design of a PET (parameter editing tool) page that provides the unit tester with all the necessary control parameters required for testing. This approach has been used for testing the horizontal plane of the Stochastic Cooling Motion Control System at RHIC. 8. Conductivity testing and evaluation Directory of Open Access Journals (Sweden) Lygita Makaravičiūtė 2015-10-01 Full Text Available Surface wastewater is consideredas effluents, which are formed on the surface of urbanized areas. Stormwater treatment is performed out using a variety of filters: sand, grass. Wastewater penetration into the deeper layers is called hydraulic conductivity. After evaluation of the hydraulic conductivity, it is possible to determine the ability of the investigated fillers to entrap the stormwater flow. The hydraulic conductivity tests can indicate which fillers of stormwater filters may influence the more effective stormwater cleaning. Four stormwater filters were tested: crushed autoclaved aerated concrete filter; crushed autoclaved aerated concrete with Meadow grass (Poa pratensis layer; silica sand filter with Meadow grass (Poa pratensis layer; silica sand filter. Under in-situ conditions hydraulic conductivity in filters is investigated using Constant-head method. Mathematical modeling program Hydrus-1D presentsthe changes of hydraulic conductivity in each filler layer of the filter. Assessed hydraulic conductivity in filters under in-situ conditions hasn‘t changed only in crushed autoclaved aerated concrete filter (30 000 mm/d. The smallest hydraulic conductivity in filters under in-situ conditions was estimated in silica sand filter with Meadow grass (Poa pratensis layer, here it was equal to 209.3 mm/d.With mathematical modeling program Hydrus-1D it was found that the hydraulic conductivity in each filter decreases, depending on the depth of filler in the filter. 9. The BNL Accelerator Test Facility and experimental program International Nuclear Information System (INIS) The Accelerator Test Facility (ATF) at BNL is a users' facility for experiments in Accelerator and Beam Physics. The ATF provides high brightness electron beams and high power laser pulses synchronized to the electron beam, suitable for studies of new methods of high gradient acceleration and state of the art free electron lasers. The electrons are produced by a laser photocathode rf gun and accelerated to 50 to 100 MeV by two traveling wave accelerator sections. The lasers include a 10 mJ, 10 ps Nd:YAG laser and a 100 mJ, 10 ps CO2 laser. A number of users from National Laboratories, universities and industry take part in experiments at the ATF. The experimental program includes various acceleration schemes, Free-Electron Laser experiments and a program on the development of high brightness electron beams. The AFT's experimental program commenced in early 1991 at an energy of about 4 MeV. The full program, with 50 MeV and the High power laser will begin operation this year. 28 refs., 4 figs 10. Experience on high voltage testing and conditioning of accelerator tube for 3 MeV DC accelerator International Nuclear Information System (INIS) In DC Electron Beam Accelerator, accelerating potentials are generated using high voltage multiplier column. Accelerating potentials are uniformly graded to the accelerator tubes for accelerating the electron to attain the required energy. 3 MeV DC Accelerator is in the advance stages of commissioning at Electron Beam Centre Kharghar, Navi Mumbai. It has 10 numbers of accelerating tube each rated for 335 kVdc in 6 kg/cm2 SF6 gas environment outside and vacuum better than 10-7 mbar inside the tube. For safe and reliable operation of the accelerator, all the dynode gaps have to be conditioned and tested for high voltage withstand capability. Accelerating Tube Test Facility (ATTF) was developed for the testing and HV Conditioning of the accelerator tube. Tubes are conditioned with plasma, baking and application of ascending high Voltages. This paper describes the experience on the high voltage conditioning and testing of the accelerator tube of 3 MeV DC Accelerator. The accelerator has been successfully tested at 1 MeV and 10 kW beam power and 1.8 MeV at no load. (author) 11. Comment on "Testing Planck-Scale Gravity with Accelerators" CERN Document Server Kalaydzhyan, Tigran 2016-01-01 We challenge the analysis and conclusions of the paper Phys. Rev. Lett. 109, 141103 (2012) by V. Gharibyan on the tests of Planck-scale gravity with accelerators. The main objective of the Comment is the observation that the explored domain of "quantum gravity" parameters is already ruled out experimentally from, e.g., absence of the vacuum Cherenkov radiation. 12. Step-Stress Accelerated Degradation Testing for Solar Reflectors: Preprint Energy Technology Data Exchange (ETDEWEB) Jones, W.; Elmore, R.; Lee, J.; Kennedy, C. 2011-09-01 To meet the challenge to reduce the cost of electricity generated with concentrating solar power (CSP) new low-cost reflector materials are being developed including metalized polymer reflectors and must be tested and validated against appropriate failure mechanisms. We explore the application of testing methods and statistical inference techniques for quantifying estimates and improving lifetimes of concentrating solar power (CSP) reflectors associated with failure mechanisms initiated by exposure to the ultraviolet (UV) part of the solar spectrum. In general, a suite of durability and reliability tests are available for testing a variety of failure mechanisms where the results of a set are required to understand overall lifetime of a CSP reflector. We will focus on the use of the Ultra-Accelerated Weathering System (UAWS) as a testing device for assessing various degradation patterns attributable to accelerated UV exposure. Depending on number of samples, test conditions, degradation and failure patterns, test results may be used to derive insight into failure mechanisms, associated physical parameters, lifetimes and uncertainties. In the most complicated case warranting advanced planning and statistical inference, step-stress accelerated degradation (SSADT) methods may be applied. 13. Optical fiber feasibility study in Accelerated Pavement Testing facility OpenAIRE Bueche, N.; Rychen, P.; Dumont, A.-G.; Santagata, E. 2009-01-01 The presented research has been carried out within the European project Intelligent Roads (INTRO). The major objective followed was to assess the potential of optical fiber for pavement monitoring in comparison with classical strain gauges. Thus, both measurement devices have been tested under the same conditions in a full scale Accelerated Pavement Testing (APT) at LAVOC. This facility allows the user to control different parameters such as loading configuration and temperature and, as a mat... 14. Free-electron laser results from the Advanced Test Accelerator International Nuclear Information System (INIS) PALADIN is a 10.6-μm FEL amplifier experiment operating at the Lawrence Livermore National Laboratory's Advanced Test Accelerator, an induction linear accelerator designed to produce a 45-MeV, 10-kA electron beam. With a 15-m long wiggler, PALADIN demonstrated 27 dB of exponential gain from a 14-kW input signal. With a 5-MW input signal, the amplifier saturated after 10 dB of gain. The exponentially growing signal in the unsaturated amplifier was clearly seen to be gain guided by the electron beam. 7 refs., 8 figs 15. Accelerating SPICE Model-Evaluation using FPGAs OpenAIRE Kapre, Nachiket; DeHon, André 2009-01-01 Single-FPGA spatial implementations can provide an order of magnitude speedup over sequential microprocessor implementations for data-parallel, floating-point computation in SPICE model-evaluation. Model-evaluation is a key component of the SPICE circuit simulator and it is characterized by large irregular floating-point compute graphs. We show how to exploit the parallelism available in these graphs on single-FPGA designs with a low-overhead VLIW-scheduled architecture. ... 16. Operation of the graded-β electron test accelerator International Nuclear Information System (INIS) The Electron Test Accelerator has been built to model the behaviour of the high energy portion of a proton linear accelerator which would be suitable for breeding fissile material. The test accelerator and its control systems have been tested at 100% duty factor producing a beam of electrons at 1.5 MeV and currents up to 20 mA where the incident rf power is shared equally between the structure dissipation and the beam loading. The structure has performed satisfactorily in all respects at dissipation power densities up to 5 kW/cell where the mean energy gradient was 1.1 MeV/m. Experiments have been done on the beam loading effects in the coupling of the transmission line to the cavity, the amplitude depression in and phase tilt along the structure, and the phase lag of the structure field. The phase acceptance, the variation of transmission with buncher-accelerator phase shift and the beam energy spread are in qualitative agreement with beam dynamics calculations. (author) 17. High-Voltage Terminal Test of Test Stand for 1-MV Electrostatic Accelerator CERN Document Server Park, Sae-Hoon 2015-01-01 The Korea Multipurpose Accelerator Complex (KOMAC) has been developing a 300-kV test stand for a 1-MV electrostatic accelerator ion source. The ion source and accelerating tube will be installed in a high-pressure vessel. The ion source in the high-pressure vessel is required to have a high reliability. The test stand has been proposed and developed to confirm the stable operating conditions of the ion source. The ion source will be tested at the test stand to verify the long-time operating conditions. The test stand comprises a 300-kV high-voltage terminal, a battery for the ion-source power, a 60-Hz inverter, 200-MHz RF power, a 5-kV extraction power supply, a 300-kV accelerating tube, and a vacuum system. The results of the 300-kV high-voltage terminal tests are presented in this paper. 18. A general Bayes weibull inference model for accelerated life testing International Nuclear Information System (INIS) This article presents the development of a general Bayes inference model for accelerated life testing. The failure times at a constant stress level are assumed to belong to a Weibull distribution, but the specification of strict adherence to a parametric time-transformation function is not required. Rather, prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels and the common shape parameter. Using the approach, Bayes point estimates as well as probability statements for use-stress (and accelerated) life parameters may be inferred from a host of testing scenarios. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known MCMC (Markov Chain Monte Carlo) methods to derive posterior approximations. The approach is illustrated with an example 19. Next Linear Collider Test Accelerator conceptual design report International Nuclear Information System (INIS) This document presents the scientific justification and the conceptual design for the open-quotes Next Linear Collider Test Acceleratorclose quotes (NLCTA) at SLAC. The goals of the NLCTA are to integrate the new technologies of X-band accelerator structures and rf systems being developed for the Next Linear Collider, to measure the growth of the open-quotes dark currentclose quotes generated by rf field emission in the accelerator, to demonstrate multi-bunch beam-loading energy compensation and suppression of higher-order deflecting modes, and to measure any transverse components of the accelerating field. The NLCTA will be a 42-meter-long beam line consisting, consecutively, of a thermionic-cathode gun, an X-band buncher, a magnetic chicane, six 1.8-meter-long sections of 11.4-GHz accelerator structure, and a magnetic spectrometer. Initially, the unloaded accelerating gradient will be 50 MV/m. A higher-gradient upgrade option eventually would increase the unloaded gradient to 100 MV/m 20. Mechanical stability study for Integrable Optics Test Accelerator at Fermilab CERN Document Server McGee, M W; Carlson, K; Leibfritz, J; Nobrega, L; Valishev, A 2016-01-01 The Integrable Optics Test Accelerator (IOTA) is proposed for operation at Fermilab. The goal of IOTA is to create practical nonlinear accelerator focusing systems with a large frequency spread and stable particle motion. The IOTA is a 40 m circumference, 150 MeV (e-), 2.5 MeV (p+) diagnostic test ring. A heavy low frequency steel floor girder is proposed as the primary tier for IOTA device component support. Two design lengths; (8) 3.96 m and (2) 3.1 m long girders with identical cross section completely encompass the ring. This study focuses on the 3.96 m length girder and the development of a working prototype. Hydrostatic Level Sensor (HLS), temperature, metrology and fast motion measurements characterize the anticipated mechanical stability of the IOTA ring. 1. European accelerator facilities for single event effects testing Energy Technology Data Exchange (ETDEWEB) Adams, L.; Nickson, R.; Harboe-Sorensen, R. [ESA-ESTEC, Noordwijk (Netherlands); Hajdas, W.; Berger, G. 1997-03-01 Single event effects are an important hazard to spacecraft and payloads. The advances in component technology, with shrinking dimensions and increasing complexity will give even more importance to single event effects in the future. The ground test facilities are complex and expensive and the complexities of installing a facility are compounded by the requirement that maximum control is to be exercised by users largely unfamiliar with accelerator technology. The PIF and the HIF are the result of experience gained in the field of single event effects testing and represent a unique collaboration between space technology and accelerator experts. Both facilities form an essential part of the European infrastructure supporting space projects. (J.P.N.) 2. Mechanical Stability Study for Integrable Optics Test Accelerator at Fermilab Energy Technology Data Exchange (ETDEWEB) McGee, Mike [Fermilab; Andrews, Richard [Fermilab; Carlson, Kermit [Fermilab; Leibfritz, Jerry [Fermilab; Nobrega, Lucy [Fermilab; Valishev, Alexander [Fermilab 2016-07-01 The Integrable Optics Test Accelerator (IOTA) is proposed for operation at Fermilab. The goal of IOTA is to create practical nonlinear accelerator focusing systems with a large frequency spread and stable particle motion. The IOTA is a 40 m circumference, 150 MeV (e-), 2.5 MeV (p⁺) diagnostic test ring. A heavy low frequency steel floor girder is proposed as the primary tier for IOTA device component support. Two design lengths; (8) 4 m and (2) 2.8 m long girders with identical cross section completely encompass the ring. This study focuses on the 4 m length girder and the development of a working prototype. Hydrostatic Level Sensor (HLS), temperature, metrology and fast motion measurements characterize the anticipated mechanical stability of the IOTA ring. 3. Design of Accelerated Fatigue Tests for Flame Free Refrigeration Fittings OpenAIRE Wilson, Michael; Bowers, Chad D. 2014-01-01 Refrigerant leakage from failed braze joints is a multi-billion dollar problem for the global HVAC&R industry. Leaks are typically caused due to mechanical fatigue from extreme pressure cycling, temperature cycling including exposure to freeze/thaw cycles, or vibrational wear induced from rotating electrical machinery. Three tests to accelerate mechanical fatigue were devised to simulate real world extreme conditions to determine possible failure modes of refrigerant components. The first tes... 4. Brookhaven Accelerator Test Facility photocathode gun and transport beamline International Nuclear Information System (INIS) We present an analysis of the electron beam emitted from a laser driven photocathode injector (Gun, operating at 2856 MHZ), through a Transport beamline, to the LINAC entrance for the Brookhaven Accelerator Test Facility (ATF). The beam parameters including beam energy, and emittance are calculated. Some of our results, are tabulated and the phase plots of the beam parameters, from Cathode, through the Transport line elements, to the LINAC entrance, are shown 5. Development of an accelerated test for Internal Sulfate Attack study Directory of Open Access Journals (Sweden) Khelil Nacim 2014-04-01 Full Text Available Internal Sulfate Attack (ISA is a pathology that occurs under certain conditions in concrete having undergone heating above 70 °C at early age (through heating in pre-casting industry or due to hydration in large concrete parts. This reaction deemed very slow, numerous methods to speed up reactions leading to delayed ettringite formation have been developed. These methods are all based on the material damage. Another type of test is currently under development. It is based on rehabilitation techniques such as electrochemical chloride extraction (ECE in order to accelerate the leaching of alkalis that could be one of the triggers of the pathology. The study presented in this paper focused on concrete specimens prepared from cement (CEM I 52.5 N enriched with Na2SO4. These concretes have undergone a heat treatment typical of those used in precast plants (up to 24 hours with a maximum temperature of 80 °C. Various paths were explored for the development of the accelerated test. The first results showed that it was necessary to use a removable titanium anode ruthenium anode instead of stainless steel embedded in the concrete. Then tests with de-ionized water as the solute to the cathode did not accelerate the onset of expansions. The experiment has been modified and potassium carbonate was added to the solution. This modification didn’t show any significant improvement, and other experiments are being carried out to explain this result. 6. Accelerated Creep Testing of High Strength Aramid Webbing Science.gov (United States) Jones, Thomas C.; Doggett, William R.; Stnfield, Clarence E.; Valverde, Omar 2012-01-01 A series of preliminary accelerated creep tests were performed on four variants of 12K and 24K lbf rated Vectran webbing to help develop an accelerated creep test methodology and analysis capability for high strength aramid webbings. The variants included pristine, aged, folded and stitched samples. This class of webbings is used in the restraint layer of habitable, inflatable space structures, for which the lifetime properties are currently not well characterized. The Stepped Isothermal Method was used to accelerate the creep life of the webbings and a novel stereo photogrammetry system was used to measure the full-field strains. A custom MATLAB code is described, and used to reduce the strain data to produce master creep curves for the test samples. Initial results show good correlation between replicates; however, it is clear that a larger number of samples are needed to build confidence in the consistency of the results. It is noted that local fiber breaks affect the creep response in a similar manner to increasing the load, thus raising the creep rate and reducing the time to creep failure. The stitched webbings produced the highest variance between replicates, due to the combination of higher local stresses and thread-on-fiber damage. Large variability in the strength of the webbings is also shown to have an impact on the range of predicted creep life. 7. An Asset Test of the CLIC Accelerating Structure International Nuclear Information System (INIS) Transverse wakefield suppression in the CLIC (Compact Linear Collider) multibunch accelerating structure, called the TDS (Tapered Damped Structure), is achieved primarily through heavy damping. In order to verify the performance of the TDS design and the validity of the theoretical tools used to model it, a 15 GHz version of the TDS has been constructed and tested in the ASSET facility at SLAC. The test has directly demonstrated transverse wakefield suppression of over a factor 100, with an excellent agreement between the measured and the calculated wakefield 8. Database requirements for the Advanced Test Accelerator project International Nuclear Information System (INIS) The database requirements for the Advanced Test Accelerator (ATA) project are outlined. ATA is a state-of-the-art electron accelerator capable of producing energetic (50 million electron volt), high current (10,000 ampere), short pulse (70 billionths of a second) beams of electrons for a wide variety of applications. Databasing is required for two applications. First, the description of the configuration of facility itself requires an extended database. Second, experimental data gathered from the facility must be organized and managed to insure its full utilization. The two applications are intimately related since the acquisition and analysis of experimental data requires knowledge of the system configuration. This report reviews the needs of the ATA program and current implementation, intentions, and desires. These database applications have several unique aspects which are of interest and will be highlighted. The features desired in an ultimate database system are outlined. 3 references, 5 figures 9. Beam loading and cavity compensation for the Ground Test Accelerator International Nuclear Information System (INIS) The Ground Test Accelerator (GTA) will be heavily beam-loaded H- linac with tight tolerances on accelerating field parameters. The methods used in modeling the effects of beam loading in this machine are described. The response of the cavity to both beam and radio-frequency (RF) drive stimulus is derived, including the effects of cavity detuning. This derivation is not restricted to a small-signal approximation. An analytical method for synthesizing a predistortion network that decouples the amplitude and phase responses of the cavity is also outline. Simulation of performance, including beam loading, is achieved through use of a control system analysis software package. A straightforward method is presented for extrapolating this work to model large coupled structures with closely spaced parasitic modes. Results to date have enabled the RF control system designs for GTA to be optimized and have given insight into their operation. 6 refs., 10 figs 10. Precise RF control system of the SCSS test accelerator International Nuclear Information System (INIS) We present development and performance of the low-level rf control system of the SCSS test accelerator. The low-level rf system consists of IQ modulators / demodulators and VME waveform generators / digitizers. Recent improvements of them established high-resolution phase and amplitude setting capabilities of 0.01 degree and 0.01%, respectively. In addition, temperature drifts of the injector acceleration cavities were reduced by tuning a precise temperature regulation system. The temperature fluctuation was improved to be 0.01 K rms. As a result, the rf phase and amplitude stabilities of sub-harmonic buncher cavities were achieved to be 0.02 degree rms and 0.03% rms, respectively. The saturated FEL radiation in the wavelength region of 50-60 nm is stably generated by this improvement. (author) 11. Accelerated stress testing of amorphous silicon solar cells Science.gov (United States) Stoddard, W. G.; Davis, C. W.; Lathrop, J. W. 1985-01-01 A technique for performing accelerated stress tests of large-area thin a-Si solar cells is presented. A computer-controlled short-interval test system employing low-cost ac-powered ELH illumination and a simulated a-Si reference cell (seven individually bandpass-filtered zero-biased crystalline PIN photodiodes) calibrated to the response of an a-Si control cell is described and illustrated with flow diagrams, drawings, and graphs. Preliminary results indicate that while most tests of a program developed for c-Si cells are applicable to a-Si cells, spurious degradation may appear in a-Si cells tested at temperatures above 130 C. 12. Simulations and Vacuum Tests of a CLIC Accelerating Structure CERN Document Server Garion, C 2011-01-01 The Compact LInear Collider, under study, is based on room temperature high gradient structures. The vacuum specificities of these cavities are low conductance, large surface areas and a non-baked system. The main issue is to reach UHV conditions (typically 10-7 Pa) in a system where the residual vacuum is driven by water outgassing. A finite element model based on an analogy thermal/vacuum has been built to estimate the vacuum profile in an accelerating structure. Vacuum tests are carried out in a dedicated set-up, the vacuum performances of different configurations are presented and compared with the predictions. 13. Testing of accelerator dipoles in pressurized superfluid helium International Nuclear Information System (INIS) Two superconducting accelerator dipole magnets, with different internal construction features, have been tested in pressurized superfluid helium (1.8K, 1.2 atmosphere) as well as in regular pool boiling helium (4.4K, 1.2 atmosphere) helium. The coils of one magnet were moderately pre-stressed, and 4.2K design performance was rapidly achieved in the superfluid. The other magnet had very low coil pre-stress, reduced helium ventilation, and displayed degraded performance, even in the superfluid helium 14. Metal and elastomer seal tests for accelerator applications International Nuclear Information System (INIS) The vacuum system of the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory has more than a thousand metal vacuum seals. Also, numerous elastomer seals are used throughout the AGS to seal large beam component chambers. An accelerator upgrade program is being implemented to reduce the AGS operating pressure by x100 and improve the reliability of the vacuum system. This paper describes work in progress on metal and elastomer vacuum seals to help meet those two objectives. Tests are reported on the sealing properties of a variety of metal seals used on different sealing surfaces. Results are also given on reversible sorption properties of certain elastomers. 16 refs., 6 figs., 4 tabs 15. Accelerated aging of IG units : North American test methods International Nuclear Information System (INIS) Both Canadian and American standards have been in place for decades to determine argon gas concentration in insulating glass (IG) units. Efforts are underway to harmonize the IG standards to have acceptable test methods for the durability of IG units and to implement a single certification program for both Canada and the United States. One way to test the durability and integrity of the edge seal on IG units is to subject them to accelerated aging cycles in a controlled environment. This paper summarizes the Canadian, American and the harmonized test methods used in testing the integrity of the seal and the determination of argon gas in IG units. The Canadian standard (CAN/CGSB 12.8) encompasses the following tests: initial seal of units, initial dew point, initial argon concentration, failure analysis (water immersion test), weather cycling, volatile fogging (UV), dew point measurement after weather cycling, high humidity cycling, and final argon concentration. American ASTM E773 and ASTM E774 differ from the Canadian standard in the sequence of testing and the rating of IG units, creating problems for certification of units being shipped across the border. It was noted that adopting a single certification program for Canada and the United States would bring economic benefits to both consumers and manufacturers. 7 refs., 5 figs 16. Advanced Vehicle Testing and Evaluation Energy Technology Data Exchange (ETDEWEB) Garetson, Thomas [The Clarity Group, Incorporated, Chicago, IL (United States) 2013-03-31 The objective of the United States (U.S.) Department of Energy's (DOEs) Advanced Vehicle Testing and Evaluation (AVTE) project was to provide test and evaluation services for advanced technology vehicles, to establish a performance baseline, to determine vehicle reliability, and to evaluate vehicle operating costs in fleet operations.Vehicles tested include light and medium-duty vehicles in conventional, hybrid, and all-electric configurations using conventional and alternative fuels, including hydrogen in internal combustion engines. Vehicles were tested on closed tracks and chassis dynamometers, as well as operated on public roads, in fleet operations, and over prescribed routes. All testing was controlled by procedures developed specifically to support such testing. 17. Bayesian optimal design of step stress accelerated degradation testing Institute of Scientific and Technical Information of China (English) Xiaoyang Li; Mohammad Rezvanizaniani; Zhengzheng Ge; Mohamed Abuali; Jay Lee 2015-01-01 This study presents a Bayesian methodology for de-signing step stress accelerated degradation testing (SSADT) and its application to batteries. First, the simulation-based Bayesian de-sign framework for SSADT is presented. Then, by considering his-torical data, specific optimal objectives oriented Kul back–Leibler (KL) divergence is established. A numerical example is discussed to il ustrate the design approach. It is assumed that the degrada-tion model (or process) fol ows a drift Brownian motion;the accele-ration model fol ows Arrhenius equation; and the corresponding parameters fol ow normal and Gamma prior distributions. Using the Markov Chain Monte Carlo (MCMC) method and WinBUGS software, the comparison shows that KL divergence is better than quadratic loss for optimal criteria. Further, the effect of simulation outliers on the optimization plan is analyzed and the preferred sur-face fitting algorithm is chosen. At the end of the paper, a NASA lithium-ion battery dataset is used as historical information and the KL divergence oriented Bayesian design is compared with maxi-mum likelihood theory oriented local y optimal design. The results show that the proposed method can provide a much better testing plan for this engineering application. 18. Characterization of Corrosion Products on Carbon Steel Exposed to Natural Weathering and to Accelerated Corrosion Tests OpenAIRE Renato Altobelli Antunes; Rodrigo Uchida Ichikawa; Luis Gallego Martinez; Isolda Costa 2014-01-01 The aim of this work was to compare the corrosion products formed on carbon steel plates submitted to atmospheric corrosion in urban and industrial atmospheres with those formed after accelerated corrosion tests. The corrosion products were characterized by X-ray diffraction, Mössbauer spectroscopy, and Raman spectroscopy. The specimens were exposed to natural weathering in both atmospheres for nine months. The morphologies of the corrosion products were evaluated using scanning electron micr... 19. Evaluating the Power of GPU Acceleration for IDW Interpolation Algorithm OpenAIRE 2014-01-01 We first present two GPU implementations of the standard Inverse Distance Weighting (IDW) interpolation algorithm, the tiled version that takes advantage of shared memory and the CDP version that is implemented using CUDA Dynamic Parallelism (CDP). Then we evaluate the power of GPU acceleration for IDW interpolation algorithm by comparing the performance of CPU implementation with three GPU implementations, that is, the naive version, the tiled version, and the CDP version. Experimental resul... 20. Cost evaluation of irradiation system with electron accelerator International Nuclear Information System (INIS) The features of electron beam irradiation system using electron accelerator are direct energy pour into the irradiated material, no third material mixture such as catalyst, suitable for mass production and easy operation and maintenance work available. These features can bring the various applications such as cross-linking action, graft polymerization, radical polymerization and others. The selection of electron accelerator ratings is made under consideration of quality, width and thickness of irradiated material, production amount, dose required for reaction and irradiation atmosphere. Especially in a case of irradiation of wire with high insulation material such as polyethylene, the consideration of maximum thickness toward irradiation direction is necessary to avoid the discharge (Lichtenberg discharge) by charged-up electrons inside insulation material. Therefore, the acceleration voltage should be selected to make the maximum penetration larger than maximum irradiation thickness. The actual model case of estimate the irradiation cost was selected that the irradiation object was polyethylene insulated wire up to AWG no.14, irradiation amount was 5,000 km/month, necessary dose was 200 kGy, operation time was 22 d/month and 8 h/day and actual operation efficiency was considered loss time such as bobbin changing as 80%. The selected ratings of electron accelerator were acceleration voltage of 800 kV, beam current of 100 mA and irradiation width of 180 cm with irradiation pulleys stand of 60 turns x 3 lanes. The initial total cost was estimated as 3 M$(US) and operation cost was evaluated as 215 k$(US). Therefore, the irradiation cost of wire was evaluated as 0.0036$/m. (author)
1. A study of erosion in die casting dies by a multiple pin accelerated erosion test
Science.gov (United States)
Shivpuri, R.; Yu, M.; Venkatesan, K.; Chu, Y.-L.
1995-04-01
An accelerated erosion test was developed to evaluate the erosion resistance of die materials and coatings for die casting application. An acceleration in wear was achieved by selecting pyramid-shaped core pins, hypereutectic aluminum silicon casting alloy, high melt temperatures and high gate velocities. Multiple pin design was selected to enable multiple test sites for comparative evaluation. Apilot run was conducted on a 300 ton commercial die casting machine at various sites (pins) to verify the thermal and flow similarities. Subsequently, campaigns were run on two different 300 ton commercial die casting machines to evaluate H13 die material and different coatings for erosive resistance. Coatings and surface treatments evaluated included surface micropeening, titanium nitride, boron carbide, vanadium carbide, and metallic coatings—tungsten, molybdenum, and platinum. Recent campaigns with different melt temperatures have indicated a possible link between soldering phenomena and erosive wear. This paper presents the details of the test set up and the results of the pilot and evaluation tests.
2. Characterization of Corrosion Products on Carbon Steel Exposed to Natural Weathering and to Accelerated Corrosion Tests
Directory of Open Access Journals (Sweden)
Renato Altobelli Antunes
2014-01-01
Full Text Available The aim of this work was to compare the corrosion products formed on carbon steel plates submitted to atmospheric corrosion in urban and industrial atmospheres with those formed after accelerated corrosion tests. The corrosion products were characterized by X-ray diffraction, Mössbauer spectroscopy, and Raman spectroscopy. The specimens were exposed to natural weathering in both atmospheres for nine months. The morphologies of the corrosion products were evaluated using scanning electron microscopy. The main product found was lepidocrocite. Goethite and magnetite were also found on the corroded specimens but in lower concentrations. The results showed that the accelerated test based on the ASTM B117 procedure presented poor correlation with the atmospheric corrosion tests whereas an alternated fog/dry cycle combined with UV radiation exposure provided better correlation.
3. Mir Cooperative Solar Array Project Accelerated Life Thermal Cycling Test
Science.gov (United States)
Hoffman, David J.; Scheiman, David A.
1996-01-01
The Mir Cooperative Solar Array (MCSA) project was a joint U.S./Russian effort to build a photovoltaic (PV) solar array and deliver it to the Russian space station Mir. The MCSA will be used to increase the electrical power on Mir and provide PV array performance data in support of Phase 1 of the International Space Station. The MCSA was brought to Mir by space shuttle Atlantis in November 1995. This report describes an accelerated thermal life cycle test which was performed on two samples of the MCSA. In eight months time, two MCSA solar array 'mini' panel test articles were simultaneously put through 24,000 thermal cycles. There was no significant degradation in the structural integrity of the test articles and no electrical degradation, not including one cell damaged early and removed from consideration. The nature of the performance degradation caused by this one cell is briefly discussed. As a result of this test, changes were made to improve some aspects of the solar cell coupon-to-support frame interface on the flight unit. It was concluded from the results that the integration of the U.S. solar cell modules with the Russian support structure would be able to withstand at least 24,000 thermal cycles (4 years on-orbit). This was considered a successful development test.
4. Evaluation of modal testing methods
Science.gov (United States)
Chen, J.-C.
1984-01-01
Modal tests are playing an increasingly important role in structural dynamics efforts which are in need of analytical model verification or trouble shootings. In the meantime, the existing modal testing methods are undergoing great changes as well as new methods are being created. Although devoted advocates of each method can be found to argue the relative advantages and disadvantages, the general superiority, if any, of one or the other is not yet evident. The Galileo spacecraft, a realistic, complex structural system, will be used as a test article for performing modal tests by various methods. The results will be used to evaluate the relative merits of the various modal testing methods.
5. Power-conditioning system for the Advanced Test Accelerator
International Nuclear Information System (INIS)
The Advanced Test Accelerator (ATA) is a pulsed, linear induction, electron accelerator currently under construction and nearing completion at Lawrence Livermore National Laboratory's Site 300 near Livermore, California. The ATA is a 50 MeV, 10 kA machine capable of generating electron beam pulses at a 1 kHz rate in a 10 pulse burst, 5 pps average, with a pulse width of 70 ns FWHM. Ten 18 kV power supplies are used to charge 25 capacitor banks with a total energy storage of 8 megajoules. Energy is transferred from the capacitor banks in 500 microsecond pulses through 25 Command Resonant Charge units (CRC) to 233 Thyratron Switch Chassis. Each Thyratron Switch Chassis contains a 2.5 microfarad capacitor and is charged to 25 kV (780 joules) with voltage regulation of +- .05%. These capacitors are switched into 10:1 step-up resonant transformers to charge 233 Blumleins to 250 kV in 20 microseconds. A magnetic modulator is used instead of a Blumlein to drive the grid of the injector
6. Cosmic acceleration without dark energy: background tests and thermodynamic analysis
International Nuclear Information System (INIS)
A cosmic scenario with gravitationally induced particle creation is proposed. In this model the Universe evolves from an early to a late time de Sitter era, with the recent accelerating phase driven only by the negative creation pressure associated with the cold dark matter component. The model can be interpreted as an attempt to reduce the so-called cosmic sector (dark matter plus dark energy) and relate the two cosmic accelerating phases (early and late time de Sitter expansions). A detailed thermodynamic analysis including possible quantum corrections is also carried out. For a very wide range of the free parameters, it is found that the model presents the expected behavior of an ordinary macroscopic system in the sense that it approaches thermodynamic equilibrium in the long run (i.e., as it nears the second de Sitter phase). Moreover, an upper bound is found for the Gibbons–Hawking temperature of the primordial de Sitter phase. Finally, when confronted with the recent observational data, the current 'quasi'-de Sitter era, as predicted by the model, is seen to pass very comfortably the cosmic background tests
7. Remote control circuit breaker evaluation testing. [for space shuttles
Science.gov (United States)
Bemko, L. M.
1974-01-01
Engineering evaluation tests were performed on several models/types of remote control circuit breakers marketed in an attempt to gain some insight into their potential suitability for use on the space shuttle vehicle. Tests included the measurement of several electrical and operational performance parameters under laboratory ambient, space simulation, acceleration and vibration environmental conditions.
8. A flexible and configurable system to test accelerator magnets
Energy Technology Data Exchange (ETDEWEB)
Jerzy M. Nogiec et al.
2001-07-20
Fermilab's accelerator magnet R and D programs, including production of superconducting high gradient quadrupoles for the LHC insertion regions, require rigorous yet flexible magnetic measurement systems. Measurement systems must be capable of handling various types of hardware and extensible to all measurement technologies and analysis algorithms. A tailorable software system that satisfies these requirements is discussed. This single system, capable of distributed parallel signal processing, is built on top of a flexible component-based framework that allows for easy reconfiguration and run-time modification. Both core and domain-specific components can be assembled into various magnet test or analysis systems. The system configured to comprise a rotating coil harmonics measurement is presented. Technologies as Java, OODB, XML, JavaBeans, software bus and component-based architectures are used.
9. Linear Accelerator Test Facility at LNF Conceptual Design Report
CERN Document Server
Valente, Paolo; Bolli, Bruno; Buonomo, Bruno; Cantarella, Sergio; Ceccarelli, Riccardo; Cecchinelli, Alberto; Cerafogli, Oreste; Clementi, Renato; Di Giulio, Claudio; Esposito, Adolfo; Frasciello, Oscar; Foggetta, Luca; Ghigo, Andrea; Incremona, Simona; Iungo, Franco; Mascio, Roberto; Martelli, Stefano; Piermarini, Graziano; Sabbatini, Lucia; Sardone, Franco; Sensolini, Giancarlo; Ricci, Ruggero; Rossi, Luis Antonio; Rotundo, Ugo; Stella, Angelo; Strabioli, Serena; Zarlenga, Raffaele
2016-01-01
Test beam and irradiation facilities are the key enabling infrastructures for research in high energy physics (HEP) and astro-particles. In the last 11 years the Beam-Test Facility (BTF) of the DA{\\Phi}NE accelerator complex in the Frascati laboratory has gained an important role in the European infrastructures devoted to the development and testing of particle detectors. At the same time the BTF operation has been largely shadowed, in terms of resources, by the running of the DA{\\Phi}NE electron-positron collider. The present proposal is aimed at improving the present performance of the facility from two different points of view: extending the range of application for the LINAC beam extracted to the BTF lines, in particular in the (in some sense opposite) directions of hosting fundamental physics and providing electron irradiation also for industrial users; extending the life of the LINAC beyond or independently from its use as injector of the DA{\\Phi}NE collider, as it is also a key element of the electron/...
10. Tests for evaluating the physiological quality of pitaya seeds
OpenAIRE
Thiago Alberto Ortiz; Aline Moritz; Lúcia Sadayo Assari Takahashi; Mariana Ragassi Urbano
2015-01-01
Germination test is used to assess the physiological quality of seeds; however, since it is carried out under ideal conditions, this test has not been shown sufficient for this purpose. Instead, it is possible to use vigor tests, although the lack of standardized methodologies has reduced their applicability and reproducibility. Thus, this study aimed to develop methodologies for conducting tests of germination, accelerated aging, and electrical conductivity for the evaluation of the physiolo...
11. Development of an accelerated aging method for evaluation of long-term irradiation effects on UHMWPE implants
International Nuclear Information System (INIS)
A general scheme for developing an accelerated aging method for irradiated biomaterials is proposed. Using UHMWPE implants as an example, an accelerated thermal diffusion oxidative aging (ATDOA) method has been developed. The method requires an optimum initial heating rate and an optimum aging temperature to accelerate oxidation reactions. Based upon oxidation-induced material property changes (crystallinity by DSC, tensile properties by ASTM D638 tensile test, and oxidation index by FTIR), correlations between accelerated aging time, shelf aging time, and implantation time can be obtained. The new ATDOA method allows a rapid evaluation of long-term irradiation effects on the material properties of UHMWPE implants
12. Life evaluation of insulating materials for electric cable by accelerated thermal-radiation combined aging. 2
International Nuclear Information System (INIS)
Energy Technology Data Exchange (ETDEWEB)
Prokop, Christopher [Northern Illinois Univ., DeKalb, IL (United States)
2014-01-01
The Advanced Superconducting Test Accelerator (ASTA) at Fermilab is a new electron accelerator currently in the commissioning stage. In addition to testing superconducting accelerating cavities for future accelerators, it is foreseen to support a variety of Advanced Accelerator R&D (AARD) experiments. Producing the required electron bunches with the expected flexibility is challenging. The goal of this dissertation is to explore via numerical simulations new accelerator beamlines that can enable the advanced manipulation of electron bunches. The work especially includes the design of a low-energy bunch compressor and a study of transverse-to-longitudinal phase space exchangers.
14. Beam test of multi-bunch energy compensation system in the accelerator test facility at KEK
International Nuclear Information System (INIS)
A beam test of the multi-bunch energy compensation system (ECS) was performed using the ΔF method with the 2856±4.327 HMz accelerating structures in the accelerator test facility (ATF) at KEK. The 1.54 GeV S-band linac of the ATF was designed to accelerate a multi-bunch beam the consists of 20 bunches with 2.8 ns spacing. The multi-bunch beam with 2.0 x 1010 electrons/bunch has an energy deviation of about 8.5% at the end of the linac due to transient beam loading without ECS. The ATF linac is the injector of the ATF damping ring (DR), whose energy acceptance is ±0.5%. The beam loading compensation system is necessary in the ATF linac for the successful injection of multi-bunch into DR. The rf system of the linac consists of 8 regular rf units with the SLED system and 2 ECS rf units without the SLED system. The accelerating structures of the regular units are driven at 2856 MHz and the 2 ECS structures are operated with slightly different rf frequencies of 2856±4.327 MHz. In the beam test, we have succeeded in compressing the multi-bunch energy spread within the energy acceptance of the DR using ΔF ECS. The principle of the beam loading compensation system of KEK-ATF and the experimental results are described in this paper. (author)
15. Accelerated atmospheric corrosion testing of electroplated gold mirror coatings
Science.gov (United States)
Chu, C.-T.; Alaan, D. R.; Taylor, D. P.
2010-08-01
Gold-coated mirrors are widely used in infrared optics for industrial, space, and military applications. These mirrors are often made of aluminum or beryllium substrates with polished nickel plating. Gold is deposited on the nickel layer by either electroplating or vacuum deposition processes. Atmospheric corrosion of gold-coated electrical connectors and contacts was a well-known problem in the electronic industry and studied extensively. However, there is limited literature data that correlates atmospheric corrosion to the optical properties of gold mirror coatings. In this paper, the atmospheric corrosion of different electroplated gold mirror coatings were investigated with an accelerated mixed flowing gas (MFG) test for up to 50 days. The MFG test utilizes a combination of low-level air pollutants, humidity, and temperatures to achieve a simulated indoor environment. Depending on the gold coating thickness, pore corrosion started to appear on samples after about 10 days of the MFG exposure. The corrosion behavior of the gold mirror coatings demonstrated the porous nature of the electroplated gold coatings as well as the variation of porosity to the coating thickness. The changes of optical properties of the gold mirrors were correlated to the morphology of corrosion features on the mirror surface.
16. Maintenance proficiency evaluation test bank
International Nuclear Information System (INIS)
The Maintenance Proficiency Evaluation Test Bank (MPETB) is an Electric Power Research Institute- (EPRJ-) operated, utility-sponsored means of developing, maintaining, and disseminating secure, high-quality written and performance maintenance proficiency tests. EPRTs charter is to ensure that all tests and test items that go into the Test Bank have been validated, screened for reliability, and evaluated to high standards of psychometric excellence. Proficiency tests of maintenance personnel.(mechanics, electricians, and instrumentation and control [I and C] technicians) are most often used to determine if an experienced employee is capable of performing maintenance tasks without further training. Such tests provide objective evidence for decisions to exempt an employee from what, for the employee, is unnecessary training. This leads to considerable savings in training costs and increased productivity because supervisors can assign personnel to tasks at which their competence is proven. The ultimate objective of proficiency evaluation is to ensure that qualified maintenance personnel are available to meet the maintenance requirements of the plant Numerous task-specific MPE tests (both written and performance) have been developed and validated using the EPRI MPE methodology by the utilities participating in the MPETB project A task-specific MPE consists of a multiple-choice written examination and a multi-step performance evaluation that can be used to assess an individual's present knowledge and skill level for a given maintenance task. The MPETB contains MPEs and test items for the mechanical, electrical, and I and C classifications that are readily available to participating utilities. Presently, utilities are placing emphasis on developing MPEs to evaluate outage-related maintenance tasks that demonstrate the competency and qualifications of plant and contractor personnel before the start of outage work. Utilities are also using the MPE methodology and process to
17. Accelerator
International Nuclear Information System (INIS)
The invention claims equipment for stabilizing the position of the front covers of the accelerator chamber in cyclic accelerators which significantly increases accelerator reliability. For stabilizing, it uses hydraulic cushions placed between the electromagnet pole pieces and the front chamber covers. The top and the bottom cushions are hydraulically connected. The cushions are disconnected and removed from the hydraulic line using valves. (J.P.)
18. 15-16 MeV electron linear accelerators for nondestructive testing
International Nuclear Information System (INIS)
15-16 MeV electron linear accelerators for nondestructive testing (ND) are described. The accelerators are intended for ND of the articles with great thickness by means of radiographic, introscopic and tomographic methods. Main characteristics of these accelerators are presented. The automatic control system based on the PC compatible controllers is described in details
19. Demonstration recommendations for accelerated testing of concrete decontamination methods
International Nuclear Information System (INIS)
A large number of aging US Department of Energy (DOE) surplus facilities located throughout the US require deactivation, decontamination, and decommissioning. Although several technologies are available commercially for concrete decontamination, emerging technologies with potential to reduce secondary waste and minimize the impact and risk to workers and the environment are needed. In response to these needs, the Accelerated Testing of Concrete Decontamination Methods project team described the nature and extent of contaminated concrete within the DOE complex and identified applicable emerging technologies. Existing information used to describe the nature and extent of contaminated concrete indicates that the most frequently occurring radiological contaminants are 137Cs, 238U (and its daughters), 60Co, 90Sr, and tritium. The total area of radionuclide-contaminated concrete within the DOE complex is estimated to be in the range of 7.9 x 108 ft2or approximately 18,000 acres. Concrete decontamination problems were matched with emerging technologies to recommend demonstrations considered to provide the most benefit to decontamination of concrete within the DOE complex. Emerging technologies with the most potential benefit were biological decontamination, electro-hydraulic scabbling, electrokinetics, and microwave scabbling
20. LeRC rail accelerators: test designs and diagnostic techniques
International Nuclear Information System (INIS)
The feasibility of using rail accelerators for various in-space and to-space propulsion applications was investigated. A 1 meter, 24 sq mm bore accelerator was designed with the goal of demonstrating projectile velocities of 15 km/sec using a peak current of 200 kA. A second rail accelerator, 1 meter long with a 156.25 sq mm bore, was designed with clear polycarbonate sidewalls to permit visual observation of the plasma arc. A study of available diagnostic techniques and their application to the rail accelerator is presented. Specific topics of discussion include the use of interferometry and spectroscopy to examine the plasma armature as well as the use of optical sensors to measure rail displacement during acceleration. Standard diagnostics such as current and voltage measurements are also discussed. 15 references
1. Status and plans for a SRF accelerator test faciliy at Fermilab
OpenAIRE
Leibfritz, J.; R. Andrews; Carlson, K.; Chase, B.; Church, M.; HARMS, E.; Klebaner, A.; Kucera, M.; Lackey, S.; Martinez, A.; Nagaitsev, S.; Nobrega, L.; Piot, P; Reid, J; Wendt, M
2012-01-01
A superconducting RF accelerator test facility is being constructed at Fermilab. The existing New Muon Lab (NML) building is being converted for this facility. The accelerator will consist of an electron gun, injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, multiple downstream beam lines for testing diagnostics and conducting various beam tests, and a high power beam dump. When completed, it is envisioned that this facility will initially be capable of gen...
2. Step-Stress Accelerated Degradation Testing (SSADT) for Photovoltaic (PV) Devices and Cells (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Lee, J.; Elmore, R.; Suh, C.; Jones, W.
2010-10-01
Presentation on step-stress accelerated degradation testing (SSADT) for photovoltaics (PV). Developed are a step-stress degradation test (SSADT) for PV reliability tests and a lifetime prediction model for PV products.
3. Evaluation of DNB test repeatability
International Nuclear Information System (INIS)
The repeatability of DNB tests was evaluated by carrying out DNB runs at the same conditions in two different test sections. The resulting matched pairs of DNB runs were then subjected to an extensive statistical analysis. This analysis indicates that individual runs using different test sections are repeatable within approximately 8 percent, and that the means of two different data sets should fall within approximately 2 percent of each other. The repeatability within a set, i.e., from the same test section, was found to be approximately 6.4 percent. An evaluation of the uncertainties by analysis of errors inherent in geometrical and physical parameters results in an estimated set-to-set repeatability for an individual run of 7.6 percent which is in good agreement with the 8 percent error found in the data analysis. For repeatability of an individual run within a set, 6.8 percent was estimated from the test parameters, compared to 6.4 percent determined by data analysis. (U.S.)
4. Error-Rate Estimation Based on Multi-Signal Flow Graph Model and Accelerated Radiation Tests.
Science.gov (United States)
He, Wei; Wang, Yueke; Xing, Kefei; Deng, Wei; Zhang, Zelong
2016-01-01
A method of evaluating the single-event effect soft-error vulnerability of space instruments before launched has been an active research topic in recent years. In this paper, a multi-signal flow graph model is introduced to analyze the fault diagnosis and meantime to failure (MTTF) for space instruments. A model for the system functional error rate (SFER) is proposed. In addition, an experimental method and accelerated radiation testing system for a signal processing platform based on the field programmable gate array (FPGA) is presented. Based on experimental results of different ions (O, Si, Cl, Ti) under the HI-13 Tandem Accelerator, the SFER of the signal processing platform is approximately 10-3(error/particle/cm2), while the MTTF is approximately 110.7 h. PMID:27583533
5. Progress on High Power Tests of Dielectric-Loaded Accelerating Structures
CERN Document Server
Jing, Chunguang; Gold, Steven H; Kinkead, Allen; Konecny, Richard; Power, John G
2005-01-01
This paper presents a progress report on a series of high-power rf experiments that were carried out to evaluate the potential of the Dielectric-Loaded Accelerating (DLA) structure for high-gradient accelerator operation. Since the last PAC meeting in 2003, we have tested DLA structures loaded with two different ceramic materials: Alumina (Al2O3) and MCT (MgxCa1-xTiO3). The alumina-based DLA experiments have concentrated on the effects of multipactor in the structures under high-power operation, and its suppression using TiN coatings, while the MCT experiments have investigated the dielectric joint breakdown observed in the structures due to local field enhancement. In both cases, physical models have been set up, and the potential engineering solutions are being investigated.
6. Status and plans for a SRF accelerator test faciliy at Fermilab
CERN Document Server
Leibfritz, J; Carlson, K; Chase, B; Church, M; Harms, E; Klebaner, A; Kucera, M; Lackey, S; Martinez, A; Nagaitsev, S; Nobrega, L; Piot, P; Reid, J; Wendt, M; Wesseln, S
2012-01-01
A superconducting RF accelerator test facility is being constructed at Fermilab. The existing New Muon Lab (NML) building is being converted for this facility. The accelerator will consist of an electron gun, injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, multiple downstream beam lines for testing diagnostics and conducting various beam tests, and a high power beam dump. When completed, it is envisioned that this facility will initially be capable of generating an 810 MeV electron beam with ILC beam intensity. Expansion plans of the facility are underway that will provide the capability to upgrade the accelerator to a total beam energy of 1.5 GeV. In addition to testing accelerator components, this facility will be used to test RF power equipment, instrumentation, LLRF and controls systems for future SRF accelerators such as the ILC and Project-X. This paper describes the current status and overall plans for this facility.
7. Integrated Test and Evaluation Flight Test 3 Flight Test Plan
Science.gov (United States)
Marston, Michael Lawrence
2015-01-01
The desire and ability to fly Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) is of increasing urgency. The application of unmanned aircraft to perform national security, defense, scientific, and emergency management are driving the critical need for less restrictive access by UAS to the NAS. UAS represent a new capability that will provide a variety of services in the government (public) and commercial (civil) aviation sectors. The growth of this potential industry has not yet been realized due to the lack of a common understanding of what is required to safely operate UAS in the NAS. NASA's UAS Integration into the NAS Project is conducting research in the areas of Separation Assurance/Sense and Avoid Interoperability, Human Systems Integration (HSI), and Communication to support reducing the barriers of UAS access to the NAS. This research is broken into two research themes namely, UAS Integration and Test Infrastructure. UAS Integration focuses on airspace integration procedures and performance standards to enable UAS integration in the air transportation system, covering Sense and Avoid (SAA) performance standards, command and control performance standards, and human systems integration. The focus of Test Infrastructure is to enable development and validation of airspace integration procedures and performance standards, including the integrated test and evaluation. In support of the integrated test and evaluation efforts, the Project will develop an adaptable, scalable, and schedulable relevant test environment capable of evaluating concepts and technologies for unmanned aircraft systems to safely operate in the NAS. To accomplish this task, the Project will conduct a series of Human-in-the-Loop and Flight Test activities that integrate key concepts, technologies and/or procedures in a relevant air traffic environment. Each of the integrated events will build on the technical achievements, fidelity and complexity of the previous tests and
8. Test of pixel detectors for laser-driven accelerated particle beams
International Nuclear Information System (INIS)
Laser-driven accelerated (LDA) particle beams have due to the unique acceleration process very special properties. In particular they are created in ultra-short bunches of high intensity exceeding more than 107 (particles)/cm2·ns per bunch. Characterization of these beams is very limited with conventional particle detectors. Non-electronic detectors such as imaging plates or nuclear track detectors are, therefore, conventionally used at present. Moreover, all these detectors give only offline information about the particle pulse position and intensity as they require minutes to hours to be processed, calling for a new highly sensitive online device. Here, we present tests of different pixel detectors for real time detection of LDA ion pulses. Experiments have been performed at the Munich 14MV Tandem accelerator with 8–20 MeV protons in dc and pulsed beam, the latter producing comparable flux as a LDA ion pulse. For detection tests we chose the position-sensitive quantum-counting semiconductor pixel detector Timepix which also provides per-pixel energy- or time-sensitivity. Additionally other types of commercially available pixel detectors are being evaluated such as the RadEye™1, a large area (25 x 50 mm2) CMOS image sensor. All of these devices are able to resolve individual ions with high spatial- and energy-resolution down to the level of μm and tens of keV, respectively. Various beam delivering parameters of the accelerator were thus evaluated and verified. The different readout modes of the Timepix detector which is operated with an integrated USB-based readout interface allow online visualization of single and time-integrated events. Therefore Timepix offers the greatest potential in analyzing the beam parameters.
9. Operational status of the Brookhaven National Laboratory Accelerator Test Facility
International Nuclear Information System (INIS)
Initial design parameters and early operational results of a 50 MeV high brightness electron linear accelerator are described. The system utilizes a radio frequency electron gun operating at a frequency of 2.856 GHz and a nominal output energy of 4.5 MeV followed by two, 2π/3 mode, disc loaded, traveling wave accelerating sections. The gun cathode is photo excited with short (6 psec) laser pulses giving design peak currents of a few hundred amperes. The system will be utilized to carry out infra-red FEL studies and investigation of new high gradient accelerating structures
10. Rapid estimation of lives of deficient superpave mixes and laboratory-based accelerated mix testing models
Science.gov (United States)
The engineers from the Kansas Department of Transportation (KDOT) often have to decide whether or not to accept non-conforming Superpave mixtures during construction. The first part of this study focused on estimating lives of deficient Superpave pavements incorporating nonconforming Superpave mixtures. These criteria were based on the Hamburg Wheel-Tracking Device (HWTD) test results and analysis. The second part of this study focused on developing accelerated mix testing models to considerably reduce test duration. To accomplish the first objective, nine fine-graded Superpave mixes of 12.5-mm nominal maximum aggregate size (NMAS) with asphalt grade PG 64-22 from six administrative districts of KDOT were selected. Specimens were prepared at three different target air void levels Ndesign gyrations and four target simulated in-place density levels with the Superpave gyratory compactor. Average number of wheel passes to 20-mm rut depth, creep slope, stripping slope, and stripping inflection point in HWTD tests were recorded and then used in the statistical analysis. Results showed that, in general, higher simulated in-place density up to a certain limit of 91% to 93%, results in a higher number of wheel passes until 20-mm rut depth in HWTD tests. A Superpave mixture with very low air voids Ndesign (2%) level performed very poorly in the HWTD test. HWTD tests were also performed on six 12.5-mm NMAS mixtures with air voids Ndesign of 4% for six projects, simulated in-place density of 93%, two temperature levels and five load levels with binder grades of PG 64-22, PG 64-28, and PG 70-22. Field cores of 150-mm in diameter from three projects in three KDOT districts with 12.5-mm NMAS and asphalt grade of PG 64-22 were also obtained and tested in HWTD for model evaluation. HWTD test results indicated as expected. Statistical analysis was performed and accelerated mix testing models were developed to determine the effect of increased temperature and load on the duration of
11. Optical system for measurement of pyrotechnic test accelerations
Science.gov (United States)
Lieberman, Paul; Czajkowski, John; Rehard, John
1992-12-01
This effort was directed at comparing the response of several different accelerometer and amplifier combinations to the pyrotechnic pulse simulating the ordnance separation of stages of multistage missiles. These pyrotechnic events can contain peak accelerations in excess of 100,000 G and a frequency content exceeding 100,000 Hz. The main thrust of this work was to compare the several accelerometer systems with each other and with a very accurate laser Doppler displacement meter in order to establish the frequency bands and acceleration amplitudes where the accelerometer systems are in error. The comparisons were made in simple sine-wave and low-acceleration amplitude environments, as well as in very severe pyroshock environments. An optical laser Doppler displacement meter (LDDM) was used to obtain the displacement velocity and acceleration histories, as well as the corresponding shock spectrum.
12. Acceleration test of heavy ion RFQ linac at TIT
International Nuclear Information System (INIS)
An 80 MHz heavy ion RFQ Linac at Tokyo Institute of Technology (TIT) was constructed for researches on inertial fusion and plasma experiments. The first acceleration was accomplished with low intensity He+ ion beam in 1993. This four vane type RFQ accelerates particles with charge to mass ratio (q/A) of 1/16 from 5 keV/amu to 214 keV/amu. Two-dimensional (2D) machining was applied for cutting of the RFQ vane-tips. The vane parameters for the RFQ were optimized considering the effects of multipole components at inter-vane field. In order to increase the acceleration efficiency synchronous phase was gradually raised from -30 degrees to -20 degrees at the open-quotes accelerator sectionclose quotes. The beam transmission is expected to be 68.4% for the beam current of 10 mA. Details of the RFQ tuning and performance will be reported
13. Evaluation of slice accelerations using multiband echo planar imaging at 3 Tesla
OpenAIRE
Xu, Junqian; Moeller, Steen; Auerbach, Edward J.; Strupp, John; Stephen M Smith; Feinberg, David A.; Yacoub, Essa; Uğurbil, Kâmil
2013-01-01
We evaluate residual aliasing among simultaneously excited and acquired slices in slice accelerated multiband (MB) echo planar imaging (EPI). No in-plane accelerations were used in order to maximize and evaluate achievable slice acceleration factors at 3 Tesla. We propose a novel leakage (L-) factor to quantify the effects of signal leakage between simultaneously acquired slices. With a standard 32-channel receiver coil at 3 Tesla, we demonstrate that slice acceleration factors of up to eight...
14. Accelerated stability testing of organic photovoltaics using concentrated sunlight
DEFF Research Database (Denmark)
Katz, Eugene A.; Manor, Assaf; Mescheloff, Asaf;
2012-01-01
We suggest to use concentrated sunlight for accelerated studies of light-induced mechanisms in the degradation of organic photovoltaics (OPV) based on the polymer (P3HT)/fullerene (PCBM) bulk heterojunctions. Two particular cases of the degradation are reported.......We suggest to use concentrated sunlight for accelerated studies of light-induced mechanisms in the degradation of organic photovoltaics (OPV) based on the polymer (P3HT)/fullerene (PCBM) bulk heterojunctions. Two particular cases of the degradation are reported....
15. Acceleration test of heavy ion RFQ linac at TIT
International Nuclear Information System (INIS)
An 80 MHz heavy ion RFQ linac at Tokyo Institute of Technology (TIT) has been constructed for research on inertial fusion and plasma experiments. Equipment for beam acceleration has been fabricated and assembled to confirm the performance with low currents of the RFQ. The linac successfully accelerated He+ and C2+ ion beams to their final energies of 219 keV/u. The obtained beam transmission was more than 89% with currents of a few tens μA. (orig.)
16. Evaluating the Power of GPU Acceleration for IDW Interpolation Algorithm
Directory of Open Access Journals (Sweden)
Gang Mei
2014-01-01
Full Text Available We first present two GPU implementations of the standard Inverse Distance Weighting (IDW interpolation algorithm, the tiled version that takes advantage of shared memory and the CDP version that is implemented using CUDA Dynamic Parallelism (CDP. Then we evaluate the power of GPU acceleration for IDW interpolation algorithm by comparing the performance of CPU implementation with three GPU implementations, that is, the naive version, the tiled version, and the CDP version. Experimental results show that the tilted version has the speedups of 120x and 670x over the CPU version when the power parameter p is set to 2 and 3.0, respectively. In addition, compared to the naive GPU implementation, the tiled version is about two times faster. However, the CDP version is 4.8x∼6.0x slower than the naive GPU version, and therefore does not have any potential advantages in practical applications.
17. Evaluating the power of GPU acceleration for IDW interpolation algorithm.
Science.gov (United States)
Mei, Gang
2014-01-01
We first present two GPU implementations of the standard Inverse Distance Weighting (IDW) interpolation algorithm, the tiled version that takes advantage of shared memory and the CDP version that is implemented using CUDA Dynamic Parallelism (CDP). Then we evaluate the power of GPU acceleration for IDW interpolation algorithm by comparing the performance of CPU implementation with three GPU implementations, that is, the naive version, the tiled version, and the CDP version. Experimental results show that the tilted version has the speedups of 120x and 670x over the CPU version when the power parameter p is set to 2 and 3.0, respectively. In addition, compared to the naive GPU implementation, the tiled version is about two times faster. However, the CDP version is 4.8x ∼ 6.0x slower than the naive GPU version, and therefore does not have any potential advantages in practical applications. PMID:24707195
18. Framework for a Comparative Accelerated Testing Standard for PV Modules: Preprint
Energy Technology Data Exchange (ETDEWEB)
Kurtz, S.; Wohlgemuth, J.; Yamamichi, M.; Sample, T.; Miller, D.; Meakin, D.; Monokroussos, C.; TamizhMani, M.; Kempe, M.; Jordan, D.; Bosco, N.; Hacke, P.; Bermudez, V.; Kondo, M.
2013-08-01
As the photovoltaic industry has grown, the interest in comparative accelerated testing has also grown. Private test labs offer testing services that apply greater stress than the standard qualification tests as tools for differentiating products and for gaining increased confidence in long-term PV investments. While the value of a single international standard for comparative accelerated testing is widely acknowledged, the development of a consensus is difficult. This paper strives to identify a technical basis for a comparative standard.
19. Lifetime Testing 700 MHz RF Windows for the Accelerator Production of Tritium Program
OpenAIRE
Cummings, K.A.; Borrego, M. D.; DeBaca, J.; Harrison, J S; Rodriguez, M. B.; Roybal, D. M.; Roybal, W. T.; Ruggles, S. C.; Torrez, P. A.; White, G. D.
2000-01-01
Radio frequency (RF) windows are historically a point where failure occurs in input-power couplers for accelerators. To understand more about the reliability of high power RF windows, lifetime testing was done on 700 MHz coaxial RF windows for the Low Energy Demonstration Accelerator (LEDA) project of the Accelerator Production of Tritium (APT) program. The RF windows, made by Marconi Applied Technologies (formerly EEV), were tested at 800 kW for an extended period of time. Changes in the ref...
20. Session: Test and Evaluation (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Marion, B.; Hanley, C.
2008-04-01
The overall goal of this presentation is: (1) provide test and evaluation of PV cells/modules/systems to TPP participants, other PV industry, labs, and universities in support of technology optimization efforts sponsored by DOE's Solar Program and the SAI; (2) support commercial and emerging technology development; (3) provide component and system performance data to improve and validate system performance models; (4) provide T and E support for reliability activities; and (5) priority is placed on TPP's and other solicitations.
1. STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING
Institute of Scientific and Technical Information of China (English)
WANG Ronghua; FEI Heliang
2004-01-01
In this note, the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time. For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull, maximum likelihood estimation is investigated.
2. Evaluating the RELM Test Results
Directory of Open Access Journals (Sweden)
Michael K. Sachs
2012-01-01
Full Text Available We consider implications of the Regional Earthquake Likelihood Models (RELM test results with regard to earthquake forecasting. Prospective forecasts were solicited for M≥4.95 earthquakes in California during the period 2006–2010. During this period 31 earthquakes occurred in the test region with M≥4.95. We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for tornadoes. We utilize a “skill score” based on the forecast scores λfi of occurrence of the test earthquakes. A perfect forecast would have λfi=1, and a random (no skill forecast would have λfi=2.86×10-3. The best forecasts (largest value of λfi for the 31 earthquakes had values of λfi=1.24×10-1 to λfi=5.49×10-3. The best mean forecast for all earthquakes was λ̅f=2.84×10-2. The best forecasts are about an order of magnitude better than random forecasts. We discuss the earthquakes, the forecasts, and alternative methods of evaluation of the performance of RELM forecasts. We also discuss the relative merits of alarm-based versus probability-based forecasts.
3. Development of laboratory acceleration test method for service life prediction of concrete structures
International Nuclear Information System (INIS)
Service life prediction of nuclear power plants depends on the application of history of structures, field inspection and test, the development of laboratory acceleration tests, their analysis method and predictive model. In this study, laboratory acceleration test method for service life prediction of concrete structures and application of experimental test results are introduced. This study is concerned with environmental condition of concrete structures and is to develop the acceleration test method for durability factors of concrete structures e.g. carbonation, sulfate attack, freeze-thaw cycles and shrinkage-expansion etc
4. Test and Evaluation of Autonomous Ground Vehicles
OpenAIRE
Yang Sun; Guangming Xiong; Weilong Song; Jianwei Gong; Huiyan Chen
2014-01-01
A preestablished test and evaluation system will benefit the development of autonomous ground vehicles. This paper proposes a design method for a scientific and comprehensive test and evaluation system for autonomous ground vehicles competitions. It can better guide and regulate the development of China’s autonomous ground vehicles. The test and evaluation system includes the test contents, the test environment, the test methods, and the evaluation methods. Using a hierarchical design approac...
5. Integrated Vibration and Acceleration Testing to Reduce Payload Mass, Cost and Mission Risk Project
Data.gov (United States)
National Aeronautics and Space Administration — We propose to develop a capability to provide integrated acceleration, vibration, and shock testing using a state-of-the-art centrifuge, allowing for the test of...
6. Experimental test accelerator: description and results of initial experiments
International Nuclear Information System (INIS)
The ETA is a high current (10,000 Amp) linear induction accelerator that produces short (30 ns) pulses of electrons at 5 MeV twice per second or in bursts of 5 pulses separated by as little as one millisecond. At this time the machine has operated at 65% of its design current and 90% of the design voltage. This report contains a description of the accelerator and its diagnostics; the results of the initial year of operation; a comparison of design codes with experiments on beam transport; and a discussion of some of the special problems and their status
7. Evaluation of Experimental Parameters in the Accelerated Aging of Closed-Cell Foam Insulation
Energy Technology Data Exchange (ETDEWEB)
Stovall, Therese K [ORNL; Vanderlan, Michael [ORNL; Atchley, Jerald Allen [ORNL
2012-12-01
The thermal conductivity of many closed-cell foam insulation products changes over time as production gases diffuse out of the cell matrix and atmospheric gases diffuse into the cells. Thin slicing has been shown to be an effective means of accelerating this process in such a way as to produce meaningful results. Efforts to produce a more prescriptive version of the ASTM C1303 standard test method led to the ruggedness test described here. This test program included the aging of full size insulation specimens for time periods of five years for direct comparison to the predicted results. Experimental parameters under investigation include: slice thickness, slice origin (at the surface or from the core of the slab), thin slice stack composition, product facings, original product thickness, product density, and product type. The test protocol has been completed and this report provides a detailed evaluation of the impact of the test parameters on the accuracy of the 5-year thermal conductivity prediction.
8. Carbon ion and high intensity acceleration test of TIT heavy ion RFQ linac
International Nuclear Information System (INIS)
The RFQ Linac at Tokyo Institute of Technology (TIT-RFQ) was constructed and acceleration test of ion beams 4He+ and 12C2+ was performed. The linac was designed to accelerate particles with charge to mass ratio(q/A) of 1-1/16 injected at 5 keV/u up to 214 keV/u. As the result of acceleration test, beam transmission was 89% for a low beam current. It is nearly design data 91% and the acceleration characteristic agrees well with a computer simulation. (author)
9. Life Prediction of DC Motor using Time Series Analysis based on Accelerated Degradation Testing
Directory of Open Access Journals (Sweden)
Li Wang
2013-12-01
Full Text Available This study presents a method of life prediction for DC motor using time series modeling procedure based on DC motor accelerated degradation testing data. DC motor accelerated degradation data are treated as time series and stochastic process are utilized to describe the degradation process for life prediction. An accelerated degradation test is processed for DC motor until they failed and the accelerated degradation data are collected for life prediction. A comparison between the predicted lifetime and the real lifetime of DC motors is processed and the results show that the life prediction of DC motors using time series analysis is effective.
10. Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring
Directory of Open Access Journals (Sweden)
M. M. Mohie EL-Din
2015-01-01
Full Text Available Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs and Bayes estimates (BEs are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.
11. Long-term storage life of light source modules by temperature cycling accelerated life test
International Nuclear Information System (INIS)
Light source modules are the most crucial and fragile devices that affect the life and reliability of the interferometric fiber optic gyroscope (IFOG). While the light emitting chips were stable in most cases, the module packaging proved to be less satisfactory. In long-term storage or the working environment, the ambient temperature changes constantly and thus the packaging and coupling performance of light source modules are more likely to degrade slowly due to different materials with different coefficients of thermal expansion in the bonding interface. A constant temperature accelerated life test cannot evaluate the impact of temperature variation on the performance of a module package, so the temperature cycling accelerated life test was studied. The main failure mechanism affecting light source modules is package failure due to solder fatigue failure including a fiber coupling shift, loss of cooling efficiency and thermal resistor degradation, so the Norris-Landzberg model was used to model solder fatigue life and determine the activation energy related to solder fatigue failure mechanism. By analyzing the test data, activation energy was determined and then the mean life of light source modules in different storage environments with a continuously changing temperature was simulated, which has provided direct reference data for the storage life prediction of IFOG. (semiconductor devices)
12. Comparative field evaluation of vehicle cruise speed and acceleration level impacts on hot stabilized emissions
International Nuclear Information System (INIS)
The main objectives of this paper are two fold. First, the paper evaluates the impact of vehicle cruise speed and acceleration levels on vehicle fuel-consumption and emission rates using field data gathered under real-world driving conditions. Second, it validates the VT-Micro model for the modeling of real-world conditions. Specifically, an on-board emission-measurement device was used to collect emissions of oxides of nitrogen, hydrocarbons, carbon monoxide, and carbon dioxide using a light-duty test vehicle. The analysis demonstrates that vehicle fuel-consumption and emission rates per-unit distance are optimum in the range of 60-90 km/h, with considerable increase outside this optimum range. The study demonstrates that as the level of aggressiveness for acceleration maneuvers increases, the fuel-consumption and emission rates per maneuver decrease because the vehicle spends less time accelerating. However, when emissions are gathered over a sufficiently long fixed distance, fuel-consumption and mobile-source emission rates per-unit distance increase as the level of acceleration increases because of the history effects that accompany rich-mode engine operations. In addition, the paper demonstrates the validity of the VT-Micro framework for modeling steady-state vehicle fuel-consumption and emission behavior. Finally, the research demonstrates that the VT-Micro framework requires further refinement to capture non-steady-state history behavior when the engine operates in rich mode. (Author)
13. Accelerated high-temperature creep tests for assessment of service life of power engineering steels
International Nuclear Information System (INIS)
Principles of accelerated constant stress - variable temperature and constant temperature - variable stress creep tests are discussed. Numerous accelerated creep tests of low-alloy Cr-Mo and Cr-Mo-V steels and high-alloy ferritic 12Cr1Mo-V steel carried out at higher-than-service temperatures and constant further service stress produced results which were in satisfactory agreement with conventional long-term creep tests. Such accelerated tests are used for practical purposes including estimation of service life, residual life and available residual life. On the other hand accelerated creep rupture tests carried out at constant service temperatures and variable stress trend to overestimate service life, create danger of unexpected failures of components under consideration and are seldom used for practical purposes. At comparable temperatures and stress levels accelerated creep tests using miniature test pieces tend to produce shorter rupture times than tests using standard specimens. The estimated life therefore shorter than that estimated on the basis of long-term tests and standard specimens. Service life estimated by means of accelerated creep tests using miniature test pieces must be calculated with the use of a corrective factor selected individually for the given type of steel. (author)
14. Optical diagnostics in the advanced test accelerator (ATA) environment
International Nuclear Information System (INIS)
The ATA is a 50-MeV, 10-kA, 70-ns pulsed electron beam accelerator that generates an extremely harsh environment for diagnostic measurements. Diagnostic targets placed in the beamline are subject to damage, frequently being destroyed by a single pulse. High radiation (x-ray, gamma, and neutron) and electromagnetic interference levels preclude placing components near the beamline that are susceptible to radiation damage. Examples of such components are integrated circuit elements, hydrocarbons such as Teflon insulation, and optical components that darken, resulting in transmission loss. Optical diagnostics play an important part in measuring experimental parameters such as the beam current density profile. A large number of optical lines of sight (LOS) are routinely deployed along the experimental beamlines that use the ATA beam. Gated TV cameras are located outside the accelerator tunnel, because the tunnel is inaccessible during operations. We will describe and discuss the difficulties, problems, and solutions encountered in making optical measurements in the ATA environment
15. Design and Simulation of IOTA - a Novel Concept of Integrable Optics Test Accelerator
OpenAIRE
Nagaitsev, S.; Valishev, A.; Danilov, V. V.; Shatilov, D. N.
2013-01-01
The use of nonlinear lattices with large betatron tune spreads can increase instability and space charge thresholds due to improved Landau damping. Unfortunately, the majority of nonlinear accelerator lattices turn out to be nonintegrable, producing chaotic motion and a complex network of stable and unstable resonances. Recent advances in finding the integrable nonlinear accelerator lattices have led to a proposal to construct at Fermilab a test accelerator with strong nonlinear focusing whic...
16. Accelerated electrochemical test of 14Kh17N2 steel susceptibility to ICC
International Nuclear Information System (INIS)
Description of the accelerated electrochemical technique used to determine susceptibility 14Kh17N2 steel of ferrite-martensite type to intercrystallite corrosion under the drop of electrolyte, is given. Convergence of the results obtained due to accelerated techniques with those of tests using the All-Union Standards 6032-84 constitutes 95%. These results demonstrate possibility to use data of the accelerated techniques for rapid estimation of susceptibility to ICC of martensite-ferrite steel-14Kh17N2
17. WAN environment test for joint development of accelerator control programs
International Nuclear Information System (INIS)
By the heightening of the processing capability of personal computers, also in the field of accelerator control, the system using personal computers as the main body can be constructed. Also it has become possible to supplement functions by combining different applications and offering the means of communication between applications by operating systems. At present, new accelerators are planned in Laboratory of Nuclear Science, Tohoku University, and National Laboratory for High Energy Physics, and the development environment using WAN was prepared for the purposes of the OMT analysis of accelerator domain from the viewpoint of control, the joint verification of the programs being made, and the efficient exchange of information. Windows NT was adopted, and its features are shown. The environment was constructed by using the personal computer on which Windows NT functions, and the specification of the used personal computer is shown. The performance was measured by using this environment, and its method and the results are reported. The operation mode for hereafter is explained. The construction of the development environment using Windows NT was completed with good results. (K.I.)
18. Understanding and evaluating bovine testes.
Science.gov (United States)
Kastelic, John P
2014-01-01
The objective is to briefly review bovine testes and how they are assessed, with an emphasis on articles from Theriogenology. Scrotal circumference (SC) is the most common method to assess testicular size; it varies among individual bulls and breeds and is highly heritable. In general, a large SC is associated with early puberty, more sperm, a higher percentage of morphologically normal sperm, and better reproductive performance in closely related females. Consequently, there are minimum requirements for SC for breeding soundness. In prepubertal bull calves, there is an early rise (10-20 weeks of age) in LH, which is critically related to onset of puberty and testicular development. Feeding bulls approximately 130% of maintenance requirements of energy and protein from approximately 8 to 30 weeks of age increased LH release during the early rise, hastened puberty (approximately 1 month), and increased mature testis size and sperm production (approximately 20%-30%). However, high-energy diets after weaning (>200 days) often reduced sperm production and semen quality. A bull's testes and scrotum have opposing (complementary) temperature gradients, which keep the testicular temperature 2 °C to 6 °C cooler than core body temperature for production of fertile sperm (increased testicular temperature reduces semen quality). Infrared thermography, a quick and noninvasive method of assessing scrotal surface temperature, may be beneficial for evaluations of breeding soundness. The primary clinical use of ultrasonography in assessment of reproductive function in the bull is characterization of grossly detectable lesions in the testes and scrotum. In conclusion, testis size and function are critical for bull fertility, affected by nutrition, and readily assessed clinically. PMID:24274406
19. Design, fabrication and first beam tests of the C-band RF acceleration unit at SINAP
Science.gov (United States)
Fang, Wencheng; Gu, Qiang; Sheng, Xing; Wang, Chaopeng; Tong, Dechun; Chen, Lifang; Zhong, Shaopeng; Tan, Jianhao; Lin, Guoqiang; Chen, Zhihao; Zhao, Zhentang
2016-07-01
C-band RF acceleration is a crucial technology for the compact Free Electron Laser (FEL) facility at the Shanghai Institute of Applied Physics (SINAP), Chinese Academy of Sciences. A project focusing on C-band RF acceleration technology was launched in 2008, based on high-gradient accelerating structures powered by klystron and pulse compressor units. The target accelerating gradient is 40 MV/m or higher. Recently one prototype of C-band RF unit, consisting of a 1.8 m accelerating structure and a klystron with a TE0115 mode pulse compressor, has been tested with high-power and electron beam. Stable operation at 40 MV/m was demonstrated and, 50 MV/m approached by the end of the test. This paper introduces the C-band R&D program at SINAP and presents the experiment results of high-power and beam tests.
20. Lifetime Testing 700 MHz RF Windows for the Accelerator Production of Tritium Program
CERN Document Server
Cummings, K A; De Baca, J; Harrison, J S; Rodríguez, M B; Roybal, D M; Roybal, W T; Ruggles, S C; Torrez, P A; White, G D
2000-01-01
Radio frequency (RF) windows are historically a point where failure occurs in input-power couplers for accelerators. To understand more about the reliability of high power RF windows, lifetime testing was done on 700 MHz coaxial RF windows for the Low Energy Demonstration Accelerator (LEDA) project of the Accelerator Production of Tritium (APT) program. The RF windows, made by Marconi Applied Technologies (formerly EEV), were tested at 800 kW for an extended period of time. Changes in the reflected power, vacuum, air outlet temperature, and surface temperature were monitored over time. The results of the life testing are summarized.
1. History of Accelerated and Qualification Testing of Terrestrial Photovoltaic Modules: A Literature Review
Energy Technology Data Exchange (ETDEWEB)
Osterwald, C. R.; McMahon, T. J.
2009-01-01
We review published literature from 1975 to the present for accelerated stress testing of flat-plate terrestrial photovoltaic (PV) modules. An important facet of this subject is the standard module test sequences that have been adopted by national and international standards organizations, especially those of the International Electrotechnical Commission (IEC). The intent and history of these qualification tests, provided in this review, shows that standard module qualification test results cannot be used to obtain or infer a product lifetime. Closely related subjects also discussed include: other limitations of qualification testing, definitions of module lifetime, module product certification, and accelerated life testing.
2. The Evaluator Effect in Usability Tests
DEFF Research Database (Denmark)
Jacobsen, Niels Ebbe; Hertzum, Morten; John, Bonnie E.
1998-01-01
Usability tests are applied in industry to evaluate systems and in research as a yardstick for other usability evaluation methods. However, one potential threat to the reliability of usability tests has been left unaddressed: the evaluator effect. In this study, four evaluators analyzed four...
3. Tests for evaluating the physiological quality of pitaya seeds
Directory of Open Access Journals (Sweden)
Thiago Alberto Ortiz
2015-12-01
Full Text Available Germination test is used to assess the physiological quality of seeds; however, since it is carried out under ideal conditions, this test has not been shown sufficient for this purpose. Instead, it is possible to use vigor tests, although the lack of standardized methodologies has reduced their applicability and reproducibility. Thus, this study aimed to develop methodologies for conducting tests of germination, accelerated aging, and electrical conductivity for the evaluation of the physiological quality of pitaya seeds. For this purpose, seeds from ripe Hylocereus undatus fruits were used. A completely randomized experimental design was used with four replications. The physiological quality of the seeds was assessed using germination, accelerated aging, and electrical conductivity tests, and the speed of germination index (SGI and mean germination time (MGT were determined for both the germination test and accelerated aging test. For the statistical analysis, we performed regression model adjustments and calculated the Pearson correlation coefficient (p < 0.05. The germination test for H. undatus seeds can be performed at 25 °C, with the aim of reaching the highest SGI and lowest MGT values. The accelerated aging test can be conducted at 43 °C for 48 h, because combining these factors favors the expression of seed vigor, allowing seeds to achieve the maximum SGI and minimum MGT, while reducing the time of the assay. The electrical conductivity test can be performed using 25 seeds at a temperature of 30 °C and a water volume of 10 mL, since under these conditions there is less interference from external factors on the leachate content of the solution.
4. Evaluation of the electrode performance for PAFC by using acid absorption, acceleration and ac-impedance measurement
Energy Technology Data Exchange (ETDEWEB)
Kim, Chang-Soo; Song, Rak-Hyun; Choi, Byung-Woo [Korea Institute of Energy Research, Taejon (Korea, Republic of)] [and others
1996-12-31
In PAFC, the degradation on cathode electrode caused by carbon corrosion, platinum dissolution and growth is especially severe. An acceleration test is a good technique for evaluating the degradation of electrode performance, because it does not need long time. Coleman et al used thermal cycling and on-off cycling as an acceleration test. Song et al showed that hydrogen shortage decreased the electrode performance more rapidly than that of air shortage in gas shortage test. Honji et al reported that the rate of coarsening of Pt particle is rapid in open circuit potential and this is one of major causes on the performance degradation of electrode. The cathode performance has been studied by using acid absorption, acceleration and ac-impedance measurements as functions of the polytetrafluoroethylene (PTFE) contents and sintering temperatures of the electrode.
5. EVALUATING SOFTWARE MAINTENANCE TESTING APPROACHES TO SUPPORT TEST CASE EVOLUTION
OpenAIRE
Othman Mohd Yusop; Suhaimi Ibrahim
2011-01-01
Software Maintenance Testing is essential during software testing phase. All defects found during testing must undergo a re-test process in order to eliminate the flaws. By doing so, test cases are absolutely needed to evolve and change accordingly. In this paper, several maintenance testing approaches namely regression test suite approach, heuristic based approach, keyword based approach, GUI based approach and model based approach are evaluated based on software evolution taxonomy framework...
6. Measuring test mass acceleration noise in space-based gravitational wave astronomy
CERN Document Server
Congedo, Giuseppe
2014-01-01
The basic constituent of interferometric gravitational wave detectors -- the test mass to test mass interferometric link -- behaves as a differential dynamometer measuring effective differential forces, comprising an integrated measure of gravity curvature, inertial effects, as well as non-gravitational spurious forces. This last contribution is going to be characterised by the LISA Pathfinder mission, a technology precursor of future space-borne detectors like eLISA. Changing the perspective from displacement to acceleration can benefit the data analysis of LISA Pathfinder and future detectors. The response in differential acceleration to gravitational waves is derived for a space-based detector's interferometric link. The acceleration formalism can also be integrated into time delay interferometry by building up the unequal-arm Michelson differential acceleration combination. The differential acceleration is nominally insensitive to the system free evolution dominating the slow displacement dynamics of low-...
7. CERN Technical training 2008 - Learning for the LHC: Special Workshop demonstrating reliability with accelerated testing
CERN Multimedia
2008-01-01
Larry Edson’s workshop will show examples of quantitative reliability predictions based upon accelerated testing and demonstrate that reliability testing during the prototyping phase will help ascertain product shortcomings. When these weak points are addressed and the redesigned product is re-tested, the reliability of that product will become much higher. These methodologies successfully used in industry might be exceedingly useful also for component development in particle physics where reliability is of the utmost importance. This training will provide participants with the skills necessary to demonstrate reliability requirements using accelerated testing methods. The workshop will focus on accelerated test design that employs increased stress levels. This approach has the advantage of reducing test time, sample size and test facility resources. The methodologies taught are applicable to all types of stresses, spanning the elec...
8. CERN Technical training 2008 - Learning for the LHC: Special Workshop demonstrating reliability with accelerated testing
CERN Multimedia
2008-01-01
Larry Edson’s workshop will show examples of quantitative reliability predictions based upon accelerated testing and demonstrates that reliability testing during the prototyping phase will help ascertain product shortcomings. When these weak points are addressed and the redesigned product is re-tested, the reliability of that product will become much higher. These methodologies successfully used in industry might be exceedingly useful also for component development in particle physics where reliability is of utmost importance. This training will provide participants with the skills necessary to demonstrate reliability requirements using accelerated testing methods. The workshop will focus on accelerated test design that employs increased stress levels. This approach has the advantage of reducing test time, sample size and test facility resources. The methodologies taught are applicable to all types of stresses, spanning the electro...
9. CERN Technical training 2008 - Learning for the LHC: Special workshop demonstrating reliability with accelerated testing
CERN Multimedia
2008-01-01
Larry Edson’s workshop will show examples of quantitative reliability predictions based upon accelerated testing and demonstrate that reliability testing during the prototyping phase will help ascertain product shortcomings. When these weak points are addressed and the redesigned product is re-tested, the reliability of that product will become much higher. These methodologies successfully used in industry might be exceedingly useful also for component development in particle physics where reliability is of the utmost importance. This training will provide participants with the skills necessary to demonstrate reliability requirements using accelerated testing methods. The workshop will focus on accelerated test design that employs increased stress levels. This approach has the advantage of reducing test time, sample size and test facility resources. The methodologies taught are applicable to all types of stresses, spanning the elec...
10. Development of an accelerated reliability test schedule for terrestrial solar cells
Science.gov (United States)
Lathrop, J. W.; Prince, J. L.
1981-01-01
An accelerated test schedule using a minimum amount of tests and a minimum number of cells has been developed on the basis of stress test results obtained from more than 1500 cells of seven different cell types. The proposed tests, which include bias-temperature, bias-temperature-humidity, power cycle, thermal cycle, and thermal shock tests, use as little as 10 and up to 25 cells, depending on the test type.
11. The Use of Conditional Probability Integral Transformation Method for Testing Accelerated Failure Time Models
OpenAIRE
Abdalla Ahmed Abdel-Ghaly; Hanan Mohamed Aly; Elham Abdel-Malik Abde-Rahman
2016-01-01
This paper suggests the use of the conditional probability integral transformation (CPIT) method as a goodness of fit (GOF) technique in the field of accelerated life testing (ALT), specifically for validating the underlying distributional assumption in accelerated failure time (AFT) model. The method is based on transforming the data into independent and identically distributed (i.i.d) Uniform (0, 1) random variables and then applying the modified Watson statistic to test the uniformity of t...
12. Cold test results of a side-coupled standing-wave electron-accelerating structure
Science.gov (United States)
Song, Ki Baek; Li, Yonggui; Lee, Sanghyun; Lee, Byeong-No; Park, Hyung Dal; Cha, Sung-Su; Lee, Byung Cheol
2013-07-01
The radio-frequency (RF) cavity for the dual-energy S-band electron linear accelerator (LINAC) is designed for a cargo inspection system (CIS) at the Korea Atomic Energy Research Institute (KAERI). The cold test results of the electron accelerator structure, which has a side-coupled standing-wave interlaced-pulse dual-energy mode, are described. The design concept, basic structure, microwave-tuning method, and cold-test procedure are described as well. The measured dispersion curve, spectrum characteristics, ρ-f relation of the power coupler, and axial field distribution of the accelerating gradient are provided.
13. Accelerated gravity testing of aquitard core permeability and implications at formation and regional scale
Science.gov (United States)
Timms, W. A.; Crane, R.; Anderson, D. J.; Bouzalakos, S.; Whelan, M.; McGeeney, D.; Rahman, P. F.; Acworth, R. I.
2016-01-01
Evaluating the possibility of leakage through low-permeability geological strata is critically important for sustainable water supplies, the extraction of fuels from coal and other strata, and the confinement of waste within the earth. The current work demonstrates that relatively rapid and realistic vertical hydraulic conductivity (Kv) measurements of aquitard cores using accelerated gravity can constrain and compliment larger-scale assessments of hydraulic connectivity. Steady-state fluid velocity through a low-K porous sample is linearly related to accelerated gravity (g level) in a centrifuge permeameter (CP) unless consolidation or geochemical reactions occur. A CP module was custom designed to fit a standard 2 m diameter geotechnical centrifuge (550 g maximum) with a capacity for sample dimensions up to 100 mm diameter and 200 mm length, and a total stress of ˜ 2 MPa at the base of the core. Formation fluids were used as influent to limit any shrink-swell phenomena, which may alter the permeability. Kv results from CP testing of minimally disturbed cores from three sites within a clayey-silt formation varied from 10-10 to 10-7 m s-1 (number of samples, n = 18). Additional tests were focussed on the Cattle Lane (CL) site, where Kv within the 99 % confidence interval (n = 9) was 1.1 × 10-9 to 2.0 × 10-9 m s-1. These Kv results were very similar to an independent in situ Kv method based on pore pressure propagation though the sequence. However, there was less certainty at two other core sites due to limited and variable Kv data. Blind standard 1 g column tests underestimated Kv compared to CP and in situ Kv data, possibly due to deionised water interactions with clay, and were more time-consuming than CP tests. Our Kv results were compared with the set-up of a flow model for the region, and considered in the context of heterogeneity and preferential flow paths at site and formation scale. Reasonable assessments of leakage and solute transport through
14. Status and Plans for a Superconducting RF Accelerator Test Facility at Fermilab
International Nuclear Information System (INIS)
The Advanced Superconducting Test Accelerator (ASTA) is being constructed at Fermilab. The existing New Muon Lab (NML) building is being converted for this facility. The accelerator will consist of an electron gun, injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, multiple downstream beam lines for testing diagnostics and conducting various beam tests, and a high power beam dump. When completed, it is envisioned that this facility will initially be capable of generating a 750 MeV electron beam with ILC beam intensity. An expansion of this facility was recently completed that will provide the capability to upgrade the accelerator to a total beam energy of 1.5 GeV. Two new buildings were also constructed adjacent to the ASTA facility to house a new cryogenic plant and multiple superconducting RF (SRF) cryomodule test stands. In addition to testing accelerator components, this facility will be used to test RF power systems, instrumentation, and control systems for future SRF accelerators such as the ILC and Project-X. This paper describes the current status and overall plans for this facility.
15. ADS-Lib/V1.0. A test library for Accelerator Driven Systems. Summary documentation
International Nuclear Information System (INIS)
The report describes the generation of a test library for a number of code systems used in the analysis of Accelerator Driven Systems (ADS). The generation of the ADS library was undertaken by IAEA-NDS and the data files are available to users at http://wwwnds. iaea.org/ads/ and also as CD-ROM (upon request).The source of the evaluated nuclear data was the JEFF-3.1 library. Processing was carried out using NJOY-99.90 with the local updates at IAEA-NDS. The resulting processed files are available in ACE format for MCNP and in MATXS format for multi-group transport calculations. (author)
16. Testing of a Loop Heat Pipe Subjective to Variable Accelerations. Part 1; Start-up
Science.gov (United States)
Ku, Jentung; Rogers, Paul; Hoff, Craig
2000-01-01
The effect of accelerating forces on the performance of loop heat pipes (LHP) is of interest and importance to terrestrial and space applications. They are being considered for cooling of military combat vehicles and for spinning spacecraft. In order to investigate the effect of an accelerating force on LHP operation, a miniature LHP was installed on a spin table. Variable accelerating forces were imposed on the LHP by spinning the table at different angular speeds. Several patterns of accelerating forces were applied, i.e. continuous spin at different speeds and periodic spin at different speeds and frequencies. The resulting accelerations ranged from 1.17 g's to 4.7 g's. This paper presents the first part of the experimental study, i.e. the effects of a centrifugal force on the LHP start-up. Tests were conducted by varying the heat load to the evaporator, sink temperature, magnitude and frequency of centrifugal force, and LHP orientation relative to the direction of the accelerating force. The accelerating force seems to have little effect on the loop start-up in terms of temperature overshoot and superheat at boiling incipience. Changes in these parameters seem to be stochastic with or without centrifugal accelerating forces. The LHP started successfully in all tests.
17. Accelerated UV Test Methods for Encapsulants of Photovoltaic Modules: Preprint
Energy Technology Data Exchange (ETDEWEB)
Kempe, M. D.
2008-05-01
This paper asserts that materials used for PV encapsulation must be evaluated for their ability to transmit light and to maintain mechanical integrity for extended periods of time under long term UV exposure.
18. Evaluation of wall thinning profile by flow accelerated corrosion in separation and union pipe
International Nuclear Information System (INIS)
Flow Accelerated Corrosion (FAC) is a pipe wall thinning phenomena to be monitored and managed in power plants with high priority. At present, its management has been conducted with conservative evaluation of thinning rate and residual lifetime of the piping based on wall thickness measurements. However, noticeable case of wall thinning was occurred at separation and union pipe. In such pipe system, it is a problem to manage section beneath reinforcing plate of T-tube pipe and 'crotch' of T-joint pipe; the region where wall thickness measurement is difficult to conduct with ordinary ultrasonic testing device. In this study, numerical analysis for separation and union part of T-tube and T-joint pipe was conducted, and wall thinning profile by Flow Accelerated Corrosion was evaluated by calculating mass transfer coefficient and geometry factor. Based on these results, we considered applicable wall thinning management for T-tube and T-joint pipe. In the case of union flow from main and branch pipe, the wall thinning profile of T-tube showed the tendency of increase at main pipe like semielliptical region. On the other hand, noticeable profile appeared at 'crotch' in T-joint. Although it was found that geometry factor of T-joint in this case was half the value of T-tube, an alternative evaluation method to previous one might be needed for the profiles of 'semielliptical region' and 'crotch'. (author)
19. Status and Plans for an SRF Accelerator Test Facility at Fermilab
CERN Document Server
Church, M; Nagaitsev, S
2012-01-01
A superconducting RF accelerator test facility is currently under construction at Fermilab. The accelerator will consist of an electron gun, 40 MeV injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, and multiple downstream beam lines for testing diagnostics and performing beam experiments. With 3 cryomodules installed this facility will initially be capable of generating an 810 MeV electron beam with ILC beam intensity. The facility can accommodate up to 6 cryomodules for a total beam energy of 1.5 GeV. This facility will be used to test SRF cryomodules under high intensity beam conditions, RF power equipment, instrumentation, and LLRF and controls systems for future SRF accelerators such as the ILC and Project-X. This paper describes the current status and overall plans for this facility.
20. Status and Plans for an SRF Accelerator Test Facility at Fermilab
Energy Technology Data Exchange (ETDEWEB)
Church, M.; Leibfritz, J.; Nagaitsev, S.; /Fermilab
2011-07-29
A superconducting RF accelerator test facility is currently under construction at Fermilab. The accelerator will consist of an electron gun, 40 MeV injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, and multiple downstream beam lines for testing diagnostics and performing beam experiments. With 3 cryomodules installed this facility will initially be capable of generating an 810 MeV electron beam with ILC beam intensity. The facility can accommodate up to 6 cryomodules for a total beam energy of 1.5 GeV. This facility will be used to test SRF cryomodules under high intensity beam conditions, RF power equipment, instrumentation, and LLRF and controls systems for future SRF accelerators such as the ILC and Project-X. This paper describes the current status and overall plans for this facility.
1. Evaluating the RELM Test Results
OpenAIRE
Sachs, Michael K.; Ya-Ting Lee; Turcotte, Donald L.; Holliday, James R.; Rundle, John B.
2012-01-01
We consider implications of the Regional Earthquake Likelihood Models (RELM) test results with regard to earthquake forecasting. Prospective forecasts were solicited for M≥4.95 earthquakes in California during the period 2006–2010. During this period 31 earthquakes occurred in the test region with M≥4.95. We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for torn...
2. On selection of optimal stochastic model for accelerated life testing
International Nuclear Information System (INIS)
This paper deals with the problem of proper lifetime model selection in the context of statistical reliability analysis. Namely, we consider regression models describing the dependence of failure intensities on a covariate, for instance, a stressor. Testing the model fit is standardly based on the so-called martingale residuals. Their analysis has already been studied by many authors. Nevertheless, the Bayes approach to the problem, in spite of its advantages, is just developing. We shall present the Bayes procedure of estimation in several semi-parametric regression models of failure intensity. Then, our main concern is the Bayes construction of residual processes and goodness-of-fit tests based on them. The method is illustrated with both artificial and real-data examples. - Highlights: • Statistical survival and reliability analysis and Bayes approach. • Bayes semi-parametric regression modeling in Cox's and AFT models. • Bayes version of martingale residuals and goodness-of-fit test
3. Novel accelerated corrosion test for LY12CZ and LC4CS aluminum alloys
Institute of Scientific and Technical Information of China (English)
CAI Jian-ping; LIU Ming
2006-01-01
A new accelerated corrosion test-comprehensive environmental test (CET) was developed in order to estimate the outdoor corrosion of aluminum alloys in marine environment. The environmental characteristics in CET were studied by atmospheric corrosion monitor (ACM), and the morphology of corrosion product was observed by SEM. The correlation between the accelerated corrosion tests and outdoor exposure was discussed. The results show that the anti-corrosion ranking for LY12CZ, LC4CS, clad LY12CZ, and clad LC4CS in CET is the same as that of the alloys exposed outdoor, and ACM study shows that CET demonstrates the same environmental characteristics as that exposed outdoor. CET is a more accurate accelerated corrosion test, and a mathematical relation was obtained to describe the relation between CET and outdoor test.
4. Accelerated fatigue testing of LM 19.1 blades
DEFF Research Database (Denmark)
Kristensen, Ole Jesper Dahl; Jørgensen, E.
2003-01-01
material. In addition to the thermal imaging surveillance the blades were instrumented with strain gauges. This report presents the temperature duringtest, calibration test results, moment range measurements, strain statistics, thermal imaging registrations and a determination of the size and cause of the...
5. Poisson simulation for high voltage terminal of test stand for 1MV electrostatic accelerator
International Nuclear Information System (INIS)
KOMAC provide ion beam to user which energy range need to expand to MeV range and develop 1 MV electrostatic accelerator. The specifications of the electrostatic accelerator are 1MV acceleration voltage, 10 mA peak current and variable gas ion. We are developing test stand before set up 1 MV electrostatic accelerator. The test stand voltage is 300 kV and operating time is 8 hours. The test stand is consist of 300 kV high voltage terminal, DC-AC-DC inverter, power supply device inside terminal, 200MHz RF power, 5 kV extraction power supply, 300 kV accelerating tube and vacuum system.. The beam measurement system and beam dump will be installed next to accelerating tube. Poisson code simulation results of the high voltage terminal are presented in this paper. Poisson code has been used to calculate the electric field for high voltage terminal. The results of simulation were verified with reasonable results. The poisson code structure could be apply to the high voltage terminal of the test stand
6. Enabling More than Moore: Accelerated Reliability Testing and Risk Analysis for Advanced Electronics Packaging
Science.gov (United States)
Ghaffarian, Reza; Evans, John W.
2014-01-01
For five decades, the semiconductor industry has distinguished itself by the rapid pace of improvement in miniaturization of electronics products-Moore's Law. Now, scaling hits a brick wall, a paradigm shift. The industry roadmaps recognized the scaling limitation and project that packaging technologies will meet further miniaturization needs or ak.a "More than Moore". This paper presents packaging technology trends and accelerated reliability testing methods currently being practiced. Then, it presents industry status on key advanced electronic packages, factors affecting accelerated solder joint reliability of area array packages, and IPC/JEDEC/Mil specifications for characterizations of assemblies under accelerated thermal and mechanical loading. Finally, it presents an examples demonstrating how Accelerated Testing and Analysis have been effectively employed in the development of complex spacecraft thereby reducing risk. Quantitative assessments necessarily involve the mathematics of probability and statistics. In addition, accelerated tests need to be designed which consider the desired risk posture and schedule for particular project. Such assessments relieve risks without imposing additional costs. and constraints that are not value added for a particular mission. Furthermore, in the course of development of complex systems, variances and defects will inevitably present themselves and require a decision concerning their disposition, necessitating quantitative assessments. In summary, this paper presents a comprehensive view point, from technology to systems, including the benefits and impact of accelerated testing in offsetting risk.
7. Evaluation of College English Test
Institute of Scientific and Technical Information of China (English)
郭奕奕
2003-01-01
There has been much heated discussion on College English Test for non-English majors Band 4 and Band 6 because it has exerted great influence on English teaching in Chinese universities. This essay is intended to explore the reliability, validity,practicality and washback of this large-scale test by focusing on CET Band 4. The author of this report discusses the merits as well as some existing problems of this test and offers some suggestions at the end of the essay.
8. Life Prediction on a T700 Carbon Fiber Reinforced Cylinder with Limited Accelerated Life Testing Data
Directory of Open Access Journals (Sweden)
Ma Xiaobing
2015-01-01
Full Text Available An accelerated life testing investigation was conducted on a composite cylinder that consists of aluminum alloy and T700 carbon fiber. The ultimate failure stress predictions of cylinders were obtained by the mixing rule and verified by the blasting static pressure method. Based on the stress prediction of cylinder under working conditions, the constant stress accelerated life test of the cylinder was designed. However, the failure data cannot be sufficiently obtained by the accelerated life test due to the time limitation. Therefore, most of the data presented to be high censored in high stress level and zero-failure data in low stress level. When using the traditional method for rupture life prediction, the results showed to be of lower confidence. In this study, the consistency of failure mechanism for carbon fiber and cylinder was analyzed firstly. According to the analysis result, the statistical test information of carbon fiber could be utilized for the accelerated model constitution. Then, rupture life prediction method for cylinder was proposed based on the accelerated life test data and carbon fiber test data. In this way, the life prediction accuracy of cylinder could be improved obviously, and the results showed that the accuracy of this method increased by 35%.
9. Development of an accelerated test for Internal Sulfate Attack study
OpenAIRE
Khelil Nacim; Aubert Jean-Emmanuel; Escadeillas Gilles
2014-01-01
Internal Sulfate Attack (ISA) is a pathology that occurs under certain conditions in concrete having undergone heating above 70 °C at early age (through heating in pre-casting industry or due to hydration in large concrete parts). This reaction deemed very slow, numerous methods to speed up reactions leading to delayed ettringite formation have been developed. These methods are all based on the material damage. Another type of test is currently under development. It is based on rehabilitation...
10. Design and Factory Test of the e+/e- Frascati Linear Accelerator for DAFNE
International Nuclear Information System (INIS)
The electron-positron accelerator for the DAFNE project has been built and is in test at Titan Beta in Dublin, CA. This S-Band RF linac system utilizes four 45 MW sledded klystrons and 16-3 m accelerating structures to achieve the required performance. It delivers a 4 ampere electron beam to the positron converter and accelerates the resulting positrons to 550 MeV. The converter design uses a 4.3T pulsed tapered flux compressor along with a pseudo-adiabatic tapered field to a 5 KG solenoid over the first two positron accelerating sections. Quadrupole focusing is used after 100 MeV. The system performance is given in Table 1. This paper briefly describes the design and development of the various subassemblies in this system and gives the initial factory test data.
11. Isolation of a piezoresistive accelerometer used in high acceleration tests
Science.gov (United States)
Bateman, V. I.; Brown, F. A.; Davie, N. T.
Both uniaxial and triaxial shock isolation techniques for a piezoresistive accelerometer have been developed for pyroshock and impact tests. The uniaxial shock isolation technique has demonstrated acceptable characteristics for a temperature range of -50 to +186 F and a frequency bandwidth of DC to 10 kHz. The triaxial shock isolation technique has demonstrated acceptable results for a temperature range of -50 to 70 F and a frequency bandwidth of DC to 10 kHz. These temperature ranges, that are beyond the accelerometer manufacturer's operational limits of -30 and +150 F, required the calibration of accelerometers at high shock levels and at the temperature extremes of -50 and +160 F. The purposes of these calibrations were to insure that the accelerometers operated at the field test temperatures and to provide an accelerometer sensitivity at each test temperature. Since there is no NIST-traceable (National Institute of Standards and Technology traceable) calibration capability at shock levels of 5,000 - 15,000 g for the temperature extremes of -50 and +160 F, a method for calibrating and certifying the Hopkinson bar with a transfer standard was developed. Time domain and frequency domain results are given that characterize the Hopkinson bar. The NIST-traceable accuracy for the standard accelerometer in shock is +\\-5%. The Hopkinson bar has been certified by the Sandia Secondary Standards Division with an uncertainty of 6%.
12. Test Ion Acceleration in the Field of Expanding Planar Electron Cloud
OpenAIRE
2006-01-01
New exact results are obtained for relativistic acceleration of test positive ions in the non-Boltzmann laminar zone of a planar electron sheath evolving from an initially mono-energetic electron distribution. The electron dynamics is analyzed against the background of motionless foil ions. The limiting gamma-factor of accelerated ions is shown to be determined primarily by the values of the ion-electron charge-over-mass ratio and the initial gamma-factor of the accelerated electrons: there e...
13. On the application of design of experiments to accelerated life testing
International Nuclear Information System (INIS)
Today, there is an increasing demand for improved quality and reliability due to increasing system complexity and increasing demands from customer. Continuous improvement of quality is not only a means of competition but also a matter of staying in the market. Accelerated life testing and statistical design of experiments are two needed methods for improvement of quality. The combined use of them is very advantageous and increases the test efficiency. Accelerated life testing is a quick way to provide information on the life distribution of materials and products. By subjecting the test unit to conditions more severe than those at normal usage, the test time can be highly reduced. Estimates of life at normal stress levels are obtained by extrapolating the available information through a reasonable acceleration model. Accelerated life testing has mostly been used to measure reliability but it is high time to use it for improvement of quality. Design of experiments serves to find out the effect of design parameters and other interesting factors on performance measure and its variability. The obtained information is essential for a continuous improvement of quality. As an illustration, two sets of experiment are designed and performed at highly increased stress levels. The results are analysed and discussed and a time saving alternative is proposed. The combination of experimental design and accelerated life testing is discussed and illustrated. The combined use of these methods can be argued for in two different cases. One is for an exploratory improvement investigation and the other is for verification of reliability. In either case, the combined use is advantageous and improves the testing efficiency. Some general conclusions are drawn to be used for planning and performance of statistically designed accelerated life testing experiments. (70 refs.) (au)
14. A Proposed Experimental Test of Proton-Driven Plasma Wakefield Acceleration Based on CERN SPS
CERN Document Server
Xia, G X; Lotov, K; Pukhov, A; Assmann, R; Zimmermann, F; Huang, C; Vieira, J; Lopes, N; Fonseca, RA; Silva, LO; An, W; Joshi, C; Mori, W; Lu, W; Muggli, P
2011-01-01
Proton-bunch driven plasma wakefield acceleration (PDPWA) has been proposed as an approach to accelerate electron beam to TeV energy regime in a single plasma section. An experimental test has recently proposed to demonstrate the capability of PDPWA by using proton beams from the CERN SPS. The layout of the experiment is introduced. Particle-in-cell simulation results based on the realistic beam parameters are presented. Presented at PAC2011 New York, 28 March - 1 April 2011.
15. Electron lenses and cooling for the Fermilab Integrable Optics Test Accelerator
OpenAIRE
Stancari, G; Burov, A.; Lebedev, V.; Nagaitsev, S.; Prebys, E.; Valishev, A.
2015-01-01
Recently, the study of integrable Hamiltonian systems has led to nonlinear accelerator lattices with one or two transverse invariants and wide stable tune spreads. These lattices may drastically improve the performance of high-intensity machines, providing Landau damping to protect the beam from instabilities, while preserving dynamic aperture. The Integrable Optics Test Accelerator (IOTA) is being built at Fermilab to study these concepts with 150-MeV pencil electron beams (single-particle d...
16. Revised evaluation of steam generator testing alternatives
International Nuclear Information System (INIS)
A scoping evaluation was made of various facility alternatives for test of LMFBR prototype steam generators and models. Recommendations are given for modifications to EBR-II and SCTI (Sodium Components Test Installation) for prototype SG testing, and for few-tube model testing
17. Evaluating an accelerated nursing program: a dashboard for diversity.
Science.gov (United States)
Schmidt, Bonnie J; MacWilliams, Brent R
2015-01-01
Diversity is a topic of increasing attention in higher education and the nursing workforce. Experts have called for a nursing workforce that mirrors the population it serves. Students in nursing programs in the United States do not reflect our country's diverse population; therefore, much work is needed before that goal can be reached. Diversity cannot be successfully achieved in nursing education without inclusion and attention to quality. The Inclusive Excellence framework can be used by nurse educators to promote inclusion, diversity, and excellence. In this framework, excellence and diversity are linked in an intentional metric-driven process. Accelerated programs offer a possible venue to promote diversity, and one accelerated program is examined using a set of metrics and a dashboard approach commonly used in business settings. Several recommendations were made for future assessment, interventions, and monitoring. Nurse educators are called to examine and adopt a diversity dashboard in all nursing programs. PMID:25839946
18. Million revolution accelerator beam instrument for logging and evaluation
International Nuclear Information System (INIS)
A data acquisition and analysis instrument for the processing of accelerator beam position monitor (BPM) signals has been assembled and used preliminarily for beam diagnosis of the Fermilab accelerators. Up to eight BPM (or other analogue) channels are digitized and transmitted to an acquisition Sun workstation and from there both to a monitor workstation and a workstation for off-line (but immediate) data analysis. A coherent data description format permits fast data object transfers to and from memory, disk and tape, across the Sun ethernet. This has helped the development of both general purpose and experiment-specific data analysis, presentation and control tools. Flexible software permits immediate graphical display in both time and frequency domains. The instrument acts simultaneously as a digital oscilloscope, as a network analyzer and as a correlating, noise-reducing spectrum analyzer. 2 refs., 3 figs
19. Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data
Directory of Open Access Journals (Sweden)
Amal S. Hassan
2015-04-01
Full Text Available Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weibull distribution. Maximum likelihood estimates are obtained for the model parameters and acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators is given. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample sizes. Simulation studies are performed to investigate the performance of the estimators.
20. Isolation of a piezoresistive accelerometer used in high acceleration tests
Energy Technology Data Exchange (ETDEWEB)
Bateman, V.I.; Brown, F.A.; Davie, N.T.
1992-12-31
Both uniaxial and triaxial shock isolation techniques for a piezoresistive accelerometer have been developed for pyroshock and impact tests. The uniaxial shock isolation technique has demonstrated acceptable characteristics for a temperature range of {minus}50{degree}F to +186{degree}F and a frequency bandwidth of DC to 10 kHz. The triaxial shock isolation technique has demonstrated acceptable results for a temperature range of {minus}50{degree}F to 70{degree}F and a frequency bandwidth of DC to 10 kHz. These temperature ranges, that are beyond the accelerometer manufacturers operational limits of {minus}30{degree}F and +150{degree}F, required the calibration of accelerometers at high shock levels and at the temperature extremes of {minus}50{degree}F and +160{degree}F. The purposes of these calibrations were to insure that the accelerometers operated at the field test temperatures and to provide an accelerometer sensitivity at each test temperature. Since there is no NIST-traceable (National Institute of Standards and Technology traceable) calibration capability at shock levels of 5,000 g - 15,000 g for the temperature extremes of {minus}50{degree}F and +160{degree}F, a method for calibrating and certifying the Hopkinson bar with a transfer standard was developed. Time domain and frequency domain results are given that characterize the Hopkinson bar. The NIST-traceable accuracy for the standard accelerometer in shock is {plus_minus}5%. The Hopkinson bar has been certified by the Sandia Secondary Standards Division with an uncertainty of 6%.
1. Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data
OpenAIRE
Amal S. Hassan; Salwa M. Assar; Ahmed N. Zaky
2015-01-01
Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weib...
2. HIV testing, staging, and evaluation.
Science.gov (United States)
Rodriguez, Carla V; Horberg, Michael A
2014-09-01
HIV testing and incidence are stable, but trends for certain populations are concerning. Primary prevention must be reinvigorated and target vulnerable populations. Science and policy have progressed to improve the accuracy, speed, privacy, and affordability of HIV testing. More potent and much better tolerated HIV treatments and a multidisciplinary approach to care have increased adherence and viral suppression. Changes to health care law in the United States seek to expand the affordability and access of improved HIV diagnostics and treatment. Continued challenges include improving long-term outcomes in people on lifetime regimens, reducing comorbidities associated with those regimens, and preventing further transmission. PMID:25151560
3. Accelerated testing of solid oxide fuel cell stacks for micro combined heat and power application
DEFF Research Database (Denmark)
Hagen, Anke; Høgh, Jens Valdemar Thorvald; Barfod, Rasmus
2015-01-01
State-of-the-art (SoA) solid oxide fuel cell (SOFC) stacks are tested using profiles relevant for use in micro combined heat and power (CHP) units. Such applications are characterised by dynamic load profiles. In order to shorten the needed testing time and to investigate potential acceleration of...
International Nuclear Information System (INIS)
Electronic components used in high energy physics experiments are subjected to a radiation background composed of high energy hadrons, mesons and photons. These particles can induce permanent and transient effects that affect the normal device operation. Ionizing dose and displacement damage can cause chronic damage which disable the device permanently. Transient effects or single event effects are in general recoverable with time intervals that depend on the nature of the failure. The magnitude of these effects is technology dependent with feature size being one of the key parameters. Analog to digital converters are components that are frequently used in detector front end electronics, generally placed as close as possible to the sensing elements to maximize signal fidelity. We report on the development of a technique for testing analog to digital converters for radiation effects, in particular for single event effects. A total of seventeen commercial ADCs were evaluated for ionizing dose tolerance and extensive SEU measurements performed on a twelve and fourteen bit ADCs. Mitigation strategies for single event effects (SEE) are discussed for their use in the large hadron collider environment
Science.gov (United States)
Chen, K.; Chen, H.; Kierstead, J.; Takai, H.; Rescia, S.; Hu, X.; Xu, H.; Mead, J.; Lanni, F.; Minelli, M.
2015-08-01
Electronic components used in high energy physics experiments are subjected to a radiation background composed of high energy hadrons, mesons and photons. These particles can induce permanent and transient effects that affect the normal device operation. Ionizing dose and displacement damage can cause chronic damage which disable the device permanently. Transient effects or single event effects are in general recoverable with time intervals that depend on the nature of the failure. The magnitude of these effects is technology dependent with feature size being one of the key parameters. Analog to digital converters are components that are frequently used in detector front end electronics, generally placed as close as possible to the sensing elements to maximize signal fidelity. We report on the development of a technique for testing analog to digital converters for radiation effects, in particular for single event effects. A total of seventeen commercial ADCs were evaluated for ionizing dose tolerance and extensive SEU measurements performed on a twelve and fourteen bit ADCs. Mitigation strategies for single event effects (SEE) are discussed for their use in the large hadron collider environment.
6. From Inspection to School Improvement? Evaluating the Accelerated Inspection Programme in Waltham Forest.
Science.gov (United States)
Hopkins, David; Harris, Alma; Watling, Rob; Beresford, John
1999-01-01
Outlines the main findings from the evaluation of the Accelerated Inspection Programme (AIP) in Waltham Forest under three main phases (pre-inspection, inspection, and post inspection). Focuses on the relationship between inspection and school improvement. Discusses the recommendations. (CMK)
7. Kerr black holes as accelerators of spinning test particles
Science.gov (United States)
Guo, Minyong; Gao, Sijie
2016-04-01
It has been shown that ultraenergetic collisions can occur near the horizon of an extremal Kerr black hole. Previous studies mainly focused on geodesic motions of particles. In this paper, we consider spinning test particles whose orbits are nongeodesic. By employing the Mathisson-Papapetrou-Dixon equation, we find the critical angular momentum satisfies J =2 E for extremal Kerr black holes. Although the conserved angular momentum J and energy E have been redefined in the presence of spin, the critical condition remains the same form. If a particle with this angular momentum collides with another particle arbitrarily close to the horizon of the black hole, the center-of-mass energy can be arbitrarily high. We also prove that arbitrarily high energies cannot be obtained for spinning particles near the horizons of nonextremal Kerr black holes.
8. Kerr black holes as accelerators of spinning test particles
CERN Document Server
Guo, Minyong
2016-01-01
It has been shown that ultraenergetic collisions can occur near the horizon of an extremal Kerr black hole. Previous studies mainly focused on geodesic motions of particles. In this paper, we consider spinning test particles whose orbits are non-geodesic. By employing the Mathisson-Papapetrou-Dixon equation, we find the critical angular momentum satisfies $J=2E$ for extremal Kerr black holes. Although the conserved angular momentum $J$ and energy $E$ have been redefined in the presence of spin, the critical condition remains the same form. If a particle with this angular momentum collides with another particle arbitrarily close to the horizon of the black hole, the center-of-mass energy can be arbitrarily high. We also prove that arbitrarily high energies cannot be obtained for spinning particles near the horizons of non-extremal Kerr black holes.
9. Evaluation of Flow Accelerated Corrosion of Carbon Steel with Rotating Cylinder
International Nuclear Information System (INIS)
Flow accelerated corrosion (FAC) of the carbon steel piping in nuclear power plants (NPPs) has been major issue in nuclear industry. Rotating cylinder FAC test facility was designed and fabricated and then performance of the facility was evaluated. The facility is very simple in design and economic in fabrication and can be used in material and chemistry screening test. The facility is equipped with on line monitoring of pH, conductivity, dissolved oxygen(DO), and temperature. Fluid velocity is controlled with rotating speed of the cylinder with a test specimen. FAC test of SA106 Gr. B carbon steel under 4 m/s flow velocity was performed with the rotating cylinder at DO concentration of less than 1 ppb and of 1.3 ppm. Also a corrosion test of the carbon steel at static condition, that is at zero fluid velocity, of test specimen and solution was performed at pH from 8 to 10 for comparison with the FAC data. For corrosion test in static condition, the amount of non adherent corrosion product was almost constant at pH ranging from 8 to 10. But adherent corrosion product decreased with increasing pH. This trend is consistent with decrease of Fe solubility with an increase in pH. For FAC test with rotating cylinder FAC test facility, the amount of non adherent corrosion product was also almost same for both DO concentrations. The rotating cylinder FAC test facility will be further improved by redesigning rotating cylinder and FAC specimen geometry for future work
10. Sustainable test cell : performance evaluation
OpenAIRE
Silva, Pedro Correia Pereira da; Bragança, L.; Mendonça, Paulo; Almeida, Manuela Guedes de
2006-01-01
Energy is one of the main causes of the environmental pollution. In the European Union, buildings are responsible for 40% of the final energy demand and 1/3 of the emissions of greenhouse gases. Therefore, in order to promote the energy consumption reduction, it is fundamental to employ sustainable development principles in the construction sector. In order to demonstrate and show the potentialities of Sustainable building technologies two Test Cells were built. Comparing the solutions obtain...
11. Performing and evaluating creep tests
Czech Academy of Sciences Publication Activity Database
Dvořák, Jiří; Blum, W.; Král, Petr; Eisenlohr, P.; Sklenička, Václav
Toulouse: Institut Carnot CIRIMAT, 2015. s. 303-304. [CREEP 2015 - International Conference on Creep and Fracture of Engineering Materials and Structures /13./. 31.05.2015-04.06.2015, Toulouse] R&D Projects: GA MŠk(CZ) ED1.1.00/02.0068 Institutional support: RVO:68081723 Keywords : creep test * inelastic strain rate * crystallite boundaries * coper * dynamic recovery Subject RIV: JG - Metallurgy
12. Life prediction of OLED for constant-stress accelerated degradation tests using luminance decaying model
International Nuclear Information System (INIS)
In order to acquire the life information of organic light emitting diode (OLED), three groups of constant stress accelerated degradation tests are performed to obtain the luminance decaying data of samples under the condition that the luminance and the current are respectively selected as the indicator of performance degradation and the test stress. Weibull function is applied to describe the relationship between luminance decaying and time, least square method (LSM) is employed to calculate the shape parameter and scale parameter, and the life prediction of OLED is achieved. The numerical results indicate that the accelerated degradation test and the luminance decaying model reveal the luminance decaying law of OLED. The luminance decaying formula fits the test data very well, and the average error of fitting value compared with the test data is small. Furthermore, the accuracy of the OLED life predicted by luminance decaying model is high, which enable rapid estimation of OLED life and provide significant guidelines to help engineers make decisions in design and manufacturing strategy from the aspect of reliability life. - Highlights: • We gain luminance decaying data by accelerated degradation tests on OLED. • The luminance decaying model objectively reveals the decaying law of OLED luminance. • The least square method (LSM) is employed to calculate Weibull parameters. • The plan designed for accelerated degradation tests proves to be feasible. • The accuracy of the OLED life and the luminance decaying fitting formula is high
13. X-band klystron modulator for the Accelerator Test Facility
International Nuclear Information System (INIS)
An X-band Klystron Modulator has been designed and constructed to drive two kinds of prototype X-band pulsed klystrons: (1) 30 MW klystron ( XB-50K) requiring a 450 kV beam voltage with a 0.5 μs flat top and (2) 120 MW klystron ( XB-72K) requiring a 550 kV beam voltage with a 0.5 μs flat top. The modulator generates 2.0 μs pulses with 37 kV voltage and 7,300 A peak current for the operation of the XB-72K. It is a conventional line-type modulator with a 6 section pulse forming network (PFN) which is resonantly charged and discharged by a thyratron switch at up to 200 pps. In order to reduce the size of the modulator, a special low inductance capacitors using a film coated thin Al-electrodes of 300 angstrom thickness has been developed for the PFN. Its output pulse voltage is stepped up to 15 times by a pulse transformer. The design, specifications and results of performance tests of the modulator are described in this paper
14. An accelerated electrochemical MIC test for stainless alloys
International Nuclear Information System (INIS)
Previous work in our laboratory and elsewhere has suggested that microbially influenced corrosion (MIC) of stainless steels and nickel-base alloys occurs in locally anaerobic regions that support the growth of sulfate-reducing bacteria (SRB). The cathodic reaction is provided by oxygen reduction at remote sites. Such a coupling between anode and cathode is difficult to reproduce in the laboratory, but can be simulated indirectly using a double electrochemical cell, as in previous work. A more realistic simulation using a single aerated electrochemical cell has now been developed, in which a second organism (P. aeruginosa) is used to provide an anoxic habitat for SRB growth and possible a source of organic carbon, within a layer of silt. A bare alloy electrode is used as the oxygen cathode. Tests of this kind using rigorous microbiological procedures have generated pitting corrosion of several alloys in low chloride media simulating freshwater heat exchanger conditions. This report discusses the adaption of these procedures to study corrosion of nuclear waste containers. (author). 20 refs., 2 tabs., 7 figs
15. Concept, implementation and commissioning of the automation system for the accelerator module test facility AMTF
International Nuclear Information System (INIS)
The European XFEL project launched on June 5, 2007 will require about 103 accelerator modules as a main part of the XFEL linear accelerator. All superconducting components constituting the accelerator module like cavities and magnets have to be tested before the assembly. For the tests of the individual cavities and the complete modules an XFEL Accelerator Module Test Facility (AMTF) has been erected at DESY. The process control system EPICS (Experimental Physics and Industrial Control System) is used to control and operate the cryogenic plant and all its subcomponents. A complementary component of EPICS is the Open Source software suit CSS (Control System Studio). CSS is an integrated engineering, maintenance and operating tool for EPICS. CSS enables local and remote operating and monitoring of the complete system and thus represents the human machine interface. More than 250 PROFIBUS nodes work at the accelerator module test facility. DESY installed an extensive diagnostic and condition monitoring system. With these diagnostic tools it is possible to examine the correct installation and configuration of all PROFIBUS nodes in real time. The condition monitoring system based on FDT/DTM technology shows the state of the PROFIBUS devices at a glance. This information can be used for preventive maintenance which is mandatory for continuous operation of the AMTF facility. The poster will describe all steps form engineering to implementation and commissioning
16. Field Operations Program Chevrolet S-10 (Lead-Acid) Accelerated Reliability Testing - Final Report
Energy Technology Data Exchange (ETDEWEB)
J. Francfort (INEEL); J. Argueta; M. Wehrey (Southern California Edison); D. Karner; L. Tyree (Electric Transportation Applications)
1999-07-01
This report summarizes the Accelerated Reliability testing of five lead-acid battery-equipped Chevrolet S-10 electric vehicles by the US Department of Energy's Field Operations Program and the Program's testing partners, Electric Transportation Applications (ETA) and Southern California Edison (SCE). ETA and SCE operated the S-10s with the goal of placing 25,000 miles on each vehicle within 1 year, providing an accelerated life-cycle analysis. The testing was performed according to established and published test procedures. The S-10s' average ranges were highest during summer months; changes in ambient temperature from night to day and from season-to-season impacted range by as much as 10 miles. Drivers also noted that excessive use of power during acceleration also had a dramatic effect on vehicle range. The spirited performance of the S-10s created a great temptation to inexperienced electric vehicle drivers to ''have a good time'' and to fully utilize the S-10's acceleration capability. The price of injudicious use of power is greatly reduced range and a long-term reduction in battery life. The range using full-power accelerations followed by rapid deceleration in city driving has been 20 miles or less.
17. 3.9 GHz superconducting accelerating 9-cell cavity vertical test results
Energy Technology Data Exchange (ETDEWEB)
Khabiboulline, Timergali; Cooper, Charles; Dhanaraj, Nandhini; Edwards, Helen; Foley, Mike; Harms, Elvin; Mitchell, Donald; Rowe, Allan; Solyak, Nikolay; /Fermilab; Moeller, Wolf-Dietrich; /DESY
2007-06-01
The 3rd harmonic 3.9GHz accelerating cavity was proposed to improve the beam performance of the FLASH (TTF/DESY) facility [1]. In the frame of a collaborative agreement, Fermilab will provide DESY with a cryomodule containing a string of four cavities. In addition, a second cryomodule with one cavity will be fabricated for installation in the Fermilab photo-injector, which will be upgraded for the ILC accelerator test facility. The first 9-cell Nb cavities were tested in a vertical setup and they didn't reach the designed accelerating gradient [2]. The main problem was a multipactor in the HOM couplers, which lead to overheating and quenching of the HOM couplers. New HOM couplers with improved design are integrated in the next 9-cell cavities. In this paper we present all results of the vertical tests.
18. High Power RF Test of the Digital Feedback Control System for the PEFP Accelerator
International Nuclear Information System (INIS)
To control the RF field in the accelerating cavity for the PEFP (Proton Engineering Frontier Project) proton accelerator, a digital feedback control system has been developed. The stability requirements of the RF field are ±1% in amplitude and ± .deg. in phase. The digital feedback control system is based on the commercial FPGA PMC board hosted in VME board. The analog front-end was also developed which contains the IQ modulator, RF mixer, attenuators etc. To check the performance of the digital feedback control system, low power test with a dummy cavity has been performed with an intentional perturbation and shown that the feedback system rejected the perturbation as expected. High power RF test with a klystron has been performed and an accelerating field profile was measured. In addition, the pulse-to-pulse stability was checked by pulse operation with 0.1 Hz repetition rate. The detailed high power test results will be given in this paper
19. Test method for position of accelerate grid of megawatt level high current ion source
International Nuclear Information System (INIS)
Background: Accelerate grid for producing several tens of MW ion beams is a critical component of the megawatt level high current ion source for the high power neutral beam injection, Purpose: To measure and analyze the position of accelerate grid. Methods: Taking the exit grid module of EAST-NBI high current ion source as the measurement object, the observation point coordinates of accelerate grid rail's actual axis are obtained by using 3 quadrant points sampling method and the point coordinates are analyzed by using MATLAB optimal function. Results: The position error that tallies with minimum zone and the distribution regularities of accelerate grid rails are obtained. Conclusions: This method has simple and stable course of evaluating, can realize automatic measurement and provide the basis for improving and finalizing the grid module's processing technic. (authors)
20. Status and Plans for a Superconducting RF Accelerator Test Facility at Fermilab
CERN Document Server
Leibfritz, J; Baffes, C M; Carlson, K; Chase, B; Church, M D; Harms, E R; Klebaner, A L; Kucera, M; Martinez, A; Nagaitsev, S; Nobrega, L E; Piot, P; Reid, J; Wendt, M; Wesseln, S J
2013-01-01
The Advanced Superconducting Test Acccelerator (ASTA) is being constructed at Fermilab. The existing New Muon Lab (NML) building is being converted for this facility. The accelerator will consist of an electron gun, injector, beam acceleration section consisting of 3 TTF-type or ILC-type cryomodules, multiple downstream beamlines for testing diagnostics and conducting various beam tests, and a high power beam dump. When completed, it is envisioned that this facility will initially be capable of generating a 750-MeV electron beam with ILC beam intensity. An expansion of this facility was recently completed that will provide the capability to upgrade the accelerator to a total beam energy of 1.5-GeV. Two new buildings were also constructed adjacent to the ASTA facility to house a new cryogenic plant and multiple superconducting RF (SRF) cryomodule test stands. In addition to testing accelerator components, this facility will be used to test RF power systems, instrumentation, and control systems for future SRF a...
1. Including test errors in evaluating surveillance test intervals
International Nuclear Information System (INIS)
To evaluate the risk impact of surveillance requirements defined in Technical Specifications, both the beneficial and negative effects of surveillance should be considered. The negative effect of surveillance testing can be caused by test errors, e.g., human errors of omission or commission including potential for common cause failures. As a consequence of the negative effect, the performance of periodic testing can have adverse impact on safety. This paper defines the various negative effects of surveillance testing from a risk perspective, and then presents a methodology to quantify the negative risk impact, i.e., the risk penalty or risk increase caused by the test. The paper presents a PRA-based method to evaluate the negative risk impact due to test-caused plant transients and a method based on a test-caused equipment degradation model and PRA to assess the negative risk impact associated with equipment wear-out. Also described in the paper are illustrative applications of the methods to specific surveillance tests conducted at boiling water reactors (BWRs) such as the tests of main steam isolation valves (MSIVs), turbine overspeed protection system, and diesel generators. Evaluation results of the risk effectiveness of the tests are presented along with the insights from the sensitivity analysis of the risk impact versus test interval
2. Metodologia para o teste de envelhecimento acelerado em sementes de ervilha Accelerated aging test on pea seeds
Directory of Open Access Journals (Sweden)
Warley Marcos Nascimento
2007-06-01
ível identificar os lotes de melhor qualidade.Pea production in Brazil uses seeds produced in the country. The objective of this study was to examine the efficiency of the accelerated aging test for vigor evaluation of pea seeds. Five seed lots of cultivar Axé (wrinkled seeds and five seed lots of cultivar Mikado (smooth seeds were used. The initial quality of each seed lot was evaluated by germination test, first counting, and seedling emergence in the field. Seed moisture content was also assessed. The accelerated aging test was set at 41ºC for periods of 24; 48; and 72 hours, with and without saturated NaCl solution. The experiment was carried out in a completely randomized design. The accelerated aging test was efficient for vigor evaluation of pea seeds, and the period of 48 hours at 41ºC, using saturated NaCl solution was the most adequate procedure to indicate vigor levels of pea seeds. However, the seed germination after this period was very low when compared to 24 hour-period (80% for both cultivars, even in higher vigor seed lots (35% for Axé and 38% for Mikado. In the saturated NaCl solution, the period of 48 hours at 41ºC was the most adequate for separate seeds through vigor levels. In these conditions, seed lots of highest vigor showed germination of 68% and 79% for Axé and Mikado, respectively. Results of the germination test, first counting, and seedling emergence were not effective in discriminating physiological seed quality when used individually. Nevertheless, when results from these tests were used all together, it was possible to identify the best seed lots.
3. Hardness evaluation of prosthetic silicones containing opacifiers following chemical disinfection and accelerated aging
Directory of Open Access Journals (Sweden)
Marcelo Coelho Goiato
2010-09-01
Full Text Available We evaluated the effects of disinfection and aging on the hardness of silicones containing opacifiers and intended for use in facial prosthetics. A total of 90 samples were produced using a cylindrical metal mold 3 mm in height and 30 mm in diameter. The samples were fabricated from Silastic MDX 4-4210 silicone in three groups: GI contained no opacifier, GII contained barium sulfate (Ba, and GIII contained titanium dioxide (Ti. The samples were disinfected using effervescent tablets (Ef, neutral soap (Ns, or 4% chlorhexidine (Cl 3 times a week for 60 days. After this period the samples underwent 1,008 hours of accelerated aging. The hardness was measured using a durometer immediately following the disinfection period and after 252, 504, and 1,008 hours of aging. The data were statistically analyzed using 3-way ANOVA and the Tukey test (p < .05. The GIII group exhibited the greatest variation in hardness regardless of elapsed time. All groups displayed greater hardness after 1,008 hours of accelerated aging independent of disinfectant type. All of the hardness values were within the clinically acceptable range.
4. Soil susceptibility to accelerated hydric erosion: geotechnical evaluation of cut slopes in residual soil profiles
Directory of Open Access Journals (Sweden)
Taciano Oliveira da Silva
2015-10-01
Full Text Available The experimental research program was developed in the Alto Paraopeba region, state of Minas Gerais, Southeastern Brazil. The main objective was to promote the geotechnical evaluation of soil samples from four cut slopes in residual soil profiles of highways and local secondary roads in order to assess the potential of the anthropic impact on the soil susceptibility to accelerated erosion processes. Soil samples were named: red residual soil (RRS; pink residual soil (PRS; yellow residual soil (YRS; and white residual soil (WRS. The methodology used consisted of geotechnical characterization tests, infiltration rate and modified mass loss by immersion tests performed on soil samples from these profiles, using the physical parameters and indirect assessment of erodibility proposed in 2000 by Bastos et al. The results of indirect assessment of erodibility, which were derived from tests based on the MCT methodology, highlighted the different susceptibility of the investigated soils to hydric erosion. The parameters proposed by the referred authors were complementary to conventional criteria for an adequate classification of tropical soils into their respective classes of erodibility. Among the tested soil samples, the highest erodibility was associated with the YRS and PRS, respectively, in the natural and pre-moistened conditions, as well as it was not detected erodibility in the RRS and WRS.
5. A high-gradient test of a 30 GHz copper accelerating structure
CERN Document Server
Corsini, Roberto; Fandos, Raquel; Grudiev, Alexei; Jensen, Erk; Mete, Oznur; Ramsvik, Trond; Rodríguez, José Alberto; Sladen, Jonathan P H; Syratchev, Igor V; Taborelli, Mauro; Tecker, Frank A; Urschütz, Peter; Wilson, Ian H; Wuensch, Walter
2006-01-01
The CLIC study is investigating a number of different materials at different frequencies in order to find ways to increase achievable accelerating gradient and to understand what are the important parameters for high-gradient operation. So far a series of rf tests have been made with a set of identical-geometry 30 GHz and X-band structures in copper, tungsten and molybdenum. A new test of a 30 GHz copper accelerating structure has been completed in CTF3 with pulse lengths up to 70 ns. The new results are presented and compared to the previous structures to determine dependencies of quantities such accelerating gradient, material, frequency, pulse length, conditioning rate, breakdown rate and surface damage.
6. Testing and interfacing intelligent power supplies for the Los Alamos National Laboratory Accelerator Complex
International Nuclear Information System (INIS)
New high-current, high precision microprocessor-controlled power supplies, built by Alpha Scientific Electronics of Hayward, CA, have been installed at the Los Alamos National Laboratory Accelerator Complex. Each unit has sophisticated microprocessor control on-board and communicates via RS-422 (serial communications). The units use a high level ASCII-based control protocol. Performance tests were conducted to verify adherence to specification and to ascertain ultimate long-term stability. The front-end software used by the accelerator control system has been written to accommodate these new devices. The supplies are interfaced to the control system through a terminal server port connected to the site-wide ethernet backbone. Test design and results as well as details of the software implementation for the analog and digital control of the supplies through the accelerator control system are presented
7. Design and beam test of a high intensity continuous wave RFQ accelerator
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhouli, E-mail: [email protected]; Sun, Liepeng; Jia, Huan; He, Yuan; Shi, Aimin; Du, Xiaonan; Wang, Jing; Jin, Xiaofeng; Pan, Gang; Xu, Xianbo; Li, Chenxing; Shi, Longbo; Lu, Liang; Zhang, Zimin; Wu, Junxia; Wang, Haoning; Zhu, Tieming; Wang, Xianwu; Guo, Yuhui; Liu, Yong; and others
2014-11-01
A four-vane continuous wave (CW) RFQ has been designed for the injector II LINAC of China ADS project. To acquire the experience of a CW RFQ on design, tuning, conditioning, running, etc., a 1-m-long RFQ accelerator prototype has been built. Working at 162.5 MHz, the RFQ prototype accelerates protons of 10 mA from 20 keV to 560 keV in one meter length with a low inter-vane voltage of 65 kV and a safe Kilpatric factor of 1.3. Conditioning and beam test of the accelerator prototype have been completed, and it shows the transmission efficiency can reach 90% with a 10 mA CW proton beam. Design, fabrication and tests of the RFQ prototype will be presented in detail in the paper.
8. Test-particle acceleration in a hierarchical three-dimensional turbulence model
Energy Technology Data Exchange (ETDEWEB)
Dalena, S.; Rappazzo, A. F.; Matthaeus, W. H. [Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, DE 19716 (United States); Dmitruk, P. [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Greco, A., E-mail: [email protected] [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy)
2014-03-10
The acceleration of charged particles is relevant to the solar corona over a broad range of scales and energies. High-energy particles are usually detected in concomitance with large energy release events like solar eruptions and flares. Nevertheless, acceleration can occur at smaller scales, characterized by dynamical activity near current sheets. To gain insight into the complex scenario of coronal charged particle acceleration, we investigate the properties of acceleration with a test-particle approach using three-dimensional magnetohydrodynamic (MHD) models. These are obtained from direct solutions of the reduced MHD equations, well suited for a plasma embedded in a strong axial magnetic field, relevant to the inner heliosphere. A multi-box, multiscale technique is used to solve the equations of motion for protons. This method allows us to resolve an extended range of scales present in the system, namely, from the ion inertial scale of the order of a meter up to macroscopic scales of the order of 10 km (1/100th of the outer scale of the system). This new technique is useful to identify the mechanisms that, acting at different scales, are responsible for acceleration to high energies of a small fraction of the particles in the coronal plasma. We report results that describe acceleration at different stages over a broad range of time, length, and energy scales.
9. Design and test results of the Low Energy Demonstration Accelerator (LEDA) RF systems
International Nuclear Information System (INIS)
The Low Energy Demonstration Accelerator (LEDA) being constructed at Los Alamos will serve as the prototype for the low energy section of the Accelerator Production of Tritium (APT) accelerator. The APT accelerator requires over 200 RF systems each with a continuous wave output power of 1 MW. The reliability and availability of these RF systems is critical to the successful operation of the APT plant and prototypes of these systems are being developed and demonstrated on LEDA. The RF system design for LEDA includes three, 1.2 MW, 350 MHz continuous wave (CW), RF systems driving a radio frequency quadrupole (RFQ) and one, 1.0 MW, CW, RF system driving a coupled-cavity drift tube linac (CCDTL). This paper presents the design and test results for these RF systems including the klystrons, cathode power supply, circulators, RF vacuum windows, accelerator field and resonance control system, and RF transmission components. The three RF systems driving the RFQ use the accelerating structure as a power combiner, and this places some unique requirements on the RF system. These requirements and corresponding operational implications will be discussed
10. The conversion of CESR to operate as the Test Accelerator, CesrTA. Part 1: overview
Science.gov (United States)
Billing, M. G.
2015-07-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper outlines the motivation, design and conversion of CESR to a test accelerator, CESRTA, enhanced to study such subjects as low emittance tuning methods, electron cloud (EC) effects, intra-beam scattering, fast ion instabilities as well as general improvements to beam instrumentation. While the initial studies of CESRTA focussed on questions related to the International Linear Collider (ILC) damping ring design, CESRTA is a very flexible storage ring, capable of studying a wide range of accelerator physics and instrumentation questions. This paper contains the outline and the basis for a set of papers documenting the reconfiguration of the storage ring and the associated instrumentation required for the studies described above. Further details may be found in these papers.
11. The conversion of CESR to operate as the Test Accelerator, CesrTA. Part 1: overview
International Nuclear Information System (INIS)
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper outlines the motivation, design and conversion of CESR to a test accelerator, CESRTA, enhanced to study such subjects as low emittance tuning methods, electron cloud (EC) effects, intra-beam scattering, fast ion instabilities as well as general improvements to beam instrumentation. While the initial studies of CESRTA focussed on questions related to the International Linear Collider (ILC) damping ring design, CESRTA is a very flexible storage ring, capable of studying a wide range of accelerator physics and instrumentation questions. This paper contains the outline and the basis for a set of papers documenting the reconfiguration of the storage ring and the associated instrumentation required for the studies described above. Further details may be found in these papers
12. Equipment for controlling test benches charged particle accelerator pulse power supply systems
International Nuclear Information System (INIS)
Composition of the off-line and manual control device system designed for experimental testing the pulse supply systems of charged particle accelereators is considered. The system includes following devices: a manual remote control desk, a sysnchronization device with fibre-optical commutation programmed pulse shape generator digital sources of reference voltage. Performances of all these devices are presented. 1 ref
13. Lifetime Prediction for Degradation of Solar Mirrors using Step-Stress Accelerated Testing (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Lee, J.; Elmore, R.; Kennedy, C.; Gray, M.; Jones, W.
2011-09-01
14. Beam Extraction for 1-MV Electrostatic Accelerator at the 300 kV Test Stand
International Nuclear Information System (INIS)
The Korea Multipurpose Accelerator Complex (KOMAC) has been developing a 300-kV test stand for a 1-MV electrostatic accelerator ion source. The ion source in the high-pressure vessel is required to have a high reliability. The test stand has been proposed and developed to confirm the stable operating conditions of the ion source. The ion source will be tested at the test stand to verify the long-time operating conditions. The test stand comprises a 300-kV high-voltage terminal, a battery for the ion-source power, a 60-Hz inverter, 200-MHz RF power, a 5-kV extraction power supply, a 300-kV accelerating tube, and a vacuum system. A beam extraction experiment for the test stand was performed, and the beam current was measured using a faraday cup in the chamber. A beam extraction results for the RF ion source will be presented. Beam extraction from the RF ion source of the test stand is verified by measuring the beam current with a faraday cup in the chamber. Thus far NI Labview, PLC and faraday cup have been used to measure the beam current. The OPC server is useful for monitoring the PLC values. The average beam current of (a), (b) and (c) shown in figure 2 are 110.241µA, 105.8597µA and 103.5278µA respectively
15. First Beam and High-Gradient Cryomodule Commissioning Results of the Advanced Superconducting Test Accelerator at Fermilab
Energy Technology Data Exchange (ETDEWEB)
Crawford, Darren; et al.
2015-06-01
The advanced superconducting test accelerator at Fermilab has accelerated electrons to 20 MeV and, separately, the International Linear Collider (ILC) style 8-cavity cryomodule has achieved the ILC performance milestone of 31.5 MV/m per cavity. When fully completed, the accelerator will consist of a photoinjector, one ILC-type cryomodule, multiple accelerator R&D beamlines, and a downstream beamline to inject 300 MeV electrons into the Integrable Optics Test Accelerator (IOTA). We report on the results of first beam, the achievement of our cryomodule to ILC gradient specifications, and near-term future plans for the facility.
16. NDT for concrete under accelerated freeze/thaw tests and surface scaling
OpenAIRE
Romero Mendoza, Héctor Leonardo; Casati Calzada, María Jesús; Gálvez Ruíz, Jaime
2011-01-01
Freezing of water or salt solution in concrete pores is a main cause for severe damage and significant reduction of the service life. Most of the freeze-thaw (F-T) accelerated tests measure the scaling of concrete by weighting. This paper presents complementary procedures based on the use of strain gages and ultrasonic pulse velocity (UPV) for measuring the deterioration of concrete due to freezing and thawing. These non-destructive testing (NDT) procedures are applied to two types of con...
17. Accelerated Test Method to Identify Freeze-Thaw Durability of Aggregates
OpenAIRE
Desta, Belayneh B.; Whiting, Nancy
2015-01-01
INDOT currently identifies freeze-thaw durable aggregate using ITM210, a 90-day concrete beam freeze-thaw test. To accelerate this procedure, the 8-day Hydraulic Fracture Test (HFT) was investigated and modified. Samples from 18 quarries and six RCA sources were subjected to HFT and ITM210. Statistical analysis demonstrated that HFT can predict the ITM210 results with reasonable accuracy. The modified HFT procedures and equipment are recommended as a quick screening tool for predicting ITM210...
18. Accelerated swell testing of artificial sulfate bearing lime stabilised cohesive soils
OpenAIRE
Buttress, A.J.; Grenfell, J.R.A.; Airey, G.D.
2014-01-01
This paper reports on the physico-chemical response of two lime stabilised sulfate bearing artificial soils subject to the European Accelerated Volumetric Swell Test (EN13286-49). At various intervals during the test, a specimen was removed and subject to compositional and microstructural analysis. Ettringite was formed by both soils types, but with significant differences in crystal morphology. Ettringite crystals formed from kaolin based soils were very small, colloidal in size and tended t...
19. Testing of a low pressure multiwire avalanche counter with heavy ions from the Pelletron accelerator, Mumbai
International Nuclear Information System (INIS)
The motivation is to investigate eta-nucleus interaction for which the available experimental information is scarce. The new system consists of two multiwire avalanche counters (MWAC) to be operated at low pressure (10-20 mbar) followed by two layers of thin plastic scintillators. The MWACs will provide position information for track reconstruction. The chambers were tested with heavy ions from the pelletron accelerator, Mumbai. The test measurement is reported here
20. ACCELERATED LABORATORY TEST OF RUBBERWOOD ORIENTED STRANDBOARD EXPOSED TO WOOD DECAY FUNGI
Directory of Open Access Journals (Sweden)
Esmeralda Yoshico Arakaki Okino
2009-10-01
Full Text Available This work aimed to evaluate the natural durability of oriented strandboards (OSB manufactured with strands of Hevea brasiliensis Müll.Arg. bonded with 5% and 8% of urea-formaldehyde (UF and phenol-formadehyde (FF resins, exposed to xilophagous fungi under laboratory conditions. In accelerated laboratory test decay, samples of OSB were exposed to the following fungi: the brown-rot fungi Gloeophyllum trabeum (Pers. ex Fries Murr., Coniophora puteana (Schumach. : Fr.P. Karst., Meruliporia incrassata (Berk. & M.A. Curtis Murrill as well as the white-rot fungi Fomes annosus (Fr. : Fr. Cooke, Trametes versicolor (L. : Fr. Pilát, Ganoderma applanatum (Pers. Pat., Bjerkandera fumosa (Pers. : Fr. P. Karst. and Phanerochaete chrysosporium Burds. Among the brown-rot fungi, the Gloeophyllum trabeum was the most aggressive, showing the highest loss of mass. Trametes versicolor and Ganoderma applanatum confirmed the preference for broadleave species. All oriented strandboards at lower UF resin contents were more degraded by Phanerochaete chrysosporium, Trametes versicolor, Ganoderma applanatum, Merulia incrassata, Coniophora puteana and Gloeophyllum trabeum, with high rate of loss of mass. Coniophora puteana showed small loss of mass when FF resin was applied. Bjerkandera fumosa showed low loss of mass only at higher resin content. Oriented strandboards exposed to Coniophora puteana showed insignificant OSB degradation.
1. Recovery mechanisms in proton exchange membrane fuel cells after accelerated stress tests
Science.gov (United States)
Zhang, Xu; Guo, Liejin; Liu, Hongtan
2015-11-01
The mechanisms of performance recovery after accelerated stress test (AST) in proton exchange membrane fuel cells (PEMFCs) are systematically studied. Experiments are carried out by incorporating a well-designed performance recovery procedure right after the AST protocol. The experiment results show that the cell performance recovers significantly from the degraded state after the AST procedure. The results from cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) measurements further show that the performance recovery can be divided into kinetic and mass transport recoveries. It is further determined that the kinetic recovery, i.e. the recovery of electrochemical active area (ECA), is due to two distinct mechanisms: the reduction of platinum oxide and the re-attachment of detached platinum nanoparticles onto the carbon surface. The mass transport resistance is probably due to reduction of hydrophilic oxide groups on the carbon surface and the microstructure change that alleviates flooding. Performance comparisons show that the recovery procedure is highly effective, indicating the results of AST significantly over-estimate the true degradation in a PEM fuel cell. Therefore, a recovery procedure is highly recommended when an AST protocol is used to evaluate cell degradations to avoid over-estimating true performance degradations in PEMFCs.
2. The Ground Test Accelerator control system database: Configuration, run-time operation, and access
International Nuclear Information System (INIS)
A database is used to implement the interface between the control system and the accelerator and to provide flexibility in configuring the I/O. This flexibility is necessary to allow the control system to keep pace with the changing requirements that are inherent in an experimental environmental environment. This is not achieved without cost. Problems often associated with using databases are painful data entry, poor performance, and embedded knowledge of the database structure in code throughout the control system. This report describes how the database configuration, access, conversion, and execution in the Ground Test Accelerator (GTA) Control System overcome these problems. 2 figs
3. LED照明产品加速衰减试验方法研究%Accelerated Luminous Depreciation Testing for LED Lighting Products
Institute of Scientific and Technical Information of China (English)
钱诚; 孙博; 曹峻松
2014-01-01
With the application of energy-saving, environmental and durable LED lighting products, the reliability testing has become a pivot point for the large scale industrialization and popularization. The paper briefly introduces two methods to be respectively applied in the accelerated depreciation testing for the luminous flex of LED lighting products and the life of outdoor LED-driving power, which can sharply shorten the time for lifetime test, providing references for the LED lighting products’ reliability evaluation.
4. ACCELERATED AGING TEST IN DETERMINING THE VIGOUR OF SUNFLOWER SEEDS WITH AND WITHOUT PERICARP
Directory of Open Access Journals (Sweden)
K. R. Ducatti
2014-09-01
Full Text Available The standard germination test alone is insufficient to attest the quality of seeds, making necessary correlation’s with vigour tests, to determine more accurately the physiological potential of a seeds lot. The accelerated aging test is an option for determine the vigour and consists in submits seeds to high temperatures and humidity, for different periods of time, has not yet standardized. The objective of this work was to analyze the efficiency of the accelerated aging test in the assessment of the effect of a lot of sunflower seed, by three periods of aging (48, 56 and 72 hours in 42 °C temperature, in seeds with and without pericarp (manually removed and relate the results with electrical conductivity test and germination first count. The experimental design was a completely randomized design and the comparison of averages made using Tukey's test at 5% probability. The results showed that standard germination, electrical conductivity and germination first count, the seeds without pericarp showed better performance. In relation to the accelerated aging, only in the period of 72 hours of aging there was no significant difference between the treatments. In this way, the appropriate period to identify differences in force between the treatments was 72 hours, which showed a positive correlation with the germination first count and electrical conductivity.
5. Corrosion Testing in Support of the Accelerator Production of Tritium Program
International Nuclear Information System (INIS)
The Accelerator Production of Tritium Project is part of the United States Department of Energy strategy to meet the nation's tritium needs. The project involves the design of a proton beam accelerator, which will produce tritium through neutron/proton interaction with helium-3. Design, construction and operation of this one-of-a-kind facility will involve the utilization of a wide variety of materials exposed to unique conditions, including elevated temperature and high-energy mixed-proton and -neutron spectra. A comprehensive materials test program was established by the APT project which includes the irradiation of structural materials by exposure to high-energy protons and neutrons at the Los Alamos Neutron Science Center at the Los Alamos National Laboratory. Real-time corrosion measurements were performed on specially designed corrosion probes in water irradiated by an 800 MeV proton beam. The water test system provided a means for measuring water chemistry, dissolved hydroge n concentration, and the effects of water radiolysis and water quality on corrosion rate. The corrosion probes were constructed of candidate APT materials alloy 718, 316L stainless steel, 304L stainless steel, and 6061 Aluminum (T6 heat treatment), and alternate materials 5052 aluminum alloy, alloy 625, and C276. Real-time corrosion rates during proton irradiation increased with proton beam current. Efforts are continuing to determine the effect of proton beam characteristics and mixed-particle flux on the corrosion rate of materials located directly in the proton beam. This paper focuses on the real-time corrosion measurements of materials located in the supply stream and return stream of the water flow line to evaluate effects of long-lived radiolysis products and water chemistry on the corrosion rates of materials. In general, the corrosion rates for the out-of-beam probes were low and were affected mainly by water conductivity. The data indicate a water conductivity threshold e xists
6. Thermal vacuum accelerated life test of the unit qualification model msds 3 marconi low speed mechanism
Energy Technology Data Exchange (ETDEWEB)
Appleton, D.A.
1975-01-01
The thermal vacuum accelerated life test of a solar array unit qualification mechanism (MSDS 3) is described. Most of the test was conducted with the shaft of the mechanism rotating at one revolution per hour, which is 24 times normal speed. The test was conducted at two different temperature conditions, and included additional thermal cycling of the shaft temperature to simulate conditions of earth eclipse of a satellite in a geostationary orbit. Throughout the test there was no change in the motor power required to drive the shaft, and the electrical noise levels on the slip rings showed no significant deterioration.
7. Travinfo Field Operational Test Evaluation Plan
OpenAIRE
Hall, Randolph; Yim, Y. B.; Khattak, Asad; Miller, Mark; Weissenberger, Stein
1995-01-01
TravInfo is a Field Operational Test (FOT) sponsored by the U.S. Federal Highway Administration. The goal of the project is to implement a centralized traveler information center to collect, integrate, and broadly disseminate timely and accurate traveler information in the San Francisco Bay Area. This evaluation plan describes the scope, methods, and procedures to measure the effectiveness of the project. The TravInfo evaluation will contain four evaluation elements: institutional, technology...
8. Data Testing CIELO Evaluations with ICSBEP Benchmarks
International Nuclear Information System (INIS)
We review criticality data testing performed at Los Alamos with a combination of ENDF/B-VII.1 + potential CIELO nuclear data evaluations. The goal of CIELO is to develop updated, best available evaluated nuclear data files for 1H, 16O, 56Fe, 235,238U and 239Pu. because the major international evaluated nuclear data libraries don't agree on the internal cross section details of these most important nuclides.
9. Tests, testing, and tested - we need to critically evaluate the meaning of tests in psychiatry.
Science.gov (United States)
Berger, Douglas M
2013-04-01
This article describes clinical pitfalls in our concepts of what it means for an illness, diagnosis, or evaluation and treatment methods to say that they have been "tested". This articles begins with the problems encountered in newborn testing for Krabbe Disease of the nervous system in New York State over the last few years as an example of a test that did not live up to its promise to help the society. Next, the article gives 3 examples of testing in psychiatry, 1. Psychological testing to make treatment decisions in children with depression, 2. Patient's and parents who have been told, or believe, that they have Asperger's disorder, and 3. The conclusions made about the efficacy of cognitive behavioral therapy based on clinical studies. The article's conclusion sums up these examples as reasons why we need to have a more practical and scientific approach to our understanding and implementation of tests used in our field. PMID:23825862
10. Testing and evaluation of light ablation decontamination
International Nuclear Information System (INIS)
This report details the testing and evaluation of light ablation decontamination. It details WINCO contracted research and application of light ablation efforts by Ames Laboratory. Tests were conducted with SIMCON (simulated contamination) coupons and REALCON (actual radioactive metal coupons) under controlled conditions to compare cleaning effectiveness, speed and application to plant process type equipment
11. Overview of the Beam diagnostics in the Medaustron Accelerator:Design choices and test Beam commissioning
CERN Document Server
Osmic, F; Gyorgy, A; Kerschbaum, A; Repovz, M; Schwarz, S; Neustadt, W; Burtin, G
2012-01-01
The MedAustron centre is a synchrotron based accelerator complex for cancer treatment and clinical and non-clinical research with protons and light ions, currently under construction in Wiener Neustadt, Austria. The accelerator complex is based on the CERN-PIMMS study [1] and its technical implementation by the Italian CNAO foundation in Pavia [2]. The MedAustron beam diagnostics system is based on sixteen different monitor types (153 devices in total) and will allow measuring all relevant beam parameters from the source to the irradiation rooms. The monitors will have to cope with large intensities and energy ranges. Currently, one ion source, the low energy beam transfer line and the RFQ are being commissioned in the Injector Test Stand (ITS) at CERN. This paper gives an overview of all beam monitors foreseen for the MedAustron accelerator, elaborates some of the design choices and reports the first beam commissioning results from the ITS.
12. Design, Construction and Test Arrangement of a Fast-Cycling HTS Accelerator Magnet
CERN Document Server
Piekarz, H; Hays, Steven; Shiltsev, Vladimir
2014-01-01
Design, fabrication and assembly of a novel fast-cycling accelerator magnet is presented. A short-sample magnet is powered with a single-turn HTS cable capable to carry 80 kA current at 20 K and generate 1.75 T field in a 40 mm magnet gap. The applied conventional leads and the power supply, however, allow only for a sin-wave 24 kA, 20 Hz current limiting test magnet to a B-field of 0.5 T and to a maximum cycling rate of 20 T/s. The critical aspects of the cable construction and the splicing connection to the power leads are described. Tentative power losses of the proposed HTS accelerator magnet in a possible application for proton and muon accelerators are presented.
13. Limited streamer chamber testing and quality evaluation in ASTRA
International Nuclear Information System (INIS)
Limited streamer chambers are extensively used for high-energy and nuclear physics experiments in accelerator and underground laboratories. The tracking system of LVD, an underground experiment to study muons and nutrino astronomy, will use roughly 15000 limited streamer chambers and 100000 external pickup strips with digital readout electronics. In the article the different aspects of chamber operation that serve to establish a testing procedure and to define acceptance criteria for selecting reliable and long-life devices, are discussed. The procedures and the results obtained from a long-term test to evaluate streamer chamber quality, based upon a sample of 2900 items, are described. The selection tests and the long-term observations have been performed in the ASTRA laboratory, established at the Laboratori Nazionali di Frascati to carry out quality control procedures for streamer chambers on a large scale and in a controlled environment
14. Setting accelerated dissolution test for PLGA microspheres containing peptide, investigation of critical parameters affecting drug release rate and mechanism.
Science.gov (United States)
Tomic, I; Vidis-Millward, A; Mueller-Zsigmondy, M; Cardot, J-M
2016-05-30
The objective of this study was development of accelerated in vitro release method for peptide loaded PLGA microspheres using flow-through apparatus and assessment of the effect of dissolution parameters (pH, temperature, medium composition) on drug release rate and mechanism. Accelerated release conditions were set as pH 2 and 45°C, in phosphate buffer saline (PBS) 0.02M. When the pH was changed from 2 to 4, diffusion controlled phases (burst and lag) were not affected, while release rate during erosion phase decreased two-fold due to slower ester bonds hydrolyses. Decreasing temperature from 45°C to 40°C, release rate showed three-fold deceleration without significant change in release mechanism. Effect of medium composition on drug release was tested in PBS 0.01M (200 mOsm/kg) and PBS 0.01M with glucose (380 mOsm/kg). Buffer concentration significantly affected drug release rate and mechanism due to the change in osmotic pressure, while ionic strength did not have any effect on peptide release. Furthermore, dialysis sac and sample-and-separate techniques were used, in order to evaluate significance of dissolution technique choice on the release process. After fitting obtained data to different mathematical models, flow-through method was confirmed as the most appropriate for accelerated in vitro dissolution testing for a given formulation. PMID:27025293
15. Biodegradable nanocomposite coatings accelerate bone healing: In vivo evaluation
OpenAIRE
2015-01-01
Background: The aim of this study was to evaluate the interaction of bioactive and biodegradable poly (lactide-co-glycolide)/bioactive glass/hydroxyapatite (PBGHA) and poly (lactide-co-glycolide)/bioactive glass (PBG) nanocomposite coatings with bone. Materials and Methods: Sol-gel derived 58S bioactive glass nanoparticles, 50/50 wt% poly (lactic acid)/poly (glycolic acid) and hydroxyapatite nanoparticles were used to prepare the coatings. The nanocomposite coatings were characterized by ...
16. Evaluation of an accelerated mineralization process for ashes - feasibility study; Evaluering av jordmaansbildande askbehandlingsprocess (EJA) - foerstudie
Energy Technology Data Exchange (ETDEWEB)
Ecke, Holger; Bjurstroem, Henrik
2005-03-01
In Japan, expenses for landfilling yield about 400 USD per ton of ash, which gives an incentive to reduce the amount of landfilled ash. At NIES (National Institute for Environmental Studies) in Tsukuba, Japan, the AMT process (Accelerated Mineralization Technology) was developed aiming at the treatment of ashes and production of soil-like material for reuse. The objective of the project EJA was to evaluate the AMT process on the basis of available information and the possibilities the process could offer with respect to the conditions present in Sweden. With support of researchers at NIES, available literature including unpublished manuscripts on the AMT process was compiled, translated and evaluated. During treatment, the ashes are washed, aged and mixed with up to 5 % by weight of biodegradable organic matter. The material is stabilized at landfill. During up to several decades, metals are demobilized through a combination of three mechanisms, viz. carbonation, clay formation, and humification. Also persistent organic pollutants (POP) are demobilized due to humification products or they are degraded anaerobically. When the treatment is completed, the reuse of the material is envisaged. Due to the long treatment period, the AMT method might not be favored by ash producers in Sweden. In the future, landfill companies could be interested in the technology, since they are experienced to handle waste at long sight. This, however, requires that the legislation does not pose any hindrance for the implementation of the method, e.g. regarding the requirement to add organic matter to the ash. Above all, it remains several years of research on the AMT process to fully understand and evaluate the underlying biological and chemical processes as well as their interaction.
17. Measuring test mass acceleration noise in space-based gravitational wave astronomy
Science.gov (United States)
Congedo, Giuseppe
2015-03-01
The basic constituent of interferometric gravitational wave detectors—the test-mass-to-test-mass interferometric link—behaves as a differential dynamometer measuring effective differential forces, comprising an integrated measure of gravity curvature, inertial effects, as well as nongravitational spurious forces. This last contribution is going to be characterized by the LISA Pathfinder mission, a technology precursor of future space-borne detectors like eLISA. Changing the perspective from displacement to acceleration can benefit the data analysis of LISA Pathfinder and future detectors. The response in differential acceleration to gravitational waves is derived for a space-based detector's interferometric link. The acceleration formalism can also be integrated into time delay interferometry by building up the unequal-arm Michelson differential acceleration combination. The differential acceleration is nominally insensitive to the system's free evolution dominating the slow displacement dynamics of low-frequency detectors. Working with acceleration also provides an effective way to subtract measured signals acting as systematics, including the actuation forces. Because of the strong similarity with the equations of motion, the optimal subtraction of systematic signals, known within some amplitude and time shift, with the focus on measuring the noise provides an effective way to solve the problem and marginalize over nuisance parameters. The F statistic, in widespread use throughout the gravitation waves community, is included in the method and suitably generalized to marginalize over linear parameters and noise at the same time. The method is applied to LPF simulator data and, thanks to its generality, can also be applied to the data reduction and analysis of future gravitational wave detectors.
18. Correlating outdoor exposure with accelerated aging tests for aluminum solar reflectors
Science.gov (United States)
Wette, Johannes; Sutter, Florian; Fernández-García, Aránzazu
2016-05-01
Guaranteeing the durability of concentrated solar power (CSP) components is crucial for the success of the technology. The reflectors of the solar field are a key component of CSP plants, requiring reliable methods for service lifetime prediction. So far, no proven correlations exist to relate accelerated aging test results in climate chambers with relevant CSP exposure sites. In this work, correlations have been derived for selected testing conditions that excite the same degradation mechanisms as for outdoor exposure. Those testing conditions have been identified by performing an extensive microscopic comparison of the appearing degradation mechanisms on reference samples that have been weathered outdoors with samples that underwent a high variety of accelerated aging experiments. The herein developed methodology is derived for aluminum reflectors and future work will study its applicability to silvered-glass mirrors.
19. The Conversion of CESR to Operate as the Test Accelerator, CesrTA, Part 1: Overview
CERN Document Server
Billing, M G
2015-01-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper outlines the motivation, design and conversion of CESR to a test accelerator, CesrTA, enhanced to study such subjects as low emittance tuning methods, electron cloud (EC) effects, intra-beam scattering, fast ion instabilities as well as general improvements to beam instrumentation. While the initial studies of CesrTA focussed on questions related to the International Linear Collider (ILC) damping ring design, CesrTA is a very flexible storage ring, capabl...
Energy Technology Data Exchange (ETDEWEB)
Czanderna, A.W.; Pern, F.J. [National Renewable Energy Lab., Golden, CO (United States)
1996-12-31
The purposes of this paper are to provide background information about encapsulants for photovoltaic (PV) modules and to evaluate estimates of the durability of different materials used in PV modules. The authors summarize the field-deployed module degradation in performance, the established degradation mechanisms of ethylene vinyl acetate (EVA) copolymer, and potential degradation mechanisms in other module components and at materials interfaces. Most of the emphasis is on estimates for the commercially used EVA formulations A9918 and 15295. These formulations have degraded in field-deployed modules to produce acetic acid and a yellow to brown color from polyenes and the module efficiencies have been reduced by 10% to 70% in 4 to 12 years. Yet, projections were made by several different research groups in the 1980s that the EVA lifetime could range from 20 to 100 years, the production of acetic acid would only be 0.006% in 20 years, and that silver metallization would survive attack from acetic acid for 300 years at 55 C. Those authors did not use appropriate variables or specimen configurations that simulate reality, and based their projections using the generalization that chemical reaction rates double for every 10 C increase in T. The authors review the inherent errors in their assumptions about the Arrhenius relation. They also show how degradation in efficiency (from current-voltage data) comparable to field experience is obtained using minimodules with a construction that simulates reality and by using appropriate variables in accelerated testing, i.e., UV, T, and RH. A test protocol is outlined that simulates reality and permits making suitable service lifetime projections.
1. A cosmic speed-trap: a gravity-independent test of cosmic acceleration using baryon acoustic oscillations
OpenAIRE
Sutherland, Will
2011-01-01
We propose a new and highly model-independent test of cosmic acceleration by comparing observations of the baryon acoustic oscillation (BAO) scale at low and intermediate redshifts: we derive a new inequality relating BAO observables at two distinct redshifts, which must be satisfied for any reasonable homogeneous non-accelerating model, but is violated by models similar to LambdaCDM, due to acceleration in the recent past. This test is fully independent of the theory of gravity (GR or otherw...
2. A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations
Science.gov (United States)
Venter, Gerhard; Sobieszczanski-Sobieski, Jaroslaw
2005-01-01
A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.
CERN Document Server
Chen, Kai; Kierstead, James; Takai, Helio; Rescia, Sergio; Hu, Xueye; Xu, Hao; Mead, Joseph; Lanni, Francesco; Minelli, Marena
2014-01-01
Electronic components used in high energy physics experiments are subjected to a radiation background composed of high energy hadrons, mesons and photons. These particles can induce permanent and transient effects that affect the normal device operation. Ionizing dose and displacement damage can cause chronic damage which disable the device permanently. Transient effects or single event effects are in general recoverable with time intervals that depend on the nature of the failure. The magnitude of these effects is technology dependent with feature size being one of the key parameters. Analog to digital converters are components that are frequently used in detector front end electronics, generally placed as close as possible to the sensing elements to maximize signal fidelity. We report on radiation effects tests conducted on 17 commercially available analog to digital converters and extensive single event effect measurements on specific twelve and fourteen bit ADCs that presented high tolerance to ionizing d...
4. Selenide isotope generator for the Galileo Mission. Axially-grooved heat pipe: accelerated life test results
International Nuclear Information System (INIS)
The results through SIG/Galileo contract close-out of accelerated life testing performed from June 1978 to June 1979 on axially-grooved, copper/water heat pipes are presented. The primary objective of the test was to determine the expected lifetime of axially-grooved copper/water heat pipes. The heat pipe failure rate, due to either a leak or a build-up of non-condensible gas, was determined. The secondary objective of the test was to determine the effects of time and temperature on the thermal performance parameters relevant to long-term (> 50,000 h) operation on a space power generator. The results showed that the gas generation rate appears to be constant with time after an initial sharp rise although there are indications that it drops to approximately zero beyond approx. 2000 h. During the life test, the following pipe-hours were accumulated: 159,000 at 1250C, 54,000 at 1650C, 48,000 at 1850C, and 8500 at 2250C. Heated hours per pipe ranged from 1000 to 7500 with an average of 4720. Applying calculated acceleration factors yields the equivalent of 930,000 pipe-h at 1250C. Including the accelerated hours on vendor tested pipes raises this number to 1,430,000 pipe-hours at 1250C. It was concluded that, for a heat pipe temperature of 1250C and a mission time of 50,000 h, the demonstrated heat pipe reliability is between 80% (based on 159,000 actual pipe-h at 1250C) and 98% (based on 1,430,000 accelerated pipe-h at 1250C). Measurements indicate some degradation of heat transfer with time, but no detectable degradation of heat transport
5. Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost
Directory of Open Access Journals (Sweden)
Heonsang Lim
2015-04-01
6. ADVANCED X-BAND TEST ACCELERATOR FOR HIGH BRIGHTNESS ELECTRON AND GAMMA RAY BEAMS
Energy Technology Data Exchange (ETDEWEB)
Marsh, R A; Anderson, S G; Barty, C P; Chu, T S; Ebbers, C A; Gibson, D J; Hartemann, F V; Adolphsen, C; Jongewaard, E N; Raubenheimer, T; Tantawi, S G; Vlieks, A E; Wang, J W
2010-05-12
In support of Compton scattering gamma-ray source efforts at LLNL, a multi-bunch test stand is being developed to investigate accelerator optimization for future upgrades. This test stand will enable work to explore the science and technology paths required to boost the current 10 Hz monoenergetic gamma-ray (MEGa-Ray) technology to an effective repetition rate exceeding 1 kHz, potentially increasing the average gamma-ray brightness by two orders of magnitude. Multiple bunches must be of exceedingly high quality to produce narrow-bandwidth gamma-rays. Modeling efforts will be presented, along with plans for a multi-bunch test stand at LLNL. The test stand will consist of a 5.5 cell X-band rf photoinjector, single accelerator section, and beam diagnostics. The photoinjector will be a high gradient standing wave structure, featuring a dual feed racetrack coupler. The accelerator will increase the electron energy so that the emittance can be measured using quadrupole scanning techniques. Multi-bunch diagnostics will be developed so that the beam quality can be measured and compared with theory. Design will be presented with modeling simulations, and layout plans.
7. Advanced X-Band Test Accelerator for High Brightness Electron and Gamma Ray Beams
Energy Technology Data Exchange (ETDEWEB)
Marsh, Roark; /LLNL, Livermore; Anderson, Scott; /LLNL, Livermore; Barty, Christopher; /LLNL, Livermore; Chu, Tak Sum; /LLNL, Livermore; Ebbers, Chris; /LLNL, Livermore; Gibson, David; /LLNL, Livermore; Hartemann, Fred; /LLNL, Livermore; Adolphsen, Chris; /SLAC; Jongewaard, Erik; /SLAC; Raubenheimer, Tor; /SLAC; Tantawi, Sami; /SLAC; Vlieks, Arnold; /SLAC; Wang, Juwen; /SLAC
2012-07-03
In support of Compton scattering gamma-ray source efforts at LLNL, a multi-bunch test stand is being developed to investigate accelerator optimization for future upgrades. This test stand will enable work to explore the science and technology paths required to boost the current 10 Hz monoenergetic gamma-ray (MEGa-Ray) technology to an effective repetition rate exceeding 1 kHz, potentially increasing the average gamma-ray brightness by two orders of magnitude. Multiple bunches must be of exceedingly high quality to produce narrow-bandwidth gamma-rays. Modeling efforts will be presented, along with plans for a multi-bunch test stand at LLNL. The test stand will consist of a 5.5 cell X-band rf photoinjector, single accelerator section, and beam diagnostics. The photoinjector will be a high gradient standing wave structure, featuring a dual feed racetrack coupler. The accelerator will increase the electron energy so that the emittance can be measured using quadrupole scanning techniques. Multi-bunch diagnostics will be developed so that the beam quality can be measured and compared with theory. Design will be presented with modeling simulations, and layout plans.
8. Accelerated corrosion test and corrosion failure distribution model of aircraft structural aluminum alloy
Institute of Scientific and Technical Information of China (English)
LIU Wen-lin; MU Zhi-tao; JIN Ping
2006-01-01
Based on corrosion damage data of 10 years for a type of aircraft aluminum alloy, the statistical analysis was conducted by Gumbel, Normal and two parameters Weibull distribution function. The results show that aluminum alloy structural member has the corrosion history of pitting corrosion-intergranular corrosion-exfoliation corrosion, and the maximum corrosion depth is in conformity to normal distribution. The accelerated corrosion test was carried out with the complied equivalent airport accelerated environment spectrum. The corrosion damage failure modes of aluminum alloy structural member indicate that the period of validity of the former protective coating is about 2.5 to 3 years, and that of the novel protective coating is about 4.0 to 4.5 years. The corrosion kinetics law of aluminum spar flange was established by fitting corrosion damage test data. The law indicates two apparent corrosion stages of high strength aluminum alloy section material: pitting corrosion and intergranular corrosion/exfoliation corrosion.The test results agree with the statistical fit result of corrosion data collected from corrosion member in service. The fractional error is 5.8% at the same calendar year. The accelerated corrosion test validates the corrosion kinetics law of aircraft aluminum alloy in service.
9. 78 FR 76410 - Request for Information on Strategies To Accelerate the Testing and Adoption of Pay for Success...
Science.gov (United States)
2013-12-17
... Strategies to Accelerate the Testing and Adoption of Pay for Success (PFS) Financing Models (78 FR 60998... Request for Information on Strategies To Accelerate the Testing and Adoption of Pay for Success (PFS... information; reopening of comment period. SUMMARY: The Department of the Treasury is reopening the...
10. Current state of X-band accelerating structure high gradient test. Be held at high energy accelerator organization on April 15, 2005
International Nuclear Information System (INIS)
XTF (X-band Test Facility, Old name is GLCTA) is the high gradient test facility for X-band acceleration. We have installed an X-band 60cm structure (KX01) in the April 2004 and have been processing it for more than 10 months. Now it is under test on long-term operation. We report here the high gradient test result to date. (author)
11. LLRF and timing system for the SCSS test accelerator at SPring-8
Science.gov (United States)
Otake, Yuji; Ohshima, Takashi; Hosoda, Naoyasu; Maesaka, Hirokazu; Fukui, Toru; Kitamura, Masanobu; Shintake, Tsumoru
2012-12-01
The 250 MeV SCSS test accelerator as an extreme-ultra violet (EUV) laser source has been built at SPring-8. The accelerator comprises a 500 kV thermionic gun, a velocity bunching system using multi-sub-harmonic bunchers (SHB) in an injector and a magnetic bunch compressor using a chicane of 4 bending magnets, a 5712 MHz main accelerator to accelerate an electron beam up to 250 MeV, and undulators to radiate the EUV laser. These bunch compression processes make short bunched electrons with a 300 A peak current and a 300 fs pulse width. The pulse width and peak current of an electron beam, which strongly affect the pulse width and intensity of the laser light, are mainly decided by the pulse compression ratio of the velocity bunching and the magnetic bunch compressing processes. The compression ratio is also determined due to an energy chirp along the beam bunch generated by an off-crest rf field at the SHB and cavities before the chicane. To constantly keep the beam pulse-width conducted by rf and timing signals, which are temporally controlled within subpicoseconds of the designed value, the low-level rf and timing system of the test accelerator has been developed. The system comprises a very low-noise and temporally stable reference signal source, in-phase and quadrature (IQ) modulators and demodulators, as well as VME type 12 bits analog-to-digital and digital-to-analog converter modules to manipulate an rf phase and amplitude by IQ functions for the cavity. We achieved that the SSB noise of the 5712 MHz reference signal source was less than -120 dBc/Hz at 1 kHz offset from the reference frequency; the phase setting and detecting resolution of the IQ-modulators and demodulators were within +/-0.5° at 5712 MHz. A master trigger VME module and a trigger delay VME module were also developed to activate the components of the test accelerator. The time jitter of the delay module was less than 0.7 ps, sufficient for our present requirement. As a result, a beam energy
12. LLRF and timing system for the SCSS test accelerator at SPring-8
International Nuclear Information System (INIS)
The 250 MeV SCSS test accelerator as an extreme-ultra violet (EUV) laser source has been built at SPring-8. The accelerator comprises a 500 kV thermionic gun, a velocity bunching system using multi-sub-harmonic bunchers (SHB) in an injector and a magnetic bunch compressor using a chicane of 4 bending magnets, a 5712 MHz main accelerator to accelerate an electron beam up to 250 MeV, and undulators to radiate the EUV laser. These bunch compression processes make short bunched electrons with a 300 A peak current and a 300 fs pulse width. The pulse width and peak current of an electron beam, which strongly affect the pulse width and intensity of the laser light, are mainly decided by the pulse compression ratio of the velocity bunching and the magnetic bunch compressing processes. The compression ratio is also determined due to an energy chirp along the beam bunch generated by an off-crest rf field at the SHB and cavities before the chicane. To constantly keep the beam pulse-width conducted by rf and timing signals, which are temporally controlled within subpicoseconds of the designed value, the low-level rf and timing system of the test accelerator has been developed. The system comprises a very low-noise and temporally stable reference signal source, in-phase and quadrature (IQ) modulators and demodulators, as well as VME type 12 bits analog-to-digital and digital-to-analog converter modules to manipulate an rf phase and amplitude by IQ functions for the cavity. We achieved that the SSB noise of the 5712 MHz reference signal source was less than −120 dBc/Hz at 1 kHz offset from the reference frequency; the phase setting and detecting resolution of the IQ-modulators and demodulators were within +/−0.5° at 5712 MHz. A master trigger VME module and a trigger delay VME module were also developed to activate the components of the test accelerator. The time jitter of the delay module was less than 0.7 ps, sufficient for our present requirement. As a result, a beam
13. Atomic oxygen ground-based accelerated tests of spacecraft materials and structures for long-term LEO missions
Science.gov (United States)
Chernik, Vladimir; Novikov, Lev; Smirnova, Tatyana; Shumov, Andrey
Spacecraft materials are degradated during long-term low earth orbit (LEO) flight. The Internation Space Station (ISS) is planed to be prolonged the term of action up to 20-25 years. To specify so long life one requires a validation of spacecraft material behaviour conservation for the period. The LEO environment includes atomic oxygen (AO) destructive incident flow. The appropriate AO fluence is proposed to be as high as 10E22-10E23 atom O/sq cm. The simulative ground-based test is evident to be acceptable if its duration is not too long usually under several hundreds of hours. In that case the rate of the test acceleration exceeds 100-200. One way to accelerate test is to increase oxygen particles energy. We test materials under oxygen plasma beam, formed by a magnetoplasmadynamic accelerator, with the oxygen particle energy of 20 -30 eV. In this way we determine an AO effective fluence by a kapton equivalent technique. The beam varies from LEO incident flow by energy, flux and rates of the oxygen dissociation / ionization/ excitation. To evaluate the test adequacy we measured and compared with LEO data erosion yields of a number of polymer materials, applied on spacecraft external surfaces. There were: polyimide (kapton), polyamide (nylon), polyethylene, polyvinyl fluoride (tedlar), polysteren, polymethyl methacrylate, epoxy, polyethylene terephthalate (mylar), graphite. Their relative erosion yields, measured and normalized by polyimide in this way, practically coincide with the data of flight experiments on the ISS. The results ground to use our plasma mode for accelerated tests of spacecraft material durability for long-term LEO flights. We tested quite a number of polymer-based materials and structures usable on ISS and another LEO spacecrafts. The effective AO fluencies ran up to 3,5 10E22 atom O/sq cm corresponding to the ISS flight duration about 20 years. We studied material behaviors like mass and thickness losses, erosion yield, surface morphology
14. Accelerated Testing of UH-60 Viscous Bearings for Degraded Grease Fault
Science.gov (United States)
Dykas, Brian; Hood, Adrian; Krantz, Timothy; Klemmer, Marko
2015-01-01
An accelerated aging investigation of critical aviation bearings lubricated with MIL-PRF- 81322 grease was conducted to derive an understanding of the mechanisms of grease degradation and loss of lubrication over time. The current study focuses on UH-60 Black Hawk viscous damper bearings supporting the tail rotor driveshaft, which were subjected to more than 5800 hours of testing in a heated environment to accelerate the deterioration of the grease. The mechanism of grease degradation is a reduction in the oil/thickener ratio rather than the expected chemical degradation of grease constituents. Over the course of testing, vibration and temperature monitoring of bearings was conducted and trends for failing bearings are presented.
15. The Use of Conditional Probability Integral Transformation Method for Testing Accelerated Failure Time Models
Directory of Open Access Journals (Sweden)
Abdalla Ahmed Abdel-Ghaly
2016-06-01
Full Text Available This paper suggests the use of the conditional probability integral transformation (CPIT method as a goodness of fit (GOF technique in the field of accelerated life testing (ALT, specifically for validating the underlying distributional assumption in accelerated failure time (AFT model. The method is based on transforming the data into independent and identically distributed (i.i.d Uniform (0, 1 random variables and then applying the modified Watson statistic to test the uniformity of the transformed random variables. This technique is used to validate each of the exponential, Weibull and lognormal distributions' assumptions in AFT model under constant stress and complete sampling. The performance of the CPIT method is investigated via a simulation study. It is concluded that this method performs well in case of exponential and lognormal distributions. Finally, a real life example is provided to illustrate the application of the proposed procedure.
16. Requirements for an evaluated nuclear data file for accelerator-based transmutation
International Nuclear Information System (INIS)
The importance of intermediate-energy nuclear data files as part of a global calculation scheme for accelerator-based transmutation of radioactive waste systems (for instance with an accelerator-driven subcritical reactor) is discussed. A proposal for three intermediate-energy data libraries for incident neutrons and protons is presented: - a data library from 0 to about 100 MeV (first priority), - a reference data library from 20 to 1500 MeV, - an activation/transmutation library from 0 to about 100 MeV. Furthermore, the proposed ENDF-6 structure of each library is given. The data needs for accelerator-based transmutation are translated in terms of the aforementioned intermediate-energy data libraries. This could be a starting point for an ''International Evaluated Nuclear Data File for Transmutation''. This library could also be of interest for other applications in science and technology. Finally, some conclusions and recommendations concerning future evaluation work are given. (orig.)
17. Real time data acquisition system for the High Current Test Facility proton accelerator
International Nuclear Information System (INIS)
A real time data acquisition system was developed to monitor and control the High Current Test Facility Proton Accelerator. It is a PDP-8/E computer system with virtual memory capability that is fully interrupt driven and operates under a real-time, multi-tasking executive. The application package includes mode selection to automatically modify programs and optimize operation under varying conditions. (U.S.)
18. Reliability Estimation based on Step-Stress Accelerated Degradation Testing by Unequal Interval Time Series Analysis
OpenAIRE
Li Wang; Zaiwen Liu; Chongchong Yu
2013-01-01
This paper proposes a reliability estimation method based on Step-Stress Accelerated Degradation Testing (SSADT) data analysis using unequal interval time series analysis. A Multi-Regression Time Varying Auto-Regressive (MRTVAR) degradation time series model is proposed. Product SSADT data are treated as unequal interval composite time series and described using MRTVAR time series model and utilized to predict long-term trend of degradation. By using the suggested method, product reliability ...
19. An experimental test of Newton's law of gravitation for small accelerations
International Nuclear Information System (INIS)
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10-10 m/s2. These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a0 ∼ 1.2.10-10 m/s2, where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
20. Evaluation of pressure transducers. Dynamic tests
International Nuclear Information System (INIS)
The evaluation of a pressure transducer consists in checking its specifications. The tests of rapidity with a shock tube are important because they allow to find out transducer response time under a pressure step and also its natural frequency and damping. These last two data define the whole dynamic work of a fast transducer as the accuracy of the amplitude versus frequency function, the phase rotation, limit of use, overload. Several tests carried out on ETCA shock tube are described
1. Evaluation of rapid diagnostic test for influenza
Directory of Open Access Journals (Sweden)
Tiziano Allice
2009-06-01
Full Text Available In high risk patients such as in eldery, newborns and immunosuppressed subjects, a timely diagnosis of influenza is required for the most appropriate antiviral strategy in order to avoid severe secondary respiratory complications and viral spreading. Influenza is preventable by vaccination and chemoprophylaxis and is treatable by specific antiviral indications. The need for a timely diagnosis has led to the introduction of numerous rapid diagnostic tests.These are mostly antigen detection test giving results within 30 minutes, a clinically relevant time-frame to complement with the use of antiviral medications or chemoprophylaxis strategy. When evaluating performances of rapid test for influenza viruses, it is important to consider the type and quality of specimen to be tested, as well as sensitivity and specificity of the assays. Nasal/nasopharyngeal swabs are the most frequently submitted specimens, but nasal/nasopharingeal aspirates and washs can improve the diagnostic sensitivity of the test. Only some rapid assays can be successful used with broncoalveolar washings. In this review,we evaluated the sensitivity, specificity, reproducibility and feasibility of the most currently licensed rapid tests for influenza virus A and B. A flow-chart for the laboratory diagnosis of influenza with rapid test in combination with confirmatory test is proposed.
2. Proficiency Testing for Evaluating Aerospace Materials Test Anomalies
Science.gov (United States)
Hirsch, D.; Motto, S.; Peyton, S.; Beeson, H.
2006-01-01
ASTM G 86 and ASTM G 74 are commonly used to evaluate materials susceptibility to ignition in liquid and gaseous oxygen systems. However, the methods have been known for their lack of repeatability. The inherent problems identified with the test logic would either not allow precise identification or the magnitude of problems related to running the tests, such as lack of consistency of systems performance, lack of adherence to procedures, etc. Excessive variability leads to increasing instances of accepting the null hypothesis erroneously, and so to the false logical deduction that problems are nonexistent when they really do exist. This paper attempts to develop and recommend an approach that could lead to increased accuracy in problem diagnostics by using the 50% reactivity point, which has been shown to be more repeatable. The initial tests conducted indicate that PTFE and Viton A (for pneumatic impact) and Buna S (for mechanical impact) would be good choices for additional testing and consideration for inter-laboratory evaluations. The approach presented could also be used to evaluate variable effects with increased confidence and tolerance optimization.
3. Data Testing CIELO Evaluations with ICSBEP Benchmarks
Energy Technology Data Exchange (ETDEWEB)
Kahler, Albert Comstock [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-03-09
We review criticality data testing performed at Los Alamos with a combination of ENDF/B-VII.1 + potential CIELO nuclear data evaluations. The goal of CIELO is to develop updated, best available evaluated nuclear data files for 1H, 16O, 56Fe, 235,238U and 239Pu. because the major international evaluated nuclear data libraries don’t agree on the internal cross section details of these most important nuclides.
4. Method for the Accelerated Testing of the Durability of a Construction Binder using the Arrhenius Approach
Directory of Open Access Journals (Sweden)
Fridrichová Marcela
2016-03-01
Full Text Available The single most reliable indicator of a material’s durability is its performance in long-term tests, which cannot always be carried out due to a limited time budget. The second option is to perform some kind of accelerated durability tests. The aim of the work described in this article was to develop a method for the accelerated durability testing of binders. It was decided that the Arrhenius equation approach and the theory of chemical reaction kinetics would be applied in this case. The degradation process has been simplified to a single quantifiable parameter, which became compressive strength. A model hydraulic binder based on fluidised bed combustion ash (FBC ash was chosen as the test subject for the development of the method. The model binder and its hydration products were tested by high-temperature X-ray diffraction analysis. The main hydration product of this binder was ettringite. Due to the thermodynamic instability of this mineral, it was possible to verify the proposed method via long term testing. In order to accelerate the chemical reactions in the binder, four combinations of two temperatures (65 and 85°C and two different relative humidities (14 and 100% were used. The upper temperature limit was chosen because of the results of the high-temperature x-ray testing of the ettringite’s decomposition. The calculation formulae for the accelerated durability tests were derived on the basis of data regarding the decrease in compressive strength under the conditions imposed by the four above-mentioned combinations. The mineralogical composition of the binder after degradation was also described. The final degradation product was gypsum under dry conditions and monosulphate under wet conditions. The validity of the method and formula was subsequently verified by means of long-term testing. A very good correspondence between the calculated and real values was achieved. The deviation of these values did not exceed 5 %. The designed
5. Method for the Accelerated Testing of the Durability of a Construction Binder using the Arrhenius Approach
Science.gov (United States)
Fridrichová, Marcela; Dvořák, Karel; Gazdič, Dominik
2016-03-01
The single most reliable indicator of a material's durability is its performance in long-term tests, which cannot always be carried out due to a limited time budget. The second option is to perform some kind of accelerated durability tests. The aim of the work described in this article was to develop a method for the accelerated durability testing of binders. It was decided that the Arrhenius equation approach and the theory of chemical reaction kinetics would be applied in this case. The degradation process has been simplified to a single quantifiable parameter, which became compressive strength. A model hydraulic binder based on fluidised bed combustion ash (FBC ash) was chosen as the test subject for the development of the method. The model binder and its hydration products were tested by high-temperature X-ray diffraction analysis. The main hydration product of this binder was ettringite. Due to the thermodynamic instability of this mineral, it was possible to verify the proposed method via long term testing. In order to accelerate the chemical reactions in the binder, four combinations of two temperatures (65 and 85°C) and two different relative humidities (14 and 100%) were used. The upper temperature limit was chosen because of the results of the high-temperature x-ray testing of the ettringite's decomposition. The calculation formulae for the accelerated durability tests were derived on the basis of data regarding the decrease in compressive strength under the conditions imposed by the four above-mentioned combinations. The mineralogical composition of the binder after degradation was also described. The final degradation product was gypsum under dry conditions and monosulphate under wet conditions. The validity of the method and formula was subsequently verified by means of long-term testing. A very good correspondence between the calculated and real values was achieved. The deviation of these values did not exceed 5 %. The designed and verified method
6. Comparison of test particle acceleration in torsional spine and fan reconnection regimes
Energy Technology Data Exchange (ETDEWEB)
Hosseinpour, M., E-mail: [email protected]; Mehdizade, M.; Mohammadi, M. A. [Plasma Physics Department, University of Tabriz, Tabriz (Iran, Islamic Republic of)
2014-10-15
Magnetic reconnection is a common phenomenon taking place in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. Torsional spine and fan reconnections are important mechanisms proposed for steady-state three-dimensional null-point reconnection. By using the magnetic and electric fields for these regimes, we numerically investigate the features of test particle acceleration in both regimes with input parameters for the solar corona. By comparison, torsional spine reconnection is found to be more efficient than torsional fan reconnection in an acceleration of a proton to a high kinetic energy. A proton can gain as high as 100 MeV of relativistic kinetic energy within only a few milliseconds. Moreover, in torsional spine reconnection, an accelerated particle can escape either along the spine axis or on the fan plane depending on its injection position. However, in torsional fan reconnection, the particle is only allowed to accelerate along the spine axis. In addition, in both regimes, the particle's trajectory and final kinetic energy depend on the injection position but adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.
7. Comparison of test particle acceleration in torsional spine and fan reconnection regimes
International Nuclear Information System (INIS)
Magnetic reconnection is a common phenomenon taking place in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. Torsional spine and fan reconnections are important mechanisms proposed for steady-state three-dimensional null-point reconnection. By using the magnetic and electric fields for these regimes, we numerically investigate the features of test particle acceleration in both regimes with input parameters for the solar corona. By comparison, torsional spine reconnection is found to be more efficient than torsional fan reconnection in an acceleration of a proton to a high kinetic energy. A proton can gain as high as 100 MeV of relativistic kinetic energy within only a few milliseconds. Moreover, in torsional spine reconnection, an accelerated particle can escape either along the spine axis or on the fan plane depending on its injection position. However, in torsional fan reconnection, the particle is only allowed to accelerate along the spine axis. In addition, in both regimes, the particle's trajectory and final kinetic energy depend on the injection position but adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory
8. Performance and Environmental Test Results of the High Voltage Hall Accelerator Engineering Development Unit
Science.gov (United States)
Kamhawi, Hani; Haag, Thomas; Huang, Wensheng; Shastry, Rohit; Pinero, Luis; Peterson, Todd; Mathers, Alex
2012-01-01
NASA Science Mission Directorate's In-Space Propulsion Technology Program is sponsoring the development of a 3.5 kW-class engineering development unit Hall thruster for implementation in NASA science and exploration missions. NASA Glenn and Aerojet are developing a high fidelity high voltage Hall accelerator that can achieve specific impulse magnitudes greater than 2,700 seconds and xenon throughput capability in excess of 300 kilograms. Performance, plume mappings, thermal characterization, and vibration tests of the high voltage Hall accelerator engineering development unit have been performed. Performance test results indicated that at 3.9 kW the thruster achieved a total thrust efficiency and specific impulse of 58%, and 2,700 sec, respectively. Thermal characterization tests indicated that the thruster component temperatures were within the prescribed material maximum operating temperature limits during full power thruster operation. Finally, thruster vibration tests indicated that the thruster survived the 3-axes qualification full-level random vibration test series. Pre and post-vibration test performance mappings indicated almost identical thruster performance. Finally, an update on the development progress of a power processing unit and a xenon feed system is provided.
9. TEST QUALITY EVALUATION FOR COMPLEX DIGITAL SYSTEMS
OpenAIRE
VLADIMIR HAHANOV; STANLEY HYDUKE; IGOR CHUGUROV
2003-01-01
A high performance Back-traced Deductive-Parallel (BDP) fault simulation method based on the superposition procedure is oriented on a using large digital designs processing. Evaluation of RT and gate level design description is proposed in this work. The data structure and program are developed for algorithms realization of proposed method and integration with automatic test pattern generation systems.
10. CMOS test and evaluation a physical perspective
CERN Document Server
Bhushan, Manjul
2015-01-01
This book extends test structure applications described in Microelectronic Test Structures for CMOS Technology (Springer 2011) to digital CMOS product chips. Intended for engineering students and professionals, this book provides a single comprehensive source for evaluating CMOS technology and product test data from a basic knowledge of the physical behavior of the constituent components. Elementary circuits that exhibit key properties of complex CMOS chips are simulated and analyzed, and an integrated view of design, test and characterization is developed. Appropriately designed circuit monitors embedded in the CMOS chip serve to correlate CMOS technology models and circuit design tools to the hardware and also aid in test debug. Impact of silicon process variability, reliability, and power and performance sensitivities to a range of product application conditions are described. Circuit simulations exemplify the methodologies presented, and problems are included at the end of the chapters.
11. Limitations of predicting in vivo biostability of multiphase polyurethane elastomers using temperature-accelerated degradation testing.
Science.gov (United States)
Padsalgikar, Ajay; Cosgriff-Hernandez, Elizabeth; Gallagher, Genevieve; Touchet, Tyler; Iacob, Ciprian; Mellin, Lisa; Norlin-Weissenrieder, Anna; Runt, James
2015-01-01
Polyurethane biostability has been the subject of intense research since the failure of polyether polyurethane pacemaker leads in the 1980s. Accelerated in vitro testing has been used to isolate degradation mechanisms and predict clinical performance of biomaterials. However, validation that in vitro methods reproduce in vivo degradation is critical to the selection of appropriate tests. High temperature has been proposed as a method to accelerate degradation. However, correlation of such data to in vivo performance is poor for polyurethanes due to the impact of temperature on microstructure. In this study, we characterize the lack of correlation between hydrolytic degradation predicted using a high temperature aging model of a polydimethylsiloxane-based polyurethane and its in vivo performance. Most notably, the predicted molecular weight and tensile property changes from the accelerated aging study did not correlate with clinical explants subjected to human biological stresses in real time through 5 years. Further, DMTA, ATR-FTIR, and SAXS experiments on samples aged for 2 weeks in PBS indicated greater phase separation in samples aged at 85°C compared to those aged at 37°C and unaged controls. These results confirm that microstructural changes occur at high temperatures that do not occur at in vivo temperatures. In addition, water absorption studies demonstrated that water saturation levels increased significantly with temperature. This study highlights that the multiphase morphology of polyurethane precludes the use of temperature accelerated biodegradation for the prediction of clinical performance and provides critical information in designing appropriate in vitro tests for this class of materials. PMID:24810790
12. An electrochemical method for accelerated testing of chloride diffusivity in concrete
Energy Technology Data Exchange (ETDEWEB)
Zhang, T.; Gjoerv, O.E. (Norwegian Inst. of Tech., Trondheim (Norway). Div. of Building Materials)
1994-01-01
In the present paper an electrochemical method for accelerated testing of chloride diffusivity in concrete is presented. The method is based on a theoretical relationship between chloride diffusivity and observed steady-state rate of chloride migration through the concrete. The concentration of the chloride source solution has a significant influence on the rate of chloride migration and, therefore, a correction factor for ionic interaction in the relationship is introduced. It is shown that the relationship can be used for calculation of chloride diffusivity under various testing conditions. Some experimental results are also presented.
13. Accelerated life tests of specimen heat pipe from Communication Technology Satellite (CTS) project
Science.gov (United States)
Tower, L. K.; Kaufman, W. B.
1977-01-01
A gas-loaded variable conductance heat pipe of stainless steel with methanol working fluid identical to one now on the CTS satellite was life tested in the laboratory at accelerated conditions for 14 200 hours, equivalent to about 70 000 hours at flight conditions. The noncondensible gas inventory increased about 20 percent over the original charge. The observed gas increase is estimated to increase operating temperature by about 2.2 C, insufficient to harm the electronic gear cooled by the heat pipes in the satellite. Tests of maximum heat input against evaporator elevation agree well with the manufacturer's predictions.
14. Liquid nitrogen tests of a Torus coil for the Jefferson Lab 12GeV accelerator upgrade
Energy Technology Data Exchange (ETDEWEB)
Fair, Ruben J. [JLAB; Ghoshal, Probir K. [JLAB; Bruhwel, Krister B. [JLAB; Kashy, David H. [JLAB; Machie, Danny [JLAB; Bachimanchi, Ramakrishna [JLAB; Taylor, William; Fischer, John W. [JLAB; Legg, Robert A. [JLAB; Powers, Jacob R. [JLAB
2015-06-01
A magnet system consisting of six superconducting trapezoidal racetrack-type coils is being built for the Jefferson Lab 12-GeV accelerator upgrade project. The magnet coils are wound with Superconducting Super Collider-36 NbTi strand Rutherford cable soldered into a copper channel. Each superconducting toroidal coil is force cooled by liquid helium, which circulates in a tube that is in good thermal contact with the inside of the coil. Thin copper sheets are soldered to the helium cooling tube and enclose the superconducting coil, providing cooling to the rest of the coil pack. As part of a rigorous risk mitigation exercise, each of the six coils is cooled with liquid nitrogen (LN2) to 80 K to validate predicted thermal stresses, verify the robustness and integrity of electrical insulation, and evaluate the efficacy of the employed conduction cooling method. This paper describes the test setup, the tests performed, and the findings.
15. Accelerated testing of solid oxide fuel cell stacks for micro combined heat and power application
Science.gov (United States)
Hagen, Anke; Høgh, Jens Valdemar Thorvald; Barfod, Rasmus
2015-12-01
State-of-the-art (SoA) solid oxide fuel cell (SOFC) stacks are tested using profiles relevant for use in micro combined heat and power (CHP) units. Such applications are characterised by dynamic load profiles. In order to shorten the needed testing time and to investigate potential acceleration of degradation, the profiles are executed faster than required for real applications. Operation with fast load cycling, both using hydrogen and methane/steam as fuels, does not accelerate degradation compared to constant operation, which demonstrates the maturity of SoA stacks and enables transferring knowledge from testing at constant conditions to dynamic operation. 7.5 times more cycles than required for 80,000 h lifetime as micro CHP are achieved on one-cell-stack level. The results also suggest that degradation mechanisms that proceed on a longer time-scale, such as creep, might have a more dominating effect for long life-times than regular short time changes of operation. In order to address lifetime testing it is suggested to build a testing program consisting of defined modules that represent different application profiles, such as one module at constant conditions, followed by modules at one set of dynamic conditions etc.
16. Power Test of the Ladder IH-RFQ Accelerator at Peking University
Institute of Scientific and Technical Information of China (English)
LU Yuan-Rong; CHEN Wei; NIE Yuan-Cun; LIU Ge; GAO Shu-Li; ZENG Hong-Jin; YAN Xue-Qing; CHEN Jia-Er
2011-01-01
A 104-MHz ladder interdigital-H radio frequency quadrupole accelerator (T-IH-RFQ) is developed for applying RFQs to heavy ion implantation and accelerator-based mass spectroscopy in recent years at the Institute of Heavy Ion Physics,Peking University.It could accelerate ions with a mass-to-charge ratio of less than 14,from 2.9 ke V/u to 35.7keV/u within a length of 1.1 m.The T-IH-RFQ cavity operating at H21(0) mode was constructed successfully.Based on a well designed rf power feeding system,the cavity was cold measured and tested with high rf power.In the case of cold measurement,the rf properties were obtained using a vector network analyzer with the help of a perturbation capacitor. During a high power test,the inter-electrode voltage was derived from the energy spectrum of x-rays measured by a high purity Ge detector.The results show that the specific shunt impedance of the T-IH-RFQ cavity reaches 178kΩm,which could meet the requirements of beam dynamics design.
17. Seismic-fragility tests of new and accelerated-aged Class 1E battery cells
International Nuclear Information System (INIS)
The seismic-fragility response of naturally-aged nuclear station safety-related batteries is of interest for two reasons: (1) to determine actual failure modes and thresholds and (2) to determine the validity of using the electrical capacity of individual cells as an indicator of the potential survivability of a battery given a seismic event. Prior reports in this series discussed the seismic-fragility tests and results for three specific naturally-aged cell types: 12-year old NCX-2250, 10-year old LCU-13, and 10-year old FHC-19. This report focuses on the complementary approach, namely, the seismic-fragility response of accelerated-aged batteries. Of particular interest is the degree to which such approaches accurately reproduce the actual failure modes and thresholds. In these tests the significant aging effects observed, in terms of seismic survivability, were: embrittlement of cell cases, positive bus material and positive plate grids; and excessive sulphation of positive plate active material causing hardening and expansion of positive plates. The IEEE Standard 535 accelerated aging method successfully reproduced seismically significant aging effects in new cells but accelerated grid embrittlement an estimated five years beyond the conditional age of other components
18. Development of a quantitative accelerated sulphate attack test for mine backfill
Science.gov (United States)
Shnorhokian, Shahe
Mining operations produce large amounts of tailings that are either disposed of in surface impoundments or used in the production of backfill to be placed underground. Their mineralogy is determined by the local geology, and it is not uncommon to come across tailings with a relatively high sulphide mineral content, including pyrite and pyrrhotite. Sulphides oxidize in the presence of oxygen and water to produce sulphate and acidity. In the concrete industry, sulphate is known to produce detrimental effects by reacting with the cement paste to produce the minerals ettringite and gypsum. Because mine backfill uses tailings and binders---including cement---it is therefore prone to sulphate attack where the required conditions are met. Currently, laboratory tests on mine backfill mostly measure mechanical properties such as strength parameters, and the study of the chemical aspects is restricted to the impact of tailings on the environment. The potential of sulphate attack in mine backfill has not been studied at length, and no tests are conducted on binders used in backfill for their resistance to attack. Current ASTM guidelines for sulphate attack tests have been deemed inadequate by several authors due to their measurement of only expansion as an indicator of attack. Furthermore, the tests take too long to perform or are restricted to cement mortars only, and not to mixed binders that include pozzolans. Based on these, an accelerated test for sulphate attack was developed in this work through modifying and compiling procedures that had been suggested by different authors. Small cubes of two different binders were fully immersed in daily-monitored sodium sulphate and sulphuric acid solutions for a total of 28 days, after 7 days of accelerated curing at 50°C. In addition, four binders were partially immersed in the same solutions for 8 days for an accelerated attack process. The two procedures were conducted in tandem with leach tests using a mixed solution of
19. Evaluation of 14C abundance in soil respiration using accelerator mass spectrometry
International Nuclear Information System (INIS)
To clarify the behavior of 14C in terrestrial ecosystems, 14C abundance in soil respiration was evaluated in an urban forest with a new method involving a closed chamber technique and 14C measurement by accelerator mass spectrometry (AMS). Soil respiration had a higher Δ14C than the contemporary atmosphere. This indicates that a significant portion of soil respiration is derived from the decomposition of soil organic matter enriched in 14C by atmospheric nuclear weapons tests, with a notable time lag between atmospheric 14C addition and re-emission from soil. On the other hand, δ14C in soil respiration demonstrated that 14C abundance ratio itself in soil-respired CO2 is not always high compared with that in atmospheric CO2 because of the isotope fractionation during plant photosynthesis and microbial decomposition of soil organic matter. The Δ14C in soil respiration was slightly lower in August than in March, suggesting a relatively high contribution of plant root respiration and decomposition of newly accumulated and/or 14C-depleted soil organic matter to the total soil respiration in August
20. WindoWorks: A flexible program for computerized testing of accelerator control system electronic circuit boards
International Nuclear Information System (INIS)
Since most accelerator control system circuit boards reside in a commercial bus architecture, such as CAMAC or VMEbus, a computerized test station is needed for exercising the boards. This test station is needed for the development of newly designed prototypes, for commissioning newly manufactured boards, for diagnosing boards which have failed in service, and for long term testing of boards with intermittent failure problems. WindoWorks was created to address these needs. It is a flexible program which runs on a PC compatible computer and uses a PC to bus crate interface. WindoWorks was designed to give the user a flexible way to test circuit boards. Each test is incapsulated into a window. By bringing up several different windows the user can run several different tests simultaneously. The windows are sizable, and moveable. They have data entry boxes so that the test can be customized to the users preference. The windows can be used in conjunction with each other in order to create supertests. There are several windows which are generic. They can be used to test basic functions on any VME (or CAMAC) board. There are other windows which have been created to test specific boards. New windows for testing specific boards can be easily created by a Pascal programmer using the WindoWorks framework
1. Generation of laser pulse trains for tests of multi-pulse laser wakefield acceleration
Science.gov (United States)
Shalloo, R. J.; Corner, L.; Arran, C.; Cowley, J.; Cheung, G.; Thornton, C.; Walczak, R.; Hooker, S. M.
2016-09-01
In multi-pulse laser wakefield acceleration (MP-LWFA) a plasma wave is driven by a train of low-energy laser pulses separated by the plasma period, an approach which offers a route to driving plasma accelerators with high efficiency and at high pulse repetition rates using emerging technologies such as fibre and thin-disk lasers. Whilst these laser technologies are in development, proof-of-principle tests of MP-LWFA require a pulse train to be generated from a single, high-energy ultrafast pulse. Here we demonstrate the generation of trains of up to 7 pulses with pulse separations in the range 150-170 fs from single 40 fs pulses produced by a Ti:sapphire laser.
2. Electron lenses and cooling for the Fermilab Integrable Optics Test Accelerator
CERN Document Server
Stancari, G; Lebedev, V; Nagaitsev, S; Prebys, E; Valishev, A
2015-01-01
Recently, the study of integrable Hamiltonian systems has led to nonlinear accelerator lattices with one or two transverse invariants and wide stable tune spreads. These lattices may drastically improve the performance of high-intensity machines, providing Landau damping to protect the beam from instabilities, while preserving dynamic aperture. The Integrable Optics Test Accelerator (IOTA) is being built at Fermilab to study these concepts with 150-MeV pencil electron beams (single-particle dynamics) and 2.5-MeV protons (dynamics with self fields). One way to obtain a nonlinear integrable lattice is by using the fields generated by a magnetically confined electron beam (electron lens) overlapping with the circulating beam. The required parameters are similar to the ones of existing devices. In addition, the electron lens will be used in cooling mode to control the brightness of the proton beam and to measure transverse profiles through recombination. More generally, it is of great interest to investigate whet...
3. Methodology to improve design of accelerated life tests in civil engineering projects.
Directory of Open Access Journals (Sweden)
Jing Lin
Full Text Available For reliability testing an Energy Expansion Tree (EET and a companion Energy Function Model (EFM are proposed and described in this paper. Different from conventional approaches, the EET provides a more comprehensive and objective way to systematically identify external energy factors affecting reliability. The EFM introduces energy loss into a traditional Function Model to identify internal energy sources affecting reliability. The combination creates a sound way to enumerate the energies to which a system may be exposed during its lifetime. We input these energies into planning an accelerated life test, a Multi Environment Over Stress Test. The test objective is to discover weak links and interactions among the system and the energies to which it is exposed, and design them out. As an example, the methods are applied to the pipe in subsea pipeline. However, they can be widely used in other civil engineering industries as well. The proposed method is compared with current methods.
4. High-Gradient test results from a CLIC prototype accelerating structure : TD26CC
CERN Document Server
Degiovanni, A; Farabolini, W; Grudiev, A; Kovermann, J; Montessinos, E; Riddone, G; Syratchev, I; Wegner, R; Wuensch, W; Solodko, A; Woolley, B
2014-01-01
The CLIC study has progressively tested prototype accelerating structures which incorporate an ever increasing number of features which are needed for a final version ready to be installed in a linear collider. The most recent high power test made in the CERN X-band test stand, Xbox-1, is of a CERN-built prototype which includes damping features but also compact input and output power couplers, which maximize the overall length to active gradient ratio of the structure. The structure’s high-gradient performance, 105 MV/m at 250 ns pulse length and low breakdown rate, matches previously tested structures validating both CERN fabrication and the compact coupler design.
5. Evaluation of influence of an earthquake acceleration upon boiling two phase flow behavior
International Nuclear Information System (INIS)
The analysis of boiling two-phase flow in a simulated fuel channel under the condition that earthquake acceleration is imposed on was performed in order to evaluate the influence of earthquake acceleration upon the boiling two-phase flow behavior in fuel bundles of nuclear reactors. From a series of numerical simulations, the following summaries were derived: when the earthquake acceleration is given to the horizontal direction, time change of the predicted void fraction aries a time lag depending on an oscillation period of earthquake and the time lag is maintained; and, the fluctuation characteristic of the predicted void fraction receives strongly the influence of lift force and turbulent force to the oscillation period of earthquake. (author)
6. Testing Einstein's time dilation under acceleration using Mössbauer spectroscopy
International Nuclear Information System (INIS)
The Einstein time dilation formula was tested in several experiments. Many trials have been conducted to measure the transverse second-order Doppler shift by Mössbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or whether the present centripetal acceleration contributes to the time dilation. We show here that because the experiment requires γ-ray emission and detection slits of finite size, the absorption line is broadened, by geometric longitudinal first-order Doppler shifts immensely. Moreover, the absorption line is non-Lorentzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results in all previous experiments which did not observe the full absorption line itself were wrong and the conclusions doubtful. The only proper experiment was done by Kündig (1963 Phys. Rev. 129 2371), who observed the broadening, but associated it with random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second-order Doppler shift by Mössbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis. (paper)
7. Evaluation of microwave oven heating for prediction of drug-excipient compatibilities and accelerated stability studies
DEFF Research Database (Denmark)
Schou-Pedersen, Anne Marie V; Østergaard, Jesper; Cornett, Claus;
2015-01-01
, if a microwave oven is applicable for accelerated drug stability testing. Chemical interactions were investigated in three selected model formulations of drug and excipients regarding the formation of ester and amide reaction products. The accelerated stability studies performed in the microwave oven using......, and sorbic acid. The model formulations were representative for oral solutions (co-solvents), parenteral solutions (buffer species) and solid dosage forms (organic acids applicable for solubility enhancement). The DoE studies showed overall that the same impurities were generated by microwave oven heating...... leading to temperatures between 150°C and 180°C as compared to accelerated stability studies performed at 40°C and 80°C using a conventional oven. Ranking of the reactivity of the excipients could be made in the DoE studies performed at 150-180°C, which was representative for the ranking obtained after...
8. Evaluation of the alignment for long linear accelerators using a level
International Nuclear Information System (INIS)
We have studied to adopt a level, which is a gravity referenced precise inclinometer, for evaluating alignment of large linear accelerators, which is several hundred meters or larger. It has advantages for evaluating large objects because it is hardly affected by shape references, which becomes difficult to be defined enough accurate as the objects becomes large. We had already evaluated the vertical aligning straightness of the reference plates for the 70-m-long part of the KEK injector linear accelerator (KEK linac) with the standard deviations of less than 49 μm by using a level on a straight bar. The results are fairly reliable having good agreement within sub-mm range with those by the other methods; however, the evaluation distances were limited by obstacles which block the measurement path. Here, we devised new method which adopts two offset bars for avoiding the obstacles. Their one ends are placed on the measurement points with their axis directed perpendicular to the measurement path. One can avoid the obstacles by measuring the slope angles between the far ends of each offset bars instead of measuring directly those between the measurement points. Error arises from the offset bars can be eliminated by reversal measurement, which considers slope angles of the offset bars. As a result, straightness for the 206-m-long part of the linac, which corresponds to the three successive accelerator sectors of the linac, could be evaluated with our new method. The reproducibility expressed by the standard deviation of the slope angles for the arbitrarily sampled measurement point was 15 μrad, which is comparable with the average of our former measurements of 10 μrad. Moreover, the result agrees with those by the alignment telescope and our laser-based alignment system partially within sub-mm range. They indicate that our new method can be applicable for evaluating alignment of large accelerators in spite of its complexity caused by the offset bars. (author)
9. 78 FR 60998 - Strategies To Accelerate the Testing and Adoption of Pay for Success (PFS) Financing Models
Science.gov (United States)
2013-10-02
... Strategies To Accelerate the Testing and Adoption of Pay for Success (PFS) Financing Models AGENCY: Office of... publicly available on the Internet. FOR FURTHER INFORMATION CONTACT: Cara Camacho by email: cara.camacho... achievement of program outcomes by accelerating adoption of PFS to improve program outcomes. What is...
10. A modified PMMA cement (Sub-cement) for accelerated fatigue testing of cemented implant constructs using cadaveric bone.
Science.gov (United States)
Race, Amos; Miller, Mark A; Mann, Kenneth A
2008-10-20
Pre-clinical screening of cemented implant systems could be improved by modeling the longer-term response of the implant/cement/bone construct to cyclic loading. We formulated bone cement with degraded fatigue fracture properties (Sub-cement) such that long-term fatigue could be simulated in short-term cadaver tests. Sub-cement was made by adding a chain-transfer agent to standard polymethylmethacrylate (PMMA) cement. This reduced the molecular weight of the inter-bead matrix without changing reaction-rate or handling characteristics. Static mechanical properties were approximately equivalent to normal cement. Over a physiologically reasonable range of stress-intensity factor, fatigue crack propagation rates for Sub-cement were higher by a factor of 25+/-19. When tested in a simplified 2 1/2-D physical model of a stem-cement-bone system, crack growth from the stem was accelerated by a factor of 100. Sub-cement accelerated both crack initiation and growth rate. Sub-cement is now being evaluated in full stem/cement/femur models. PMID:18774136
11. The Performance of Multileaf Collimators Evaluated by the Stripe Test
International Nuclear Information System (INIS)
The performance of 3 multileaf collimator (MLC) systems (Varian Medical Systems, Elekta, and Siemens Medical Solutions) mounted on 7 different radiotherapy linear accelerators was investigated by a stripe test. The stripe test consisted of 8 adjacent multileaf segments of 2.5 x 40 cm2, enclosed by all leaf pairs. With 6-MV photons, the segments were used to irradiate Agfa CR films. The optical density profile of the irradiated film in the travel direction of the MLC was used to estimate the short- and long-term leaf positioning reproducibility. The short-term reproducibility was found by analyzing 6 consecutive stripe tests. The long-term reproducibility was obtained by performing 3 to 5 stripe tests over 2 months. The short-term reproducibility was mainly within 0.3 mm for all systems. For the long-term reproducibility, the Varian and Elekta MLCs were within 0.4 to 0.5 mm, while the Siemens MLC showed a wider distribution, with values up to 1 mm for some leaf pairs. The inferior long-term reproducibility of the Siemens MLCs was mainly due to a decrease of the segment size with time. In conclusion, the stripe test is a useful method for evaluating MLC performance. Furthermore, the long-term reproducibility varied among the MLC systems investigated.
12. The performance of multileaf collimators evaluated by the stripe test.
Science.gov (United States)
Sastre-Padro, Maria; Lervåg, Christoffer; Eilertsen, Karsten; Malinen, Eirik
2009-01-01
The performance of 3 multileaf collimator (MLC) systems (Varian Medical Systems, Elekta, and Siemens Medical Solutions) mounted on 7 different radiotherapy linear accelerators was investigated by a stripe test. The stripe test consisted of 8 adjacent multileaf segments of 2.5 x 40 cm(2), enclosed by all leaf pairs. With 6-MV photons, the segments were used to irradiate Agfa CR films. The optical density profile of the irradiated film in the travel direction of the MLC was used to estimate the short- and long-term leaf positioning reproducibility. The short-term reproducibility was found by analyzing 6 consecutive stripe tests. The long-term reproducibility was obtained by performing 3 to 5 stripe tests over 2 months. The short-term reproducibility was mainly within 0.3 mm for all systems. For the long-term reproducibility, the Varian and Elekta MLCs were within 0.4 to 0.5 mm, while the Siemens MLC showed a wider distribution, with values up to 1 mm for some leaf pairs. The inferior long-term reproducibility of the Siemens MLCs was mainly due to a decrease of the segment size with time. In conclusion, the stripe test is a useful method for evaluating MLC performance. Furthermore, the long-term reproducibility varied among the MLC systems investigated. PMID:19647629
13. Experimental high gradient testing of a 17.1 GHz photonic band-gap accelerator structure
Science.gov (United States)
Munroe, Brian J.; Zhang, JieXi; Xu, Haoran; Shapiro, Michael A.; Temkin, Richard J.
2016-03-01
We report the design, fabrication, and high gradient testing of a 17.1 GHz photonic band-gap (PBG) accelerator structure. Photonic band-gap (PBG) structures are promising candidates for electron accelerators capable of high-gradient operation because they have the inherent damping of high order modes required to avoid beam breakup instabilities. The 17.1 GHz PBG structure tested was a single cell structure composed of a triangular array of round copper rods of radius 1.45 mm spaced by 8.05 mm. The test assembly consisted of the test PBG cell located between conventional (pillbox) input and output cells, with input power of up to 4 MW from a klystron supplied via a TM01 mode launcher. Breakdown at high gradient was observed by diagnostics including reflected power, downstream and upstream current monitors and visible light emission. The testing procedure was first benchmarked with a conventional disc-loaded waveguide structure, which reached a gradient of 87 MV /m at a breakdown probability of 1.19 ×10-1 per pulse per meter. The PBG structure was tested with 100 ns pulses at gradient levels of less than 90 MV /m in order to limit the surface temperature rise to 120 K. The PBG structure reached up to 89 MV /m at a breakdown probability of 1.09 ×10-1 per pulse per meter. These test results show that a PBG structure can simultaneously operate at high gradients and low breakdown probability, while also providing wakefield damping.
14. Extensive multiple test centre evaluation of the VecTest malaria antigen panel assay.
Science.gov (United States)
Ryan, J R; Davé, K; Collins, K M; Hochberg, L; Sattabongkot, Jetsumon; Coleman, R E; Dunton, R F; Bangs, M J; Mbogo, C M; Cooper, R D; Schoeler, G B; Rubio-Palis, Y; Magris, M; Romer, L I; Padilla, N; Quakyi, I A; Bigoga, J; Leke, R G; Akinpelu, O; Evans, B; Walsey, M; Patterson, P; Wirtz, R A; Chan, A S T
2002-09-01
To determine which species and populations of Anopheles transmit malaria in any given situation, immunological assays for malaria sporozoite antigen can replace traditional microscopical examination of freshly dissected Anopheles. We developed a wicking assay for use with mosquitoes that identifies the presence or absence of specific peptide epitopes of circumsporozoite (CS) protein of Plasmodium falciparum and two strains of Plasmodium vivax (variants 210 and 247). The resulting assay (VecTest Malaria) is a rapid, one-step procedure using a 'dipstick' test strip capable of detecting and distinguishing between P. falciparum and P. vivax infections in mosquitoes. The objective of the present study was to test the efficacy, sensitivity, stability and field-user acceptability of this wicking dipstick assay. In collaboration with 16 test centres world-wide, we evaluated more than 40 000 units of this assay, comparing it to the standard CS ELISA. The 'VecTest Malaria' was found to show 92% sensitivity and 98.1% specificity, with 97.8% accuracy overall. In accelerated storage tests, the dipsticks remained stable for > 15 weeks in dry conditions up to 45 degrees C and in humid conditions up to 37 degrees C. Evidently, this quick and easy dipstick test performs at an acceptable level of reliability and offers practical advantages for field workers needing to make rapid surveys of malaria vectors. PMID:12243234
15. Development of an accelerated pavement test reproducing the effect of natural ageing on skid resistance
OpenAIRE
Kane, M.; D. Zhao; Chailleux, E.; Delarrard, F.; Do, M. T.
2013-01-01
This study deals with the development of a new test method simulating the effect of ageing on skid resistance. This test is applied to bituminous mixes in this study, but can also be applied to concrete. This test relies on two machines, the Wehner–Schulze machine, to measure the friction, and the Weatherometer sunset machine, to simulate weather effects (rain, wind, sunlight, etc.). The relevance of this test is evaluated from comparisons between changes in friction and a chemical func...
16. Beam Profile Measurement of 300 kV Ion Source Test Stand for 1 MV Electrostatic Accelerator
Energy Technology Data Exchange (ETDEWEB)
Park, Sae-Hoon; Kim, Yu-Seok [Dongguk University, Gyeonju (Korea, Republic of); Kim, Dae-Il; Kwon, Hyeok-Jung; Cho, Yong-Sub [Korea Multipurpose Accelerator Complex, Gyeongju (Korea, Republic of)
2015-10-15
In this paper, RF ion source, test stand of the ion source and its test results are presented. Beam profile was measured at the downstream from the accelerating tube and at the beam dump by using BPM and wire scanner. The RF ion source of the test stand is verified by measuring the total beam current with a faraday cup in the chamber. The KOMAC (KOrea Multi-purpose Accelerator Complex) has been developing a 300 kV ion source test stand for a 1 MV electrostatic accelerator. An ion source and accelerating tube will be installed in a high pressure vessel. The ion source in a high pressure vessel requires high reliability. To confirm the stable operation of the ion source, a test stand was proposed and developed. The ion source will be tested at the test stand to verify its long-term operation conditions. The test stand consists of a 300 kV high voltage terminal, a battery for the ion source power, a 60 Hz inverter, a 200 MHz RF power, a 5 kV extraction power supply, a 300 kV accelerating tube, and a vacuum system. The beam profile monitor was installed at the downstream from the accelerating tube. Wire scanner and faraday-cup was installed at the end of the chamber.
17. An accelerated step test to assess dancer pre-season aerobic fitness.
Science.gov (United States)
Bronner, Shaw; Rakov, Sara
2014-03-01
As the technical performance demands of dance increase, professional companies and pre-professional schools are implementing pre-season screenings that require an efficient, cost effective way to measure dancer aerobic fitness. The aim of this study was to assess an accelerated 3-minute step test (112 beats·min(-1)) by comparing it to the well-studied YMCA step test (96 beats·min(-1)) and a benchmark standard, an incremental treadmill test, using heart rate (HR) and oxygen consumption (VO2) as variables. Twenty-six professional and pre- professional dancers (age 20 ± 2.02 years) were fitted with a telemetric gas analysis system and HR monitor. They were tested in the following order: 96 step, 112 step, and treadmill test, with rest to return to baseline heart rate between each test. The step and treadmill tests were compared using Intra-class Correlation Coefficients [ICC (3, k)] calculated with analysis of variance (p dance populations, though further testing in larger groups of dancers representing a diverse range of genres and training levels is needed. PMID:24568799
18. Test results of a Nb3Al/Nb3Sn subscale magnet for accelerator application
International Nuclear Information System (INIS)
The High Energy Accelerator Research Organization (KEK) has been developing a Nb3Al and Nb3Sn subscale magnet to establish the technology for a high-field accelerator magnet. The development goals are a feasibility demonstration for a Nb3Al cable and the technology acquisition of magnet fabrication with Nb3Al superconductors. KEK developed two double-pancake racetrack coils with Rutherford-type cables composed of 28 Nb3Al wires processed by rapid heating, quenching, and transformation in collaboration with the National Institute for Materials Science and the Fermi National Accelerator Laboratory. The magnet was fabricated to efficiently generate a high magnetic field in a minimum-gap common-coil configuration with two Nb3Al coils sandwiched between two Nb3Sn coils produced by the Lawrence Berkeley National Laboratory. A shell-based structure and a 'bladder and key' technique have been used for adjusting coil prestress during both the magnet assembly and the cool down. In the first excitation test of the magnet at 4.5 K performed in June 2014, the highest quench current of the Nb3Sn coil, i.e., 9667 A, was reached at 40 A/s corresponding to 9.0 T in the Nb3Sn coil and 8.2 T in the Nb3Al coil. The quench characteristics of the magnet were studied
19. The Conversion of CESR to Operate as the Test Accelerator, CesrTA, Part 4: Superconducting Wiggler Diagnostics
CERN Document Server
Billing, M G; Liu, X; Li, Y; Sabol, D; Smith, E N; Strohman, C R; Palmer, M A; Munson, D V
2016-01-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it appropriate for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper, the last in a series of four, describes the vacuum system modifications of the superconducting wigglers to accommodate the diagnostic instrumentation for the study of electron cloud (EC) behavior within wigglers. Earlier papers provided an overview of the accelerator physics program, the general modifications of CESR, the modifications of the vacuum system necessary for the conversion of CESR to the test accelerator, CesrTA, enhanced to study such ...
20. Evaluation of corrosion damage of aluminum alloy using acoustic emission testing
Institute of Scientific and Technical Information of China (English)
GENG Rongsheng; FU Gangqiang
2004-01-01
Current studies are aiming at monitoring corrosion damage of aircraft main structures by using acoustic emission (AE) technique and at supplying useful data for determining calendar life of the aircraft. The characteristics of AE signals produced during accelerating corrosion process are described, and methods for evaluating corrosion damages and determining remaining life of main structures of aircraft using AE testing are outlined. Experimental results have shown that AE technique can detect corrosion damage of aluminum alloy much earlier than conventional non-destructive testing means, such as ultrasonic testing and eddy current testing. Relationship between corrosion damage and AE parameters was obtained through investigating corrosion damage extent and changes of AE signals during accelerating corrosion test, and showing that AE technique can be used to detect early corrosion, investigating corrosion developing trend, and in monitoring and evaluating corrosion damages.
1. Electrical Testing of Cement-Based Materials: Role of Testing Techniques, Sample Conditioning, and Accelerated Curing
OpenAIRE
Spragg, Robert; Bu, Yiwen; Snyder, Kenneth; Bentz, Dale; Weiss, Jason
2013-01-01
These projects examined the potential for using electrical testing on concrete as a potential surrogate for obtaining information on ion and fluid transport. Electrical measurements are particularly attractive for use in quality control as they are easy to perform, are performed rapidly, and can be directly related to fluid transport. This work describes how electrical resistance measurements should be corrected for geometry to obtain a geometry independent resistivity or conductivity. Furthe...
2. Simulation and steering in the intertank matching section of the ground test accelerator
International Nuclear Information System (INIS)
The Intertank Matching Section (IMS) of the Ground Test Accelerator (GTA) is a short (36 cm) beamline designed to match the Radio Frequency Quadrupole (RFQ) exit beam into the first Drift Tube LINAC (DTL) tank. The IMS contains two steering quadrupoles (SMQs) and four variable-field focussing quads (VFQs). The SMQs are fixed strength permanent magnet quadrupoles on mechanical actuators capable of transverse movement for the purpose of steering the beam. The upstream and downstream steering quadrupoles are labelled SMQ1 and SMQ4 respectively. Also contained in the IMS are two RF cavities for longitudinal matching
3. Using a Tandem Pelletron accelerator to produce a thermal neutron beam for detector testing purposes.
Science.gov (United States)
Irazola, L; Praena, J; Fernández, B; Macías, M; Bedogni, R; Terrón, J A; Sánchez-Nieto, B; Arias de Saavedra, F; Porras, I; Sánchez-Doblado, F
2016-01-01
Active thermal neutron detectors are used in a wide range of measuring devices in medicine, industry and research. For many applications, the long-term stability of these devices is crucial, so that very well controlled neutron fields are needed to perform calibrations and repeatability tests. A way to achieve such reference neutron fields, relying on a 3 MV Tandem Pelletron accelerator available at the CNA (Seville, Spain), is reported here. This paper shows thermal neutron field production and reproducibility characteristics over few days. PMID:26595777
4. Instrumentation and control system for the AT-2 accelerator test stand
International Nuclear Information System (INIS)
A data-driven subroutine package, written for our accelerator test stand (ATS), is described. This flexible package permits the rapid writing and modifying of data acquisition, control, and analysis programs for the many diverse experiments performed on the ATS. These structurally simple and easy to maintain routines help to control administratively the integrity of the ATS through the use of the database. Our operating experience indicates that the original design goals have been met. We describe the subroutines, database, and our experiences with this system
5. Design, fabrication and testing of a large cylindrical vacuum vessel for proton linear accelerator
International Nuclear Information System (INIS)
The paper deals with engineering design, fabrication, copper plating and vacuum design and leak testing of the first prototype segment of Alveraz type drift tube Proton Linear Accelerator (DTL) being developed at CAT. The prototype drift tube linac segment is a long horizontal cylindrical vacuum vessel. The cylindrical cavity is internally machined and copper plated from inside and operates at 202 MHz (RF) with a vacuum better than 1 x 10-6 mbar. There are 34 openings provided for vacuum pumps, RF input and monitoring loops, piston tuners etc. and a large openings for insertions of drift tubes from top of the tank. (author)
6. Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case
Institute of Scientific and Technical Information of China (English)
2006-01-01
In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution,and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.
7. Constant-step stress accelerated life test of VFD under Weibull distribution case
Institute of Scientific and Technical Information of China (English)
ZHANG Jian-ping; GENG Xin-min
2005-01-01
Constant-step stress accelerated life test of Vacuum Fluorescent Display (VFD) was conducted with increased cathode temperature. Statistical analysis was done by applying Weibull distribution for describing the life, and Least Square Method (LSM)for estimating Weibull parameters. Self-designed special software was used to predict the VFD life. Numerical results showed that the average life of VFD is over 30000 h, that the VFD life follows Weibull distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. Accurate calculation of the key parameter enabled rapid estimation of VFD life.
8. Accelerated leaching of cementitious materials using ammonium nitrate (6 M): influence of test conditions
International Nuclear Information System (INIS)
We have focused on the test conditions influence on accelerated degradation of cementitious materials using ammonium nitrate. PH-buffering and renewal of the leaching solution were studied. PH-buffering appeared not to be very important when the renewal pH remains under eight. Renewal appeared to be the most influential feature. Its absence leads to calcium accumulation in the leaching solution inducing aggressiveness fall. Degradation is then less marked in terms of depth, flux and mineralogy. The resulting porosity increase is also smaller. (authors)
9. Laserwire at the Accelerator Test Facility 2 with Sub-Micrometre Resolution
OpenAIRE
Nevay, L. J.; Boogert, S.T.; Karataev, P.; Kruchinin, K.; Corner, L; Howell, D. F.; Walczak, R.; Aryshev, A.; Urakawa, J.; Terunuma, N.
2014-01-01
A laserwire transverse electron beam size measurement system has been developed and operated at the Accelerator Test Facility 2 (ATF2) at KEK. Special electron beam optics were developed to create an approximately 1 x 100 {\\mu}m (vertical x horizontal) electron beam at the laserwire location, which was profiled using a 150 mJ, 71 ps laser pulse with a wavelength of 532 nm. The precise characterisation of the laser propagation allows the non-Gaussian transverse profiles of the electron beam ca...
10. An experimental test of Newton's law of gravitation for small accelerations
Energy Technology Data Exchange (ETDEWEB)
Schubert, Sven
2011-10-15
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10{sup -10} m/s{sup 2}. These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a{sub 0} {approx} 1.2.10{sup -10} m/s{sup 2}, where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
11. Field Work Proposal: PUBLIC OUTREACH EVENT FOR ACCELERATOR STEWARDSHIP TEST FACILITY PILOT PROGRAM
Energy Technology Data Exchange (ETDEWEB)
Hutton, Andrew [TJNAF; Areti, Hari [TJNAF
2015-03-05
Jefferson Lab’s outreach efforts towards the goals of Accelerator Stewardship Test Facility Pilot Program consist of the lab’s efforts in three venues. The first venue, at the end of March is to meet with the members of Virginia Tech Corporate Research Center (VTCRC) (http://www.vtcrc.com/tenant-directory/) in Blacksburg, Virginia. Of the nearly 160 members, we expect that many engineering companies (including mechanical, electrical, bio, software) will be present. To this group, we will describe the capabilities of Jefferson Lab’s accelerator infrastructure. The description will include not only the facilities but also the intellectual expertise. No funding is requested for this effort. The second venue is to reach the industrial exhibitors at the 6th International Particle Accelerator Conference (IPAC’15). Jefferson Lab will host a booth at the conference to reach out to the >75 industrial exhibitors (https://www.jlab.org/conferences/ipac2015/SponsorsExhibitors.php) who represent a wide range of technologies. A number of these industries could benefit if they can access Jefferson Lab’s accelerator infrastructure. In addition to the booth, where written material will be available, we plan to arrange a session A/V presentation to the industry exhibitors. The booth will be hosted by Jefferson Lab’s Public Relations staff, assisted on a rotating basis by the lab’s scientists and engineers. The budget with IPAC’15 designations represents the request for funds for this effort. The third venue is the gathering of Southeastern Universities Research Association (SURA) university presidents. Here we plan to reach the research departments of the universities who can benefit by availing themselves to the infrastructure (material sciences, engineering, medical schools, material sciences, to name a few). Funding is requested to allow for attendance at the SURA Board Meeting. We are coordinating with DOE regarding these costs to raise the projected conference
12. Tolerable Limits of Oscillatory Accelerations Due to Rolling Motions Experienced by One Pilot During Automatic-Interceptor Flight Tests
Science.gov (United States)
Brissenden, Roy F.; Cheatham, Donald C.; Champine, Robert A.
1961-01-01
Limited flight - test data obtained from an automatically controlled interceptor during runs in which oscillatory rolling motions were encountered have been correlated with the pilot's comments regarding his ability to tolerate the imposed lateral accelerations.
13. ZZ ADS-LIB/V1.0, test library for Accelerator Driven Systems
International Nuclear Information System (INIS)
1 - Description: This test library can be used for a number of code systems in the analysis of Accelerator Driven Systems (ADS). The library is restricted to those materials needed for benchmarking efforts linked to short and mid-term ADS experimental results and design concepts. The 30 materials selected and the upper energy limit of the evaluation of each of them is given in parentheses. Format: ENDF-6. Number of groups: continuous energy for ACE library, 421 neutron groups for MATXS library. Nuclides: H1 (150), O16 (150), Al27 (150), Ti46 (20), Ti47 (20), Ti48 (20), Ti49 (20), Ti50 (20), Cr50 (20), Cr52 (20), Cr53 (20), Cr54 (20), Mn55 (20), Fe54 (200), Fe56 (200), Fe57 (200), Fe58 (200), Ni58 (20), Ni60 (20), Ni61 (150), Ni62 (150), Ni64 (150), Pb204 (200), Pb206 (200), Pb207 (200), Pb208 (200), Th232 (20), U234 (20), U235 (20), U238 (30). Thermal scattering: Thermal scattering Data for Hydrogen bound in water, 293.6 K, 323.6 K, 373.6 K, 423.6 K, 473.6 K, 523.6 K, 573.6 K, 623.6 K. Temperatures: for H1: [293.6, 323.6, 373.6, 423.6, 473.6, 523.6, 573.6, 623.6 K]; for Actinides and O-16: [293.6, 400, 500, 600, 700, 800, 900, 1200 K]; and for the rest of materials: [293.6, 400, 500, 600, 700, 800, 900 K]. Origin: JEFF3.1. Neutron weighting spectrum: standard PWR spectrum included in the GROUPR module of NJOY, modified in such a way that follows the 1/E shape from 4.0 eV to 9.811 KeV and from 10 to 20 MeV. Background scattering: sigma-0, between 5 and 10, depending on the nuclide in the range 1-10 E10. Legendre order: P-6 for transport correction to P-5. 2 - Methods: Processing was carried out using NJOY-99.90 with the local updates at IAEA-NDS. The resulting processed files are available in ACE format for Monte Carlo transport calculations and in MATXS format for deterministic transport calculations
14. Evaluation of the effectiveness of packed red blood cell irradiation by a linear accelerator
OpenAIRE
Olivo, Ricardo Aparecido; da Silva, Marcus Vinícius; Garcia, Fernanda Bernadelli; Soares, Sheila; Rodrigues Junior, Virmondes; Moraes-Souza, Helio
2015-01-01
Irradiation of blood components with ionizing radiation generated by a specific device is recommended to prevent transfusion-associated graft-versus-host disease. However, a linear accelerator can also be used in the absence of such a device, which is the case of the blood bank facility studied herein. In order to evaluate the quality of the irradiated packed red blood cells, this study aimed to determine whether the procedure currently employed in the facility is effective in inhibiting the ...
15. Some methods of the stop-band width evaluation in the compensated accelerating
International Nuclear Information System (INIS)
Several methods of the stop-band width δf evaluation in compensated structures are briefly observed. Simple for practical usage methods based on dispersion curve behavior in the vicinity of operating mode, are proposed. The methods are preferable for structures with large group velocity. The numerical simulation proved them to provide the high accuracy of δf determination. The application of the developed methods is given for the DAW structure in the case of proton and electron linear accelerators
16. Accelerated Degradation Test and Predictive Failure Analysis of B10 Copper-Nickel Alloy under Marine Environmental Conditions
OpenAIRE
Bo Sun; Tianyuan Ye; Qiang Feng; Jinghua Yao; Mumeng Wei
2015-01-01
This paper studies the corrosion behavior of B10 copper-nickel alloy in marine environment. Accelerated degradation test under marine environmental conditions was designed and performed based on the accelerated testing principle and the corrosion degradation mechanism. With the prolongation of marine corrosion time, the thickness of Cu2O film increased gradually. Its corrosion product was Cu2(OH)3Cl, which increased in quantity over time. Cl− was the major factor responsible for the marine c...
17. High power testing of the multiple-loop radio-frequency drive concept for the FMIT accelerator
International Nuclear Information System (INIS)
The Fusion Materials Irradiation Test (FMIT) accelerator requires several 600-kW rf systems to simultaneously supply rf power to a single accelerator tank. Each rf-system output must be carefully phase and amplitude controlled to achieve the proper system performance. Two 80-MHz, 600-kW rf amplifiers with phase- and amplitude-control systems have been tested into a single, high-Q resonant cavity. Experimental results are presented
18. ANALYSIS OF ACCELERATED LIFE TESTING USING LOG-LOGISTIC GEOMETRIC PROCESS MODEL IN CASE OF CENSORED DATA
Directory of Open Access Journals (Sweden)
S. SAXENA
2013-07-01
Full Text Available Geometric process model has been used in a variety of situations such as the determination of the optimal replacement policy and the optimal inspection-repair replacement policy for standby systems, and the analysis of data with trends. This study deals with the analysis of accelerated life testing for Log-Logistic distribution using geometric process model. The case of type-I censoring is considered in this study. It is assumed that the lifetimes under increasing stress levels form a geometric process. The maximum likelihood estimates of the parameters and their confidence intervals using the asymptotic method are derived. The performance of the estimators is evaluated by a simulation study with different pre-fixed parameters.
19. Application of the EXPERT consultation system to accelerated laboratory testing and interpretation.
Science.gov (United States)
Van Lente, F; Castellani, W; Chou, D; Matzen, R N; Galen, R S
1986-09-01
The EXPERT consultation system-building tool, a knowledge-based artificial intelligence program developed at Rutgers University, has been applied to the development of a laboratory consultation system facilitating sequential laboratory testing and interpretation. Depending on the results of a basic panel of laboratory tests, the system requests that specific secondary tests be performed. Input of these secondary findings can result in requests for tertiary testing, to complete the database necessary for interpretation. Interpretation of all results is based upon final inferences from the collected findings through a series of rules, a hierarchical network that yields an efficient production system not easily obtained through conventional programming. The rules included in this model are based upon initial results for total protein, calcium, glucose, total bilirubin, alkaline phosphatase, lactate dehydrogenase, aspartate aminotransferase, thyroxin, hemoglobin, mean corpuscular volume, and the concentrations of four drugs. Pertinent clinical history items included are jaundice, diabetes, thyroid disease, medications, and ethanol. Implementing this system in a laboratory-based accelerated testing program involving outpatients maximized the effective use of laboratory resources, eliminated useless testing, and provided the patient with low-cost laboratory information. PMID:3527478
20. Lessons from two field tests on pipeline damage detection using acceleration measurement
Science.gov (United States)
Shinozuka, Masanobu; Lee, Sungchil; Kim, Sehwan; Chou, Pai H.
2011-04-01
Early detection of pipeline damages has been highlighted in water supply industry. Water pressure change in pipeline due to a sudden rupture causes pipe to vibrate and the pressure change propagates through the pipeline. From the measurement of pipe vibration the rupture can be detected. In this paper, the field test results and observations are provided for implementing next generation of SCADA system for pipeline rupture detection. Two field tests were performed on real buried plastic and metal pipelines for rupture detection. The rupture was simulated by introducing sudden water pressure drop caused by water blow-off and valve control. The measured acceleration data at the pipe surfaces were analyzed in both time and frequency domain. In time domain, the sudden narrow increase of acceleration amplitude was used as an indication of rupture event. For the frequency domain analysis, correlation function and the short time Fourier Transform technique were adopted to trace the dominant frequency shift. The success of rupture detection was found to be dependent on several factors. From the frequency analysis, the dominant frequency of metal water pipe was shifted by the water pressure drop, however, it was hard to identify from the plastic pipeline. Also the influence of existing facility such as airvac on pipe vibrations was observed. Finally, several critical lessons learned in the viewpoint of field measurement are discussed in this paper.
1. Performance testing of the LUEhR-40M structure with an accelerated beam
International Nuclear Information System (INIS)
The results of experimental investigation of the prototype of the accelerating structure of the therapeutic linear accelerator of the LUEhR-40M model with an accelerating beam are presented. The accelerating structure is the standing wave biperiodic structure with inner coupling cells of 1.6 m length. The design energy of accelerated electrons equalling 20 MeV (during single electron beam passage through an accelerating structure) is obtained. 60 % of accelerated particles are accumulated in the energy interval of (20±1) MeV at 20 mA pulse current and at 3.6 MW SHF-power at the structure input
2. Accelerated atmospheric corrosion testing using a cyclic wet/dry exposure test
International Nuclear Information System (INIS)
Aluminum corrosion is important in overhead electrical conductors constructed from aluminum wire centrally reinforced by galvanized steel strands. Inspection of conductor after long service has implicated rubber bushing material, on the outside, and the galvanized strands, on the inside, as providing potential galvanic sites for the initiation of rapid aluminum corrosion. Therefore, the galvanic corrosion of aluminum in contact with graphite-loaded neoprene rubber, hot-dip galvanized steel and steel was assessed in a cyclic wet/dry exposure test using mixed-salts spray solutions containing appropriate ratios of sulfate and chloride ion. Aluminum was found to corrode at between 3 to 6 times its uncoupled rate when associated with the rubber material. While the eta-phase, relatively pure Zn, galvanized layer remained intact, galvanic corrosion of aluminum was slow. However, on exposure of the zeta-phase, Zn/Fe intermetallic layer, aluminum corroded about 35 times faster than expected in a solution with a high level of Cl- ion. The importance of these data to conductor lifetime is discussed
3. Effects of UV on power degradation of photovoltaic modules in combined acceleration tests
Science.gov (United States)
Ngo, Trang; Heta, Yushi; Doi, Takuya; Masuda, Atsushi
2016-05-01
UV exposure and other factors such as high/low temperature, humidity and mechanical stress have been reported to degrade photovoltaic (PV) module materials. By focusing on the combined effects of UV stress and moisture on PV modules, two new acceleration tests of light irradiation and damp heat (DH) were designed and conducted. The effects of UV exposure were validated through a change in irradiation time (UV dosage) and a change of the light irradiation side (glass side vs backsheet side) in the UV-preconditioned DH and cyclic sequential tests, respectively. The chemical corrosion of finger electrodes in the presence of acetic acid generated from ethylene vinyl acetate used as an encapsulant was considered to be the main origin of degradation. The module performance characterized by electroluminescence images was confirmed to correlate with the measured acetic acid concentration and Ag finger electrode resistance.
4. Benchmark testing of 233U evaluations
International Nuclear Information System (INIS)
In this paper we investigate the adequacy of available 233U cross-section data (ENDF/B-VI and JENDL-3) for calculation of critical experiments. An ad hoc revised 233U evaluation is also tested and appears to give results which are improved relative to those obtained with either ENDF/B-VI or JENDL-3 cross sections. Calculations of keff were performed for ten fast benchmarks and six thermal benchmarks using the three cross-section sets. Central reaction-rate-ratio calculations were also performed
5. Rapid evaluation of the durability of cortical neural implants using accelerated aging with reactive oxygen species
Science.gov (United States)
Takmakov, Pavel; Ruda, Kiersten; Phillips, K. Scott; Isayeva, Irada S.; Krauthamer, Victor; Welle, Cristin G.
2015-04-01
Objective. A challenge for implementing high bandwidth cortical brain-machine interface devices in patients is the limited functional lifespan of implanted recording electrodes. Development of implant technology currently requires extensive non-clinical testing to demonstrate device performance. However, testing the durability of the implants in vivo is time-consuming and expensive. Validated in vitro methodologies may reduce the need for extensive testing in animal models. Approach. Here we describe an in vitro platform for rapid evaluation of implant stability. We designed a reactive accelerated aging (RAA) protocol that employs elevated temperature and reactive oxygen species (ROS) to create a harsh aging environment. Commercially available microelectrode arrays (MEAs) were placed in a solution of hydrogen peroxide at 87 °C for a period of 7 days. We monitored changes to the implants with scanning electron microscopy and broad spectrum electrochemical impedance spectroscopy (1 Hz-1 MHz) and correlated the physical changes with impedance data to identify markers associated with implant failure. Main results. RAA produced a diverse range of effects on the structural integrity and electrochemical properties of electrodes. Temperature and ROS appeared to have different effects on structural elements, with increased temperature causing insulation loss from the electrode microwires, and ROS concentration correlating with tungsten metal dissolution. All array types experienced impedance declines, consistent with published literature showing chronic (>30 days) declines in array impedance in vivo. Impedance change was greatest at frequencies <10 Hz, and smallest at frequencies 1 kHz and above. Though electrode performance is traditionally characterized by impedance at 1 kHz, our results indicate that an impedance change at 1 kHz is not a reliable predictive marker of implant degradation or failure. Significance. ROS, which are known to be present in vivo, can create
6. THE MECHANICAL AND SHIELDING DESIGN OF A PORTABLE SPECTROMETER AND BEAM DUMP ASSEMBLY AT BNLS ACCELERATOR TEST FACILITY
International Nuclear Information System (INIS)
A portable assembly containing a vertical-bend dipole magnet has been designed and installed immediately down-beam of the Compton electron-laser interaction chamber on beamline 1 of the Accelerator Test Facility (ATF) at Brookhaven National Laboratory (BNL). The water-cooled magnet designed with field strength of up to 0.7 Tesla will be used as a spectrometer in the Thompson scattering and vacuum acceleration experiments, where field-dependent electron scattering, beam focusing and energy spread will be analyzed. This magnet will deflect the ATF's 60 MeV electron-beam 90o downward, as a vertical beam dump for the Compton scattering experiment. The dipole magnet assembly is portable, and can be relocated to other beamlines at the ATF or other accelerator facilities to be used as a spectrometer or a beam dump. The mechanical and shielding calculations are presented in this paper. The structural rigidity and stability of the assembly were studied. A square lead shield surrounding the assembly's Faraday Cup was designed to attenuate the radiation emerging from the 1 inch-copper beam stop. All photons produced were assumed to be sufficiently energetic to generate photoneutrons. A safety evaluation of groundwater tritium contamination due to the thermal neutron capturing by the deuterium in water was performed, using updated Monte Carlo neutron-photon coupled transport code (MCNP). High-energy neutron spallation, which is a potential source to directly generate radioactive tritium and sodium-22 in soil, was conservatively assessed in verifying personal and environmental safety
7. ASSESSMENT OF THE PCFBC-EXPOSED AND ACCELERATED LIFE-TESTED CANDLE FILTERS; TOPICAL
International Nuclear Information System (INIS)
Development of the hot gas filtration technology has been the focus of DOE/FETC and Siemens Westinghouse Power Corporation during the past twenty years. Systems development during this time has successfully lead to the generation and implementation of high temperature Siemens Westinghouse particulate filtration systems that are currently installed and are operational at Demonstration Plant sites, and which are ready for installation at commercial plant sites. Concurrently, materials development has advanced the use of commercially available oxide- and nonoxide-based monoliths, and has fostered the manufacture and use of second generation, oxide-based, continuous fiber reinforced ceramic composites and filament wound materials. This report summarizes the material characterization results for commercially available and second generation filter materials tested in Siemens Westinghouse's advanced, high temperature, particulate removal system at the Foster Wheeler, pressurized circulating fluidized-bed combustion, pilot-scale test facility in Karhula, Finland, and subsequent extended accelerated life testing of aged elements in Siemens Westinghouse pressurized fluidized-bed combustion simulator test facility in Pittsburgh, PA. The viability of operating candle filters successfully for over 1 year of service life has been shown in these efforts. Continued testing to demonstrate the feasibility of acquiring three years of service operation on aged filter elements is recommended
8. Using student satisfaction data to evaluate a new online accelerated nursing education program.
Science.gov (United States)
Gazza, Elizabeth A; Matthias, April
2016-10-01
As increasing numbers of students enroll in online education, institutions of higher education are responsible for delivering quality online courses and programs. Agencies that accredit institutions and programs require evidence of program quality, including student satisfaction. A large state university in the Southeastern United States transitioned an online nursing education degree completion, or Registered Nurse-to-Bachelor of Science in Nursing, program to an online accelerated format in order to meet the needs of working nurses and ultimately, increase the number of nurses prepared at the baccalaureate level. This article describes a descriptive, cross-sectional study that evaluated the effectiveness of the new online accelerated program using the quality indicator of student satisfaction. Ninety-one (32%) of the 284 students who were enrolled or had been enrolled in a course within the online accelerated degree completion program between fall 2013 session 1 and summer 2014 session participated in the study. The electronic Noel-Levitz Priorities Survey for Online Learners™ was used to measure student satisfaction with the program and associated services. Results provided insight into the students' satisfaction with the new program format and served as the basis for an interdepartmental program enhancement plan aimed at maintaining and enhancing student satisfaction and overall program quality. Findings indicated that measuring and evaluating student satisfaction can provide valuable information about the effectiveness of an online program. Recommendations for using the measurement tool in online program planning and studying student satisfaction in relation to retention and program completion were identified. PMID:27419621
9. SwissFEL injector conceptual design report. Accelerator test facility for SwissFEL
International Nuclear Information System (INIS)
This comprehensive report issued by the Paul Scherrer Institute (PSI) in Switzerland takes a look at the design concepts behind the institute's SwissFEL X-ray Laser facility - in particular concerning the conceptual design of the injector system. The SwissFEL X-ray FEL project at PSI, involves the development of an injector complex that enables operation of a FEL system operating at 0.1 - 7 nm with permanent-magnet undulator technology and minimum beam energy. The injector pre-project was motivated by the challenging electron beam requirements necessary to drive the SwissFEL accelerator facility. The report takes a look at the mission of the test facility and its performance goals. The accelerator layout and the electron source are described, as are the low-level radio-frequency power systems and the synchronisation concept. The general strategy for beam diagnostics is introduced. Low energy electron beam diagnostics, the linear accelerator (Linac) and bunch compressor diagnostics are discussed, as are high-energy electron beam diagnostics. Wavelength selection for the laser system and UV pulse shaping are discussed. The laser room for the SwissFEL Injector and constructional concepts such as the girder system and alignment concepts involved are looked at. A further chapter deals with beam dynamics, simulated performance and injector optimisation. The facility's commissioning and operation program is examined, as are operating regimes, software applications and data storage. The control system structure and architecture is discussed and special subsystems are described. Radiation safety, protection systems and shielding calculations are presented and the lateral shielding of the silo roof examined
10. Test setup for accelerated test of high power IGBT modules with online monitoring of Vce and Vf voltage during converter operation
DEFF Research Database (Denmark)
de Vega, Angel Ruiz; Ghimire, Pramod; Pedersen, Kristian Bonderup;
2014-01-01
Several accelerated test methods exist in order to study the failures mechanisms of the high power IGBT modules like temperature cycling test or power cycles based on DC current pulses. The main drawback is that the test conditions do not represent the real performance and stress conditions of th...
11. On the compressibility effect in test particle acceleration by magnetohydrodynamic turbulence
Science.gov (United States)
González, C. A.; Dmitruk, P.; Mininni, P. D.; Matthaeus, W. H.
2016-08-01
The effect of compressibility in a charged particle energization by magnetohydrodynamic (MHD) fields is studied in the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the flow compressibility effect over the particle dynamics, we performed different numerical experiments: an incompressible case and two weak compressible cases with Mach number M = 0.1 and M = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. What we call protons and electrons are test particles with scales comparable to (for protons) and much smaller than (for electrons) the dissipative scale of MHD turbulence, maintaining the correct mass ratio m e / m i . For these test particles, we show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the other hand, electrons remain magnetized and display an almost adiabatic motion, with no effect of compressibility observed. Another set of numerical experiments takes into account two fluid modifications, namely, electric field due to Hall effect and electron pressure gradient. We show that the electron pressure has an important contribution to electron acceleration allowing highly parallel energization. In contrast, no significant effect of these additional terms is observed for the protons.
12. The Cornell-BNL FFAG-ERL Test Accelerator: White Paper
CERN Document Server
Bazarov, Ivan; Dunham, Bruce; Hoffstaetter, Georg; Mayes, Christopher; Patterson, Ritchie; Sagan, David; Ben-Zvi, Ilan; Berg, Scott; Blaskiewicz, Michael; Brooks, Stephen; Brown, Kevin; Fischer, Wolfram; Hao, Yue; Meng, Wuzheng; Méot, François; Minty, Michiko; Peggs, Stephen; Ptitsin, Vadim; Roser, Thomas; Thieberger, Peter; Trbojevic, Dejan; Tsoupas, Nick
2015-01-01
The Cornell-BNL FFAG-ERL Test Accelerator (C$\\beta$) will comprise the first ever Energy Recovery Linac (ERL) based on a Fixed Field Alternating Gradient (FFAG) lattice. In particular, we plan to use a Non Scaling FFAG (NS-FFAG) lattice that is very compact and thus space- and cost- effective, enabling multiple passes of the electron beam in a single recirculation beam line, using the superconducting RF (SRF) linac multiple times. The FFAG-ERL moves the cost optimized linac and recirculation lattice to a dramatically better optimum. The prime accelerator science motivation for C$\\beta$ is proving that the FFAG-ERL concept works. This is an important milestone for the Brookhaven National Laboratory (BNL) plans to build a major Nuclear Physics facility, eRHIC, based on producing 21 GeV electron beams to collide with the RHIC ion beams. A consequence of the C$\\beta$ work would be the availability of significantly better, cost-effective, compact CW high-brightness electron beams for a plethora of scientific inves...
13. Lattice design of the integrable optics test accelerator and optical stochastic cooling experiment at Fermilab
Energy Technology Data Exchange (ETDEWEB)
Kafka, Gene [Illinois Inst. of Technology, Chicago, IL (United States)
2015-05-01
The Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab will serve as the backbone for a broad spectrum of Advanced Accelerator R&D (AARD) experiments, and as such, must be designed with signi cant exibility in mind, but without compromising cost e ciency. The nonlinear experiments at IOTA will include: achievement of a large nonlinear tune shift/spread without degradation of dynamic aperture; suppression of strong lattice resonances; study of stability of nonlinear systems to perturbations; and studies of di erent variants of nonlinear magnet design. The ring optics control has challenging requirements that reach or exceed the present state of the art. The development of a complete self-consistent design of the IOTA ring optics, meeting the demands of all planned AARD experiments, is presented. Of particular interest are the precise control for nonlinear integrable optics experiments and the transverse-to-longitudinal coupling and phase stability for the Optical Stochastic Cooling Experiment (OSC). Since the beam time-of- ight must be tightly controlled in the OSC section, studies of second order corrections in this section are presented.
14. Design and evaluation for the shielding system of the 9 MeV travelling wave linear electron accelerator
International Nuclear Information System (INIS)
The authors use EGS4 code, a generally known Monte Carlo computer simulation package, to carry out the simulation analysis of the radiation dose distribution around the head shielding system and inside the accelerator hall of the 9 MeV travelling wave linear electron accelerator. The accelerator is used for the large container inspecting system. The comparison of experience formulae evaluation and practical data was made. The results show that, at the main reference points in the accelerator hall, the dose calculated by EEG's is well coincided with the results measured. It serves as a good example for flexible application of EGS4
15. Evaluation of High Energy Nuclear Data of Importance for Use in Accelerator and Space Technology
Energy Technology Data Exchange (ETDEWEB)
Lee, Young Ouk
2005-10-15
New evaluation were performed for neutron- and proton-induced reactions for energies up to 250 400 MeV on C-12, N-14, O-16, Al-27, Si-28, Ca-40, Ar-40, Fe-54,58, Ni-64, Cu-63,65, Zr-90, Pb-208, Th-232, U-233,234,236, and Cm-243246. The evaluated results are then applied to the accelerator and space technology. A set of optical model parameters were optimized by searching a number of adjustable coefficients with the Simulated Annealing(SA) method for the spherical nuclei. A parameterization of the empirical formula was proposed to describe the proton-nucleus non-elastic cross sections of high-priority elements for space shielding purpose for proton energies from reaction threshold up to 400 MeV, which was then implemented into the fast scoping space shielding code CHARGE, based on the results of the optical model analysis utilizing up-to-date measurements. For proton energies up to 400 MeV covering most of the incident spectrum for trapped protons and solar energetic particle events, energy-angle spectra of secondary neutrons produced from the proton-induced neutron production reaction were prepared. The evaluated cross section set was applied to the thick target yield (TTY) and promp radiation benchmarks for the accelerator shielding. As for the assessment of the radiological impact of the accelerator to the environment, relevant nuclear reaction cross sections for the activation of the air were recommended among the author's evaluations and existing library based on the available measurements.
16. Evaluation of High Energy Nuclear Data of Importance for Use in Accelerator and Space Technology
International Nuclear Information System (INIS)
New evaluation were performed for neutron- and proton-induced reactions for energies up to 250 400 MeV on C-12, N-14, O-16, Al-27, Si-28, Ca-40, Ar-40, Fe-54,58, Ni-64, Cu-63,65, Zr-90, Pb-208, Th-232, U-233,234,236, and Cm-243246. The evaluated results are then applied to the accelerator and space technology. A set of optical model parameters were optimized by searching a number of adjustable coefficients with the Simulated Annealing(SA) method for the spherical nuclei. A parameterization of the empirical formula was proposed to describe the proton-nucleus non-elastic cross sections of high-priority elements for space shielding purpose for proton energies from reaction threshold up to 400 MeV, which was then implemented into the fast scoping space shielding code CHARGE, based on the results of the optical model analysis utilizing up-to-date measurements. For proton energies up to 400 MeV covering most of the incident spectrum for trapped protons and solar energetic particle events, energy-angle spectra of secondary neutrons produced from the proton-induced neutron production reaction were prepared. The evaluated cross section set was applied to the thick target yield (TTY) and promp radiation benchmarks for the accelerator shielding. As for the assessment of the radiological impact of the accelerator to the environment, relevant nuclear reaction cross sections for the activation of the air were recommended among the author's evaluations and existing library based on the available measurements
17. Los Alamos transmutation research: heavy liquid metal coolant technology and accelerator-driven materials test station
International Nuclear Information System (INIS)
The US Department of Energy is developing technologies needed to reduce the quantity of high-level nuclear waste bound for deep geologic disposal. Los Alamos National Laboratory has a long history of transmutation research in support of this mission. This report summarises two research programmes in the portfolio development of lead-alloy coolant technology and materials, and the Materials Test Station (MTS) using an accelerator-driven spallation target. We have been developing lead and lead-bismuth coolant technology and materials for advanced transmutation and nuclear energy systems since the mid-1990. Our programme mainly consists of operating a medium-scale lead-bismuth eutectic materials and thermal-hydraulic test loop (DELTA), conducting tests and experiments, developing associated coolant chemistry and liquid metal flow measurement and control sensors, instrumentation and systems, building and validating system corrosion models. We are also building a high-temperature natural convection lead test loop using an advanced material (Al-rich oxide dispersion strengthened steel). Key activities and an assessment of the technological readiness level will be given. (authors)
18. Allowance for insulation aging in the new concept of accelerated life tests of high-voltage power transformers
International Nuclear Information System (INIS)
This paper reports that the existing system of type and acceptance tests of high-voltage transformer insulation does not take into account insulation ageing, which is particularly objectionable with respect to equip-met with reduced insulation levels. Suggested in the paper is a new concept of accelerated life tests based on integrated simulation of basic operating loads, both periodic (surge) and long-term ones; by making a long-term accelerated test simulating the working conditions, with exposure of test object and/or its insulation to periodic operating surges (overvoltages and overcurrents). This test replaces a group of conventional individual acceptance tests and provides more ample and more precise information on performance and dependability of the equipment. The test procedure was checked in test of a small lot of 1600 kVA 35 kV power transformers
19. Test of new accelerator superconducting dipoles suitable for high precision field
International Nuclear Information System (INIS)
Field homogeneity of superconducting dipoles for accelerators is still difficult to achieve. To reach the required homogeneity level of 10-4 the conductors must be located within a few hundreths of mm. At present all the superconducting machines in construction or in project use the most developed technique of the double shell configuration. This technique is very sensitive to conductor size and a great care must be taken to reach the needed field homogeneity. The design proposed in this paper is a current block configuration which uses accuratly punched laminations with slots for conductor location. The design is then much less sensitive to conductor size. Furthermore the tooling needed to build such magnets is much less expensive than the one needed for the shell design. Three short dipoles have been constructed and tested. Very good results in field homogeneity have been obtained directly from the original design
20. Design of CEBAF's [Continuous Electron Beam Accelerator Facility] rf separator and results of cold tests
International Nuclear Information System (INIS)
The design of the CEBAF accelerator system is based upon a multipass racetrack configuration, the straight sections of which will utilize 1497-MHz superconducting linac sections with independent magnetic transport at the end of each linac segment. Room temperature SW rf separators operating at a frequency of 998 MHz will be used in each independent transport channel at one end of the racetrack to extract a portion of the recirculating current. With the frequency chosen and appropriate phasing, three independent beams of correlated energy may be extracted for use in the three experimental areas. The design of the rf separators, abased on an alternating periodic structure (APS), will be described and some preliminary prototype cold test results will be given. 11 refs., 10 figs., 2 tabs
1. Cavity beam position monitor system for the Accelerator Test Facility 2
CERN Document Server
Kim, Y I; Aryshev, A; Boogert, S T; Boorman, G; Frisch, J; Heo, A; Honda, Y; Hwang, W H; Huang, J Y; Kim, E -S; Kim, S H; Lyapin, A; Naito, T; May, J; McCormick, D; Mellor, R E; Molloy, S; Nelson, J; Park, S J; Park, Y J; Ross, M; Shin, S; Swinson, C; Smith, T; Terunuma, N; Tauchi, T; Urakawa, J; White, G R
2013-01-01
The Accelerator Test Facility 2 (ATF2) is a scaled demonstrator system for final focus beam lines of linear high energy colliders. This paper describes the high resolution cavity beam position monitor (BPM) system, which is a part of the ATF2 diagnostics. Two types of cavity BPMs are used, C-band operating at 6.423 GHz, and S-band at 2.888 GHz with an increased beam aperture. The cavities, electronics, and digital processing are described. The resolution of the C-band system with attenuators was determined to be approximately 250 nm and 1 m for the S-band system. Without attenuation the best recorded C-band cavity resolution was 27 nm.
2. Final safety analysis report for the Ground Test Accelerator (GTA), Phase 2
Energy Technology Data Exchange (ETDEWEB)
NONE
1994-10-01
This document is the first volume of a 3 volume safety analysis report on the Ground Test Accelerator (GTA). The GTA program at the Los Alamos National Laboratory (LANL) is the major element of the national Neutral Particle Beam (NPB) program, which is supported by the Strategic Defense Initiative Office (SDIO). A principal goal of the national NPB program is to assess the feasibility of using hydrogen and deuterium neutral particle beams outside the Earths atmosphere. The main effort of the NPB program at Los Alamos concentrates on developing the GTA. The GTA is classified as a low-hazard facility, except for the cryogenic-cooling system, which is classified as a moderate-hazard facility. This volume consists of an introduction, summary/conclusion, site description and assessment, description of facility, and description of operation.
3. Accelerated testing of metal foil tape joints and their effect of photovoltaic module reliability
Science.gov (United States)
Sorensen, N. Robert; Quintana, Michael A.; Puskar, Joseph D.; Lucero, Samuel J.
2009-08-01
A program is underway at Sandia National Laboratories to predict long-term reliability of photovoltaic (PV) systems. The vehicle for the reliability predictions is a Reliability Block Diagram (RBD), which models system behavior. Because this model is based mainly on field failure and repair times, it can be used to predict current reliability, but it cannot currently be used to accurately predict lifetime. In order to be truly predictive, physics-informed degradation processes and failure mechanisms need to be included in the model. This paper describes accelerated life testing of metal foil tapes used in thin-film PV modules, and how tape joint degradation, a possible failure mode, can be incorporated into the model.
4. On the Use of Accelerated Test Methods for Characterization of Advanced Composite Materials
Science.gov (United States)
Gates, Thomas S.
2003-01-01
A rational approach to the problem of accelerated testing for material characterization of advanced polymer matrix composites is discussed. The experimental and analytical methods provided should be viewed as a set of tools useful in the screening of material systems for long-term engineering properties in aerospace applications. Consideration is given to long-term exposure in extreme environments that include elevated temperature, reduced temperature, moisture, oxygen, and mechanical load. Analytical formulations useful for predictive models that are based on the principles of time-based superposition are presented. The need for reproducible mechanisms, indicator properties, and real-time data are outlined as well as the methodologies for determining specific aging mechanisms.
5. On the compressibility effect in test particle acceleration by magnetohydrodynamic turbulence
CERN Document Server
González, C A; Mininni, P D; Matthaeus, W H
2016-01-01
The effect of compressibility in charged particle energization by magnetohydrodynamic (MHD) fields is studied in the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the compressibilty effect over the particle dynamics we performed different numerical experiments: an incompressible case, and two weak compressible cases with Mach number M = 0.1 and M = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. We show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the ot...
6. Final safety analysis report for the Ground Test Accelerator (GTA), Phase 2
Energy Technology Data Exchange (ETDEWEB)
NONE
1994-10-01
This document is the third volume of a 3 volume safety analysis report on the Ground Test Accelerator (GTA). The GTA program at the Los Alamos National Laboratory (LANL) is the major element of the national Neutral Particle Beam (NPB) program, which is supported by the Strategic Defense Initiative Office (SDIO). A principal goal of the national NPB program is to assess the feasibility of using hydrogen and deuterium neutral particle beams outside the Earths atmosphere. The main effort of the NPB program at Los Alamos concentrates on developing the GTA. The GTA is classified as a low-hazard facility, except for the cryogenic-cooling system, which is classified as a moderate-hazard facility. This volume consists of appendices C through U of the report
7. Extremely low vertical-emittance beam in accelerator-test facility at KEK
International Nuclear Information System (INIS)
Electron beams with the lowest, normalized transverse emittance recorded so far were produced and confirmed in single-bunch-mode operation of the Accelerator Test Facility at KEK. We established a tuning method of the damping rings which achieves a small vertical dispersion and small x-y orbit coupling. The vertical emittance was less than 1 percent of the horizontal emittance. At the zero-intensity limit, the vertical normalized emittance was less than 2.8 x 10-8 rad m at beam energy 1.3 GeV. At high intensity, strong effects of intrabeam scattering were observed, which had been expected in view of the extremely high particle density due to the small transverse emittance
8. Accelerated lifetime testing methodology for lifetime estimation of Lithium-ion batteries used in augmented wind power plants
DEFF Research Database (Denmark)
Stroe, Daniel Ioan; Swierczynski, Maciej Jozef; Stan, Ana-Irina;
2013-01-01
The development of lifetime estimation models for Lithium-ion battery cells, which are working under highly variable mission profiles characteristic for wind power plant applications, requires a lot of expenditures and time resources. Therefore, batteries have to be tested under accelerated...... lifetime ageing conditions. This paper presents a three-stage methodology used for accelerated lifetime testing of Lithium-ion batteries. The results obtained at the end of the accelerated ageing process can be used for the parametrization of a performance-degradation lifetime model. In the proposed...... methodology both calendar and cycling lifetime tests are considered since both components are influencing the lifetime of Lithium-ion batteries. The methodology proposes also a lifetime model verification stage, where Lithium-ion battery cells are tested at normal operating conditions using an application...
9. Design, testing and modifications of the Pelletron accelerator and future uses
International Nuclear Information System (INIS)
Solutions to various problems in the design of high voltage generator and acceleration units of the Pelletron electron accelerator designed and constructed at ININ are presented. Information on the design of the control system of the electron beams, activities proposed for utilization of sulfur hexafluoride as an accelerator isolating gas as well as some future uses of the Pelletron. (Author). 7 refs, 3 figs
Energy Technology Data Exchange (ETDEWEB)
Temkin, Richard [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics. Plasma Science and Fusion Center
2016-07-12
The goal of the MIT program of research on high gradient acceleration is the development of advanced acceleration concepts that lead to a practical and affordable next generation linear collider at the TeV energy level. Other applications, which are more near-term, include accelerators for materials processing; medicine; defense; mining; security; and inspection. The specific goals of the MIT program are: • Pioneering theoretical research on advanced structures for high gradient acceleration, including photonic structures and metamaterial structures; evaluation of the wakefields in these advanced structures • Experimental research to demonstrate the properties of advanced structures both in low-power microwave cold test and high-power, high-gradient test at megawatt power levels • Experimental research on microwave breakdown at high gradient including studies of breakdown phenomena induced by RF electric fields and RF magnetic fields; development of new diagnostics of the breakdown process • Theoretical research on the physics and engineering features of RF vacuum breakdown • Maintaining and improving the Haimson / MIT 17 GHz accelerator, the highest frequency operational accelerator in the world, a unique facility for accelerator research • Providing the Haimson / MIT 17 GHz accelerator facility as a facility for outside users • Active participation in the US DOE program of High Gradient Collaboration, including joint work with SLAC and with Los Alamos National Laboratory; participation of MIT students in research at the national laboratories • Training the next generation of Ph. D. students in the field of accelerator physics.
11. Development of an accelerated test design for predicting the service life of the solar array at Mead, Nebraska
Energy Technology Data Exchange (ETDEWEB)
Gaines, G.B.; Thomas, R.E.; Noel, G.T.; Shilliday, T.S.; Wood, V.E.; Carmichael, D.C.
1979-06-07
This report describes an accelerated test which is designed to predict the life of the 25-kW photovoltaic array installed near Mead, Nebraska. Emphasis is placed on the power-output degradation at the module level and on long-term degradation modes, as appropriate for life prediction of mature devices for which infant failures are few. A quantitative model for accelerating testing using multiple environmental stresses is used to develop the test design. The model accounts for the effects of thermal stress by a relation of the Arrhenius form. This relation is then corrected for the effects of nonthermal environmental stresses such as relative humidity, atmospheric pollutants, and ultraviolet radiation. The test conditions, measurements, and data analyses for the accelerated tests are presented for determining the predicted life of the modules in service at Mead. Constant-temperature, cyclic-temperature, and uv types of tests are specified, incorporating selected levels of relative humidity and chemical contamination and an imposed forward-bias current and static electric field. It is recommended that as a first step in test implementation, the model be selectively validated using identified portions of the accelerated test design.
12. Accelerating the design and testing of LEU fuel assemblies for conversion of Russian-designed research reactors outside Russia
International Nuclear Information System (INIS)
This paper identifies proposed geometries and loading specifications of LEU tube-type and pin-type test assemblies that would be suitable for accelerating the conversion of Russian-designed research reactors outside of Russia if these fuels are manufactured, qualified by irradiation testing, and made commercially available in Russia. (author)
13. Optimal design of accelerated life tests for an extension of the exponential distribution
International Nuclear Information System (INIS)
Accelerated life tests provide information quickly on the lifetime distribution of the products by testing them at higher than usual levels of stress. In this paper, the lifetime of a product at any level of stress is assumed to have an extension of the exponential distribution. This new family has been recently introduced by Nadarajah and Haghighi (2011 [1]); it can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. The scale parameter of lifetime distribution at constant stress levels is assumed to be a log-linear function of the stress levels and a cumulative exposure model holds. For this model, the maximum likelihood estimates (MLEs) of the parameters, as well as the Fisher information matrix, are derived. The asymptotic variance of the scale parameter at a design stress is adopted as an optimization objective and its expression formula is provided using the maximum likelihood method. A Monte Carlo simulation study is carried out to examine the performance of these methods. The asymptotic confidence intervals for the parameters and hypothesis test for the parameter of interest are constructed
14. Evaluation of the effectiveness of packed red blood cell irradiation by a linear accelerator
OpenAIRE
Ricardo Aparecido Olivo; Marcus Vinícius da Silva; Fernanda Bernadelli Garcia; Sheila Soares; Virmondes Rodrigues Junior; Helio Moraes-Souza
2015-01-01
Irradiation of blood components with ionizing radiation generated by a specific device is recommended to prevent transfusion-associated graft-versus-host disease. However, a lin- ear accelerator can also be used in the absence of such a device, which is the case of the blood bank facility studied herein. In order to evaluate the quality of the irradiated packed red blood cells, this study aimed to determine whether the procedure currently employed in the facility is effective in inhibiting the...
15. Reliability demonstration methodology for products with Gamma Process by optimal accelerated degradation testing
International Nuclear Information System (INIS)
16. The conversion of CESR to operate as the Test Accelerator, CesrTA. Part 3: electron cloud diagnostics
Science.gov (United States)
Billing, M. G.; Conway, J. V.; Crittenden, J. A.; Greenwald, S.; Li, Y.; Meller, R. E.; Strohman, C. R.; Sikora, J. P.; Calvey, J. R.; Palmer, M. A.
2016-04-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper is the third in a series of four describing the conversion of CESR to the test accelerator, CESRTA. The first two papers discuss the overall plan for the conversion of the storage ring to an instrument capable of studying advanced accelerator physics issues [1] and the details of the vacuum system upgrades [2]. This paper focusses on the necessary development of new instrumentation, situated in four dedicated experimental regions, capable of studying such phenomena as electron clouds (ECs) and methods to mitigate EC effects. The fourth paper in this series describes the vacuum system modifications of the superconducting wigglers to accommodate the diagnostic instrumentation for the study of EC behavior within wigglers. While the initial studies of CESRTA focussed on questions related to the International Linear Collider damping ring design, CESRTA is a very versatile storage ring, capable of studying a wide range of accelerator physics and instrumentation questions.
17. Measurement of induced radioactivities for the evaluation of internal exposure at high energy accelerator facilities
International Nuclear Information System (INIS)
18. Accelerated Lifetime Testing Methodology for Lifetime Estimation of Lithium-ion Batteries used in Augmented Wind Power Plants
DEFF Research Database (Denmark)
Stroe, Daniel Ioan; Swierczynski, Maciej Jozef; Stan, Ana-Irina;
2014-01-01
The development of lifetime estimation models for Lithium-ion battery cells, which are working under highly variable mission profiles characteristic for wind power plant applications, requires a lot of expenditures and time resources. Therefore, batteries have to be tested under accelerated...... lifetime ageing conditions. This paper presents a three-stage methodology used for accelerated lifetime testing of Lithium ion batteries. The results obtained at the end of the accelerated ageing process were used for the parametrization of a performance-degradation lifetime model, which is able to predict...... both the capacity fade and the power capability decrease of the selected Lithium-ion battery cells. In the proposed methodology both calendar and cycling lifetime tests were considered since both components are influencing the lifetime of Lithium-ion batteries. Furthermore, the proposed methodology was...
19. Alternative filtration testing program: Pre-evaluation of test results
Energy Technology Data Exchange (ETDEWEB)
Georgeton, G.K.; Poirier, M.R.
1990-09-28
Based on results of testing eight solids removal technologies and one pretreatment option, it is recommended that a centrifugal ultrafilter and polymeric ultrafilter undergo further testing as possible alternatives to the Norton Ceramic filters. Deep bed filtration should be considered as a third alternative, if a backwashable cartridge filter is shown to be inefficient in separate testing.
20. Alternative filtration testing program: Pre-evaluation of test results
International Nuclear Information System (INIS)
Based on results of testing eight solids removal technologies and one pretreatment option, it is recommended that a centrifugal ultrafilter and polymeric ultrafilter undergo further testing as possible alternatives to the Norton Ceramic filters. Deep bed filtration should be considered as a third alternative, if a backwashable cartridge filter is shown to be inefficient in separate testing
1. VMAT linear accelerator commissioning and quality assurance: dose control and gantry speed tests.
Science.gov (United States)
Barnes, Michael P; Rowshanfarzad, Pejman; Greer, Peter B
2016-01-01
In VMAT treatment delivery the ability of the linear accelerator (linac) to accurately control dose versus gantry angle is critical to delivering the plan correctly. A new VMAT test delivery was developed to specifically test the dose versus gantry angle with the full range of allowed gantry speeds and dose rates. The gantry-mounted IBA MatriXX with attached inclinometer was used in movie mode to measure the instantaneous relative dose versus gantry angle during the plan every 0.54 s. The results were compared to the expected relative dose at each gantry angle calculated from the plan. The same dataset was also used to compare the instantaneous gan-try speeds throughout the delivery compared to the expected gantry speeds from the plan. Measurements performed across four linacs generally show agreement between measurement and plan to within 1.5% in the constant dose rate regions and dose rate modulation within 0.1 s of the plan. Instantaneous gantry speed was measured to be within 0.11°/s of the plan (1 SD). An error in one linac was detected in that the nominal gantry speed was incorrectly calibrated. This test provides a practical method to quality-assure critical aspects of VMAT delivery including dose versus gantry angle and gantry speed control. The method can be performed with any detector that can acquire time-resolved dosimetric information that can be synchronized with a measurement of gantry angle. The test fulfils several of the aims of the recent Netherlands Commission on Radiation Dosimetry (NCS) Report 24, which provides recommendations for comprehensive VMAT quality assurance. PMID:27167282
2. Testing MOND over a large acceleration range in x-ray ellipticals
CERN Document Server
Milgrom, Mordehai
2012-01-01
The gravitational fields of two isolated ellipticals, NGC 720 and NGC 1521, have been recently measured, assuming hydrostatic balance of the hot gas enshrouding them. These galaxies are worthy of special interest: They afford, for the first time to my knowledge, testing MOND in ellipticals with force and quality that, arguably, approach those of rotation-curve tests in disc galaxies: The fields have been probed to very large galactic radii, revealing a large range of mass discrepancies. In the context of MOND, it is noteworthy that the measured accelerations span a wide range, from more than 10a0 to about a0/10, unprecedented in individual ellipticals. I compare the predictions of MOND, based on only the baryonic mass, for reasonable stellar M/L values, with the deduced dynamical mass runs of these galaxies. I find that MOND predicts correctly the runs of the mass discrepancies: from no discrepancy in the inner parts, to approximately a-factor-of-ten discrepancy in the outermost regions probed. For NGC 1521, ...
3. Estimating service lifetimes of a polymer encapsulant for photovoltaic modules from accelerated testing
Energy Technology Data Exchange (ETDEWEB)
Czanderna, A.W.; Pern, F.J. [National Renewable Energy Lab., Golden, CO (United States)
1996-05-01
In this paper, most of the emphasis is on A9918 ethylene vinyl acetate (EVA) used commercially as the pottant for encapsulating photovoltaic (PV) modules, in which the efficiencies in field-deployed modules have been reduced by 10-70% in 4-12 years. Yet, projections were made by several different research groups in the 1980s that the EVA lifetime could range from 2-100 years. The authors (1) elucidate the complexity of the encapsulation problem, (2) indicate the performance losses reported for PV systems deployed since 1981, (3) critically assess the service lifetime predictions for EVA as a PV pottant based on studies by others for which they review the inherent errors in their assumptions about the Arrhenius relation, (4) show how degradation of minimodules in laboratory experiments that simulate reality can produce efficiency losses comparable to those in field-degraded PV modules reported in the literature, and (5) outline an acceptable methodology for making a service lifetime prediction of the polymer encapsulant, including the essential need for relating accelerated lifetime testing to real-time testing with a sufficient number of samples.
4. Testing MOND over a wide acceleration range in x-ray ellipticals.
Science.gov (United States)
Milgrom, Mordehai
2012-09-28
The gravitational fields of two isolated ellipticals, NGC 720 and NGC 1521, have been recently measured to very large galactic radii (~100 and ~200 kpc), assuming hydrostatic balance of the hot gas enshrouding them. They afford, for the first time to my knowledge, testing modified Newtonian dynamics (MOND) in ellipticals with force and quality that, arguably, approach those of rotation-curve tests in disk galaxies. In the context of MOND, it is noteworthy that the measured accelerations span a wide range, from more than 10a(0) to about 0.1a(0), unprecedented in individual ellipticals. I find that MOND predicts correctly the measured dynamical mass runs (apart from a possible minor tension in the inner few kpc of NGC 720, which might be due to departure from hydrostatic equilibrium): The predicted mass discrepancy increases outward from none near the center, to ~10 at the outermost radii. The implications for the MOND-versus-dark-matter controversy go far beyond the simple fact of two more galaxies conforming to MOND. PMID:23030078
5. Development of accelerated test design for service-life prediction of solar array at Mead, Nebraska. Quarterly report
Energy Technology Data Exchange (ETDEWEB)
Gaines, G.B.; Thomas, R.E.; Noel, G.T.; Shilliday, T.S.; Wood, V.E.; Carmichael, D.C.
1978-11-03
As a significant beginning in applying accelerated tests to solar arrays for life-prediction purposes, this study is directed toward (a) developing a plan for predicting the service life of a specific solar array in a specific geographic site - viz., the 25-KW flat-plate array installed near Mead, Nebraska, and (b) developing technical information from laboratory and field measurements for designing an accelerated test that can be carried out in 2 years and have predictive validity for a service life as long as 20 years. Status of the program is described.
6. Estimation of the Parameters of the Bivariate Generalized Exponential Distribution using Accelerated Life Testing with Censoring Data
Directory of Open Access Journals (Sweden)
Salwa Asser
2014-06-01
Full Text Available In this paper, the estimation for the bivariate generalized exponential (BVGE distribution under type-I censored with constant stress accelerated life testing (CSALT are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The unknown parameters are estimated by the maximum likelihood approach and their approximate variance-covariance matrix is obtained. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the bivariate generalized exponential distribution. Keywords: Accelerated life testing, Bivariate generalized exponential distribution, Constant stress, Type-I censoring, Maximum likelihood estimation.
7. Technical Evaluation of Oak Ridge Filter Test Facility
CERN Document Server
Kriskovich, J R
2002-01-01
Two evaluations of the Oak Ridge Department of Energy (DOE) Filter Test Facility (FTF) were performed on December 11 and 12, 2001, and consisted of a quality assurance and a technical evaluation. This report documents results of the technical evaluation.
8. Finds in Testing Experiments for Model Evaluation
Institute of Scientific and Technical Information of China (English)
WU Ji; JIA Xiaoxia; LIU Chang; YANG Haiyan; LIU Chao
2005-01-01
To evaluate the fault location and the failure prediction models, simulation-based and code-based experiments were conducted to collect the required failure data. The PIE model was applied to simulate failures in the simulation-based experiment. Based on syntax and semantic level fault injections, a hybrid fault injection model is presented. To analyze the injected faults, the difficulty to inject (DTI) and difficulty to detect (DTD) are introduced and are measured from the programs used in the code-based experiment. Three interesting results were obtained from the experiments: 1) Failures simulated by the PIE model without consideration of the program and testing features are unreliably predicted; 2) There is no obvious correlation between the DTI and DTD parameters; 3) The DTD for syntax level faults changes in a different pattern to that for semantic level faults when the DTI increases. The results show that the parameters have a strong effect on the failures simulated, and the measurement of DTD is not strict.
9. Test and evaluation capabilities at NAVELEXCEN Charleston
Energy Technology Data Exchange (ETDEWEB)
Stalvey, T.W.; Anderson, G.B.; Hinson, T.L. [Naval Electronic Systems Engineering Center, Charleston, SC (United States)
1993-12-31
The Environmental Systems and Instrumentation Engineering Department is located within the Special Programs Directorate of the Naval Electronic Systems Engineering Center (NAVELEXCEN Charleston). This Center is an echelon 4 Command under the Naval Command Control and Ocean Surveillance Center, San Diego (NCCOSC). NCCOSC is an echelon 3 Command under the Space and Warfare Systems Command (SPAWAR) which is located in Washington DC. Radiation Detection, Indication and Computation (RDIAC) equipment life-cycle management for the entire Navy falls under the auspices of the Naval Sea Systems Command (SEA 04R). The RADIAC Program provides centralized management for the execution of research, development, test, evaluation, maintenance, procurement, allowance, and equipment support for all Navy RADIAC instrumentation and assigned special monitoring equipments. RADIAC equipment is used throughout the Navy to support various functions associated with radioactivity, potential contamination, and personnel exposure to sources of ionizing radiation. Common sources in todays Navy include nuclear reactors, nuclear weapons, industrial radiography, and nuclear medicine. Types of radiation includes gamma, x-ray, alpha, and beta.
10. Tested by Fire - How two recent Wildfires affected Accelerator Operations at LANL
International Nuclear Information System (INIS)
In a little more than a decade two large wild fires threatened Los Alamos and impacted accelerator operations at LANL. In 2000 the Cerro Grande Fire destroyed hundreds of homes, as well as structures and equipment at the DARHT facility. The DARHT accelerators were safe in a fire-proof building. In 2011 the Las Conchas Fire burned about 630 square kilometers (250 square miles) and came dangerously close to Los Alamos/LANL. LANSCE accelerator operations Lessons Learned during Las Conchas fire: (1) Develop a plan to efficiently shut down the accelerator on short notice; (2) Establish clear lines of communication in emergency situations; and (3) Plan recovery and keep squirrels out.
11. Diagnosis and Tests: Evaluating a Fall or Risk of Falling
Science.gov (United States)
... Get Up and Go” test, the Berg Balance Scale, or similar simple tests of mobility and balance. ... memory testing Physical therapy assessment A home safety evaluation. Updated: March 2012 Posted: March 2012 © 2016 Health ...
12. Imbibitions, energy test and accelerated ageing in primed and non-primed seeds of Peltophorum dubium
Institute of Scientific and Technical Information of China (English)
LILei-hong; ZHANGWan-li; ZUYuan-gang; SONIAPerez
2005-01-01
Peltophorum dubium seeds were set to imbibe with four treatments, soaked with solution Captan 0.2% under 10and 27℃,PEG 6000 -1.0 MPa under 10 and 27℃. For each treatment there were four replicates with 40 seeds incubated in 9-cm Petri dishes with double filter paper moistened with testing solution. The imbibition curves showed that the final weight increase were from 70% to 150% in the treatments when imbibition entered a lag phase. Seeds were tested for effects on germination of five treatments: control group (nonprimed), primed with PEG6000 -1.0 MPa at 10 and 27℃, primed with Captan 0.2% at 10 and 27℃. For each treatment, there were three sub-treatments: seeds were soaked in distilled water for 12, 24 and 36h before the energy test. Germination percentages of nonprimed seeds and primed in PEG 27℃ soaked in distilled water during 12 h were the highest, reaching 100%. The lowest germination percentage occurred primed seeds with PEG6000 27℃ and soaked in distilled water during 36 h, which was only 52%. Germination mean time of primed seeds in PEG at 10℃, soaked 24 h was 1.08 days, mean time of primed seeds in PEG at 27℃ soaked 12 h was 2.42 days. Accelerated ageing results showed low or no germination after ageing 72 h. Control group had a higher germination percentage and seeds were more resistant to deterioration than those in primed groups, both in Petri dish (27℃) and vermiculate (room temperature).
13. Coating and Interface Degradation of Coated steel, Part 2: Accelerated Laboratory Tests
International Nuclear Information System (INIS)
14. Stress corrosion evaluation of powder metallurgy aluminum alloy 7091 with the breaking load test method
Science.gov (United States)
Domack, Marcia S.
1987-01-01
The stress corrosion behavior of the P/M aluminum alloy 7091 is evaluated in two overaged heat treatment conditions, T7E69 and T7E70, using an accelerated test technique known as the breaking load test method. The breaking load data obtained in this study indicate that P/M 7091 alloy is highly resistant to stress corrosion in both longitudinal and transverse orientations at stress levels up to 90 percent of the material yield strength. The reduction in mean breaking stress as a result of corrosive attack is smallest for the more overaged T7E70 condition. Details of the test procedure are included.
15. The conversion of CESR to operate as the Test Accelerator, CesrTA. Part 2: vacuum modifications
International Nuclear Information System (INIS)
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper, the second in a series of four, discusses the modifications of the vacuum system necessary for the conversion of CESR to the test accelerator, CESR-TA, enhanced to study such subjects as low emittance tuning methods, electron cloud (EC) effects, intra-beam scattering, fast ion instabilities as well as general improvements to beam instrumentation. A separate paper describes the vacuum system modifications of the superconducting wigglers to accommodate the diagnostic instrumentation for the study of EC behavior within wigglers. While the initial studies of CESR-TA focussed on questions related to the International Linear Collider (ILC) damping ring design, CESR-TA is a very flexible storage ring, capable of studying a wide range of accelerator physics and instrumentation questions
16. The Conversion of CESR to Operate as the Test Accelerator, CesrTA, Part 3: Electron Cloud Diagnostics
CERN Document Server
Billing, M G; Crittendan, J A; Greenwald, S; Li, Y; Meller, R E; Strohman, C R; Sikora, J P; Calvey, J R; Palmer, M A
2015-01-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper is the third in a series of four describing the the conversion of CESR to the test accelerator, CesrTA. The first two papers discuss the overall plan for the conversion of the storage ring to an instrument capable of studying advanced accelerator physics issues and the details of the vacuum system upgrades. This paper focusses on the necessary development of new instrumentation, situated in four dedicated experimental regions, capable of studying such phe...
17. Razor UAS Test and Evaluation System Project
Data.gov (United States)
National Aeronautics and Space Administration — Adsys Controls' Razor UAS Test System is a high fidelity simulation and Hardware-in-the-Loop (HIL) test system. Razor provides extensive existing capability for...
18. On the design and testing of solid armatures for rail accelerator applications
Energy Technology Data Exchange (ETDEWEB)
Karthaus, W.; de Zeeuw, W.A.; Kolkert, W.J. (TNO PML-Pulse Physics (NL))
1991-01-01
Two different armature designs, for rail accelerator applications have been studied during electromagnetic launch experiments. The designs investigated are an aluminium multi-finger monoblock and a copper fiber brush armature. The experimental set-up used and the results obtained together with an electro-thermal model that describes the armature interface behavior during the acceleration process itself are presented in this paper.
19. An evaluation of a test scheduling solution
OpenAIRE
Kelly, Timothy James
1993-01-01
As recognized in the software engineering process, software testing during development is an aspect that must be improved to accurately predict and reduce probabilities of future software failures. A possible method of improving software reliability is to concentrate on the scheduling of the test process to reduce costs and increase coverage. Software test scheduling is the process of sequencing the test procedures to manage costs and maximize verification and validation of the system being e...
20. Monitoring accelerated carbonation on standard Portland cement mortar by nonlinear resonance acoustic test
Science.gov (United States)
Eiras, J. N.; Kundu, T.; Popovics, J. S.; Monzó, J.; Borrachero, M. V.; Payá, J.
2015-03-01
Carbonation is an important deleterious process for concrete structures. Carbonation begins when carbon dioxide (CO2) present in the atmosphere reacts with portlandite producing calcium carbonate (CaCO3). In severe carbonation conditions, C-S-H gel is decomposed into silica gel (SiO2.nH2O) and CaCO3. As a result, concrete pore water pH decreases (usually below 10) and eventually steel reinforcing bars become unprotected from corrosion agents. Usually, the carbonation of the cementing matrix reduces the porosity, because CaCO3 crystals (calcite and vaterite) occupy more volume than portlandite. In this study, an accelerated carbonation-ageing process is conducted on Portland cement mortar samples with water to cement ratio of 0.5. The evolution of the carbonation process on mortar is monitored at different levels of ageing until the mortar is almost fully carbonated. A nondestructive technique based on nonlinear acoustic resonance is used to monitor the variation of the constitutive properties upon carbonation. At selected levels of ageing, the compressive strength is obtained. From fractured surfaces the depth of carbonation is determined with phenolphthalein solution. An image analysis of the fractured surfaces is used to quantify the depth of carbonation. The results from resonant acoustic tests revealed a progressive increase of stiffness and a decrease of material nonlinearity.
1. Final safety analysis report for the Ground Test Accelerator (GTA), Phase 2
Energy Technology Data Exchange (ETDEWEB)
NONE
1994-10-01
This document is the second volume of a 3 volume safety analysis report on the Ground Test Accelerator (GTA). The GTA program at the Los Alamos National Laboratory (LANL) is the major element of the national Neutral Particle Beam (NPB) program, which is supported by the Strategic Defense Initiative Office (SDIO). A principal goal of the national NPB program is to assess the feasibility of using hydrogen and deuterium neutral particle beams outside the Earth`s atmosphere. The main effort of the NPB program at Los Alamos concentrates on developing the GTA. The GTA is classified as a low-hazard facility, except for the cryogenic-cooling system, which is classified as a moderate-hazard facility. This volume consists of failure modes and effects analysis; accident analysis; operational safety requirements; quality assurance program; ES&H management program; environmental, safety, and health systems critical to safety; summary of waste-management program; environmental monitoring program; facility expansion, decontamination, and decommissioning; summary of emergency response plan; summary plan for employee training; summary plan for operating procedures; glossary; and appendices A and B.
2. Operation and postirradiation examination of ORR capsule OF-2: accelerated testing of HTGR fuel
International Nuclear Information System (INIS)
Irradiation capsule OF-2 was a test of High-Temperature Gas-Cooled Reactor fuel types under accelerated irradiation conditions in the Oak Ridge Research Reactor. The results showed good irradiation performance of Triso-coated weak-acid-resin fissile particles and Biso-coated fertile particles. These particles had been coated by a fritted gas distributor in the 0.13-m-diam furnace. Fast-neutron damage (E > 0.18 MeV) and matrix-particle interaction caused the outer pyrocarbon coating on the Triso-coated particles to fail. Such failure depended on the optical anisotropy, density, and open porosity of the outer pyrocarbon coating, as well as on the coke yield of the matrix. Irradiation of specimens with values outside prescribed limits for these properties increased the failure rate of their outer pyrocarbon coating. Good irradiation performance was observed for weak-acid-resin particles with conversions in the range from 15 to 75% UC2
3. Utilization of optical image data from the Advanced Test Accelerator (ATA)
International Nuclear Information System (INIS)
Extensive use is made of optical diagnostics to obtain information on the 50-MeV, 10-kA, 70-ns pulsed-electron beam produced by the Advanced Test Accelerator (ATA). Light is generated by the beam striking a foil inserted in the beamline or through excitation of the gas when the beamline is filled with air. The emitted light is collected and digitized. Two-dimensional images are recorded by either a gated framing camera or a streak camera. Extraction of relevant beam parameters, such as current density, current, and beam size, requires an understanding of the physics of the light-generation mechanism and an ability to handle and properly exploit a large digital database of image data. We will present a brief overview of the present understanding of the light-generation mechanisms in foil and gas, with emphasis on experimental observations and trends. We will review our data management and analysis techniques and indicate successful approaches for extracting beam parameters
4. Test of the Pauli exclusion principle for nucleons and atomic electrons by accelerator mass spectrometry
International Nuclear Information System (INIS)
The Pauli exclusion principle was tested by searching with accelerator mass spectrometry for non-Paulian atoms with three electrons in the K-shell and for non-Paulian nuclei with three protons or three neutrons in the nuclear 1 s1/2 shell. For non-Paulian atoms of 20Ne and 36Ar the following limits have been obtained: N(20Ne)/N(20Ne)-21 and N(36Ar)/N(36Ar)-17. For non-Paulian nuclei of 5Li and 5He with three protons or three neutrons, respectively, in the nuclear 1 s1/2 shell the following limits have been measured: N(5Li)/N(6Li)-17 for a range of proton separation energies of 5Li between 0 and 50 MeV and N(5He)/N(4He)-15 for neutron separation energies between 0 and 32 MeV. The result for 5Li is used to deduce a limit for the probability β2/2 of finding two colliding protons in the symmetric state with respect to exchange to be β2/2-32. (orig.)
5. A modified feed-forward control system at the Accelerator Test Facility
International Nuclear Information System (INIS)
A modified feed-forward control system has been operated at the Brookhaven Accelerator Test Facility to control the phase and amplitude of two high power klystron rf systems used to power a photocathode rf gun and a traveling wave electron linac. The changes to the control algorithm include an improved handling of cross coupling between the amplitude and the phase channels, an improved calibration routine that allows for changes in the matrix elements due to the variable base-line and improved filtering. The modifications to the software include modularity, portability, and user-friendliness. Improvements to the hardware include a linearized phase and amplitude controller with dc biasing for an improved dynamic range. The feed-forward system can handle nonlinear and noninstantaneous systems. With simultaneous regulation of two channels, the phase and the amplitude fluctuations over a time span of more than 3 μS were reduced to less than ±0.2 degree and ±0.2%, from the initial ±2.7 degree and ±1.8%, respectively. copyright 1997 American Institute of Physics
6. Accelerated aging tests of radiation damaged lasers and photodiodes for the CMS tracker optical links
CERN Document Server
Gill, K; Batten, J; Cervelli, G; Grabit, R; Jensen, F; Troska, Jan K; Vasey, F
1999-01-01
7. Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator
CERN Document Server
Ehrlichman, M P; Hartung, W; Peterson, D P; Rider, N; Rubin, D; Sagan, D; Shanks, J P; Wang, S T
2013-01-01
In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal ($xz$) coupling, contributing to beam tilt in the $xz$ plane. This coupling can be characterized by a "crabbing" dispersion term $\\zeta_a$ that comes from decomposing the $1$-turn transfer matrix. $\\zeta_a$ is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where $xz$ coupling was explored using three lattices with distinct crabbing properties. We characterize the $xz$ coupling for each case by measuring the horizontal projection of the beam with a beam size monitor. The three lattice configurations correspond to a) $16$ mrad $xz$ tilt at the beam size monitor source point, b) compensation of the $\\zeta_a$ introduced by one of two pairs of RF cavities with the second, and c) zero dispersion in RF cavities, eliminating $\\zeta_a$ entirely. Additionally, intrabeam scattering (IBS) is evident in our mea...
8. Particle acceleration and plasma energization in substorms: MHD and test particle studies
Energy Technology Data Exchange (ETDEWEB)
Birn, Joachim [Los Alamos National Laboratory
2015-07-16
The author organizes his slide presentation under the following topics: background, MHD simulation, orbit integration, typical orbits, spatial and temporal features, acceleration mechanisms, source locations, and source energies. Field-aligned energetic particle fluxes are shown for 45-keV electrons and 80-keV protons. It is concluded that the onset from local thin current sheet is electron tearing. Acceleration is mainly from field collapse, governed by Ey = -vxXBz: importance of localization; betatron acceleration (similar if nonadiabatic); 1st order Fermi, type B (or A; current sheet acceleration). There are two source regions (of comparable importance in magnetotail): - flanks, inner tail - drift entry - early, higher energy - outer plasma sheet - reconnection entry - later, lower energy. Both thermal and suprathermal sources are important, with limited energy range for acceleration
9. Development of an accelerated test design for predicting the service life of the solar array at Mead, Nebraska. Quarterly report
Energy Technology Data Exchange (ETDEWEB)
Gaines, G.B.; Thomas, R.E.; Noel, G.T.; Shilliday, T.S.; Wood, V.E.; Carmichael, D.C.
1979-02-06
10. Evaluation of a new IR-guided system for mechanical QA of linear accelerators
International Nuclear Information System (INIS)
The authors report the development of a new procedure for mechanical quality assurance of linear accelerators using an infrared-guided system. The system consists of an infrared (IR) camera and an IR-reflective marker that can be attached to a gantry, a collimator, or a treatment table. The trace of this marker can be obtained in three dimensions (3D) for a full or partial rotation of the mechanical devices. The software is written to localize rotational axes of the gantry, collimator, and the treatment table based on the marker traces. The separation of these axes characterizes the size of the sphere defining the mechanical isocenter. Additional information on anomalies in gantry movement such as degree of gantry sag and hysteresis can also be obtained. An intrinsic uncertainty of the system to localize rotational axis is 0.35 mm or less. Tests on a linear accelerator demonstrated the ability of this system to detect the separation between rotational axes of less than 1 mm and to confirm orthogonality of the planes of gantry, collimator, and table rotation.
11. Glass durability evaluation using multiple test methods
International Nuclear Information System (INIS)
The high content of Na2O in Hanford Site low-level tank wastes, averaging about 80 wt % on an oxide basis, necessitates the development of durable high-sodium glasses. Pacific Northwest Laboratory (PNL) is providing glass formulation support for this program. Glass development entails testing many glasses in a short time; it is not practical to perform long-term durability tests on every glass. The current approach on chemical durability focuses on a suite of short-term laboratory tests such as dynamic single-pass flow-through (SPFT) tests, static product consistency tests (PCT), and vapor hydration tests. The preliminary results from the three types of tests are quite different, but each provides insight into the glass corrosion process. The PCT data showed that at the same alumina, silica, and sodium levels the glass durability order for different glass systems is: Boron-only > Mixture > Calcium-only, while the opposite order is observed in SPFT tests. The order for vapor hydration tests is: Boron-only > Mixture = Calcium-only. Understanding of the glass durability order requires knowledge of the glass corrosion mechanism under specific test conditions. Integration of the three types of tests used in this program provides a more nearly complete picture of glass corrosion progress and the needed confidence for a glass optimization program. The 7-day PCT tests may provide one of the best means for preliminary screening of glass compositions within short development time. The results are relevant to long-term (or final stage corrosion) durability, as assessed by vapor hydration tests
12. Test and evaluation of pressure vessel materials
International Nuclear Information System (INIS)
We have prepared a method for analyzing the Charpy impact test data, which is deduced from ''the standard anelastic solid equation''. The theoretical expression for the absorbed energy is in a form of W=Wsub(U)+(Wsub(R)-Wsub(U))/ [1+(ωtau)2] showing the Debye characteristics and where tau is given by the Arrhenius equation; tau=tau0 exp(ΔH/ksub(B)T). Four measurable parameters, at the present stage, can characterize the dynamic hehavior of cracking (Charpy impact result). They are the upper shelf energy(Wsub(R), the lower shelf energy (Wsub(U)), the activation energy of crack (ΔH, and wtau(0) where w tau(0) are the resonance frequency of the specimen and the jumping pre-exponential factor of propagating crack respectively. However the states of R (relaxed) and U (un-relaxed) should be defined from reasonable physical conditions in the future and it is possible that Wsub(U) is small enough to be taken as zero. The effects of irradiation, alloying elements, and heat treatment on the impact results should be interpreted as changes in the above characteristic parameters. The present method has been applied for weld metal of SA 508-2 irradiated up to a fluence of 4x1018n/cm2, E>1.0Mev, resulting in about 29% decrease in Wsub(R), negligible change in Wsub(U), 5.6 times increase in ωtau0, and no change in ΔH. This seems to indicate that irradiation degrades an average value of YOUNG's modulus so that cracks propagate more easily and it does not effect on breaking the lattice bond. However much more systematic analyses should be necessary for correct judgment. It is concluded that the present method is quite adequate for analyzing the Charpy impact data even though plastic deformation in the specimen was not considered separately so that the method should be applied for various cases in order to evaluate the proper trend of effects of irradiation, alloying elements, and heat treatment on the Charpy impact results. (Author)
13. Development and test of an accelerating cavity shape for a superconducting linear collider
International Nuclear Information System (INIS)
In order to use superconducting RF accelerating structures in the construction of a linear collider certain criteria must be addressed. Foremost of these criteria is the high accelerating gradient. This requirement might be more accurately expressed as the accelerating gradient per unit cost. The authors see therefore that cost/unit length is also a primary criteria. The cavity must be designed so that input power can be coupled in and higher order mode (HOM) power may be coupled out to the degree required by beam stability considerations. At this time in the development of superconducting RF accelerating cavities, the accelerating gradient is limited by two phenomena, electron field emission and thermal breakdown. The first of these makes it imperative to choose a cell shape that minimizes Epk/Eacc and the second phenomena to minimize Hpk/Eacc (the ratio of the peak surface fields to the accelerating gradient). As field emission is the dominant gradient limitation, there is considerable premium in lowering Epk/Eacc. The cell to cell coupling (K) is also effected by the shape. This is true of the coupling of the HOM's as well as the fundamental TM010 mode. Because of this, the number of coupled cells comprising an accelerating unit is limited. A larger number of cells/module helps reduce the structure cost by reducing the number of couplers as well as by improving the filling factor for the machine. An effort is made here to increase the number of cells per module to 10
14. Accelerated tests for the soft error rate determination of single radiation particles in components of terrestrial and avionic electronic systems
International Nuclear Information System (INIS)
This paper describes the main features of the accelerated test procedures used to determine reliability data of microelectronics devices used in terrestrial environment.This paper focuses on the high energy particle test that could be performed through spallation neutron source or quasi-mono-energetic neutron or proton. Improvements of standards are illustrated with respect to the state of the art of knowledge in radiation effects and scaling down of microelectronics technologies. (authors)
15. Corrosion Embrittlement of Duralumin II Accelerated Corrosion Tests and the Behavior of High-Strength Aluminum Alloys of Different Compositions
Science.gov (United States)
Rawdon, Henry S
1928-01-01
The permanence, with respect to corrosion, of light aluminum alloy sheets of the duralumin type, that is, heat-treatable alloys containing Cu, Mg, Mn, and Si is discussed. Alloys of this type are subject to surface corrosion and corrosion of the interior by intercrystalline paths. Results are given of accelerated corrosion tests, tensile tests, the effect on corrosion of various alloying elements and heat treatments, electrical resistance measurements, and X-ray examinations.
16. Test and evaluation of isotope identifiers
International Nuclear Information System (INIS)
Three devices were tested against eighteen radio-isotopes ranging in activity from 0.37 kBq (K-40) to 93.24 GBq (Pu-239) to determine their effectiveness as isotope identifiers. Two of the devices were hand-held instruments using NaI(Tl) detectors and the third one was a bench-top instrument using a mechanically-cooled Ge detector. Details of the test and the test results are presented in this paper. (author)
17. Installation, tests and start up of the Tandetron positive ions accelerator
International Nuclear Information System (INIS)
The National Institute of Nuclear Research acquired a Positive ions accelerator type Tandetron 2MV of the Dutch Company High Voltage Engineering, Europe B.V. (H.V.E.E.) which was installed in the building named Irradiator Nave which is occupied by the Gamma irradiator and the Pelletron accelerator. Starting from the accelerator selection it was defined the conditions required for the operation of this as well as: electric feeding, water quality and quantity, air compressed, temperature, humidity, etc.; as well as the necessary modifications of the installation area. (Author)
18. Status of the visible Free-Electron Laser at the Brookhaven Accelerator Test Facility
International Nuclear Information System (INIS)
The 500 nm Free-Electron Laser (ATF) of the Brookhaven National Laboratory is reviewed. We present an overview of the ATF, a high-brightness, 50-MeV, electron accelerator and laser complex which is a users' facility for accelerator and beam physics. A number of laser acceleration and FEL experiments are under construction at the ATF. The visible FEL experiment is based on a novel superferric 8.8 mm period undulator. The electron beam parameters, the undulator, the optical resonator, optical and electron beam diagnostics are discussed. The operational status of the experiment is presented. 22 refs., 7 figs
19. Deuteron cross section evaluation for safety and radioprotection calculations of IFMIF/EVEDA accelerator prototype
International Nuclear Information System (INIS)
In the frame of IFMIF/EVEDA activities, a prototype accelerator delivering a high power deuteron beam is under construction in Japan. Interaction of these deuterons with matter will generate high levels of neutrons and induced activation, whose predicted yields depend strongly on the models used to calculate the different cross sections. A benchmark test was performed to validate these data for deuteron energies up to 20 MeV and to define a reasonable methodology for calculating the cross sections needed for EVEDA. Calculations were performed using the nuclear models included in MCNPX and PHITS, and the dedicated nuclear model code TALYS. Although the results obtained using TALYS (global parameters) or Monte Carlo codes disagree with experimental values, a solution is proposed to compute cross sections that are a good fit to experimental data. A consistent computational procedure is also suggested to improve both transport simulations/prompt dose and activation/residual dose calculations required for EVEDA.
20. Deuteron cross section evaluation for safety and radioprotection calculations of IFMIF/EVEDA accelerator prototype
Energy Technology Data Exchange (ETDEWEB)
2011-10-01
In the frame of IFMIF/EVEDA activities, a prototype accelerator delivering a high power deuteron beam is under construction in Japan. Interaction of these deuterons with matter will generate high levels of neutrons and induced activation, whose predicted yields depend strongly on the models used to calculate the different cross sections. A benchmark test was performed to validate these data for deuteron energies up to 20 MeV and to define a reasonable methodology for calculating the cross sections needed for EVEDA. Calculations were performed using the nuclear models included in MCNPX and PHITS, and the dedicated nuclear model code TALYS. Although the results obtained using TALYS (global parameters) or Monte Carlo codes disagree with experimental values, a solution is proposed to compute cross sections that are a good fit to experimental data. A consistent computational procedure is also suggested to improve both transport simulations/prompt dose and activation/residual dose calculations required for EVEDA.
1. Life prediction of 808nm high power semiconductor laser by accelerated life test of constant current stress
Science.gov (United States)
Yao, Nan; Li, Wei; Zhao, Yihao; Zhong, Li; Liu, Suping; Ma, Xiaoyu
2015-10-01
High power semiconductor laser is widely used because of its high transformation efficiency, good working stability, compact volume and simple driving requirements. Laser's lifetime is very long, but tests at high levels of stress can speed up the failure process and shorten the times to failure significantly. So accelerated life test is used here for forecasting the lifetime of 808nm CW GaAs/AlGaAs high power semiconductor laser that has an output power of 1W under 1.04A. Accelerated life test of constant current stress based on the Inverse Power Law Relationship was designed. Tests were conducted under 1.3A, 1.6A and 1.9A at room temperature. It is the first time that this method is used in the domestic research of laser's lifetime prediction. Applying Weibull Distribution to describe the lifetime distribution and analyzing the data of times to failure, characteristics lifetime's functional relationship model with current is achieved. Then the characteristics lifetime under normal current is extrapolated, which is 9473h. Besides, to confirm the validity of the functional relationship model, we conduct an additional accelerated life test under 1.75A. Based on this experimental data we calculated the characteristics lifetime corresponding to 1.75A that is 171h, while the extrapolated characteristics lifetime from the former functional relationship model is 162h. The two results shows 5% deviation that is very low and acceptable, which indicates that the test design is reasonable and authentic.
2. Accelerated multi-source remedial approach using field sample evaluation for site characterization and closure
International Nuclear Information System (INIS)
An active 128-acre industrial site, which has been operating since 1868, located in southern New Jersey was effectively remediated in three months using an accelerated multi-source remedial approach which uses field sample evaluation for site characterization and closure. Through extensive multi-remedial investigations consisting of the collection and laboratory analysis of 849 soil samples, and the installation and subsequent sampling of 60 ground water monitoring wells, 73 areas of environmental concern were identified and subsequently designated for remedial action. An aggressive remedial approach was conducted which consisted of soil excavation, including post-excavation sampling to ensure that compliance with applicable New Jersey soil cleanup criteria was achieved. Waste loading, transportation and proper disposal at a designated facility, and the use of a full service mobile laboratory for post-excavation soil sample characterization was achieved within the project time-frame. The mobile laboratory was an integral component of the remedial approach. It provided volatile organic, base-neutral, total petroleum hydrocarbon, and priority pollutant metals analyses on post-excavation soil samples using approved laboratory methods. Use of the mobile laboratory provided multiparameter sample results for field evaluation within 24 hours of collection, which expedited remediation activities allowing areas to be evaluated and backfilled immediately, as appropriate. This approach allowed rapid restoration of the remediation areas, thereby greatly reducing disruptions in facility operations. Quality Assurance/Quality Control methods consisted of the use of a fixed base laboratory for confirmation sample analysis of 10% of the samples collected
3. Coanda hydro intake screen testing and evaluation
Energy Technology Data Exchange (ETDEWEB)
Howarth, J.
2001-07-01
The objective of this project has been to evaluate the effectiveness, suitability and cost benefit of the Aquashear Coanda effect, maintenance free intake screen for use in small hydro system intakes. (author)
4. Electron cloud dynamics in the Cornell Electron Storage Ring Test Accelerator wiggler
OpenAIRE
Celata, C. M.
2011-01-01
The interference of stray electrons (also called “electron clouds”) with accelerator beams is important in modern intense-beam accelerators, especially those with beams of positive charge. In magnetic wigglers, used, for instance, for transverse emittance damping, the intense synchrotron radiation produced by the beam can generate an electron cloud of relatively high density. In this paper the complicated dynamics of electron clouds in wigglers is examined using the example of a wiggler in th...
5. Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
OpenAIRE
Borowiec, Andrzej; Godlowski, Wlodzimierz; Szydlowski, Marek
2006-01-01
Recent supernovae of type Ia measurements and other astronomical observations suggest that our universe is in accelerating phase of evolution at the present epoch. While a dark energy of unknown form is usually proposed as the most feasible mechanism for the acceleration, there are appears some alternative conception that some effects arising from generalization of Einstein equation can mimic dark energy through a modified Friedmann equation. In this work we investigate some observational con...
6. An End-to-End Test of Neutron Stars as Particle Accelerators
OpenAIRE
CARAVEO, PATRIZIA A.
2005-01-01
Combining resolved spectroscopy with deep imaging, XMM-Newton is providing new insights on the particle acceleration processes long known to be at work in the magnetospheres of isolated neutron stars. According to a standard theoretical interpretation, in neutron stars' magnetospheres particles are accelerated along the B field lines and, depending on their charge, they can either move outward, to propagate in space, or be funnelled back, towards the star surface. While particles impinging on...
7. Testing Assumptions about Evaluating Strategic Alliance Performance
OpenAIRE
Olk, Paul; Ariño, Africa
2003-01-01
Researchers have used a variety of measures to evaluate strategic alliance performance. In this paper we use data collected on performance of R&D consortia in the U.S. and of Spain-based equity and non-equity dyadic alliances to investigate empirically five basic assumptions made by strategic alliance researchers. We find that while several assumptions are supported, others are not. Results are consistent across samples. We conclude with recommendations for how to evaluate performance in futu...
International Nuclear Information System (INIS)
A design methodology for the lead-bismuth eutectic (LBE) spallation target has been developed and applied for the accelerator-driven test facility (ADTF) target. This methodology includes the target interface with the subcritical multiplier (SCM) of the ADTF and the different engineering aspects of the target design, physics, heat-transfer, hydraulics, structural, radiological, and safety analyses. Several design constrains were defined and utilised for the target design process to satisfy different engineering requirements and to minimise the time and the cost of the design development. Interface requirements with the subcritical multiplier were defined based on target performance parameters and material damage issues to enhance the lifetime of the target structure. Different structural materials were considered to define the most promising candidate based on the current database including radiation effects. The developed target design has a coaxial geometrical configuration to minimise the target footprint and it is installed vertically along the SCM axis. LBE is the target material and the target coolant with ferritic steel (HT-9 Alloy) structural material. The proton beam has 8.33 mA current uniformly distributed and 8.14 cm beam radius resulting in a current density of 40 μA/cm2. The beam power is 5 MW and the proton energy is 600 MeV. The beam tube has 10 cm radius to accommodate the halo current. A hemi-spherical geometry is used for the target window, which is connected to the beam tube. The beam tube is enclosed inside two coaxial tubes to provide inlet and outlet manifolds for the LBE coolant. The inlet and the outlet coolant manifolds and the proton beam are entered from the top above the SCM. The paper describes the design criteria, engineering constraints, and the developed target design for the ADTF. (authors)
9. Experimental test of a new antiproton acceleration scheme in the Fermilab Main Injector
International Nuclear Information System (INIS)
In an effort to provide higher intensity and lower emittance antiproton beam to the Tevatron collider for high luminosity operation, a new Main Injector (MI) antiproton acceleration scheme has been developed [1-4]. In this scheme, beam is accelerated from 8 to 27 GeV using the 2.5 MHz rf system and from 27 to 150 GeV using the 53 MHz rf system. This paper reports the experimental results of beam study. Simulation results are reported in a different PAC'05 paper [5]. Experiments are conducted with proton beam from the Booster. Acceleration efficiency, emittance growth and beam harmonic transfer between 2.5 MHz (h=28) and 53 MHz (h=588) buckets have been studied. Beam study shows that one can achieve an overall acceleration efficiency of about 100%, longitudinal emittance growth less than 20% and negligible transverse emittance growth. accelerated to 150 GeV and injected to the Tevatron. The multi-bunch coalescing process is eliminated in this acceleration scheme. Consequently, longitudinal emittance growth is reduced. Smaller emittance growth reduces beam loss
10. The Conversion of CESR to Operate as the Test Accelerator, CesrTA, Part 2: Vacuum Modifications
CERN Document Server
Billing, M G
2015-01-01
Cornell's electron/positron storage ring (CESR) was modified over a series of accelerator shutdowns beginning in May 2008, which substantially improves its capability for research and development for particle accelerators. CESR's energy span from 1.8 to 5.6 GeV with both electrons and positrons makes it ideal for the study of a wide spectrum of accelerator physics issues and instrumentation related to present light sources and future lepton damping rings. Additionally a number of these are also relevant for the beam physics of proton accelerators. This paper, the second in a series of four, discusses the modifications of the vacuum system necessary for the conversion of CESR to the test accelerator, CesrTA, enhanced to study such subjects as low emittance tuning methods, electron cloud (EC) effects, intra-beam scattering, fast ion instabilities as well as general improvements to beam instrumentation. A separate paper describes the vacuum system modifications of the superconducting wigglers to accommodate the ...
11. Accuracy evaluation of the optical surface monitoring system on EDGE linear accelerator in a phantom study.
Science.gov (United States)
Mancosu, Pietro; Fogliata, Antonella; Stravato, Antonella; Tomatis, Stefano; Cozzi, Luca; Scorsetti, Marta
2016-01-01
Frameless stereotactic radiosurgery (SRS) requires dedicated systems to monitor the patient position during the treatment to avoid target underdosage due to involuntary shift. The optical surface monitoring system (OSMS) is here evaluated in a phantom-based study. The new EDGE linear accelerator from Varian (Varian, Palo Alto, CA) integrates, for cranial lesions, the common cone beam computed tomography (CBCT) and kV-MV portal images to the optical surface monitoring system (OSMS), a device able to detect real-time patient׳s face movements in all 6 couch axes (vertical, longitudinal, lateral, rotation along the vertical axis, pitch, and roll). We have evaluated the OSMS imaging capability in checking the phantoms׳ position and monitoring its motion. With this aim, a home-made cranial phantom was developed to evaluate the OSMS accuracy in 4 different experiments: (1) comparison with CBCT in isocenter location, (2) capability to recognize predefined shifts up to 2° or 3cm, (3) evaluation at different couch angles, (4) ability to properly reconstruct the surface when the linac gantry visually block one of the cameras. The OSMS system showed, with a phantom, to be accurate for positioning in respect to the CBCT imaging system with differences of 0.6 ± 0.3mm for linear vector displacement, with a maximum rotational inaccuracy of 0.3°. OSMS presented an accuracy of 0.3mm for displacement up to 1cm and 1°, and 0.5mm for larger displacements. Different couch angles (45° and 90°) induced a mean vector uncertainty < 0.4mm. Coverage of 1 camera produced an uncertainty < 0.5mm. Translations and rotations of a phantom can be accurately detect with the optical surface detector system. PMID:26994827
12. Evaluation of Cermet Fuels Test Data
International Nuclear Information System (INIS)
Test results characterizing ceramic-metallic (cermet) fuels are available from fuel development programs conducted for the ANP project, the 710 reactor program and the Argonne National Laboratory (ANL) nuclear rocket program. There is some overlap in the materials candidates tested in these programs. Test conditions were however significantly different due to wide variation in intended applications of these high temperature cermet fuels. This paper provides an overview of these development efforts, define (where possible) the damage mechanisms thought to be responsible for fuel operating limitations, and identify the fundamental physical mechanisms thought to be responsible. In more recent years, a new form of cermet fuels based on uranium-zirconium carbonitride (U,Zr)CN was developed and tested by the Innovative Nuclear Space Power and Propulsion Institute, University of Florida, and the Scientific Research Associates 'LUTCH' of Russia. The most significant outcome of the joint INSPILUTCH program was the establishment of the high temperature characteristics of the uranium-zirconium carbonitride, (U,Zr)CN and its long term compatibility with the metallic matrix. The improved features of uranium-zirconium carbonitride include chemical compatibility with tungsten matrix and stability at temperatures as high as 3300 K, high uranium density, and high thermal conductivity. The paper also presents a brief summary of the (U,Zr)CN base cermet fuel test results. (authors)
13. Evaluation of the technique 'wire on the screw' in laboratory accelerated essays
International Nuclear Information System (INIS)
The CLIMAT essay has been employed as for the micro climate corrosiveness determination as for large geographic zones, allowing the qualification of corrosiveness of the interesting sites, the maps raising, the materials evaluation and the pollution focus localization. However, its utility, this has not been deepen in the understanding of his characteristics and corrosive process that it experiments. With the purpose in order to deepen in its knowledge and evaluating the useful possibilities in an immersion-emersion accelerated essay, it was accomplishment the present work. For this, was employed spiral aluminium manometers forming a galvanized pair with copper and steel screws, which were exposed to representative dissolutions of rainwater of the rural, urban and marine environment. It was measured the electrode potential for the essays, the corrosion velocities were determined gravimetrically, it was drawing polarization curves and they were characterized the corrosion products by X-ray diffraction (XRD), Infrared spectrometry (Ftir), Scanning Electron Microscopy (Sem) and stereoscopic microscope. The results allow to conclude that must pass sometime for what galvanic action was established. The potential evolution after that initial time, is approximately the same for the two pairs, for which the main losing of mass obtained in the Al-Cu screw has to be explained with kinetic arguments offered for polarization curves. The main corrosion product is bayerite (Al(OH)3), with greater crystallinity in Cl- dissolution than in SO4(2-) and with morphologies very influenced by environment. (Author)
14. LIBO accelerates
CERN Multimedia
2002-01-01
The prototype module of LIBO, a linear accelerator project designed for cancer therapy, has passed its first proton-beam acceleration test. In parallel a new version - LIBO-30 - is being developed, which promises to open up even more interesting avenues.
15. Neural Network Models of Simple Mechanical Systems Illustrating the Feasibility of Accelerated Life Testing
Science.gov (United States)
Fusaro, Robert L.; Jones, Steven P.; Jansen, Ralph
1996-01-01
A complete evaluation of the tribological characteristics of a given material/mechanical system is a time-consuming operation since the friction and wear process is extremely systems sensitive. As a result, experimental designs (i.e., Latin Square, Taguchi) have been implemented in an attempt to not only reduce the total number of experimental combinations needed to fully characterize a material/mechanical system, but also to acquire life data for a system without having to perform an actual life test. Unfortunately, these experimental designs still require a great deal of experimental testing and the output does not always produce meaningful information. In order to further reduce the amount of experimental testing required, this study employs a computer neural network model to investigate different material/mechanical systems. The work focuses on the modeling of the wear behavior, while showing the feasibility of using neural networks to predict life data. The model is capable of defining which input variables will influence the tribological behavior of the particular material/mechanical system being studied based on the specifications of the overall system.
16. Testability integrated evaluation method based on testability virtual test data
Institute of Scientific and Technical Information of China (English)
Liu Guanjun; Zhao Chenxu; Qiu Jing; Zhang Yong
2014-01-01
Testability virtual test is a new test method for testability verification, which has the advantages such as low cost, few restrictions and large sample of test data. It can be used to make up the deficiency of testability physical test. In order to take the advantage of testability virtual test data effectively and to improve the accuracy of testability evaluation, a testability integrated eval-uation method is proposed in this paper based on testability virtual test data. Considering the char-acteristic of testability virtual test data, the credibility analysis method for testability virtual test data is studied firstly. Then the integrated calculation method is proposed fusing the testability vir-tual and physical test data. Finally, certain helicopter heading and attitude system is presented to demonstrate the proposed method. The results show that the testability integrated evaluation method is feasible and effective.
17. Testability integrated evaluation method based on testability virtual test data
Directory of Open Access Journals (Sweden)
Liu Guanjun
2014-02-01
Full Text Available Testability virtual test is a new test method for testability verification, which has the advantages such as low cost, few restrictions and large sample of test data. It can be used to make up the deficiency of testability physical test. In order to take the advantage of testability virtual test data effectively and to improve the accuracy of testability evaluation, a testability integrated evaluation method is proposed in this paper based on testability virtual test data. Considering the characteristic of testability virtual test data, the credibility analysis method for testability virtual test data is studied firstly. Then the integrated calculation method is proposed fusing the testability virtual and physical test data. Finally, certain helicopter heading and attitude system is presented to demonstrate the proposed method. The results show that the testability integrated evaluation method is feasible and effective.
18. Assembly Test of Elastic Averaging Technique to Improve Mechanical Alignment for Accelerating Structure Assemblies in CLIC
CERN Document Server
Huopana, J
2010-01-01
The CLIC (Compact LInear Collider) is being studied at CERN as a potential multi-TeV e+e- collider [1]. The manufacturing and assembly tolerances for the required RF-components are important for the final efficiency and for the operation of CLIC. The proper function of an accelerating structure is very sensitive to errors in shape and location of the accelerating cavity. This causes considerable issues in the field of mechanical design and manufacturing. Currently the design of the accelerating structures is a disk design. Alternatively it is possible to create the accelerating assembly from quadrants, which favour the mass manufacturing. The functional shape inside of the accelerating structure remains the same and a single assembly uses less parts. The alignment of these quadrants has been previously made kinematic by using steel pins or spheres to align the pieces together. This method proved to be a quite tedious and time consuming method of assembly. To limit the number of different error sources, a meth...
19. A null test of the metric nature of the cosmic acceleration
International Nuclear Information System (INIS)
We discuss the testable predictions of a phenomenological model in which the accelerated expansion of the universe is the result of the action of a non-gravitational force field, rather than the effect of a negative-pressure dark energy fluid or a modification of general relativity. We show, through the equivalence principle, that in such a scenario the cosmic acceleration felt by distant standard candles like SNIa (type Ia supernovae (SNe)) depends on the mass of the host system, being larger in isolated galaxies than in rich clusters. As a consequence, the scatter in the observed SNIa Hubble diagram has mostly a physical origin in this scenario: in fact, the SNIa distance modulus is increasing, at fixed redshift, for SNe that are hosted in isolated galaxies with respect to the case of SNe hosted in rich galaxy clusters. Due to its strong dependence on the astrophysical environments of standard candles, we conclude that alternative non-gravitational mechanisms for the observed accelerated expansion of the universe can be interestingly contrasted against the standard metric interpretation of the cosmological acceleration by means of an environmental analysis of the cosmic structures in which SNIa are found. The possible absence of such environmental effects would definitely exclude the possibility of non-gravitational mechanisms being responsible for the accelerated cosmological expansion and will therefore reinforce a metric interpretation
20. Evaluation of high density polyethylene composite filled with bagasse after accelerated weathering followed by biodegradation
Directory of Open Access Journals (Sweden)
Peyvand Darabi
2012-11-01
Full Text Available Wood-plastic composites (WPC have many applications as structural and non-structural material. As their outdoor application becomes more widespread, their resistance against weathering, particularly ultraviolet light and biodegradation becomes of more concern. In the present study, natural fiber composites (NFPC made of bagasse and high density polyethylene, with and without pigments, were prepared by extrusion and subjected to accelerated weathering for 1440 h; then weathered and un-weathered samples were exposed to fungal and termite resistance tests. The chemical and surface qualities of samples were studied by ATR-FTIR spectroscopy, colorimetry, contact angle, and roughness tests before and after weathering. Using bagasse as filler does reduce the discoloration of weathered samples. Adding pigments may reduce the effect of weathering on lignin degradation, although it favors polymer oxidation, but it increases the weight loss caused by fungi. Despite the high resistance of samples against biological attack, weathering triggers attack by termites and fungi on the surface and causes surface quality loss.
1. Testing and evaluation of eight decontamination chemicals
International Nuclear Information System (INIS)
This report covers experimental work comparing eight different decontamination chemicals. Seven of these chemicals have some novelty, or are not currently in use at the ICPP. The eighth is a common ICPP decontamination reagent used as a baseline for effective comparison. Decontamination factors, waste generation values, and corrosion rates are tabulated for these chemicals. Recommendations are given for effective methods of non-sodium or low-sodium decontamination chemicals. The two most effective chemical for decontamination found in these test were a dilute hydrofluoric and nitric acid (HF/HNO3) mixture and a fluoroboric acid solution. The fluoroboric acid solution (1 molar) was by far the most effective decontamination reagent, but suffered the problem of generating significant final calcine volume. The HF/HNO3 solution performed a very good decontamination of the SIMCON coupons while generating only small amounts of calcine volume. Concentration variables were also tested, and optimized for these two solutions. Several oxidation/reduction decon chemical systems were also tested. These systems were similar to the TURCO 4502 and TURCO 4521 solutions used for general decontamination at the ICPP. A low sodium alternative, nitric acid/potassium permanganate, to the ''high sodium'' TURCO 4502 was tested extensively, optimized and recommended for general ICPP use. A reductive chemical solution, oxalic acid/nitric acid was also shown to have significant advantages
2. Interactive Test Analysis: Development, Implementation, and Evaluation.
Science.gov (United States)
Lipe, Gary
An interactive test analysis system was developed which interfaces a 3M DATRONICS system with a XEROX Sigma 9 computer. The computer programs were written in A Programming Language (APL). The current implementation of the program is characterized by its capability to: read responses from a DATRONIC answer sheet; allow the faculty member the option…
3. Accelerated safety analyses - structural analyses Phase I - structural sensitivity evaluation of single- and double-shell waste storage tanks
International Nuclear Information System (INIS)
Accelerated Safety Analyses - Phase I (ASA-Phase I) have been conducted to assess the appropriateness of existing tank farm operational controls and/or limits as now stipulated in the Operational Safety Requirements (OSRs) and Operating Specification Documents, and to establish a technical basis for the waste tank operating safety envelope. Structural sensitivity analyses were performed to assess the response of the different waste tank configurations to variations in loading conditions, uncertainties in loading parameters, and uncertainties in material characteristics. Extensive documentation of the sensitivity analyses conducted and results obtained are provided in the detailed ASA-Phase I report, Structural Sensitivity Evaluation of Single- and Double-Shell Waste Tanks for Accelerated Safety Analysis - Phase I. This document provides a summary of the accelerated safety analyses sensitivity evaluations and the resulting findings
4. Laboratory test of Newton's law of gravity for small accelerations
International Nuclear Information System (INIS)
The rotation curves of spiral galaxies suggest that either a considerable fraction of the galactic mass must be dark matter, or that one of Newton's laws needs revision at accelerations less than 1×10−10 m s−2. We have endeavored to search for evidence of the latter in a terrestrial laboratory. A sensitive torsion balance was employed to measure small accelerations due to gravity. No deviations from the predictions of Newton's law were found down to 1 × 10−12 m s−2. (paper)
5. Evaluation of Apoptosis in Immunotoxicity Testing
OpenAIRE
Nagarkatti, Mitzi; Rieder, Sadiye Amcaoglu; Vakharia, Dilip; Nagarkatti, Prakash S.
2010-01-01
Immunotoxicity testing is important in determining the toxic effects of chemical substances, medicinal products, airborne pollutants, cosmetics, medical devices, and food additives. The immune system of the host is a direct target of these toxicants, and the adverse effects include serious health complications such as susceptibility to infections, cancer, allergic reactions, and autoimmune diseases. One way to investigate the harmful effects of different chemicals is to study apoptosis in imm...
6. Evaluation of rapid diagnostic test for influenza
OpenAIRE
Tiziano Allice; Valeria Ghisetti
2009-01-01
In high risk patients such as in eldery, newborns and immunosuppressed subjects, a timely diagnosis of influenza is required for the most appropriate antiviral strategy in order to avoid severe secondary respiratory complications and viral spreading. Influenza is preventable by vaccination and chemoprophylaxis and is treatable by specific antiviral indications. The need for a timely diagnosis has led to the introduction of numerous rapid diagnostic tests.These are mostly antigen detection tes...
7. Foucault test: a quantitative evaluation method.
Science.gov (United States)
Rodríguez, Gustavo; Villa, Jesús; Ivanov, Rumen; González, Efrén; Martínez, Geminiano
2016-08-01
Reliable and accurate testing methods are essential to guiding the polishing process during the figuring of optical telescope mirrors. With the natural advancement of technology, the procedures and instruments used to carry out this delicate task have consistently increased in sensitivity, but also in complexity and cost. Fortunately, throughout history, the Foucault knife-edge test has shown the potential to measure transverse aberrations in the order of the wavelength, mainly when described in terms of physical theory, which allows a quantitative interpretation of its characteristic shadowmaps. Our previous publication on this topic derived a closed mathematical formulation that directly relates the knife-edge position with the observed irradiance pattern. The present work addresses the quite unexplored problem of the wavefront's gradient estimation from experimental captures of the test, which is achieved by means of an optimization algorithm featuring a proposed ad hoc cost function. The partial derivatives thereby calculated are then integrated by means of a Fourier-based algorithm to retrieve the mirror's actual surface profile. To date and to the best of our knowledge, this is the very first time that a complete mathematical-grounded treatment of this optical phenomenon is presented, complemented by an image-processing algorithm which allows a quantitative calculation of the corresponding slope at any given point of the mirror's surface, so that it becomes possible to accurately estimate the aberrations present in the analyzed concave device just through its associated foucaultgrams. PMID:27505659
8. Evaluation and testing of computed radiography systems
International Nuclear Information System (INIS)
The implementation of film replacement digital radiographic imaging systems throughout Europe is now gathering momentum. Such systems create the foundations for totally digital departments of radiology, since radiographic examinations constitute the most prevalent modality. Although this type of development will lead to improvements in the delivery and management of radiological service, such widespread implementation of new technology must be carefully monitored. The implementation of effective QA tests on installation, at periodic intervals and as part of a routine programme will aid this process. This paper presents the results of commissioning tests undertaken on a number of computed radiography imaging systems provided by different manufacturers. The aim of these tests was not only to provide baseline performance measurements against which subsequent measurements can be compared but also to explore any differences in performance, which might exist between different units. Results of measurements will be presented for (1) monitor and laser printer setup; (2) imaging plates, including sensitivity, consistency and uniformity; (3) resolution and contrast detectability; and (4) signal and noise performance. Results from the latter are analysed in relationship with both system and quantum noise components. (authors)
9. Evaluation and testing of computed radiography systems.
Science.gov (United States)
Charnock, P; Connolly, P A; Hughes, D; Moores, B M
2005-01-01
The implementation of film replacement digital radiographic imaging systems throughout Europe is now gathering momentum. Such systems create the foundations for totally digital departments of radiology, since radiographic examinations constitute the most prevalent modality. Although this type of development will lead to improvements in the delivery and management of radiological service, such widespread implementation of new technology must be carefully monitored. The implementation of effective QA tests on installation, at periodic intervals and as part of a routine programme will aid this process. This paper presents the results of commissioning tests undertaken on a number of computed radiography imaging systems provided by different manufacturers. The aim of these tests was not only to provide baseline performance measurements against which subsequent measurements can be compared but also to explore any differences in performance, which might exist between different units. Results of measurements will be presented for (1) monitor and laser printer set-up; (2) imaging plates, including sensitivity, consistency and uniformity; (3) resolution and contrast detectability; and (4) signal and noise performance. Results from the latter are analysed in relationship with both system and quantum noise components. PMID:15933109
10. Electron Lenses for Experiments on Nonlinear Dynamics with Wide Stable Tune Spreads in the Fermilab Integrable Optics Test Accelerator
Energy Technology Data Exchange (ETDEWEB)
Stancari, G. [Fermilab; Carlson, K. [Fermilab; McGee, M. W. [Fermilab; Nobrega, L. E. [Fermilab; Romanov, A. L. [Fermilab; Ruan, J. [Fermilab; Valishev, A. [Fermilab; Noll, D. [Frankfurt U.
2015-06-01
Recent developments in the study of integrable Hamiltonian systems have led to nonlinear accelerator lattice designs with two transverse invariants. These lattices may drastically improve the performance of high-power machines, providing wide tune spreads and Landau damping to protect the beam from instabilities, while preserving dynamic aperture. To test the feasibility of these concepts, the Integrable Optics Test Accelerator (IOTA) is being designed and built at Fermilab. One way to obtain a nonlinear integrable lattice is by using the fields generated by a magnetically confined electron beam (electron lens) overlapping with the circulating beam. The parameters of the required device are similar to the ones of existing electron lenses. We present theory, numerical simulations, and first design studies of electron lenses for nonlinear integrable optics.
11. Application of gamma-ray radiography and gravimetric measurements after accelerated corrosion tests of steel embedded in mortar
International Nuclear Information System (INIS)
The accelerated corrosion by the impressed current technique is widely used in studies of concrete durability since it has the advantage that tests can be carried out within reasonable periods of time. In the present work the relationship between the applied current density and the resulting damage on the reinforcing steel, by applying optical microscopy, scanning electron microscopy, gamma-ray radiography and gravimetric measurements, was studied by means of the implementation of accelerated corrosion tests on reinforced mortar. The results show that the efficiency of the applied current is between 1 and 77%, regardless of the applied current density, the water/cement ratio and the mortar cover depth of the specimens. The results show the applicability of the gamma-ray radiography technique to detect localized corrosion of steel rebars in laboratory specimens
12. Application of gamma-ray radiography and gravimetric measurements after accelerated corrosion tests of steel embedded in mortar
Energy Technology Data Exchange (ETDEWEB)
Duffó, Gustavo, E-mail: [email protected] [Comisión Nacional de Energía Atómica, Gerencia Materiales, Depto. Corrosión, Av. Gral. Paz 1499, 1650 San Martín, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Av. Rivadavia 1917, 1033 Buenos Aires (Argentina); Universidad Nacional de San Martín, Av. Gral. Paz 1499, 1650 San Martín, Buenos Aires (Argentina); Gaillard, Natalia [Universidad Nacional de San Martín, Av. Gral. Paz 1499, 1650 San Martín, Buenos Aires (Argentina); Mariscotti, Mario; Ruffolo, Marcelo [Tomografía de Hormigón Armado S.A. (THASA), Reclus 2017, 1609 Boulogne, Buenos Aires (Argentina)
2015-08-15
The accelerated corrosion by the impressed current technique is widely used in studies of concrete durability since it has the advantage that tests can be carried out within reasonable periods of time. In the present work the relationship between the applied current density and the resulting damage on the reinforcing steel, by applying optical microscopy, scanning electron microscopy, gamma-ray radiography and gravimetric measurements, was studied by means of the implementation of accelerated corrosion tests on reinforced mortar. The results show that the efficiency of the applied current is between 1 and 77%, regardless of the applied current density, the water/cement ratio and the mortar cover depth of the specimens. The results show the applicability of the gamma-ray radiography technique to detect localized corrosion of steel rebars in laboratory specimens.
13. Design of an accelerated test to determine the attack of the sulphates on concrete structures, and the suggest alternative to design a container
International Nuclear Information System (INIS)
This work at demonstrating one of the accelerated tests in the frame of the Norm ASTM E-632-82, in order to evaluate the life of service for Reinforced Concrete Structures with High Performance.These will be used as barriers of engineering in containers for Radioactive Wastes.The results of the evaluation are necessary for the probabilistic and deterministic analysis, which are required to obtain licentiate for the emplacement and construction of this type of installations.Since concrete is the principal material used in this type of containers, its properties, in particular, its durability must be evaluated taking into accounts both, intrinsic factors and the extrinsic factors.Within the intrinsic factors we can mention your formulation, including design of armors of steel, production, treated and structural design.As extrinsic factors, weather and environmental, soil characteristic and service operation must be considered.It is important to emphasize that within the criteria used in the conceptual design of these types of repositories, the structures that act of barrier must not alter their insulation properties during all the period of service, which may be several hundreds of years.Although it is not possible to guarantee that repository's performance will not be altered throughout its time of service, the fact to obtain results of accelerated tests and the long term, it will enable us to estimate the durability of such structures, across the support of mathematical suitable models.The different stages which should be taken into account for the development of the evaluation tests, determining the relevant parameters to be considered in them and results obtained so far, are showing in this work
14. Software Test And Evaluation Center Of CASC Established
Institute of Scientific and Technical Information of China (English)
2008-01-01
@@ The software Test and Evaluation Center of CASC(CASC-STEC) was established recently.The establishment of the CASC-STEC is an important measure to strengthen the capability of software test and evaluation,to ensure the quality of software products and improve the level of software engineering.
15. An Accelerated Test Method of Simultaneous Carbonation and Chloride Ion Ingress: Durability of Silica Fume Concrete in Severe Environments
OpenAIRE
Ghahari, S. A.; Ramezanianpour, A. M.; Ramezanianpour, A. A.; Esmaeili, M
2016-01-01
The effects of simultaneous carbonation and chloride ion attack on mechanical characteristics and durability of concrete containing silica fume have been investigated through an accelerated test method. Specimens containing different amounts of silica fume were maintained in an apparatus in which carbon dioxide pressure and concentration and relative humidity were kept constant, and wetting and drying cycles in saline water were applied. Surface resistivity, sorptivity, CO2 consumption, and c...
16. Testing prototypes of high-temperature superconducting current leads of cryogenic stand for testing magnetic elements of the NICA accelerating complex
Science.gov (United States)
Kres, E. V.; Kadenko, I. N.; Bessheiko, O. A.; Belov, D. V.; Blinov, N. A.; Galimov, A. R.; Zorin, A. G.; Karpinsky, V. N.; Nikiforov, D. N.; Pivin, R. V.; Smirnov, A. V.; Shevchenko, E. V.; Smirnov, S. A.; Khodzhibagiyan, G. G.; Liu, Cheng Lian
2014-09-01
In the Laboratory of High Energies at the Joint Institute for Nuclear Research, as part of the NICA-MPD [1] project, tests of two prototypes of HTSC current leads prepared at ASIPP institute (Hefei, China) have been performed [2, 3] to measure electric and heat parameters and to search for structural and physical drawbacks. Based on the experimental results, necessary changes are made in the structure of HTSC current leads of the testing stand for the magnetic element testing of the NICA accelerating complex and its basic setups: the Nuclotron, Booster, and Collider.
17. Vacuum seals design and testing for a linear accelerator of the National Spallation Neutron Source
Energy Technology Data Exchange (ETDEWEB)
Z. Chen; C. Gautier; F. Hemez; N. K. Bultman
2000-02-01
Vacuum seals are very important to ensure that the Spallation Neutron Source (SNS) Linac has an optimum vacuum system. The vacuum joints between flanges must have reliable seals to minimize the leak rate and meet vacuum and electrical requirements. In addition, it is desirable to simplify the installation and thereby also simplify the maintenance required. This report summarizes an investigation of the metal vacuum seals that include the metal C-seal, Energized Spring seal, Helcoflex Copper Delta seal, Aluminum Delta seal, delta seal with limiting ring, and the prototype of the copper diamond seals. The report also contains the material certifications, design, finite element analysis, and testing for all of these seals. It is a valuable reference for any vacuum system design. To evaluate the suitability of several types of metal seals for use in the SNS Linac and to determine the torque applied on the bolts, a series of vacuum leak rate tests on the metal seals have been completed at Los Alamos Laboratory. A copper plated flange, using the same type of delta seal that was used for testing with the stainless steel flange, has also been studied and tested. A vacuum seal is desired that requires significantly less loading than a standard ConFlat flange with a copper gasket for the coupling cavity assembly. To save the intersegment space the authors use thinner flanges in the design. The leak rate of the thin ConFlat flange with a copper gasket is a baseline for the vacuum test on all seals and thin flanges. A finite element analysis of a long coupling cavity flange with a copper delta seal has been performed in order to confirm the design of the long coupling cavity flange and the welded area of a cavity body with the flange. This analysis is also necessary to predict a potential deformation of the cavity under the combined force of atmospheric pressure and the seating load of the seal. Modeling of this assembly has been achieved using both HKS/Abaqus and COSMOS
18. Vacuum seals design and testing for a linear accelerator of the National Spallation Neutron Source
International Nuclear Information System (INIS)
Vacuum seals are very important to ensure that the Spallation Neutron Source (SNS) Linac has an optimum vacuum system. The vacuum joints between flanges must have reliable seals to minimize the leak rate and meet vacuum and electrical requirements. In addition, it is desirable to simplify the installation and thereby also simplify the maintenance required. This report summarizes an investigation of the metal vacuum seals that include the metal C-seal, Energized Spring seal, Helcoflex Copper Delta seal, Aluminum Delta seal, delta seal with limiting ring, and the prototype of the copper diamond seals. The report also contains the material certifications, design, finite element analysis, and testing for all of these seals. It is a valuable reference for any vacuum system design. To evaluate the suitability of several types of metal seals for use in the SNS Linac and to determine the torque applied on the bolts, a series of vacuum leak rate tests on the metal seals have been completed at Los Alamos Laboratory. A copper plated flange, using the same type of delta seal that was used for testing with the stainless steel flange, has also been studied and tested. A vacuum seal is desired that requires significantly less loading than a standard ConFlat flange with a copper gasket for the coupling cavity assembly. To save the intersegment space the authors use thinner flanges in the design. The leak rate of the thin ConFlat flange with a copper gasket is a baseline for the vacuum test on all seals and thin flanges. A finite element analysis of a long coupling cavity flange with a copper delta seal has been performed in order to confirm the design of the long coupling cavity flange and the welded area of a cavity body with the flange. This analysis is also necessary to predict a potential deformation of the cavity under the combined force of atmospheric pressure and the seating load of the seal. Modeling of this assembly has been achieved using both HKS/Abaqus and COSMOS
19. TravInfo Field Operational Test Institutional Evaluation Final Results
OpenAIRE
Yim, Youngbin; Deakin, Elizabeth
2000-01-01
This paper documents the final analysis of a three part series of institutional evaluations of the TravInfo Field Operational Test from its inception in 1992 through its completion in 1998. The Field Operational Test was performed over a two-year period from September 1996 to September 1998. Funding for the TravInfo evaluation was from the Federal Highway Administration with a matching grant from the California Department of Transportation (Caltrans). The institutional evaluation examined Tra...
20. High power testing of the RF accelerating cavity for the positron damping ring at SuperKEKB
International Nuclear Information System (INIS)
A positron damping ring (DR) is under construction to meet the requirement of the low-emittance positron-beam injection to the main ring of SuperKEKB based on the nano-beam scheme. We have proposed and developed a radiofrequency (RF) accelerating structure for the DR, which can supply 2 MV accelerating voltage at maximum with three accelerating cavities to be installed in a limited space, forming “multi single cell” structure. This structure is based on the higher-order-mode (HOM) damped structure of the normal-conducting accelerating cavity system ARES, where 32 ARES cavities had been successfully operated at the KEKB main rings with extremely low trip rates. Last fiscal year, we made the first production-version cavity (hereafter called cavity No.1) based on the development of the prototype cavity (hereafter called prototype). In this paper, we present results of low-power and high-power tests of the cavity No.1, compared with the results of the prototype. (author)
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6843140721321106, "perplexity": 4087.950037232058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172050.87/warc/CC-MAIN-20170219104612-00020-ip-10-171-10-108.ec2.internal.warc.gz"}
|
https://livingthing.danmackinlay.name/musical_metrics.html
|
# The Living Thing / Notebooks : Musical metrics and manifolds
Features, descriptors, metrics, kernels and affinities and the spaces and topologies they induce and what they reveal about composition. This has considerable overlap with machine listening, but there I start from audio signals, and here I usually think about more “symbolic” data such as musical scores, and with rhythm, but there I care only about the time axis. There is overlap also with psychoacoustic units, which are the pure elements from which these amalgams are made.
This is a specialized area with many fine careers built on it, and many schools with long and proud histories of calling adherents of other schools wrong. A short literature search will find many worth distinctions drawn between differences, cultural versus the biological, general versus individual, the different models applicable at different time scales, of masking effects and such.
I will largely pass over these fine contrasts here, in my quest for some pragmatically useful, minimally complex features for using in machine-learning algorithms, which do not require truth but functionality.
## General musically-motivated metric spaces
Chords etc.
Consider grouping chords played on a piano with some known (idealised) 16-harmonic spectrum. How can we understand the harmonic relations of chords played upon this keyboard?
We know a-priori that this projection can be naturally embedded in a Euclidean space with something less than $$16\times 12 = 192$$ dimensions, since there are at most that many spectral bands. In fact, since there are only 12 notes, we can get this down to 12 dimensions. The question is, can we get to an even smaller number of dimensions? How small? By “small” here, I mean, can I group chords on a lower number of dimensions than this in some musically interesting way? For bonus points, can I group chords into several different such maps and switch between them?
Without explanation, here is one similarity-distance embedding of all the chords using an ad hoc metric based on thinking about this question. (Brightness: The more notes in the chord, the darker. Hue: I forget.)
Question: can we use word-bag models for note adjacency representation? Since I asked that question I discovered the Chord2vec model of Walder’s lab, whose answer is “yes”. See MaQW16.
## To understand
• Basic group theory: What are the symmetries of the group of all pitch class co-occurrences in the 12-tet? The most common pitch class co-occurrence is a 12-vector over the Boolean algebra where a “1” in the first entry means “the note C was played”, in pos 2, “C-sharp was played” etc Symmetries we care about are, for example, that (under equal temperament) chord harmonic relationships should be invariant under transposition - i.e. rotation of the entries of the vector. (this last is not so in the case of Sethares/Terhardt style dissonance theory, which considers only unwrapped harmonics.)
• Dmitri Tymoczko’s Geometrical Methods in Recent Music Theory
• Henjan Honing’s Musical Cognition: any good?
## “Spectral roughness” Dissonance
A particular empirically-motivated metric, with good predictive performance despite its simplicity, and willful lack of concern for the actual mechanisms of the ear and the brain, or modern nuances such as masking effects and the influence of duration on sound perception etc. Invented by Plomp and Levelt (PlLe65), and developed by variously, Sethares, Terhardt and Parncutt and others.
Some sources seem to distinguish roughness in the sense of Sethares from the Plomp and Levelt sense, although they use qualitatively equations. I suspect therefore that the distinction is philosophical, or possibly pointed failure to cite one another because someone said something rude at the after-conference drinkies.
An overview by Vassilakis might help, or the app based on his work by Dr Kelly Fitz.
Juan Sebastian Lach Lau’s produced some actual open-source software (DissonanceLib) that attempts to action this stuff in a musical setting. There is a slightly different version below attributed to Parncutt.
A convenient summary of both is in the DissonanceLib code.
It’s most useful for things where you are given the harmonics a priori; I’m not especially convinced about the tenability of directly inferring this metric from an audio signal (“how dissonant is this signal?”). We should be cautious about the identifiability of this statistic from signals nonparametrically e.g. windowed DTFT power-spectrogram peaks, just because beat frequency stuff is complicated and runs into the uncertainty principle. Lach11, Seth98b and TeSS82 give it a go, though. Inferring dissonance between two signals known to be not dissonant might work though, or parametric approaches, as in linear system identification
Dissonance an interesting measure, despite these problems, though because it is very much like a Mercer kernel, in that it constructs a distance defined on an (explicit) high-dimensional space; Also, the “nearly circular” geometry it induces is interesting; For harmonic spectra, you recover the equal-tempered 12-tone scale and the 2:1 octave by minimising dissonance between twelve notes with harmonic spectra (i.e. plucked string spectra), which is suggestive that it might do other useful things.
Also, it’s almost-everywhere differentiable with respect to your signal parameters, which makes fitting it or optimising its value easy.
Anyway, details.
### Plomp and Levelt’s dissonance curves
Attributed to Plomp and Levelt’s (PlLe65), here is Sethares’ version (Seth98a), also summarised on Sethares’ web page.
Dissonance between two pure sinusoidal frequencies, $$f_1 \leq f_2$$, with amplitudes respectively $$v_1, v_2$$, is given by:
\begin{equation*} d_\text{PL}(f_1,f_2, v_1,v_2) := v_1v_2\left[ \exp\left( -as(f_2-f_1) \right) - \exp\left( -bs(f_2-f_1) \right) \right] \end{equation*}
Where
\begin{equation*} s=\frac{d^*}{s_1 f_1+s_2} \end{equation*}
and $$a=3.5, b=5.75, d^*=.24, s_1=0.21, s_2= 19$$, the constants being fit by least-squares from experimental data.
If your note has more than one frequency, one sums the pairwise dissonances of all contributing frequencies to find the total dissonance, which is not biologically plausible but seems to work ok. Other ways of working out differences between two composite sounds could be possible (Hausdorff metric etc). [1]
This looks to me like the kind of situation where the actual details of the curve are not so important as getting the points of maximal and minimal dissonance right. Clearly we have a minimal value at $$f_1=f_2$$. We solve for the maximally dissonant frequency $$f_2$$ with respect to a fixed $$f_1, v_1, v_2$$:
\begin{align*} -as\exp( -as(f_2-f_1) ) &= -bs\exp( -bs(f_2-f_1) )\\ a\exp( -as(f_2-f_1) ) &= b\exp( -bs(f_2-f_1) )\\ \ln a - as(f_2-f_1) &= \ln b -bs(f_2-f_1)\\ \ln a - \ln b &= as(f_2-f_1) -bs(f_2-f_1)\\ \ln a - \ln b &= s(a-b)(f_2-f_1) \\ f_2 &= f_1+\frac{\ln b - \ln a}{s(b-a)}\\ f_2 &= f_1(s_1+C)+s_2C \end{align*}
where
\begin{equation*} C:=\frac{\ln b - \ln a}{d^*(b-a)} \end{equation*}
That affine difference is reminiscent of resolvability criteria in functional bases.
### Parncutt and Barlow dissonance
Differences of exponentials are computationally tedious because of numerical concerns with large frequency values; this is suggestive of approximation by something more convenient, maybe of this form:
\begin{equation*} d_\text{simple}(f_1,f_2,v_1, v_2):=C_1(f_2-f_1)\exp -C_2(f_2-f_1) \end{equation*}
The Parncutt approximation takes this approach and additionally transforms the units into heuristically preferable psychoacoustic ones.
Cribbed from Lach Lau’s source code and thesis (Lach12), where he attributes it to Parncutt and Barlow, although I can’t find any actual articles by Parncutt and/or Barlow which use this. Mash06 implies it might be unpublished. Hans14 gives a squared version of the same formula.
For this we take frequencies $$b_1\leq b_2$$ and volumes $$s_1, s_2$$ in, respectively, barks and sones. Then
\begin{align*} d_\text{PB}(b_1, b_2, s_1, s_2) &:=\sqrt{(s_1 s_2)}(4 ( b_2- b_1) \exp(1 - 4 ( b_2- b_1)))\\ &= \sqrt{(s_1 s_2)}(4 ( b_2- b_1) e \exp( - 4 ( b_2- b_1))) \end{align*}
Since this scale is relative, I’m not quite sure why we have constants everywhere. Why not
\begin{equation*} d_\text{PB}'(b_1, b_2, s_1, s_2) := \sqrt{(s_1 s_2)}\frac{ b_2- b_1}{ \exp(b_2-b_1)}? \end{equation*}
Possibly in order to more closely approximate Sethares?
[1] I thought I was being clever to consider such alternatives, but Budney and Sethares (BuSe14) scooped me.
## Induced topologies
TBD. Nestke (2004) and Mazzola (2012). Tymozcko.
BaLo87
Barlow, C., & Lohner, H. (1987) Two Essays on Theory. Computer Music Journal, 11(1), 44. DOI.
BaMe55
Bartlett, M. S., & Medhi, J. (1955) On the Efficiency of Procedures for Smoothing Periodograms from Time Series with Continuous Spectra. Biometrika, 42(1/2), 143. DOI.
BiPa99
Bigand, E., & Parncutt, R. (1999) Perceiving musical tension in long chord sequences. Psychological Research, 62(4), 237–254.
BiPL96
Bigand, E., Parncutt, R., & Lerdahl, F. (1996) Perception of musical tension in short chord sequences: The influence of harmonic function, sensory dissonance, horizontal motion, and musical training. Perception & Psychophysics, 58(1), 125–141. DOI.
BiGS11
Bigo, L., Giavitto, J.-L., & Spicher, A. (2011) Building Topological Spaces for Musical Objects. In Proceedings of the Third International Conference on Mathematics and Computation in Music (pp. 13–28). Berlin, Heidelberg: Springer-Verlag DOI.
BiGT67
Bingham, C., Godfrey, M., & Tukey, J. W.(1967) Modern techniques of power spectrum estimation. Audio and Electroacoustics, IEEE Transactions on, 15(2), 56–66.
Bod02
Bod, R. (2002) Memory-based models of melodic analysis: Challenging the Gestalt principles. Journal of New Music Research, 31(1), 27–36. DOI.
BoRo90
Boggs, P. T., & Rogers, J. E.(1990) Orthogonal distance regression. Contemporary Mathematics, 112, 183–194.
BuSe14
Budney, R., & Sethares, W. (2014) Topology of Musical Data. Journal of Mathematics and Music, 8(1), 73–92. DOI.
CaQT08
Callender, C., Quinn, I., & Tymoczko, D. (2008) Generalized voice-leading spaces. Science (New York, N.Y.), 320(5874), 346–348. DOI.
CaSo03
Cancho, R. F. i, & Solé, R. V.(2003) Least effort and the origins of scaling in human language. Proceedings of the National Academy of Sciences, 100(3), 788–791. DOI.
Carl87
Carlos, W. (1987) Tuning: At the Crossroads. Computer Music Journal, 11(1), 29–43. DOI.
CVGL08
Casey, M. A., Veltkamp, R., Goto, M., Leman, M., Rhodes, C., & Slaney, M. (2008) Content-Based Music Information Retrieval: Current Directions and Future Challenges. Proceedings of the IEEE, 96(4), 668–696. DOI.
CaRS08
Casey, M., Rhodes, C., & Slaney, M. (2008) Analysis of Minimum Distances in High-Dimensional Musical Spaces. IEEE Transactions on Audio, Speech, and Language Processing, 16(5), 1015–1028. DOI.
Chon08
Chon, S. H.(2008) Quantifying the consonance of complex tones with missing fundamentals.
CoDu97
Cohen, D., & Dubnov, S. (1997) Gestalt phenomena in musical texture. In M. Leman (Ed.), Music, Gestalt, and Computing (pp. 386–405). Springer Berlin Heidelberg
CoFK07
Cook, N. D., Fujisawa, T. X., & Konaka, H. (2007) Why Not Study Polytonal Psychophysics?. Empirical Musicology Review, 2(1).
CoFa84
Cooper, J., & Fazio, R. H.(1984) A new look at dissonance. Advances in Experimental Social Psychology, 17, 229–268.
CoLL09
Corral, A. del, León, T., & Liern, V. (2009) Compatibility of the Different Tuning Systems in an Orchestra. In E. Chew, A. Childs, & C.-H. Chuan (Eds.), Mathematics and Computation in Music (pp. 93–103). Springer Berlin Heidelberg
CoMP12
Cousineau, M., McDermott, J. H., & Peretz, I. (2012) The basis of musical consonance as revealed by congenital amusia. Proceedings of the National Academy of Sciences, 109(48), 19858–19863. DOI.
Chev05
de Cheveigné, A. (2005) Pitch Perception Models. In C. J. Plack, R. R. Fay, A. J. Oxenham, & A. N. Popper (Eds.), Pitch (pp. 169–233). Springer New York DOI.
DGMR05
Demaine, E. D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G. T., … Wood, D. R.(2005) The Distance Geometry of Deep Rhythms and Scales. In CCCG (pp. 163–166).
DGMR09
Demaine, E. D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G. T., … Wood, D. R.(2009) The distance geometry of music. In Computational Geometry (Vol. 42, pp. 429–454). DOI.
DeKa07
Demopoulos, R. J., & Katchabaw, M. J.(2007) Music Information Retrieval: A Survey of Issues and Approaches. . Technical Report
DuKL06
Du, P., Kibbe, W. A., & Lin, S. M.(2006) Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching. Bioinformatics, 22(17), 2059–2065. DOI.
Duff48
Duffin, R. J.(1948) Function classes invariant under the Fourier transform. Duke Mathematical Journal, 15(3), 781–785. DOI.
FePa04
Ferguson, S., & Parncutt, R. (2004) Composing In the Flesh: Perceptually-Informed Harmonic Syntax. In Proceedings of Sound and Music Computing.
FéBD08
Févotte, C., Bertin, N., & Durrieu, J.-L. (2008) Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis. Neural Computation, 21(3), 793–830. DOI.
FiHM00
Fitzpatrick, J. M., Hill, D. L. G., & Maurer, Jr., C. R.(2000) Image Registration. In M. Sonka & J. M. Fitzpatrick (Eds.), Handbook of Medical Imaging, Volume 2. Medical Image Processing and Analysis (p. Chapter 8). 1000 20th Street, Bellingham, WA 98227-0010 USA: SPIE
FFCE16
Flamary, R., Févotte, C., Courty, N., & Emiya, V. (2016) Optimal spectral transportation with application to music transcription. In arXiv:1609.09799 [cs, stat] (pp. 703–711). Curran Associates, Inc.
Fokk69
Fokker, A. D.(1969) Unison vectors and periodicity blocks in 3-dimensional (3-5-7-) harmonic lattice of notes. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen Series B-Physical Sciences, 72(3), 153.
GaMa11
Gashler, M., & Martinez, T. (2011) Tangent space guided intelligent neighbor finding. (pp. 2617–2624). IEEE DOI.
GaMa12
Gashler, M., & Martinez, T. (2012) Robust manifold learning with CycleCut. Connection Science, 24(1), 57–69. DOI.
Hall08
Hall, R. W.(2008) Geometrical Music Theory. Science, 320(5874), 328–329. DOI.
Hans14
Hansen, B. (2014) Spatial Utilization of Sensory Dissonance and the Creation of Sonic Sculpture. . Ann Arbor, MI: Michigan Publishing, University of Michigan Library
Haus99
Haussler, D. (1999) Convolution kernels on discrete structures. . Technical report, UC Santa Cruz
HaKD13
Hawe, S., Kleinsteuber, M., & Diepold, K. (2013) Analysis operator learning and its application to image reconstruction. IEEE Transactions on Image Processing, 22(6), 2138–2150. DOI.
HeVo13
Hemmen, J. L. van, & Vollmayr, A. N.(2013) Resonating vector strength: what happens when we vary the “probing” frequency while keeping the spike times fixed. Biological Cybernetics, 107(4), 491–494. DOI.
Herm88
Hermes, D. J.(1988) Measurement of pitch by subharmonic summation. The Journal of the Acoustical Society of America, 83(1), 257–264. DOI.
HoBo11
Honingh, A., & Bod, R. (2011) In Search of Universal Properties of Musical Scales. Journal of New Music Research, 40(1), 81–89. DOI.
Huro94
Huron, D. (1994) Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance. Music Perception: An Interdisciplinary Journal, 11(3), 289–305. DOI.
HuPa93
Huron, D., & Parncutt, R. (1993) An improved model of tonality perception incorporating pitch salience and echoic memory. Psychomusicology: A Journal of Research in Music Cognition, 12(2), 154–171. DOI.
JeRI10
Jewell, M. O., Rhodes, C., & d’Inverno, M. (2010) Querying improvised music: Do you sound like yourself?. In ISMIR (pp. 483–488). International Society for Music Information Retrieval
KaKu69a
Kameoka, A., & Kuriyagawa, M. (1969a) Consonance theory part I: Consonance of dyads. The Journal of the Acoustical Society of America, 45(6), 1451–1459. DOI.
KaKu69b
Kameoka, A., & Kuriyagawa, M. (1969b) Consonance theory part II: Consonance of complex tones and its calculation method. The Journal of the Acoustical Society of America, 45(6), 1460–1469. DOI.
KaPe09
Katz, J., & Pesetsky, D. (2009) The recursive syntax and prosody of tonal music. Ms., Massachusetts Institute of Technology.
Krum00
Krumhansl, C. L.(2000) Rhythm and pitch in music cognition. Psychological Bulletin, 126(1), 159. DOI.
Kusw11
Kuswanto, Heru. (2011) Comparison Study of Saron Ricik Instruments’ Sound Color (Timbre) on the Gamelans of Nagawilaga and Gunturmadu from. International Journal of Basic & Applied Sciences.
Kusw12
Kuswanto, H. (2012) Saron demung’s timbre and sonogram of gamelans gunturmadu from Keraton Ngayogyakarta. Jurnal Pendidikan Fisika Indonesia, 8(1).
KSPC12
Kuswanto, Heru, Sumarna, Purwanto, A., & Cipto Budy Handoyo. (2012) Saron demung instruments timbre spectrum comparison study on the gamelans sekati from Karaton Ngayogyakarta. International Journal of Basic & Applied Sciences.
Lach11
Lach Lau, J. S.(2011) Dissonance Curves as Generating Devices for Dealing With Harmony. ICMC2011.
Lach12
Lach Lau, J. S.(2012, December 13) Harmonic duality : from interval ratios and pitch distance to spectra and sensory dissonance (Dissertatie).
Lema97
Leman, M. (1997) Music, Gestalt, and computing: studies in cognitive and systematic musicology. (Vol. 1317). Springer
Lerd88
Lerdahl, F. (1988) Tonal Pitch Space. Music Perception: An Interdisciplinary Journal, 5(3), 315–349. DOI.
Lerd96
Lerdahl, F. (1996) Calculating Tonal Tension. Music Perception: An Interdisciplinary Journal, 13(3), 319–363. DOI.
LeCM12
Levitin, D. J., Chordia, P., & Menon, V. (2012) Musical rhythm spectra from Bach to Joplin obey a 1/f power law. Proceedings of the National Academy of Sciences of the United States of America, 109(10), 3716–3720. DOI.
Li06
Li, G. (2006) The effect of inharmonic and harmonic spectra in Javanese gamelan tuning (1): a theory of the sléndro. In Proceedings of the 7th WSEAS International Conference on Acoustics & Music: Theory & Applications (pp. 65–71). World Scientific and Engineering Academy and Society (WSEAS)
MBET09
Macke, J. H., Berens, P., Ecker, A. S., Tolias, A. S., & Bethge, M. (2009) Generating spike trains with specified correlation coefficients. Neural Computation, 21(2), 397–423. DOI.
MaQW16
Madjiheurem, S., Qu, L., & Walder, C. (2016) Chord2Vec: Learning Musical Chord Embeddings.
MMMR05
Manaris, B., Machado, P., McCauley, C., Romero, J., & Krehbiel, D. (2005) Developing Fitness Functions for Pleasant Music: Zipf’s Law and Interactive Evolution Systems. In F. Rothlauf, J. Branke, S. Cagnoni, D. W. Corne, R. Drechsler, Y. Jin, … G. Squillero (Eds.), Applications of Evolutionary Computing (pp. 498–507). Springer Berlin Heidelberg
Mash06
Mashinter, K. (2006) Calculating sensory dissonance: Some discrepancies arising from the models of Kameoka & Kuriyagawa, and Hutchinson & Knopoff.
Mazz12
Mazzola, G. (2012) Singular homology on hypergestures. Journal of Mathematics and Music, 6(1), 49–60. DOI.
McEl11
McFee, B., & Ellis, D. P.(2011) Analyzing song structure with spectral clustering. In IEEE conference on Computer Vision and Pattern Recognition (CVPR).
Mcki01
McKinney, M. F.(2001) Neural correlates of pitch and roughness: toward the neural code for melody and harmony. . Massachusetts Institute of Technology
MoSF13
Moustafa, K. A.-, Schuurmans, D., & Ferrie, F. (2013) Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning. In Journal of Machine Learning Research (pp. 341–356).
NiJa01
Nicolls, F., & de Jager, G. (2001) Uniformly most powerful cyclic permutation invariant detection for discrete-time signals. (Vol. 5, pp. 3165–3168). IEEE DOI.
NoFa88
Nordmark, J., & Fahlen, L. E.(1988) Beat theories of musical consonance. Speech Transmission Laboratory, Quarterly Progress and Status Report.
Park04
Park, C. G. C. G.(2004) Construction of random vectors of heterogeneous component variables under specified correlation structures. Computational Statistics & Data Analysis, 46(4), 621–630. DOI.
Parn89
Parncutt, R. (1989) Harmony: a psychoacoustical approach. . Berlin ; New York: Springer-Verlag
Parn94
Parncutt, R. (1994) A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms. Music Perception: An Interdisciplinary Journal, 11(4), 409–464. DOI.
Parn97
Parncutt, R. (1997) A model of the perceptual root(s) of a chord accounting for voicing and prevailing tonality. In M. Leman (Ed.), Music, Gestalt, and Computing (pp. 181–199). Springer Berlin Heidelberg
Parn05
Parncutt, R. (2005) Psychoacoustics and music perception. Musikpsychologie–das Neue Handbuch.
Parn06
Parncutt, R. (2006) Commentary on Keith Mashinter’s “Calculating Sensory Dissonance: Some Discrepancies Arising from the Models of Kameoka & Kuriyagawa, and Hutchinson & Knopoff”.
Parn13
Parncutt, R. (2013) Psychoacoustics and cognition for musicians. Sound Musicianship: Understanding the Crafts of Music, 2.
PaHa11
Parncutt, R., & Hair, G. (2011) Consonance and dissonance in music theory and psychology: disentangling dissonant dichotomies. J. Interdiscipl. Music Stud, 5, 119–166.
PaSt94
Parncutt, R., & Strasburger, H. (1994) Applying Psychoacoustics in Composition: “Harmonic” Progressions of “Nonharmonic” Sonorities. Perspectives of New Music, 32(2), 88–129. DOI.
PeSa09
Perchy, S., & Sarria, G. (2009) Dissonances: Brief description and its computational representation in the RTCC calculus. In Proc. of SMC2009, Porto, Portugal.
PlLe65
Plomp, R., & Levelt, W. J.(1965) Tonal consonance and critical bandwidth. The Journal of the Acoustical Society of America, 38(4), 548–560. DOI.
RaPl99
Rasch, R., & Plomp, R. (1999) The perception of musical tones. The Psychology of Music, 2, 89–112.
ReYE12
Reese, K., Yampolskiy, R., & Elmaghraby, A. (2012) A framework for interactive generation of music for games. In 2012 17th International Conference on Computer Games (CGAMES) (pp. 131–137). Washington, DC, USA: IEEE Computer Society DOI.
ReBr69
Reitboeck, H., & Brody, T. P.(1969) A transformation with invariance under cyclic permutation for applications in pattern recognition. Information and Control, 15(2), 130–154. DOI.
Reut97
Reuter, C. (1997) Karl Erich Schumann’s principles of timbre as a helpful tool in stream segregation research. In M. Leman (Ed.), Music, Gestalt, and Computing (pp. 362–374). Springer Berlin Heidelberg
RZWS15
Rohrmeier, M., Zuidema, W., Wiggins, G. A., & Scharff, C. (2015) Principles of structure building in music, language and animal song. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 370(1664), 20140097. DOI.
SCBH12
Serrà, J., Corral, Á., Boguñá, M., Haro, M., & Arcos, J. L.(2012) Measuring the Evolution of Contemporary Western Popular Music. Scientific Reports, 2. DOI.
Seth97
Sethares, W. A.(1997) Specifying spectra for musical scales. The Journal of the Acoustical Society of America, 102(4), 2422–2431. DOI.
Seth98a
Sethares, W. A.(1998a) Consonance-Based Spectral Mappings. Computer Music Journal, 22(1), 56. DOI.
Seth98b
Sethares, W. A.(1998b) Tuning, Timbre, Spectrum, Scale. . Springer London
SMTP09
Sethares, W. A., Milne, A. J., Tiedje, S., Prechtl, A., & Plamondon, J. (2009) Spectral Tools for Dynamic Tonality and Audio Morphing. Computer Music Journal, 33(2), 71–84. DOI.
Shiv11
Shiv, V. L.(2011) Improved frequency estimation in sinusoidal models through iterative linear programming schemes. In Sound and Music Computing Conference, Proceedings.
SWMS99
Smola, A. J., Williamson, R. C., Mika, S., & Schölkopf, B. (1999) Regularized Principal Manifolds. In P. Fischer & H. U. Simon (Eds.), Computational Learning Theory (pp. 214–229). Springer Berlin Heidelberg
SFGS12
Sriperumbudur, B. K., Fukumizu, K., Gretton, A., Schölkopf, B., & Lanckriet, G. R. G.(2012) On the empirical estimation of integral probability metrics. Electronic Journal of Statistics, 6, 1550–1599. DOI.
StVo40
Stevens, S. S., & Volkmann, J. (1940) The Relation of Pitch to Frequency: A Revised Scale. The American Journal of Psychology, 53(3), 329–353. DOI.
Stol13
Stolzenburg, F. (2013) Harmony Perception by Periodicity Detection. arXiv:1306.6458 [Cs].
Terh74
Terhardt, E. (1974) Pitch, consonance, and harmony. The Journal of the Acoustical Society of America, 55(5), 1061–1069. DOI.
TeSS82
Terhardt, E., Stoll, G., & Seewann, M. (1982) Algorithm for extraction of pitch and pitch salience from complex tonal signals. The Journal of the Acoustical Society of America, 71(3), 679–688. DOI.
ThPa97
Thompson, W. F., & Parncutt, R. (1997) Perceptual judgments of triads and dyads: Assessment of a psychoacoustic model. Music Perception, 263–280.
TiBB00
Tillmann, B., Bharucha, J. J., & Bigand, E. (2000) Implicit learning of tonality: a self-organizing approach. Psychological Review, 107(4), 885.
Toiv97
Toiviainen, P. (1997) Optimizing self-organizing timbre maps: Two approaches. In M. Leman (Ed.), Music, Gestalt, and Computing (pp. 335–350). Springer Berlin Heidelberg
Tous05
Toussaint, G. (2005) Mathematical Features for Recognizing Preference in Sub-saharan African Traditional Rhythm Timelines. In S. Singh, M. Singh, C. Apte, & P. Perner (Eds.), Pattern Recognition and Data Mining (Vol. 3686, pp. 18–27). Berlin, Heidelberg: Springer Berlin Heidelberg
Tous04
Toussaint, G. T.(2004) A Comparison of Rhythmic Similarity Measures. In ISMIR.
Tymo06
Tymoczko, D. (2006) The Geometry of Musical Chords. Science, 313(5783), 72–74. DOI.
Tymo09a
Tymoczko, D. (2009a) Generalizing Musical Intervals. Journal of Music Theory, 53(2), 227–254. DOI.
Tymo09b
Tymoczko, D. (2009b) Three Conceptions of Musical Distance. In E. Chew, A. Childs, & C.-H. Chuan (Eds.), Mathematics and Computation in Music (pp. 258–272). Springer Berlin Heidelberg DOI.
Tymo11a
Tymoczko, D. (2011a) A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. (1 edition.). New York: Oxford University Press
Tymo11b
Tymoczko, D. (2011b) Mazzola’s Counterpoint Theory. Mathematics and Computation in Music, Springer, 297–310.
Tymo12
Tymoczko, D. (2012) The Generalized Tonnetz. Journal of Music Theory, 56(1), 1–52. DOI.
Tymo13
Tymoczko, D. (2013) Geometry and the quest for theoretical generality. Journal of Mathematics and Music, 7(2), 127–144. DOI.
VaKe10
Vassilakis, P. N., & Kendall, R. A.(2010) Psychoacoustic and cognitive aspects of auditory roughness: definitions, models, and applications. In IS&T/SPIE Electronic Imaging (p. 75270O–75270O). International Society for Optics and Photonics
Wagh76
Wagh, M. D.(1976) Cyclic autocorrelation as a translation invariant transform. India, IEE-IERE Proceedings, 14(5), 185–191. DOI.
XiQi06
Xin, J., & Qi, Y. (2006) A Many to One Discrete Auditory Transform. arXiv:math/0603174.
Zane06
Zanette, D. H.(2006) Zipf’s law and the creation of musical context. Musicae Scientiae, 10(1), 3–18. DOI.
ZhSi13
Zhao, Z., & Singer, A. (2013) Fourier–Bessel rotational invariant eigenimages. Journal of the Optical Society of America A, 30(5), 871. DOI.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6475211977958679, "perplexity": 10859.085259161133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122619.71/warc/CC-MAIN-20170423031202-00389-ip-10-145-167-34.ec2.internal.warc.gz"}
|
http://mymathforum.com/geometry/341446-please-help-me-about-problem.html
|
Geometry Geometry Math Forum
August 14th, 2017, 10:34 AM #1
Newbie
Joined: Aug 2016
From: Pakistan
Posts: 6
Thanks: 0
Attached Images
20170814_232243.jpg (85.3 KB, 13 views)
August 14th, 2017, 01:00 PM #2 Global Moderator Joined: May 2007 Posts: 6,342 Thanks: 534 Your note is very hard to read. I suggest you type it in directly. Thanks from Hammad
August 14th, 2017, 03:01 PM #3 Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 Your solution is correct. Thanks from Hammad
August 14th, 2017, 03:24 PM #4 Global Moderator Joined: Dec 2006 Posts: 18,048 Thanks: 1395 The answer is essentially correct, but it should be stated that angle A is calculated based on the fact that the angles of a triangle sum to 180°. The theorem about angles subtended is stated inaccurately. The reflex angle subtended by the major arc AC at O is 360° - 60° - 60° = 240°. Hence (by the inscribed angle theorem) the angle subtended by that arc at B (the angle you want to find) is 240°/2, which is 120°. Thanks from Hammad
Tags problem
Thread Tools Display Modes Linear Mode
Contact - Home - Forums - Cryptocurrency Forum - Top
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.834251344203949, "perplexity": 5734.068884193045}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824618.72/warc/CC-MAIN-20171021062002-20171021082002-00896.warc.gz"}
|
https://www.physicsforums.com/threads/is-it-true-photons-will-not-produce-an-interference-pattern-in-a-vacuum.353724/
|
# Is it true photons will not produce an interference pattern in a vacuum?
1. Nov 11, 2009
### CosmicVoyager
"In this study, it is shown with reasons that superposition principle does not work in vacuum. This case can be observed by Young type double slit experiment to be carried out. Since field-field interaction is carried through charged particles, in the absence of charged particles linear superposition of two fields is not possible and interference will not be observed."
http://arxiv.org/abs/physics/0212103
2. Nov 11, 2009
### ZapperZ
Staff Emeritus
Please note that while we do tolerate certain arxiv references for high energy physics and string/etc. subject areas (because that is a common practice within that community), the rest of the physics subject areas still adhere to peer-reviewed publications. This applies to these types of articles as well in areas of basic QM. Arxiv is not immune to having strange stuff that goes nowhere fast.
So unless it has been published, it should not be a topic of discussion on here just yet.
Zz.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8766918182373047, "perplexity": 827.0301592632717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589757.30/warc/CC-MAIN-20180717164437-20180717184437-00382.warc.gz"}
|
http://www.data-automaton.com/2018/01/09/nonlinear-regression/
|
# Nonlinear Regression
##### January 9, 2018
Written by Boutros El-Gamil
# 1. Idea
[watch video]
In a previous post, we saw the linear relationship between heights and weights of a group of persons (see the below figure), where both variables are growing together and shrinking together as well.
This is however not the case with every two variables. For instance, the average heart beats of a person has a nonlinear relationship with the number of minutes that person is spending in physical exercising. Number of heart beats is rapidly increasing during the first 5 minutes. Afterwards, it starts to decrease.
As another example, levels of testosterone hormone increase in men in the age between 25 and 44 years old (on average). Afterwards, testosterone level starts to decrease monotonically as men become older.
In such scenarios, a linear function can not express the relation between these variables, and a non-linear (polynomial) function should be used instead.
Suppose we have a set of observations represented by two dimensions $$x$$ and $$y$$, where these observations have non-linear relation, like the below figures.
Now suppose you need to find a function to represent the relation between these 2 variables (also called features). In this case, the function should be nonlinear (polynomial of degree $$>1$$) function.
As a reminder, a polynomial function of degree $$>1$$ is a function that has more than one direction. In the below figure, the left-side function has two directions, while the right-hand function has three directions.
# 2. Theory
As we explained in linear regression article,we want to find a nonlinear regression function (like the blue function below) that minimize distances (vertical green lines) between true and predicted values of dependent variable $$y$$ (i.e Least Squares approach).
The error function we need to minimize is defined as:
E(\mathbf{w}) = \frac{1}{N} \sum\limits_{i=1}^N [y^{(i)}-f(x^{(i)},\mathbf{w})]^2\tag{1}
which is the same as that of linear regression. The only difference is with hypothesis function $$f(x^{(i)},\mathbf{w})$$. This function will be nonlinear with respect to predictor $$x$$:
f(x^{(i)},\mathbf{w}) = w_0 {x^{(i)}}^0 + w_1 {x^{(i)}}^1 + w_2 {x^{(i)}}^2 + w_3 {x^{(i)}}^3 + … + w_P {x^{(i)}}^P\tag{2}
Or in a compact form:
f(x^{(i)},\mathbf{w}) = \sum\limits_{p=0}^P w_p {x^{(i)}}^p\tag{3}
where $$P$$ is the polynomial degree of function $$f(x^{(i)},\mathbf{w})$$.
In order to minimize function $$E(\mathbf{w})$$ (Equation 1), we need to put its derivatives with respect to $$\mathbf{w}$$ to $$0$$:
\nabla E(\mathbf{w})= 0\tag{4}
Let’s compute the derivative of $$E(\mathbf{w})$$ with respect to each coefficient $$w \in \mathbf{w}$$:
• For $$w_0$$:
\frac{\partial E(\mathbf{w})}{\partial w_0}= \frac{1}{N} \sum\limits_{i=1}^N \frac{\partial [y^{(i)} – (w_0 + w_1 {x^{(i)}} + w_2 {x^{(i)}}^2 + w_3 {x^{(i)}}^3 + … + w_P {x^{(i)}}^P)]^2}{\partial w_0}\tag{5}
\frac{\partial E(\mathbf{w})}{\partial w_0}= \frac{1}{N} \sum\limits_{i=1}^N \frac{\partial [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)]^2}{\partial w_0}\tag{6}
\frac{\partial E(\mathbf{w})}{\partial w_0}= \frac{1}{N} \sum\limits_{i=1}^N \frac{\partial [{y^{(i)}}^2 -2 w_0 y^{(i)} – 2 y^{(i)} \sum\limits_{p=1}^P w_p {x^{(i)}}^p + w_0^2 + 2w_0 \sum\limits_{p=1}^P w_p {x^{(i)}}^p + \sum\limits_{p=1}^P w_p {x^{(i)}}^{2p}]}{\partial w_0}\tag{7}
\frac{\partial E(\mathbf{w})}{\partial w_0}= \frac{1}{N} \sum\limits_{i=1}^N -2 y^{(i)} + 2w_0 + 2 \sum\limits_{p=1}^P w_p {x^{(i)}}^p\tag{8}
\frac{\partial E(\mathbf{w})}{\partial w_0}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)]\tag{9}
• For $$w_1$$:
\frac{\partial E(\mathbf{w})}{\partial w_1}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)]x^{(i)}\tag{10}
• For $$w_2$$:
\frac{\partial E(\mathbf{w})}{\partial w_2}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)]{x^{(i)}}^2\tag{11}
• For $$w_p$$ of any polynomial degree $$p \in [0:P]$$:
\frac{\partial E(\mathbf{w})}{\partial w_p}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)] {x^{(i)}}^p,
\forall p \in [0:P]\tag{12}
# 3. Closed Form Approach
[watch video]
In this method, we convert equation (12) into $$P+1$$ non-linear system, and solve the generated equations system using metrics’ operations. Let’s equalize equation (12) to 0 and re-order it:
\frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)] {x^{(i)}}^p = 0\tag{13}
\sum\limits_{i=1}^N {x^{(i)}}^p y^{(i)} = \sum\limits_{i=1}^N {x^{(i)}}^p (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)\tag{14}
\sum\limits_{i=1}^N {x^{(i)}}^p y^{(i)} = w_0 N + \sum\limits_{p=1}^P w_p {x^{(i)}}^{2p}\tag{15}
This non-linear equation system is written in matrix form as:
\begin{gather}
\begin{bmatrix}
\sum\limits_{i=1}^N y^{(i)} \\\\
\sum\limits_{i=1}^N x^{(i)} y^{(i)} \\\\
\sum\limits_{i=1}^N {x^{(i)}}^2 y^{(i)} \\\\
\vdots \\\\
\sum\limits_{i=1}^N {x^{(i)}}^p y^{(i)}
\end{bmatrix}
=
\begin{bmatrix}
w_0 \\\\
w_1 \\\\
w_2 \\\\
\vdots \\\\
w_p
\end{bmatrix}
\begin{bmatrix}
N & \sum\limits_{i=1}^N x^{(i)} & \sum\limits_{i=1}^N {x^{(i)}}^2 & … & \sum\limits_{i=1}^N {x^{(i)}}^p \\\\
\sum\limits_{i=1}^N x^{(i)} & \sum\limits_{i=1}^N {x^{(i)}}^2 & \sum\limits_{i=1}^N {x^{(i)}}^3 & … & \sum\limits_{i=1}^N {x^{(i)}}^{p+1} \\\\
\sum\limits_{i=1}^N {x^{(i)}}^2 & \sum\limits_{i=1}^N {x^{(i)}}^3 & \sum\limits_{i=1}^N {x^{(i)}}^4 & … & \sum\limits_{i=1}^N {x^{(i)}}^{p+2} \\\\
\vdots & \vdots & \vdots & \vdots\\\\
\sum\limits_{i=1}^N {x^{(i)}}^p & \sum\limits_{i=1}^N {x^{(i)}}^{p+1} & \sum\limits_{i=1}^N {x^{(i)}}^{p+2} & … & \sum\limits_{i=1}^N {x^{(i)}}^{2p}
\end{bmatrix} \tag{16}
\end{gather}
which simulates the form:
\mathbf{B} = \mathbf{wA}\tag{17}
then the vector $$\mathbf{w}$$ is computed as:
\mathbf{w} = \mathbf{A}^{-1} \mathbf{B}\tag{18}
We follow the same gradient descent algorithm of linear regression (listed below). The only difference will be with the new error function defined in equation (3) and its derivatives (equation (12)).
Algorithm1 GradientDescent($$E(\mathbf{w}),\mathbf{w},\eta$$)
1. Input:
2. $$E(\mathbf{w})$$: cost function
3. $$\mathbf{w}$$: initial values of coefficients vector
4. $$\eta$$: learning rate
5. Output:
6. $$\mathbf{w}$$: updated values of coefficients vector
7. Procedure:
8. repeat
1. $$w_p=w_p – \eta \frac{\partial E(\mathbf{w})}{\partial w_p}, \forall w_p \in \mathbf{w}$$
9. until $$\nabla E(\mathbf{w})= 0$$
10. return $$\mathbf{w}$$
Coefficients $$w_p$$’s in step (8.A.) are updated as follows:
w_p = w_p – \eta \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)] {x^{(i)}}^p\tag{19}
# 5. Multivariate Nonlinear Regression
Let’s consider the following multivariate nonlinear function (equation 20) between dependent variable $$y$$, and vector of independent variables $$\mathbf{x} = [x_1,x_2]$$:
f(\mathbf{x}^{(i)},\mathbf{w}) = w_0 + w_1 x_1^{(i)} + w_2 x_2^{(i)} + w_3 {x_1^{(i)}}^2 + w_4 x_1^{(i)} x_2^{(i)} + w_5 {x_2^{(i)}}^2\tag{20}
This nonlinear equation can be transformed to linear equation, by introducing a new vector $$\mathbf{z}$$:
\mathbf{z} = [x_1^{(i)},x_2^{(i)}, {x_1^{(i)}}^2, x_1^{(i)} x_2^{(i)}, {x_2^{(i)}}^2]\tag{21}
By substituting $$\mathbf{z}$$ with it’s corresponded values in equation (20), we obtain the following linear equation:
f(\mathbf{z},\mathbf{w}) = w_0 + w_1 z_1 + w_2 z_2 + w_3 z_3 + w_4 z_4 + w_5 z_5\tag{22}
Equation (22) converts the multivariate nonlinear regression into linear regression, where we can use the same methods of multivariate linear regression.
## 5.1 Closed Form Approach
We build the following $$N \times (M+1)$$ matrix $$\mathbf{X}$$:
\begin{gather}
\mathbf{X}
= \begin{bmatrix}
1 & z_1^{(1)} & z_2^{(1)} & z_3^{(1)} & z_4^{(1)} & z_5^{(1)} \\\\
1 & z_1^{(2)} & z_2^{(2)} & z_3^{(2)} & z_4^{(2)} & z_5^{(2)} \\\\
\vdots \\\\
1 & z_1^{(N)} & z_2^{(N)} & z_3^{(N)} & z_4^{(N)} & z_5^{(N)}
\end{bmatrix}
= \begin{bmatrix}
1 & x_1^{(1)} & x_2^{(1)} & {x_1^{(1)}}^2 & x_1^{(1)} x_2^{(1)} & {x_2^{(1)}}^2 \\\\
1 & x_1^{(2)} & x_2^{(2)} & {x_1^{(2)}}^2 & x_1^{(2)} x_2^{(2)} & {x_2^{(2)}}^2 \\\\
\vdots \\\\
1 & x_1^{(N)} & x_2^{(N)} & {x_1^{(N)}}^2 & x_1^{(N)} x_2^{(N)} & {x_2^{(N)}}^2
\end{bmatrix}\tag{23}
\end{gather}
and a $$N\times 1$$ target vector $$\mathbf{Y}$$:
\begin{gather}
\mathbf{Y}
= \begin{bmatrix}
y^{(1)} \\\\
y^{(2)} \\\\
\vdots \\\\
y^{(N)}
\end{bmatrix}\tag{24}
\end{gather}
The vector of coefficients $$\mathbf{w}$$ is calculated as:
\mathbf{w} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{Y}\tag{25}
We use the same algorithm above with the following coefficients’ updates:
w_0= w_0 – \eta\frac{-2}{N} \sum\limits_{i=1}^N y^{(i)} – (w_0 + \sum\limits_{j=1}^5 w_j z_j)\tag{26}
w_j= w_j – \eta\frac{-2}{N} \sum\limits_{i=1}^N z_j [y^{(i)} – (w_0 + \sum\limits_{j=1}^5 w_j z_j)]\tag{27}
We also substitute each $$z_j$$ in equations (26) and (27) with it’s corresponded value in $$\mathbf{x}$$ in equation (21).
# 6. Polynomial Degree Selection (Bias -Variance Tradeoff)
[watch video]
A question may rise in the discussion of nonlinear regression: which polynomial degree ($$p$$) should we use to build our regression function? There is no standard answer to this question. A good way to estimate the value of $$p$$ is to try out different values and select between. Your selection should be in the middle between underfitting and overfitting situations.
On the one hand, the case of underfitting (e.g. $$p=1$$) generate a regression function which is highly biased toward erroneous assumptions of training data (like the case of below figure, where nonlinear variable is predicted by linear function), and thus is far from simulating the relationship between target and predictor variables.
On the other hand, the case of overfitting (e.g. $$p=N-1$$ in below figure) generates regression function with high variance, makes it highly sensitive to small fluctuations in the training data, and accordingly recording error rate close to $$0$$. Overfitting is usually generating models that can not precisely interact with unseen data, as these models are highly biased to the training set of observations, and the corresponded regression functions are usually quite complicated.
The proper regression model (like the one in the following figure) is usually estimated by making a tradeoff between underfitting and overfitting scenarios, where the regression function is minimizing the error rate, while keeping itself as simple as possible (i.e. with lowest possible number of coefficients).
## 6.1 Regularization
A common technique to overcome the problem of overfitting is to add a penalty term to the error function $$E(\mathbf{w})$$. The role of this penalty term – sometimes called also smooth term – is to minimize the number of coefficients used in regression function. Now, we define the new error function ($$\tilde{E}$$) to be:
\tilde{E}(\mathbf{w}) = \frac{1}{N} \sum\limits_{i=1}^N [y^{(i)}-f(x^{(i)},\mathbf{w})]^2 + \frac{1}{2} \lambda \sum\limits_{p=1}^P w_p^2\tag{28}
The $$\lambda$$ term in equation (28) is called the regularization coefficient, and its role is to control the simplicity of the error function in terms of $$\mathbf{w}$$ length. If $$\lambda$$ is large, the function tends to be simple, and we move to the underfitting situation, while if $$\lambda$$ is small, the function tends to be complex and we move to the overfitting situation. If $$\lambda = 0$$, the regularization term is deleted and we return to the definition (1) of error function. The following plots show nonlinear regression functions generated by equation (28) with different $$\lambda$$ values.
Please note also, that the intercept coefficient $$w_0$$ is excluded from the penalty term in (28), to make our error function independent from the origin of target variable $$y$$. The intercept coefficient $$w_0$$ has nothing to do with the simplicity or complexity degree of the regression function. The only effect of changing $$w_0$$ is to move the fitted curve from it’s place into one direction of the target axis. Therefore, $$w_0$$ does not need to be regularized with other coefficients.
Now, we will expand equation (28) by substituting the hypothesis function with the compact form of nonlinear regression formula in equation (3):
\tilde{E}(\mathbf{w}) = \frac{1}{N} \sum\limits_{i=1}^N [y^{(i)}-(\sum\limits_{p=0}^P w_p {x^{(i)}}^p)]^2 + \frac{1}{2} \lambda \sum\limits_{p=1}^P w_p^2\tag{29}
and compute the derivative with respect to each $$w_p \in \mathbf{w}$$:
\frac{\partial \tilde{E}(\mathbf{w})}{\partial w_p}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)] {x^{(i)}}^p + \frac{\partial (\frac{1}{2} \lambda w_p^2)}{\partial w_p}\tag{30}
which is reduced to:
\frac{\partial \tilde{E}(\mathbf{w})}{\partial w_p}= \frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)] {x^{(i)}}^p + \lambda w_p\tag{31}
Putting equation (31) to zero will generate:
\frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – \sum\limits_{p=0}^P w_p {x^{(i)}}^p] {x^{(i)}}^p + \lambda w_p = 0\tag{32}
### 6.1.1 Closed Form Approach
Let’s re-write function (32) into matrix form:
[\mathbf{Y} – \mathbf{wX}] \mathbf{X}^T + \lambda \mathbf{w} = 0\tag{33}
where $$\mathbf{X}$$, $$\mathbf{Y}$$, and $$\mathbf{w}$$ are defined in equation (16). Now we re-arrange equation (33):
\mathbf{X}^T \mathbf{Y}= \mathbf{X}^T \mathbf{Xw} – \lambda \mathbf{w}\tag{34}
\mathbf{X}^T \mathbf{Y}= \mathbf{w} [\mathbf{X}^T \mathbf{X} – \lambda\mathbf{I}] \tag{35}
Coefficients are calculated as:
\mathbf{w} = [\mathbf{X}^T \mathbf{X} – \lambda\mathbf{I}]^{-1} \mathbf{X}^T \mathbf{Y} \tag{36}
For your convenience, putting $$\lambda = 0$$ in (36) will give us same solution as equation (25).
Please note, that both (25) and (36) equations are valid for both uni- and multivariate regression as closed-form.
In order to apply gradient descent algorithm, we add the penalty term $$\lambda w_p$$ to equation (27):
w_0= w_0 – \eta\frac{-2}{N} \sum\limits_{i=1}^N y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p) \tag{37}
w_p= w_p – \eta\frac{-2}{N} \sum\limits_{i=1}^N [y^{(i)} – (w_0 + \sum\limits_{p=1}^P w_p {x^{(i)}}^p)]{x^{(i)}}^p + \lambda w_p,
The intercept coefficient $$w_0$$ is computed the same as in equation (26). The formulas (37) and (38) are valid for both uni- and multivariate regressions.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8866828680038452, "perplexity": 3210.760999957583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540547165.98/warc/CC-MAIN-20191212205036-20191212233036-00200.warc.gz"}
|
https://4gravitons.com/2019/11/22/qcd-and-reductionism-stranger-than-youd-think/?like_comment=12279&_wpnonce=6b37fbf842
|
# QCD and Reductionism: Stranger Than You’d Think
Earlier this year, I made a list of topics I wanted to understand. The most abstract and technical of them was something called “Wilsonian effective field theory”. I still don’t understand Wilsonian effective field theory. But while thinking about it, I noticed something that seemed weird. It’s something I think many physicists already understand, but that hasn’t really sunk in with the public yet.
There’s an old problem in particle physics, described in many different ways over the years. Take our theories and try to calculate some reasonable number (say, the angle an electron turns in a magnetic field), and instead of that reasonable number we get infinity. We fix this problem with a process called renormalization that hides that infinity away, changing the “normalization” of some constant like a mass or a charge. While renormalization first seemed like a shady trick, physicists eventually understood it better. First, we thought of it as a way to work around our ignorance, that the true final theory would have no infinities at all. Later, physicists instead thought about renormalization in terms of scaling.
Imagine looking at the world on a camera screen. You can zoom in, or zoom out. The further you zoom out, the more details you’ll miss: they’re just too small to be visible on your screen. You can guess what they might be, but your picture will be different depending on how you zoom.
In particle physics, many of our theories are like that camera. They come with a choice of “zoom setting”, a minimum scale where they still effectively tell the whole story. We call theories like these effective field theories. Some physicists argue that these are all we can ever have: since our experiments are never perfect, there will always be a scale so small we have no evidence about it.
In general, theories can be quite different at different scales. Some theories, though, are especially nice: they look almost the same as we zoom in to smaller scales. The only things that change are the mass of different particles, and their charges.
One theory like this is Quantum Chromodynamics (or QCD), the theory of quarks and gluons. Zoom in, and the theory looks pretty much the same, with one crucial change: the force between particles get weaker. There’s a number, called the “coupling constant“, that describes how strong a force is, think of it as sort of like an electric charge. As you zoom in to quarks and gluons, you find you can still describe them with QCD, just with a smaller coupling constant. If you could zoom “all the way in”, the constant (and thus the force between particles) would be zero.
This makes QCD a rare kind of theory: one that could be complete to any scale. No matter how far you zoom in, QCD still “makes sense”. It never gives contradictions or nonsense results. That doesn’t mean it’s actually true: it interacts with other forces, like gravity, that don’t have complete theories, so it probably isn’t complete either. But if we didn’t have gravity or electricity or magnetism, if all we had were quarks and gluons, then QCD could have been the final theory that described them.
And this starts feeling a little weird, when you think about reductionism.
Philosophers define reductionism in many different ways. I won’t be that sophisticated. Instead, I’ll suggest the following naive definition: Reductionism is the claim that theories on larger scales reduce to theories on smaller scales.
Here “reduce to” is intentionally a bit vague. It might mean “are caused by” or “can be derived from” or “are explained by”. I’m gesturing at the sort of thing people mean when they say that biology reduces to chemistry, or chemistry to physics.
What happens when we think about QCD, with this intuition?
QCD on larger scales does indeed reduce to QCD on smaller scales. If you want to ask why QCD on some scale has some coupling constant, you can explain it by looking at the (smaller) QCD coupling constant on a smaller scale. If you have equations for QCD on a smaller scale, you can derive the right equations for a larger scale. In some sense, everything you observe in your larger-scale theory of QCD is caused by what happens in your smaller-scale theory of QCD.
But this isn’t quite the reductionism you’re used to. When we say biology reduces to chemistry, or chemistry reduces to physics, we’re thinking of just a few layers: one specific theory reduces to another specific theory. Here, we have an infinite number of layers, every point on the scale from large to small, each one explained by the next.
Maybe you think you can get out of this, by saying that everything should reduce to the smallest scale. But remember, the smaller the scale the smaller our “coupling constant”, and the weaker the forces between particles. At “the smallest scale”, the coupling constant is zero, and there is no force. It’s only when you put your hand on the zoom nob and start turning that the force starts to exist.
It’s reductionism, perhaps, but not as we know it.
Now that I understand this a bit better, I get some of the objections to my post about naturalness a while back. I was being too naive about this kind of thing, as some of the commenters (particularly Jacques Distler) noted. I believe there’s a way to rephrase the argument so that it still works, but I’d have to think harder about how.
I also get why I was uneasy about Sabine Hossenfelder’s FQXi essay on reductionism. She considered a more complicated case, where the chain from large to small scale could be broken, a more elaborate variant of a problem in Quantum Electrodynamics. But if I’m right here, then it’s not clear that scaling in effective field theories is even the right way to think about this. When you have an infinite series of theories that reduce to other theories, you’re pretty far removed from what most people mean by reductionism.
Finally, this is the clearest reason I can find why you can’t do science without an observer. The “zoom” is just a choice we scientists make, an arbitrary scale describing our ignorance. But without it, there’s no way to describe QCD. The notion of scale is an inherent and inextricable part of the theory, and it doesn’t have to mean our theory is incomplete.
Experts, please chime in here if I’m wrong on the physics here. As I mentioned at the beginning, I still don’t think I understand Wilsonian effective field theory. If I’m right though, this seems genuinely weird, and something more of the public should appreciate.
## 27 thoughts on “QCD and Reductionism: Stranger Than You’d Think”
1. Wouter M.
hi,
for those of us not in Particle Physics, it would be helpful to give an example or analogy for a case where the scale factor changes the physical effect of an interaction. As I see it, the familiar physical laws like electromagnetism are independent of scale : E = c q1 q2 /r as the electrostatic potential between two charges. The value of E changes as r changes, but the constant c does not change. So, this is not a good example of the effect you discuss. But what is?
What is the simplest case where renormalisation is required?
Is there an analogue in pure mathematics where a similar “technique” is used to get rid of infinities? Surely not the old L’Hopital’s rule?
Like
1. 4gravitons Post author
This is a tricky question to answer, in part because some of what I’m talking about is genuinely a quantum effect. So it’s hard to find a physics analogy…but here’s a vaguer one:
Let’s say instead of physics, you’re studying international relations. You could think about different nations as having their own interests and desires, communicating and competing with each other. Alternatively, you could zoom in to a smaller scale, and look at the behavior of individual people. Once again, you’d model them with their own interests and desires, communicating and competing. Your models might look very similar, but some aspects would be different: maybe nations have more trouble communicating than people do, or have stronger “desires”. You’ve changed the scale and you’ve got almost the same theory, but a few of your “constants” have changed.
Quantum field theory is like that, but instead of just two “scales” it’s continuous. You need to do this in pretty much every quantum field theory. Only a few special ones have no infinities, and none of those are ones we use for everyday physics. Quantum electrodynamics, quantum chromodynamics, the Higgs boson, they all need renormalization.
There are lots of cases in mathematics where one regularizes to avoid infinities in one way or another. There are many different ways of doing this, depending on what you’re interested in doing. Here’s just one context.
Like
2. itaibn
I’d say that the scaling laws of classical materials can be considered a simpler example of this phenomenon. There is the classic fact, which I believe is due to Galileo, that if you have an object that’s a certain size you cannot scale all of its parts proportionally and expect this resized object to behave the same way. Compare a pillar in some cathedral that supports a certain weight, with its matching pillar in the doubled cathedral, which is twice as long and broad and must support a larger weight. If we imagine it is a square pillar then the doubled pillar can be thought of as being made of eight versions of the original pillar bunched together. Since placing one pillar on top of the other doesn’t affect how much weight it can support, the doubled pillar is equivalent to four of the original pillar placed side-by-side, and can support four times as much weight. On the other hand, the structure the doubled pillar is supporting can also be thought of as eight versions of the original structure, so has eight times the weight. So even if the original pillar can support its weight doesn’t mean that the pillar in the twice-as-large cathedral can.
To put it in a more idealized setting, if we consider a cube of some material with side-length L, and let $f (L)$ be the its weight and $g (L)$ be the weight it can support, then $f (2 L) = 8 f (L)$ and $g (2 L) = 4 g (L)$. More important than the actual formulas is how they are derived: By imagining a cube with side-length 2L as being made up of eight cubes with side-length L. In fact, for any length L’ much smaller than L we can model the cube of length L as being made up of many smaller cubes of length L’. The smaller L’ is, the better the model for the cube is, because it can account for things such the cube stretching and bending in a very detailed way or small pieces breaking off of it. However, for this to work the properties (strength weight, …) of the cube of length L’ need to be set to be compatible with the properties of the cube of length L.
Like
3. Iliody
Pure speculattion, maybe (almost surelly wrong):
If really don’t have E=c q_1 q_2/r, but instead you have E=k q_1 q_2/(r^1.3), but you supposed it was like the first law and made an experiment with a typical scale L in which you measured “c”. Then, when you Made again your experiment ay different scales you saw that E≈c q_1 q_2/r -c ln(L’/L)q_1 q_2/r=(c-c ln(r/L)) q_1 q_2 as if your constant c wasn’t constant, but ir was something like c(r)≈c(L)-0.3 c(L) ln(r/L). The thing here is that your theory classically looks as if it behaved well only if you put the first thing, but then Quantum field theory rules moved your theory to behave un the second way.
Like
1. 4gravitons Post author
This is kind of what’s going on, but there’s a key subtlety. In your example, the scientist doesn’t have to keep trying to measure “c”: if they’re smart enough they can figure out the real scaling and measure “k” instead.
The difference is that in quantum field theory, the equivalent “k” would have to be infinite. There just isn’t a “bare constant” that makes sense in theories like QCD. So the “c version” is our only choice in those cases.
Like
1. Iliody
I am not sure if it’s necesarelly Infinity. c and k have different scalling dimensions and c(lenght scale) will diverge if what’s really going on is k-like, but for knowing about k we need a nonperturbative definition on the theory, thing that we ussually don’t have.
In some CFT’s in two dimensions you know that you have that exactly.
I don’t know if that happens in QCD (I find really unlikely that it was the case, because of mass gap and that kind ir things). In N=4 is known what are the two point functions at nonperturbative level?
Like
1. 4gravitons Post author
Ah sure. Yeah, if your theory is integrable or otherwise has a closed-form nonperturbative description then yeah, the analogy is much better. But indeed as you say QCD probably isn’t like that.
At least in planar N=4 the operator dimensions are known nonperturbatively yeah.
Like
4. Schmelzer
Water near the point of boiling. You have already small bubbles of vapor. The average size of these bubbles depends on temperature and increases if one comes close to the boiling temperature. The mathematics to handle this is the mathematics of renormalization.
The point of this type of renormalization is not to get rid of infinities. It is the atomic structure which regularizes the theory.
Like
2. Kevin Zhou
As a phenomenologist, this post sounds odd to me, because it seems to be conflating what could be consistent mathematically with what is true physically. Yes, it’s possible that QCD (or more realistically the SM) could be correct up to very high energy scales, in the sense that it wouldn’t be mathematically inconsistent.
But the point of parametrizing things with cutoff scales is that we don’t know if that actually is the case, in our universe! It is, after all, the point of science to figure out what actually exists. So the fact that QCD has a continuum limit and QED has a Landau pole just isn’t relevant from this point of view. We don’t care about extrapolating up to 10^100 TeV when qualitatively new stuff could appear at 10 TeV. The cutoff is meant to stand in for any number of unknown effects, which could range from just the same old boring scaling, to new particles, to even a breakdown of quantum field theory itself.
Like
1. 4gravitons Post author
I agree, and I’m not saying that we should take QCD seriously as a theory to 10^100 TeV or whatever.
But some theory should be valid up to 10^100 TeV (even if all the theory says is “10^100 TeV doesn’t make sense”). It’s worth thinking about what sort of properties such a theory would need to have. And the impression I get (from people who seem to know Wilsonian EFT more than I do) is that one way such a theory could be is that it could be like QCD. That is, one type of theory that can be valid up to 10^100 TeV and beyond is an asymptotically free theory. Again, that doesn’t mean QCD itself is valid that far, just that when we do have a “final theory” it may well be asymptotically free (or I suppose asymptotically safe). Not the only option, but one of them.
And my point in this post is that’s weird! If the real world really was described by an asymptotically free theory up to arbitrarily high energies, that clashes with our naive intuitions about reductionism pretty heavily.
So does that mean the real world cannot be asymptotically free? I don’t think so, not on the basis of this at least. Does it mean our intuitions about reductionism are wrong? Probably! Does it mean quantum field theory itself is going to break down? Not because of this I don’t think, though it might break down anyway!
And yeah, it’s perfectly fine to approach all this by saying “we never have access to the far UV so who cares?” I don’t object to that attitude. But I think some people will still care, and it’s worth thinking about what to tell them.
Like
3. clayton
I’m not sure there’s really any weirdness — there is no energy E at which a sufficiently precise experiment would be compatible with alpha_s(E) = 0. You’d always measure some deflection if you fired two quarks at one another from asymptotically far away (for example). Such an energy simply does not exist, given the input that alpha_s=4pi at some other energy. Thus, alpha_s always has somewhere to run from. Perhaps there’s an ambiguity about what “asymptotically far away” and “some deflection” mean in my sentence above, but those are IR questions, not UV ones, and those need to be dealt with to create a sensible S-matrix at any energy (which presumably, you’ve done if you’re talking about scattering and so forth)
Like
1. 4gravitons Post author
I think that’s part of the weirdness though: yes, at any given energy, there’s a finite higher energy to run there from. The weirdness is that there’s no “final energy”, no lowest-level theory that your low-energy theories “reduce to”. It’s just an infinite (continuous) chain of one theory reducing to another. There’s nothing illogical or impossible about that, but it’s weird! I think it’s very much not something the average person would have expected to be possible.
Like
1. clayton
Not trying to be obtuse, but: what is the alternative that you think is most satisfying? QED runs to a Landau pole, but maybe it’s just electronballs behaving like billiard balls at higher energy. Imagine QCD turning into nuclear physics (which itself is in some sense “residual” QCD forces between nucleons), just reversed as a function of energy — it doesn’t have to be something “heartier” like string theory (or the physics that underlies chemistry) up there to resolve the Landau pole. It might “just be”. This, too, is probably not “maximally classic reductionism,” but we don’t know which is the answer until we run an experiment at a sufficiently high energy. One case is equivalent to saying “there’s a few constants we can’t predict (like the electronball mass gap or electronball spectroscopic splittings),” while the other is saying “we were totally misled by what appeared to simple organizing principles at low energy, which have very different interpretations at high energies.”
Having a theory that is replaced (in a predictable way) by the same theory is a little simpler than either of these, but I think one way or another this points to the fact that there’s a continuum (or, if you prefer: “a wide range”) of possibility for UV completions. Perhaps this only reinforces your claim that the real picture is “very much not something the average person would have expected to be possible,” but I think you overestimate “what the average person would have expected to be possible” in the sense that the “average person” probably doesn’t even know that chemistry is derived from physics. I’d wager that understanding thermodynamic limits already puts someone in sufficiently rarefied company that they can accept that EFT is complicated 🙂
(As an unrelated quibble, let me say also that I think that your definition “Reductionism is the claim that theories on larger scales reduce to theories on smaller scales” uses “reduce to” in exactly the opposite way that most phenomenologists use it. To go to high energies is to “complete” the theory; to go to low energies is to “reduce” the theory. Think about the a- or c-theorems: the function monotonically decreases as energy decreases, which sounds like a reduction to me…)
Like
1. 4gravitons Post author
There’s two uses of the word reduction that are clashing here, yes, and I’m leaning on the philosophical one (though I’ll admit I’ve never heard of going to the IR as “reducing” a theory, but maybe I just don’t talk to enough phenomenologists).
I think I see what you’re getting at here, but let me know if I’m misunderstanding. You’re saying that, if there are going to be some “physical accidents” in your theory anyway (value of the coupling, mass gaps, etc.) that can’t be explained by a more fundamental theory, then it shouldn’t really matter whether they’re continuously varying with scale (like QCD) or whether there is a final scale where they are defined (“electronballs”). Either way we have some high-energy theory that has unexplained properties.
In my view there is a meaningful difference, and it is that you can define your electronball theory without RG. That is, you can specify all the theory’s parameters without adding an artificial cutoff scale. The theory you get won’t necessarily be useful at all scales, but at least in principle physics at any scale would be derivable from a scale-agnostic theory.
That’s not true of QCD. You can’t define QCD without adding in a cutoff scale. If you don’t, you have no way of specifying the coupling. The theory depends on what is essentially a subjective quantity, the scale at which you choose to cut off your description.
I don’t blame you for being comfortable with that, I think as physicists have learned to accept it. But I think most people would find it strange, in the same way they find quantum mechanics strange. And I find it interesting that we don’t emphasize this when we talk about physics, in the same way we emphasize the weirdness of say quantum mechanics.
(As an aside: yes, the average person doesn’t care about physics at all. That’s a fully general argument against any point about “intuition” at all. For now, maybe it’s better to think about an “average reader of this blog”. I think my non-physicist readers would find this behavior of QCD interesting and weird, even if the literal average person wouldn’t.)
Like
1. clayton
So, I guess where we part ways is the statement “you can define your electronball theory without RG” — why do you think that’s true? There are some (dimensionful) “high energy constants” in that theory, but there’s also running couplings that have threshold corrections and the whole works. The nuclear EFT, which can be defined at many scales (a “full” EFT, a pionless one, etc.), certainly has these properties (and they’re certainly not fully understood! RGEs in the nuclear EFT are an area of active research).
Perhaps QCD feels weird because, despite going to higher energies, the degrees of freedom remain the same — I think that’s ultimately the difference between QCD and electronball (or electronstring) theory: it just so happens that with QCD we’ve identified good degrees of freedom at what feels like a low scale. QED has a definite cutoff beyond which the degrees of freedom change to those of electronball/electronstring theory (whichever one is verified at the Nth collider after this one, I’m agnostic until then 🙂 ), but what that means to me is that when you say QCD “depends on what is essentially a subjective quantity, the scale at which you choose to cut off your description”, I’d say “so does QED” — you need to know how far you are from the Landau pole to know how good your calculation of electron scattering angles can possibly be, since there will be fractional corrections of order s/Lambda_Landau^2. This is why the prediction of the muon’s g-2 is less precise than the electron’s — schematically, alpha_EMalpha_sm_mu^2/Lambda_QCD^2 is a larger number than alpha_EMalpha_sm_e^2/Lambda_QCD^2, and hadronic matrix elements can’t be ignored in the muon calculation even though they can be in the electron one. If QCD-charged particles didn’t couple to the photon (say), then we would only have fractional uncertainties of order alpha_EMalpha_sm_mu^2/v_EW^2, which is quite a bit smaller. Ergo, the “scale at which you choose to cut off your description” matters here, too.
Let me say: I appreciate the back and forth, I’m glad you’re learning about EFT, and I’m by no means an expert in all this, so please keep at it if I’m being unclear or inconsistent!
Like
1. 4gravitons Post author
Likewise, glad for the enlightening discussion!
I think in retrospect I was confused by whether in your last comment you were literally thinking of the electronballs behaving like (classical? quantum?) billiard balls, or whether you were thinking of a distinct QFT taking over there. Literal classical billiard balls can be certainly be defined without RG: you still might find RG useful for handling them, but you can specify all the “parameters of your theory” without it. I agree if you ended up with something more analogous to nuclear EFT then you likely can’t avoid RG, so my point is closer to “QFT is weird” than “specifically QCD is weird”. The latter just felt like a cleaner example.
That said, I think your argument about precision is missing the point. Yes, you don’t want to do perturbation theory in the bare coupling, even if you had one. That’s a good reason to use RG in practice. But when I pointed that out in a post explaining running couplings a while back, I got some (deserved!) pushback. RG isn’t just some pragmatic thing we do to make sure our perturbation theory works, in many cases it’s part of how the nonperturbative theory is defined. In the context of this post, the need to use RG to do perturbation theory isn’t particularly strange: you’re using something subjective (cutoff scale) to do something else subjective (get a good approximation under certain experimental conditions). What’s strange is if subjectivity is baked into the physics at its core, so that even if you could calculate everything exactly and nonperturbatively you’d need to add an arbitrary choice of scale.
Like
1. clayton
Ah, sorry — by “like billiard balls” I just meant “without a long-range force.” But I didn’t mean for that to be taken too literally. Anything could happen above the Landau pole; we’d need to do experiments to figure out the right theory up there!
Anyway, I’m still not getting the point you’re trying to make. I simply don’t see a qualitative difference between QED/electronballology and QCD/nuclear physics. QED gives us an unambiguous Landau pole, QCD gives us an unambiguous strong coupling scale. The centrality of that energy doesn’t seem (to me) to be subjective in either theory. In some sense there’s a direction of RG flow that makes asymptotic freedom feel different, but in both cases there’s a strong coupling energy and simple prescription for what you do away from that energy.
Like
1. 4gravitons Post author
There’s a particular loophole I was worried about that it sounds like you might be invoking, so to clarify: are you saying that once you specify the strong-coupling scale, QCD is unambiguous? I.E., there are no other free parameters, and the only difference between QCD with different couplings is the choice of units you use for energy?
If that’s the case, I agree that my argument doesn’t work. If it is, is the same true for QCD with massive quarks? I would think that at some point you’d need to consider a theory with multiple scales and there would be a free parameter that wouldn’t just come down to a choice of units.
If that’s not what you were getting at (or in a sufficiently complicated theory if QCD doesn’t work for this), then I’d argue that the direction of the flow actually does matter, at least if we still care about philosophical reductionism. If we do, then we expect parameters at low energy to be determined by parameters at high energy, and not the reverse. Even if we can do the math either way, one direction has a causal meaning that the other doesn’t.
Again, this may well mean we shouldn’t care about philosophical reductionism. It also may just mean, as I comment in the post, that it’s wrong to think about EFT in terms of low-energy scale EFTs philosophically reducing to high-energy scale EFTs, and that really we should be thinking of reductionism in terms of non-QFT theories reducing to QFT, and not of different scales of the same EFT reducing to each other.
Like
1. clayton
To answer the question as cleanly as possible (and according to my best understanding, which, again, may not be perfect): once you specify Lambda_QCD and the numbers and masses of quarks*, then QCD is unique. It just so happens that QCD appears “simple” at energies above strong coupling and QED appears “simple” at energies below; the “aboveness or belowness” is determined by the gauge group and matter content, but each is unique, and (to me) neither is weirder or less scale-sensitive than the other. Interestingly, going to more supersymmetric QFTs typically allows one to formulate a duality between theories with different matter and gauge content such that there’s a “simple” calculation at any scale (one theory is weakly coupled when the other is strongly coupled) — this, I think, is where some of the truest “weirdness” (or beauty) of QFT lurks 🙂
*you need to know the masses to know when to add threshold corrections and alter the running
Like
1. 4gravitons Post author
Hmm. Ok, so is one way to think about this that a theory is defined by the shape of its RG trajectories? So I draw some curve for the behavior of the coupling, it diverges at some point and its running changes at other points, and the ratio between the point where it diverges and the point its running changes is the ratio between Lambda_QCD and one of the quark masses?
I think that works from one of the perspectives I was describing: if you call QCD itself a “theory”, then you’re fine: you have a well-defined theory, and theories at lower energies (pion models, chemistry…) (philosophically) reduce to that theory.
It’s still confusing from the other perspective, where the individual theories are things like “QCD at scale 1 TeV” instead of “QCD as a whole”. From that perspective, you ask “why does the coupling diverge at Lambda_QCD?” and the answer is “because the coupling was X at Y energy above Lambda_QCD”, and you get the weird infinite regress of “why X? Because Y” that was bugging me earlier. (Again, maybe that means this perspective is just wrong!)
Overall, there’s something deeper that bugs me, which is the statement that you need RG to define (not just use in practice, but define) any of these theories in the first place. But maybe I’m mistaken about that, and you can imagine one of these theories just defined by all its correlation functions with no mention of RG?
I agree that there’s a lot of weirdness once duality enters the picture, but on a certain level (at least from my perspective), it’s not as weird, because the theories related are usually CFTs, or otherwise theories without UV divergences (and often, integrable theories). So you’ve got two perspectives, one where the coupling is strong and the other where it is weak, but ultimately you can think about the theory as defined by correlation functions with some parameters, and the duality just corresponding to how you interpret the “meaning” of those parameters and correlation functions.
Like
2. clayton
I think I’d agree that “a theory is defined by the shape of its RG trajectories,” but if you want to literally define a theory which is “QCD at scale 1 TeV” instead of “QCD as a whole”, then you are no longer allowed to ask “why does the coupling diverge at Lambda_QCD?” — you only have one energy, which is 1 TeV. The coupling is well-defined for this “candidate theory,” but you can’t access Lambda_QCD. Only “QCD as a whole” allows you to run between energies and ask questions about different energies
As for “Overall, there’s something deeper that bugs me, which is the statement that you need RG to define (not just use in practice, but define) any of these theories in the first place. But maybe I’m mistaken about that, and you can imagine one of these theories just defined by all its correlation functions with no mention of RG?” — I’ll hazard that an alternate “complete” definition of a theory is via its correlation functions as well as every operator’s (exact) scaling dimension (which in a weakly coupled limit tells you how it behaves under RG evolution), but now I’m really out of my element 🙂
Like
3. 4gravitons Post author
Wouldn’t you still be able to access Lambda_QCD from the “QCD at scale 1 TeV” theory, though? The higher-energy theories on the trajectory should have all the information about what happens at lower energies (barring a version of a Landau pole that presents an essential singularity like Hossenfelder was speculating about).
Fair enough about correlation functions+scaling dimensions. In CFT indeed all you need is the dimension of each operator and the structure constants (both as exact functions of the coupling). But I had the impression that there’s an issue with this for non-CFTs. I’m out of my element there too so I may just be misremembering!
Like
4. clayton
I was just being pedantic about accessing Lambda_QCD from 1 TeV — if you define a theory in which sqrt(s) = 10 TeV but all other facts about QCD obtain, then, well: this is a theory where sqrt(s) is always 10 TeV. You can change the number of incoming states that you prepare when you run an experiment, perhaps, and you can speculate about an alternate universe where sqrt(s) sometimes reaches as low as Lambda_QCD, but sqrt(s) for you is always 10 TeV, so you’ll never test those speculations. But, yes, you’d get the right energy scale when you (and your 10 TeV pencil) did the calculation 🙂
Like
5. 4gravitons Post author
Ok, now I’m confused. I had the impression that the “scale” of a theory wasn’t literally sqrt(s) (after all, if you aren’t computing a scattering amplitude you don’t even have an “s”!) Rather, it was a cutoff scale that characterizes how you’ve coarse-grained. Calculating things at other energies will introduce large logarithms and make your perturbation theory worse, but the theory isn’t inapplicable at those energies, it’s just less useful. Am I mistaken?
Like
6. clayton
Ah — I misunderstood. Yes, what you’ve written is correct: there are higher-twist operators and so forth which would seem to blow up beyond X TeV, but which you can calculate with at any energy below X TeV. I thought you were describing something narrower — indeed, you’re using totally standard terminology, I just misinterpreted. Carry on 🙂
Like
4. Andrew Oh-Willeke
I’m not sure that I buy your line of reasoning in the case of QCD.
Generally speaking, the theory that most people would think about reducing to QCD would be effective theories of nuclear physics involving atoms made up of multiple nucleons.
In theory, you can explain the behavior of these atoms predominantly with QCD from first principles, with a little sprinkling of electroweak theory. But, in practice, we have a hard enough time explaining the behavior of single hadrons or two to four hadrons with QCD from first principles without resorting to numerical or analytical approximations because the math involved in QCD is so hard (in part because it is a strong non-abelian force in which gluons interact with each other, unlike photons which carry an abelian force without self-interactions and the weak force that usually gets summarized as a black box set of input-output matrixes).
So, instead we resort to a phenomenological residual nuclear force inspired by our qualitative understanding of QCD to understand bigger atoms (hadrons compounds made of hadron other than nucleons don’t seem to be observed at scales large than meson and baryon molecules with a couple of hadrons in a non-confined system anyway, and quark-gluon plasma can be thought of a single special case with the mix of quarks in it and the temperature as parameters for that special case). At the most basic level, the phenomenology is done crudely by estimating based upon measured atomic isotope masses the nuclear binding energy in an atomic isotope to determine the exothermic or endothermic properties of possible nuclear fusion and nuclear fission reactions involve them. At a more advanced level, we model it as one or several Yukawa forces mediated by several massive but light mesons, but mostly by pions.
Likewise, at the next discrete level, we then turn to chemistry and condensed matter physics, which is dominated by underlying QED interactions, to understand molecules and ionic compounds, as opposed to single atoms, since the residual nuclear force and weak force are rarely important in understanding chemistry and condensed matter physics at this scale.
In basic structure (e.g. in path integrals and boson propagators), QED and QCD are very similar, except for the self-interaction terms and the fact that the QCD infinite series require far more terms than the parallel infinite series in QED, to produce meaningful results. So, I’m a bit puzzled while QED or weak force theory would be singled out in the same way as a mere effective field theory relative to QCD.
Also, while QCD is, in theory, generalizable up to arbitrary scales, in practice, the twin boundaries of confinement and asymptotic freedom, tightly defines the scale at which it applies in the context of the fundamental masses (subject to only modest renormalization in most circumstances) of the hadronizing quarks (i.e. u, d, s, c and b), with confinement preventing pure, direct gluon-quark interactions between hadrons from being important, and asymptotic freedom preventing very small distance QCD interactions from being very interesting.
Further, above the roughly 1 GeV temperature scale, you get a phase shift into quark-gluon plasma and a discrete change in the effective phenomenological outcome into the QGP special case with one vector parameter representing the relative proportions of different quark types and one scalar parameter representing temperature, as a very precise first order approximation.
It is still stunning how much structure can arise from the naively very simple rules of QCD and its modest number of experimentally determined parameters. But, I also don’t know how much time I’ve squandered puzzling over why it is that the universe has scores of hadrons and hadron molecules, that somehow end up boiling down to two kinds of baryons (the proton and the neutron), and a few light mesons to carry the residual nuclear force, for all but the first few moments after the big bang, and some isolated and sporadic interactions that take mere moments in the history of the universe in particle colliders and perhaps in supernovae, in and around black holes, neutron stars and perhaps a few other hypothetic stellar creatures like quark stars. How did we end up with a universe that gets so little mileage out of such a simple yet rich fundamental theory like QCD?
Like
1. 4gravitons Post author
Actually deriving the full behavior of a theory on large scales from its small-scale properties is almost always out of reach, and QCD is indeed no exception. What’s bothering me in this post is less what we can calculate in practice, and more what our theories determine in principle. If the world was QCD, what would that mean? Is QCD the kind of thing the world can be?
And with that in mind, it bothers me that once we get down to our supposedly most fundamental theory, it’s not actually one theory. It’s a series of theories, each one at a different scale, stretching off to the (infinite) limit of asymptotic freedom. And it’s not clear that we can define it in any other way, not just in practice but perhaps in principle. That’s weird!
(By the way, I think you’re conflating “QCD becomes QGP at high energies” with “QCD isn’t described by field theory at high energies”. QCD collectively behaves as QGP at high energies, but an individual quark inside QGP is basically as close to nice perturbative QCD behavior as you can get.)
Like
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8561882376670837, "perplexity": 699.7383339937073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487647232.60/warc/CC-MAIN-20210619081502-20210619111502-00370.warc.gz"}
|
https://www.physicsforums.com/threads/beginner-calculus-help.646540/
|
# Beginner calculus help
1. Oct 23, 2012
### Murph84
I realize this question will probably be too easy for people who are good at it.
But I can't figure this out.
I'm trying to find the limit for
lim x→7 (sin(x − 7))/(x2 + 2x − 63)
Sorry, I don't know how to make it look like the proper equation.
Thanks for any help....
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Oct 23, 2012
### lanedance
welcome to PF!
now what have you tried, or what relevant equations/theorems do you know?
Similar Discussions: Beginner calculus help
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8658963441848755, "perplexity": 2231.721676513243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813712.73/warc/CC-MAIN-20180221182824-20180221202824-00641.warc.gz"}
|
https://arrayfire.org/arrayfire-rust/arrayfire/fn.eq.html
|
# [−][src]Function arrayfire::eq
pub fn eq<T, U>(arg1: &T, arg2: &U, batch: bool) -> Array<bool> where T: Convertable, U: Convertable, <T as Convertable>::OutType: ImplicitPromote<<U as Convertable>::OutType>, <U as Convertable>::OutType: ImplicitPromote<<T as Convertable>::OutType>,
Perform equals comparison operation
This is a comparison operation.
# Parameters
• arg1is an argument that implements an internal trait Convertable.
• arg2is an argument that implements an internal trait Convertable.
• batch is an boolean that indicates if the current operation is an batch operation.
Both parameters arg1 and arg2 can be either an Array or a value of rust integral type.
# Return Values
An Array with results of the comparison operation a.k.a an Array of boolean values.
# Important Notes
• If shape/dimensions of arg1 and arg2 are same, the value of batch parameter has no effect.
• If shape/dimensions of arg1 and arg2 are different, the value of batch has to be set to true. In this case, the shapes of arg1 and arg2 have to satisfy the following criteria:
• Same number of elements in arg1 and arg2 along a given dimension/axis
• Only one element in arg1 or arg2 along a given dimension/axis
• The trait Convertable essentially translates to a scalar native type on rust or Array.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5692281126976013, "perplexity": 10860.373275700473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305288.57/warc/CC-MAIN-20220127193303-20220127223303-00138.warc.gz"}
|
http://forums.mtbr.com/bike-frame-discussion/any-luck-painting-anodised-bike-components-747607.html
|
Thread: Any luck painting anodised bike components?
1. Any luck painting anodised bike components?
I have a 2011 Giant Reign X0, while I love the bike, I am not a fan of the Gold anodised linkages - they don't sit well with my conservative mid 40's image, a bit more bling than I can handle
Personally I think natural alloy or flat black would look better
If I was to pull them off, give them a good going over with fine sandpaper then etch prime and spray with good quality aerosol can auto colour does any one know if it would last over the anodising?
I am pretty good with my hands [I am a tradesman] so it would be as good a job as possible without trade/spray shop skills
2. Never did it, but....
... a quick Google search and you'll see it can be done.
How to Paint Over Anodized Aluminum | eHow.com
Personally, I say leave it be and ride it, but I also am very particulat about color, so I can relate. Let us know how you make out.
3. I've read that certain solvents eat the color off of anodized parts. You don't want to beat up the surface finish too much because surface condition is a critical component of fatigue life.
4. Oven cleaner removes anodizing, once used it to convert some purple components to polished.
5. Anodize is the perfect base for a paint job. There is no need
to remove it or sand it. Just clean it with a solvent of some kind,
prime, then paint it the color you want.
Best, John
6. Painting aluminum, or anodized aluminum can be tricky. At the minimum you should use self etching primer.
7. Originally Posted by John Kuhl
Anodize is the perfect base for a paint job. There is no need
to remove it or sand it. Just clean it with a solvent of some kind,
prime, then paint it the color you want.
Best, John
Originally Posted by ljsmith
Painting aluminum, or anodized aluminum can be tricky. At the minimum you should use self etching primer.
Hmmm...
Conflicting information.
More research on my part is required I think
8. Maybe this will help. I anodized and painted parts for
Navy aircraft for over 35 years and this is what we did.
Best, John
9. Originally Posted by John Kuhl
Maybe this will help. I anodized and painted parts for
Navy aircraft for over 35 years and this is what we did.
Best, John
John
Am I missing something? did you forget a link?
10. Originally Posted by John Kuhl
Maybe this will help. I anodized and painted parts for
Navy aircraft for over 35 years and this is what we did.
Best, John
John
Am I missing something? did you forget a link?
11. well if you can spend like $20, i would say use a de-ano from the hardware store... then just bring it to your local ano shop, and they should charge roughly$20 per link..
unless you dont mind painting over and getting scratches
12. Sorry jeffgre_6163, but sometimes I don't explain myself very well. What I
was trying to say is in the aircraft industry the way we would finish a aluminum
part is first anodize or alodine it, then prime, and last color. We never painted
bare aluminum. It is not easy to get paint to stick on bare aluminum. Also
getting the part reanodized is another choice like Mattlikestobike said, but
they will strip the old anodize as part of the process to reanodize it. How
ever you need to be carefull when getting a part reanodized because every
time you remove the old anodize you will remove some base metal. If the
whole process isn't done right you can end up with oversized holes for things
like the pivot bearings. So make sure you have a good shop do the work.
Best, John
13. Originally Posted by John Kuhl
Sorry jeffgre_6163, but sometimes I don't explain myself very well. What I
was trying to say is in the aircraft industry the way we would finish a aluminum
part is first anodize or alodine it, then prime, and last color. We never painted
bare aluminum. It is not easy to get paint to stick on bare aluminum. Also
getting the part reanodized is another choice like Mattlikestobike said, but
they will strip the old anodize as part of the process to reanodize it. How
ever you need to be carefull when getting a part reanodized because every
time you remove the old anodize you will remove some base metal. If the
whole process isn't done right you can end up with oversized holes for things
like the pivot bearings. So make sure you have a good shop do the work.
Best, John
Cheers
thanks for the clarification
14. What if the part is small, delicate and non-removable?
Hey all, sorry to dig up an old post but I have a related problem that's got me in a dilemma.
I have had success in the past using a procedure of removing anodizing using oven cleaner (from those blingy Crankbrothers seatpost saddle rail clamps!) and this is all well and good and fairly straightforward to do if you can completely remove and disassemble the parts to be recoloured.
BUT, what are we to do if the parts cannot be removed, are small and/or fiddly to reach, and/or allowing any harsh chemicals to move outside the part to be recoloured would cause damage?
I am in this situation with two parts that give me the creeps, and these are the rebound dials on both my front suspension (Cannondale Lefty XLR) and my rear shock (RockShox Monarch RT3 Relay). \begin{rant} BRIGHT RED. I HATE IT! Seriously bike industry, leave the whole bright red thing alone, I don't have any red on my bike! \end{rant}
I was told by my Lefty specialist that for my particular model (Lefty 1.0, MY2015) the rebound dial cannot be removed easily by a home mechanic and is a lot of work. Furthermore I recently took off my Monarch Relay from the frame and whilst I got better access to the rebound dial, I couldn't figure out an easy way of removing it without disassembling the entire shock.
Thus I think we can take it for granted that these dials cannot be removed from their locations without serious work (though, I'm happy to be corrected, if anyone can provide me with a guide!), they are small and have fiddly areas to access (in terms of painting) and if some harsh chemical were to spill or seep into surrounding areas, it could cause trouble.
I'll attach a couple of pictures below:
Lefty XLR
Monarch Relay
Whatever 'treatment' were to be applied to the dials, we would certainly like the colour to be somewhat resilient to handling (turning with our fingers) and the weather (water and dirt), so simply using a 'Sharpie' (permanent marker) is probably out of the equation since it won't really last that long and will probably have purple hues.
Anyone have any suggestions? My first preference would be BLACK, so what about simply painting them on top of their anodizing with some special black paint with a tiny paint brush or cotton tip, would that work? If so, what kind of paint would I need to use? I have heard that anodized aluminium is an excellent surface to paint on top of, but I suspect that these dials have some sort of clear coat over the top of the anodizing, so would I have to remove the clear coat with a solvent and cotton tip, or just sand it a tiny bit lightly? Folks from the USA seem to have varying success with using a 'paint pen' like this for the aluminium parts on firearms: https://www.birchwoodcasey.com/Clean...ch-Up-Pen.aspx
My second preference would be to just remove the anodizing and get a dull grey from the natural oxidation of the aluminium after which I can just apply a clear coat to seal it (I ended up doing this go get a weathered gun-metal grey look on my Crankbrothers clamps so it looks alright). I could probably very very gently rub oven cleaner with a cotton bud and persist until the red all comes off, but then I'd be left with this bare aluminium and wouldn't have a means to seal the surface as the clear coat could seep into surrounding crevices and cause trouble!
Obviously 'leave it' is the best advice and simplest solution, but can anyone offer some advice as to how I could remove these red bling bits in a fairly safe and easy way?
Thanks guys!
Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25184154510498047, "perplexity": 2564.1488141619875}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280133.2/warc/CC-MAIN-20170116095120-00312-ip-10-171-10-70.ec2.internal.warc.gz"}
|
http://mathbabe.org/2013/11/09/aunt-pythias-advice-29/
|
Home > Aunt Pythia > Aunt Pythia’s advice
November 9, 2013
Aunt Pythia is well-slept and excited to be here to answer your wonderful and thoughtful ethical conundrums. Please do comment on my answers, if you disagree but especially if you agree wholeheartedly and want me to keep up the good work. Love that kind of encouraging comment.
And please, don’t forget to ask me a question at the bottom of the page!
By the way, if you don’t know what the hell I’m talking about, go here for past advice columns and here for an explanation of the name Pythia.
——
Dear Aunt Pythia,
What is your text editor of choice? The most popular ones, the ones in which I know die-hard fans, are for Emacs, Vi/Vim, and Sublime. I am personally an Emacs user, but I haven’t given any other editors a chance, to be honest. Which do you prefer to use, and why?
Text Editor
Dear TE,
I use emacs mostly, and xemacs when it’s available. It’s easy, it “knows” about python and other languages, and the drop-down menu is easier than remembering keystroke commands. I’ve been known to use an IDE or two depending on codebase context. For me it’s all about ease of use and, since I’ve never been a professional engineer and so I’ve never spent a large majority of my time with source code, vim doesn’t attract me, even though everything is keystroke and you never need to use your mouse.
As an aside, I’d like to argue this point, because it’s often shrouded in weird macho crap: why not use your mouse? Does it really waste that much time? I honestly have never been prevented from coding efficiently because my arm is too tired from moving from the keyboard to the mouse and back. Is the goal really to be able to stay in the exact same position for as long as possible? I’m the kind of person that is too fidgety for such ideas. I take the “stand up and walk around every 20 minutes” rule seriously, at least before 4pm, when I become a zombie.
Aunt Pythia
——
Dear Aunt Pythia,
What are your thoughts on the famous (infamous?) two-daughter problem? I have three PhDs who give different answers all of which appear to be statistically correct. Modinow says the answer is 1/2. The chair of the stats department at local university says the answer is 3/7, and a chap at Fl Coastal College has yet a 3rd answer which I have lost.
How can this be?
Tombs
Dear Tombs,
OK I’m pretty sure there’s only one answer to this if it’s stated precisely. So let’s try to do that. Here’s the question:
Suppose I have two children. One of them is a girl who was born on a Friday. What are the chances of both children being girls?
Now I’m a big fan of making things incredibly easy and visual. So what I’m going to do here is identify the fact that, as far as children go, there are two attributes of interest in this question, namely gender and day of birth. I will assume that all options are equally likely and that they are independent from each other as well as between kids, and in my first iteration I’ll draw up a list of equally likely bins for a given child, namely of either gender and of any day born. That’s 14 equally likely bins for a given single child, and that means they happen with probability 1/14.
Now, for the second iteration, let’s talk about having two kids. You have a 2-dimensional array of bins, which you arrange to be 14-by-14, and you assume that any of those 14*14 = 196 bins is a priori equally likely.
Label the bins with ordered pairs (gender, day). The x-axis is first kid, y-axis is 2nd kid. Each bin equally likely.
If you label the first bin as “(Female, Friday)” and the second bin as “(Female, Saturday)” and so on, you realize that the condition that “one of the two kids is a girl who was born on Friday” means that we already know we are working in the context where we are either in the left-most column or the bottom row. Here’s my awesome rendition of this area:
The pink parts show where there’s a girl born on a Friday among the two children.
Specifically, the left bottom corner is the case where there are two girls, both born on Friday. The one to the right and above that corner refers to the case where there are two girls, one born on Friday and one born on Saturday. The stuff on the right and in the upper part of the column refers to the case where there’s a Friday girl and a boy.
Altogether we have 13 pink bins with two girls and 14 pink bins of a boy and a girl. So the overall chances of two girls, given one Friday girl, is 13/27.
I hope that’s convincing!
Aunt Pythia
——
Dear Auntie P,
What do you think about topological data analysis (some info here). Should we trust people who can’t tell the difference between their rear end and a coffee cup because the two are topologically equivalent?
Topological Fear
Dear TF,
Geez I don’t know about you but my rear end is not topologically equivalent to my coffee cups. You either need to go to a doctor or buy some coffee cups that don’t leak.
So, I don’t know very much about this stuff, but I do think it’s potentially interesting, and it’s maybe close to an idea I’ve had for a while now but for which I haven’t found a practical use. Yet.
The idea I have had, if it’s close to this idea, and I think from short conversations with people that it is, is that if you draw a bunch of scatter plots of, say, two attributes x1 and x2 and an outcome y (so you need numerical data for this), then you’ll notice in the resulting 3-dimensional blob of points some interesting topological properties. Namely, there seem to be pretty well-defined boundaries, and those boundaries might have certain kinds of curves, and there may possibly even be well-defined holes in the blob, at least if you “fatten up” the points (sufficiently but not more than necessary) and then take the union of all of the resulting spheres to be some kind of 3-d manifold. You can then play with the relationship between, say, the radius of these fattened points and the topological properties of the resulting blob.
Anyhoo, the idea could be that, if you see x1 and x2 then you can exclude a y that lives in a hole, or rather where point (x1, x2, y) would live in a hole. This is more than most kinds of modern models can do for you, but even so I’ve never seen this actually come in handy.
I hope that helps, and please do see a doctor!
Auntie P
——
Dear Aunt Pythia,
This is a reaction to a previous post (maybe Oct 12?) where you said the following:
My kids, to be clear, hate team sports and suck at them, like good nerds.
Now, as a nerd whose parents never let play team sports growing up and now plays one in college (a “nerd” sport, but still…), I have a question for you: Why do “good nerds” have to hate sports and/or suck at them? What classifies a “good nerd”? Does this generalize to other things that nerds are stereotypically bad at, like sex lives? Is there another category that should be created for nerdy type people that are also jocky-er, like a nerock or a jord?
With Love,
Great question, and you’re not the only nerd that called me out on my outrageous discrimination. I wasn’t being fair to my nerock and jord friends, and that ‘aint cool. Although, statistically I believe I still have a point, there’s no reason to limit people in arbitrary ways like that, and it’s fundamentally un-nerdy of me to do so.
For all you nerocks and jords out there: you go, girls! and boys!
But just for the record, nerds are categorically excellent at sex. We all know that. Say yes.
Love,
Aunt Pythia
——
Please submit your well-specified, fun-loving, cleverly-abbreviated question to Aunt Pythia!
Categories: Aunt Pythia
1. November 9, 2013 at 10:22 am
I’m feeling good that I got the same answer as Auntie Pi to the 2 daughter problem – and I didn’t even have to look. Unfortunately, my approach lacked Auntie P’s cool visualization. Hopefully, the profs alluded to were working different problems.
2. November 9, 2013 at 10:28 am
I just want to defend the answer 1/2 to the two daughters problem. I’m not sure either is completely correct – it depends on subtle issues of language.
Suppose the question read, “I have two children – Taylor and Morgan. Traylor is a girl born on a Friday; what is the probability that Morgan is a girl?”
Here I believe the answer is unambiguously 1/2. Indeed, if when specifying the gender and day of birth you are referring to a *particular* child (first born, better at math, etc.) then the genders are independent. The answer 13/27 only makes sense if your children are completely interchangeable, which might make sense if you are doing statistics on families with two children including a daughter born on a Friday.
Overall I think I prefer the answer 1/2 since when somebody says “one of my children” they usually have a specific child in mind.
• November 9, 2013 at 11:02 am
Sorry but no. Of course it’s true that, when somebody says “one of my children” they usually have a specific child in mind, it is not clear to the listener whether it’s the older or younger child.
• November 9, 2013 at 1:13 pm
As with most such probability puzzles, the problem really needs to be stated even more precisely than the supposedly precise statement above for either answer to be unambiguously correct. (At least the statement should contain the words “at least.”)
If the question is about a family selected at random from all families with exactly two children, at least one of whom is a girl born on a Friday – perhaps there is an annual convention of such families – then obviously the answer given above with the pretty pictures is correct.
OTOH if some random parent randomly starts telling you about some random child of theirs – as parents are wont to do – and it emerges that this child was a girl born on a Friday and has exactly one sibling, then the 1/2 answer is correct. In this case the diagonal parents will perforce always say the same (sex, day), while the off-diagonal parents will have had a choice and only pick (girl, Friday) half of the time. It’s the same as the principle of restricted choice in bridge, or the Monty Hall problem.
• November 9, 2013 at 1:16 pm
I agree with the answer of 1/2 to pwsiegel’s reworded problem. With the rewording, the kids have been distinguished. If supplied with identifiers up front – names, birth positions, hair color, etc. and then you tell me the kid identified as “Taylor” or “First” or “Blonde” is a girl born on Friday then that changes the conditioning on the problem – and the answer. Let
GF = girl born on Friday
GF’ = girl born on a day other than Friday
B = boy
ID1 = kid with identifier #1 (“Taylor” or “First”,,,)
ID2 = kid with identifier #2 (“Morgan” or “Second” or…)
Probabilities for each of the possible outcomes (should add to 1:)
ID1 ID2 Probability
1. GF GF (1/14)(1/14)
2. GF GF’ (1/14)(6/14)
3. GF’ GF (6/14)(1/14)
4. GF’ GF’ (6/14)(6/14)
5. GF B (1/14)(7/14)
6. GF’ B (6/14)(7/14)
7. B GF (7/14)(1/14)
8. B GF’ (7/14)(6/14)
9. B B (7/14)(7/14)
In the original problem, one kid is a girl born on Friday in cases 1,2,3,5 and 7 above. The probability of one of the kids being a Friday-born girl is the sum of the probabilities associated with these cases, 27/196. The probability of 2 girls given one is a girl born on Friday is then the probability of case 1 or 2 or 3 (13/196) divided by 27/196 = 13/27.
In pwsiegel’s reformulation, ID1 is a Friday girl – only true in cases 1,2, and 5. The probability of one of these 3 cases occurring is 14/196. Of these, cases 1 and 2 result in two girls. So, the desired probability is 7/196 divided by 14/196 = 1/2.
I can’t see how the original problem can be read as pwsiegal’s formulation though. It seems pretty clear that the reformulation excludes cases 3 and 7 while the original includes them.
Regarding Cathy’s comment – I’m not convinced that birth position gives one any different information than the identifiers proposed by pwsiegel.
• November 9, 2013 at 2:40 pm
The only role that providing names played in changing the solution to the problem was to distinguish the children, and so the answer is still 1/2 if the setup for the puzzle is “I have two children. The older child is a girl born on a Friday…” Indeed, the solution to this puzzle can be reduced to your analysis if you imagine that the speaker is a weird parent who named his or her children “Firstchild” and “Secondchild” instead of “Taylor” and “Morgan”.
So in the original puzzle, it all comes down to how you interpret the phrase “one of my children is X”. If you interpret this phrase to mean “it is not true that both of my children are not X” then 13/27 is correct. But if you interpret it to mean “A specific element of the set containing my two children is X” then 1/2 is correct. The first interpretation is usually correct in statistical language, but the second seems more correct in colloquial language. The puzzle is confusing because it is hard to decide which linguistic environment takes pecedence.
• November 9, 2013 at 3:08 pm
(After thinking a little bit more about this, I realized that the issue here is whether or not the speaker has chosen a coordinate system on his or her family. The answer is 1/2 in any fixed in any fixed choice of coordinates, but if one works intrinsically – as those trained in algebraic geometry are known to do – then the answer is 13/27.)
3. November 9, 2013 at 3:25 pm
Wow if “weird macho crap” isn’t bait then I don’t know what is! Some jord here needs to defend it. Might as well be me.
Quite frankly keystrokes are, to use a kinder Pythian term, awesome! Here’s just one lovely thing about them: for anyone like myself who prefers to automate repetitive tasks whenever possible, the ease with which keystrokes go into keyboard macros makes them absolutely adorable. Entering menu selections in macros can be a big pain, button presses an even bigger one. Mice have their place, but in my opinion keyboard shortcuts rank right up there with some of the best UI features of all time, including modern touchscreen ones.
Though I haven’t tried a bunch, my favorite text editors are the commercial ones Epsilon (Windows) and BBEdit (Mac). My favorite keyboard macro app of all time is Winbatch (Windows). Lately I’ve been using Keyboard Maestro (Mac) and have found it to be impressive and reliable.
4. November 9, 2013 at 8:55 pm
I don’t like using the mouse because it takes more precision, and I’m clumsy (getting the pointer exactly where I want it is hard for me). Also, I find taking my hands on and off the keyboard takes time, and for some reason interrupts my train of thought.
Macho non-jock
5. November 9, 2013 at 11:49 pm
pwsiegel, andeux, and greg, beat me to some points I think are very important about the conditional probability puzzle. The most important thing as with any model, is to know when the calculations would apply, and they covered this well, but let me sum up in my own words: To be sure $P(A|B) \equiv P(A \cap B)/ P(B)$ is the applicable answer to such a problem, it must be the case that you would have received your current information in *all worlds* and *only those worlds* where B is true. It is the *all worlds* direction of this condition which is often overlooked and which leads to errors, most famously in the Monty Hall problem. It is relevant here also, because we we don’t know how the information provided to us was chosen. It is hard to imagine, for instance, that someone would make the statement in the problem and in fact have two daughters both born on Friday. One way to make it unambiguous would be “You ask someone if event B has happened and she says yes. You are sure she is accurate and truthful, would never refuse to answer, *and* would never volunteer additional information beyond Yes/No.” That’s a lot of conditions, but they are all necessary, and the last two especially are easily overlooked.
This is a very relevant topic on mathbabe’s blog because selectively provided information is a major way to manipulate models!
6. November 10, 2013 at 7:56 pm
There is not enough room in this space for me to give a complete proof, so here is my last (and first) theorem:
1) We all know that each person is born on one of seven days, and for that matter, one of many times. If adding the information that the daughter was born on a Friday is truly meaningful (or whatever the correct mathematical/statistical term may be), then adding the precise time of birth is also meaningful.
2) Suppose we add that the birth time was 12:01 am on Friday.
3) By the reasoning above, there would be a much larger collection of possible combinations.
4) By arbitrarily revealing more accurate information as to the precise time of birth (e. g. Monday, 2:00000001 pm), the solution becomes arbitrarily close to 1/2.
7. November 11, 2013 at 3:30 am
5) Therefore, the correct probability that the other child is a girl is 1/3.
8. November 12, 2013 at 11:00 pm
I liked that probability problem! For a little while it bugged me that if you know one kid is a girl, the probability of both kids being girls is 1/3, while if you know one kid is a girl born on a Friday, then it’s much closer to 1/2 (13/27). I finally got some decent intuition for it by filling in more of your picture:
P(2 girls | 1 girl born on a Friday) = 13 / (13+14)
P(2 girls | 1 girl born on a Friday or Saturday) = (13+11) / (13+11+2*14)
P(2 girls | 1 girl born on a Friday or Saturday or Sunday = (13+11+9) / (13+11+9+3*14)
P(2 girls | 1 girl) = P(2 girls | 1 girl born on Fri, Sat, Sun, Mon, Tue, Wed, or Thu)
= (13+11+9+7+5+3+1) / (13+11+9+7+5+3+1+7*14) = 7*7 / (7*7 + 7*14) = 1/3.
In the other direction, as you extend the number of characteristics (probability of having two girls given that you have one girl born on Friday in March with red hair and freckles), the probability goes to 1/2. The best intuition I can come up with for that is that the more characteristics you know, the more likely it is that you’ve pinned down which kid you’re talking about, as the probability that both kids have those characteristics gets lower and lower. In other words, you’ve gotten closer and closer to saying that Kid A is a girl, which reduces the probability of both kids being girls to the probability of Kid B being a girl, which is 1/2.
My probabilist undergrad advisor always used to say that our brains weren’t wired right to think about probability!
1. November 11, 2013 at 6:29 pm
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4636412560939789, "perplexity": 952.7700717442615}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737916324.63/warc/CC-MAIN-20151001221836-00131-ip-10-137-6-227.ec2.internal.warc.gz"}
|
http://expressionengine.stackexchange.com/questions/23625/conditional-with-variable-gives-php-error
|
# Conditional with variable gives php error
I'm using channel:categories and would like to show only child categories so I added the following conditional {if {parent_id} != 0}...{/if} but get php errors as soon as I add it to the template. I tried any sort of variable check {category_description} and get errors.
The above conditional was taken from an accepted answer on another thread.
Parse error: syntax error, unexpected '{' in path\to\system\expressionengine\libraries\Functions.php(689) : eval()'d code on line 43
My template looks like this:
{!--stash 1st level category list--}
{exp:stash:set name="categories" parse_tags="yes"}{exp:gwcode_categories channel="products" depth="1" style="linear" backspace="1"}{cat_url_title}|{/exp:gwcode_categories}{/exp:stash:set}
{!--category ids for sub cats--}
{exp:stash:set name="sub_category_ids" parse_tags="yes"}{exp:gwcode_categories channel="products" output_depth="2" style="linear" backspace="1" cat_url_title="{segment_3}"}{cat_id}|{/exp:gwcode_categories}{/exp:stash:set}
{exp:stash:parse}
{exp:switchee variable="{segment_2}" parse="inward"}
{case value="#^P(/d+)\$#|category|''"}
{switchee variable="{segment_3}" parse="inward"}
{case value="{stash:categories}"}{!--level 1 category listing filtered by stashed list --}
{exp:low_variables:single var="lv-products-cat-tier1"
preparse:pre_seg_id="{stash:sub_category_ids}"
preparse:pre_single_cat_id="{segment_3_category_id}"
}
{/case}{!--level 1 category listing--}
some more case checks here
{/switchee}{!--end nested switchee--}
{/case}{!--listing & category listing--}
some more case checks here
{/exp:switchee}
Finally my lv-products-cat-tier1 is a low variable with the following code where the parent conditional will wrapp the double-square div when it is working:
{!--list sub categories--}
{exp:channel:categories channel="products" show="{pre_single_cat_id}|{pre_seg_id}" style="linear"}
{if {parent_id} != 0}
yo
{/if}
<div class="col-xs-6 double-square">
<img src="http://lorempixel.com/545/270/people" alt="" class="img-responsive">
<div class="row">
<div class="pos-ab">
<div class="col-xs-6 left">
<div>
<h4><a href="/products/category/{category_url_title}">{category_name}</a></h4>
</div>
</div>
<div class="col-xs-6 right">
<div class="content">
{exp:eehive_hacksaw chars="" words="15" cutoff="" append="" allow="<p><b><a>"}
{category_description}
{/exp:eehive_hacksaw}
</div>
</div><!--right-->
</div><!--pos-ab-->
</div><!--row-->
</div><!--double square-->
{/exp:channel:categories}
-
The problem with that is that if {parent_id} doesn't get replaced with a number before the conditional is evaluated, then EE will choke because when converted to PHP it becomes:
if ({parent_id} == 0)
Either this
{if parent_id != 0}
Or this
{if "{parent_id}" != "0"}
Is more fault tolerant when the variable doesn't exist.
But, you may wonder, why is your conditional getting parsed before {parent_id} has been replaced in the first place? Because by default {exp:stash:parse} parses conditionals after it has parsed the layers of tags it wraps to a "depth" of 3 (parse_conditionals="yes" and parse_depth="3" by default).
It so happens that in your code the {exp:low_variables} tag is on the deepest layer to be parsed (layer 3). This tag gets replaced with your {exp:channel:categories} tag pair which is NOT parsed, because at this point Stash is done parsing and will now parse any conditionals that have been exposed. See the problem?
To stop this undesirable behaviour you can either set parse_conditionals="no" on the {exp:stash:parse} tag or increase the parse depth with parse_depth="4" so that the categories tag is fully parsed before the conditionals are evaluated.
-
Mark, brillant. Thanks. – CreateSean Jun 11 at 17:42
That's a proper answer. – foamcow Jun 12 at 8:55
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21706224977970123, "perplexity": 21175.58675769808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802765698.11/warc/CC-MAIN-20141217075245-00042-ip-10-231-17-201.ec2.internal.warc.gz"}
|
https://www.birs.ca/events/2016/5-day-workshops/16w5152
|
# Complexity and Analysis of Distributed Algorithms (16w5152)
Arriving in Oaxaca, Mexico Sunday, November 27 and departing Friday December 2, 2016
## Organizers
(University of Calgary)
(Technion - Israel Institute of Technology)
## Objectives
One of the main challenges faced today is to enable algorithms to fully exploit the parallelism provided by hardware. Shared memory algorithms need to cope with the inherent asynchrony and faulty process behavior in parallel systems. In the light of recent technological developments, most conspicuously, multi-core processors, distributed shared memory algorithms have gained huge importance for every-day and high-performance computing. The design of correct shared memory algorithms, as well as their efficiency analysis and correctness proofs remain a challenging task.
This workshop will bring together international experts, promising junior researchers, and some exceptional graduate students and postdocs, to exchange ideas on how the research on the design and analysis of fundamental algorithmic problems in shared memory systems can be advanced. Invitees will cover a broad area of expertise. While the emphasis will be on the theory of shared memory algorithms, experts on other areas of concurrent and distributed computing (e.g., networks and message passing systems) and mathematics (combinatorics and topology) will be invited. We will also invite some researchers with systems background and from industry research labs, whose expertise will help identify problems and approaches that are relevant for practical applications. This will on one hand allow shared memory researchers to benefit from techniques and experiences present in other fields, and on the other hand enable dissemination of new results and ideas to related research areas.
One goal is to identify novel techniques to design and analyze efficient randomized algorithms, and to understand limits of their efficiency. Questions of interest include, but are not limited to:
• Present and discuss novel randomized algorithms or impossibility results for fundamental problems of distributed computing.
• Can randomized algorithms and analysis techniques used in other models (e.g., message passing) be applied to shared memory models and vice versa?
• How variations in the model affect the efficiency of possible algorithms?
• How much does the possible gain in speedup depend on the choice of adversary? Which adversaries permit efficient algorithms but don't at the same time underestimate the effects of randomized choices on the schedule.
• Explore techniques to prove lower bounds for randomized shared memory algorithms.
• In sequential computing, Yao's Min-Max [Yao1977a} principle is used frequently for algorithm analysis. Even though there are some ad-hoc lower bound results relying on Yao's principle for shared memory problems (e.g., \cite{GW2012a]), the general applicability of that technique is not well understood.
A related objective is to advance the research on heuristics and alternative complexity measures for shared memory algorithms. Since this research is still in its infancy, many basic questions remain to be answered. The workshop will provide a unique opportunity to shape the direction this research will take, and to solicit and disseminate ideas of leading distributed computing researchers. Possible questions that will be discussed are
• What are suitable models in which shared memory heuristics can be analyzed? Is there a good notion of average-case complexity for distributed problems? Is something similar to Smoothed analysis possible for concurrent algorithms?
• Develop design principles and analysis techniques for shared memory heuristics using randomized adversaries.
• What is the complexity of fundamental shared memory problems in such models? Can we find efficient solutions to practical data-structure problems, e.g., concurrent binary search trees, using randomized adversary models?
• (How) can we test the practical performance of heuristics, and whether theoretical models yield accurate predictions in real systems?
The workshop attempts to promote and advance new methods for analyzing and understanding shared memory algorithms. Combinatorial topology provides an exciting tool to obtain insights which seem otherwise difficult or impossible to achieve. The initial hurdle to learn the mathematical background is high, but recent advances make the framework more accessible to non-topologists [HKR2013a]. One of the workshop's objectives is to engage researchers in this research direction, and to raise awareness for recent developments. Another objective is to come to a better understanding of the tool, and to advance progress on problems that eluded researchers so far. Examples are:
• Many impossibility results for distributed computing were established using conventional methods (i.e., not using combinatorial topology) [AE2014a:impossibility].
• Can topology be used to explain, unify, and perhaps improve those results?
• Explore the application of combinatorial topology to more models and problems. Computabiity of one-shot tasks has been studied in many distributed computing models, such as message-passing, synchronous, asynchronous and partially synchronous models with both crash failures and byzantine failures. However, few research results based on topology are known for other models and problems, such as long-lived tasks (as opposed to one-shot ones) and systems with multi-reader multi-writer registers.
• Combinatorial topology tools have been applied mostly for computability, and in systems where processes can communicate directly with each other.
• It would be interesting to study the applicability of these techniques in situations, where processes communicate through point-to-point channels defined by a graph, a very active research area pursued by other communities. Also, it would be interesting to study through topology other aspects besides computability, such as complexity and the alternatives to worst-case analysis described above, where algorithms adapt to the actual conditions of the system.
The connection between distributed computing and topology is essential, and gained the attention not only from computer scientists, but also from mathematicians. New topology questions have arisen, and there is already work by researchers in topology motivated by distributed computing questions (e.g.~[FFH2012dagstuhl,MR2955101,kozlov2012]). The workshop will provide a forum for further cross-fertilization between these two fields.
\def\DISC#1{Proc. of \#1 {DISC}} \def\PODC#1{Proc. of \#1 {PODC}} \def\SODA#1{Proc. of \#1 {SODA}} \def\JACM{J.\ of the {ACM}} \def\FOCS#1{Proc. of \#1 {FOCS}} \def\STOC#1{Proc. of \#1 {ACM} {STOC}} \def\JALG{J.\ of Alg.} \def\SIAMJC{{SIAM} J.\ on Comp.} \def\DistComp{Distr.\ Comp.} \def\TOPLAS{ACM Trans. Program. Lang. Syst.} \def\CACM{Commun. {ACM}}
#### Bibliography
1. [Abr1988] K.~Abrahamson.
On achieving consensus using a shared memory.
In \PODC{7th}, pp. 291--302. 1988.
2. [AA2011a] D.~Alistarh and J.~Aspnes.
Sub-logarithmic test-and-set against a weak adversary.
In \DISC{25th}, pp. 97--109. 2011.
3. [AABGG2014a] D.~Alistarh, J.~Aspnes, M.~A. Bender, R.~Gelashvili, and S.~Gilbert.
Dynamic task allocation in asynchronous shared memory.
In \SODA{25th}, pp. 416--435. 2014.
4. [AACGG2014a] D.~Alistarh, J.~Aspnes, K.~Censor{-}Hillel, S.~Gilbert, and R.~Guerraoui.
Tight bounds for asynchronous renaming.
\JACM, 61:18, 2014.
Optimal-time adaptive strong renaming, with applications to counting.
In \PODC{30th}, pp. 239--248. 2011.
6. [AAGW2013a} D.~Alistarh, J.~Aspnes, G.~Giakkoupis, and P.~Woelfel.
Randomized loose renaming in {$O(\log\log n)$] time.
In \PODC{32nd}, pp. 200--209. 2013.
7. [AAGGG2010a] D.~Alistarh, H.~Attiya, S.~Gilbert, A.~Giurgiu, and R.~Guerraoui.
Fast randomized test-and-set and renaming.
In \DISC{24th}, pp. 94--108. 2010.
8. [ABGG2012a] D.~Alistarh, M.~A. Bender, S.~Gilbert, and R.~Guerraoui.
In \FOCS{53rd}, pp. 331--340. 2012.
9. [ACS2014a] D.~Alistarh, K.~Censor{-}Hillel, and N.~Shavit.
Are lock-free concurrent algorithms practically wait-free?
In \STOC{46th}, pp. 714--723. 2014.
10. [AAC2012a] J.~Aspnes, H.~Attiya, and K.~Censor-Hillel.
Polylogarithmic concurrent data structures from monotone circuits.
\JACM, 59:2, 2012.
11. [AC2010a] J.~Aspnes and K.~Censor.
Approximate shared-memory counting despite a strong adversary.
ACM Transactions on Algorithms, 6:1--23, 2010.
12. [AC2013a} J.~Aspnes and K.~Censor-Hillel.
Atomic snapshots in {$O(\log^3 n)$] steps using randomized helping.
In \DISC{27th}, pp. 254--268. 2013.
13. [AH1990a] J.~Aspnes and M.~Herlihy.
Fast randomized consensus using shared memory.
\JALG, 11:441--461, 1990.
14. [AE2014a:impossibility] H.~Attiya and F.~Ellen.
Impossibility Results for Distributed Computing.
Morgan and Claypool, 2014.
15. [BG2011a} M.~Bender and S.~Gilbert.
Mutual exclusion with {$O(\log^2\log n)$] amortized work.
In \FOCS{52nd}, pp. 728--737. 2011.
16. [CR2012a] A.~Casta{\~{n}}eda and S.~Rajsbaum.
New combinatorial topology bounds for renaming: The upper bound.
\JACM, 59:3, 2012.
17. [GHHW2013a} G.~Giakkoupis, M.~Helmi, L.~Higham, and P.~Woelfel.
An {$O(\sqrt{n})$] space bound for obstruction-free leader election.
In \DISC{27th}, pp. 46--60. 2013.
18. [GW2012b] G.~Giakkoupis and P.~Woelfel.
On the time and space complexity of randomized test-and-set.
In \PODC{31st}, pp. 19--28. 2012.
19. [GW2012a} G.~Giakkoupis and P.~Woelfel.
A tight {RMR] lower bound for randomized mutual exclusion.
In \STOC{44th}, pp. 983--1002. 2012.
20. [GW2014a} G.~Giakkoupis and P.~Woelfel.
Randomized mutual exclusion with constant amortized {RMR] complexity on the {DSM}.
In \FOCS{55nd}. 2014.
To appear.
21. [GHW2010a} W.~Golab, D.~Hendler, and P.~Woelfel.
An {$O(1)$] {RMR}s leader election algorithm.
\SIAMJC, 39:2726--2760, 2010.
22. [HW2010a] D.~Hendler and P.~Woelfel.
Adaptive randomized mutual exclusion in sub-logarithmic expected time.
In \PODC{29th}, pp. 141--150. 2010.
23. [HW2011a] D.~Hendler and P.~Woelfel.
Randomized mutual exclusion with sub-logarithmic {RMR}-complexity.
\DistComp, 24:3--19, 2011.
24. [Her1991a] M.~Herlihy.
Wait-free synchronization.
\TOPLAS, 13:124--149, 1991.
25. [HKR2013a] M.~Herlihy, D.~Kozlov, and S.~Rajsbaum.
Distributed Computing Through Combinatorial Topology.
Morgan Kaufmann, 2013.
26. [kozlov2012] D.~N. Kozlov.
Chromatic subdivision of a simplicial complex.
Homology, Homotopy and Applications, 14:197--209, 2012.
27. [MR2955101} D.~N. Kozlov.
Some conjectures concerning complexity of {PL] subdivisions.
In Proceedings of the {W}orkshop on {Geometric and {T}opological {M}ethods in {C}omputer {S}cience ({GETCO})}, volume 283 of Electron. Notes Theor. Comput. Sci., pp. 153--157. Elsevier Sci. B. V., Amsterdam, 2012.
28. [Lev1986a] L.~A. Levin.
Average case complete problems.
\SIAMJC, 15:285--286, 1986.
29. [FFH2012dagstuhl] M.~H. Lisbeth~Fajstrup, Dmitry Feichtner-Kozlov, editor.
\emph{Applications of Combinatorial Topology to Computer Science (Dagstuhl Seminar 12121)}, volume~2 of Dagstuhl Reports. 2012.
30. [MF2004a:heuristics] Z.~Michalewicz and D.~Fogel.
How to solve it - modern heuristics.
Springer, second edition, 2004.
31. [PW2012a] A.~Pareek and P.~Woelfel.
{RMR}-efficient randomized abortable mutual exclusion.
In \DISC{26th}, pp. 267--281. 2012.
32. [ST2004a] D.~A. Spielman and S.~Teng.
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time.
\JACM, 51:385--463, 2004.
33. [ST2009a] D.~A. Spielman and S.~Teng.
Smoothed analysis: an attempt to explain the behavior of algorithms in practice.
\CACM, 52:76--84, 2009.
34. [Yao1977a] A.~C.-C. Yao.
Probabilistic computations: Towards a unified measure of complexity.
In \FOCS{17th}, pp. 222--227. 1977.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8928526043891907, "perplexity": 8943.33588527462}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128329344.98/warc/CC-MAIN-20170629135715-20170629155715-00359.warc.gz"}
|
https://questioncove.com/updates/5665eb4ee4b0525915ef7f18
|
OpenStudy (princessaurora):
** Will Fan and Medal ** What is the asymptote of the function: f(x) = (3^x + 1) – 2? A) y=-2 B) y=-1 C) y=1 D) y=2
2 years ago
OpenStudy (anonymous):
Y=-1
2 years ago
OpenStudy (princessaurora):
2 years ago
OpenStudy (princessaurora):
@whpalmer4 is this right?
2 years ago
OpenStudy (whpalmer4):
Yes, $$y=-1$$ is correct. Think about what happens to the value of $$f(x)$$ as $$x$$ moves to the left of $$0$$: $f(-1) = 3^{-1}+1-2 = \frac{1}{3}-1$ $f(-2) = 3^{-2} +1 -2 = \frac{1}{3^2} -1$ $f(-100) = 3^{-100}+1-2 = \frac{1}{3^{100}}-1$That $$3^x$$ term gets arbitrarily close to $$0$$, so the overall value gets arbitrarily close to $$y = f(x) = -1$$
2 years ago
OpenStudy (whpalmer4):
@PrincessAurora
2 years ago
OpenStudy (princessaurora):
@whpalmer4 thanks a lot for the help :)
2 years ago
OpenStudy (anonymous):
@lildanny2025 OpenStudy isn't a place where you go to "get answers", it's a place where you go to learn how to find your own answers. The OpenStudy code of conduct ( http://openstudy.com/code-of-conduct) includes the line: "Don’t post only answers - guide the asker to a solution." @PrincessAurora specifically asked how you got that answer, but you didn't provide that information, which is the only valuable part of the exercise. How is knowing the answer to this particular problem is $$y=-1$$ (without knowing how to find it) going to be any help solving the next problem of this sort?
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4746181070804596, "perplexity": 1527.4383759441273}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257649627.3/warc/CC-MAIN-20180324015136-20180324035136-00599.warc.gz"}
|
http://mathhelpforum.com/calculus/128602-differentiate.html
|
1. ## Differentiate
Differentiate this function f(x)= (4x)/(sqrt2x).
I know I use the quotient rule to differentiate this, this is what I have done so far:
(2x)^1/2 (0) - (4) [1/2(2x)^-1/2] divided by (2x)
0 - 2(2x)^-1/2 divided by (2x)
-(2x)^-1/2 divided by x
-2 divided by x^1/2 * x
-2 divided by sqrtx^3
Please help if something here is confusing because i dont know how to use Latex please tell I will try to show it more better.
Thanks
2. fastter than that, is note that: $f(x)=\dfrac{4}{\sqrt{2}}\cdot \dfrac{x}{\sqrt{x}}$
3. but what I have done is not right. Tha answer given is (2)/(sqrt2x)
4. Originally Posted by Nacho
fastter than that, is note that: $f(x)=\dfrac{4}{\sqrt{2}}\cdot \dfrac{x}{\sqrt{x}}$
Nacho is pointing out that his approach and hint will work better. Instead, split it into a constant ( $\frac{4}{\sqrt 2}$) multiplied by a term in x ( $\frac{x}{\sqrt x}=\sqrt x$)
So then you can just use the power rule. So before differentiating you have changed the function to $y=\frac{4\sqrt x}{\sqrt2}$
Can you differentiate that more easily?
5. ok, I don´t undestand why you multiplicate by zero in the first line, if the quotient rule says: $
\left( {\frac{h}
{g}} \right)^\prime = \frac{{h'g - hg'}}
{{g^2 }}
$
In your example $h=4x$ and $g=\sqrt{2x}$
Whit my way is easy $
f(x) = \frac{4}
{{\sqrt 2 }} \cdot x^{1/2} \Rightarrow f'(x) = \frac{4}
{{\sqrt 2 }} \cdot \frac{1}
{2} \cdot x^{ - 1/2} = \frac{{\sqrt 2 }}
{{\sqrt x }}
$
6. Originally Posted by Nacho
ok, I don´t undestand why you multiplicate by zero in the first line, if the quotient rule says: $
\left( {\frac{h}
{g}} \right)^\prime = \frac{{h'g - hg'}}
{{g^2 }}
$
In your example $h=4x$ and $g=\sqrt{2x}$
Whit my way is easy $
f(x) = \frac{4}
{{\sqrt 2 }} \cdot x^{1/2} \Rightarrow f'(x) = \frac{4}
{{\sqrt 2 }} \cdot \frac{1}
{2} \cdot x^{ - 1/2} = \frac{{\sqrt 2 }}
{{\sqrt x }}
$
Just pointing out simplification
$\frac{4}{\sqrt{2}}\cdot \frac{1}{2}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2}}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2x}}$
7. Originally Posted by Keithfert488
Just pointing out an error in simplification
$\frac{4}{\sqrt{2}}\cdot \frac{1}{2}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2}}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2x}}$
I just continue the simplification
$
\frac{2}
{{\sqrt 2 }} = \frac{{\sqrt 2 \sqrt 2 }}
{{\sqrt 2 }} = \sqrt 2
$
8. Originally Posted by Keithfert488
Just pointing out an error in simplification
$\frac{4}{\sqrt{2}}\cdot \frac{1}{2}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2}}\cdot x^{-\frac{1}{2}}=\frac{2}{\sqrt{2x}}$
Your solution and his solution are equal.
9. Originally Posted by drumist
Your solution and his solution are equal.
Wow. I feel stupid. Well...I was doing it so we can see it through to the answer that he gave us.
10. lols thanks guys.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.929263174533844, "perplexity": 1127.3102303596384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822822.66/warc/CC-MAIN-20171018070528-20171018090528-00071.warc.gz"}
|
https://socratic.org/questions/for-what-values-of-x-if-any-does-f-x-1-x-6-x-2-9-have-vertical-asymptotes
|
Calculus
Topics
# For what values of x, if any, does f(x) = 1/((x-6)(x^2-9)) have vertical asymptotes?
Jan 11, 2016
$x = 6 , x = 3 , x = - 3$
#### Explanation:
Vertical asymptotes occur when the denominator equals zero.
$\left(x - 6\right) \left({x}^{2} - 9\right) = 0$
$\left(x - 6\right) \left(x - 3\right) \left(x + 3\right) = 0$
$x = 6 , x = 3 , x = - 3$
##### Impact of this question
102 views around the world
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9183963537216187, "perplexity": 6507.260424516343}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204885.27/warc/CC-MAIN-20190326075019-20190326101019-00412.warc.gz"}
|
http://genealogy.math.ndsu.nodak.edu/id.php?id=27154
|
Janos Edvard Hanson
Ph.D. The George Washington University 1960
Dissertation: On Linear Sequence Spaces Which Permit Omission and Adjunction and Have Finite Dimension Modulo Convergence
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8999829292297363, "perplexity": 10741.482885782132}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657135597.56/warc/CC-MAIN-20140914011215-00226-ip-10-234-18-248.ec2.internal.warc.gz"}
|
http://www.mathworks.com/help/matlab/ref/gamma.html?s_tid=gn_loc_drop&requestedDomain=www.mathworks.com&nocookie=true
|
Documentation
This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.
gamma
Gamma function
Syntax
``Y = gamma(X)``
Description
example
````Y = gamma(X)` returns the `gamma` function evaluated at the elements of `X`. ```
Examples
collapse all
Evaluate the gamma function with a scalar and a vector.
Evaluate , which is equal to .
`y = gamma(0.5)`
```y = 1.7725 ```
Evaluate several values of the gamma function between `[-3.5 3.5]`.
```x = -3.5:3.5; y = gamma(x)```
```y = Columns 1 through 7 0.2701 -0.9453 2.3633 -3.5449 1.7725 0.8862 1.3293 Column 8 3.3234 ```
Plot the gamma function and its inverse.
Use `fplot` to plot the gamma function and its inverse. The gamma function increases quickly for positive arguments and has simple poles at all negative integer arguments (as well as 0). The function does not have any zeros. Conversely, the inverse gamma function has zeros at all negative integer arguments (as well as 0).
```fplot(@gamma) hold on fplot(@(x) 1./gamma(x)) legend('\Gamma(x)','1/\Gamma(x)') hold off grid on```
Input Arguments
collapse all
Input array, specified as a scalar, vector, matrix, or multidimensional array. The elements of `X` must be real.
Data Types: `single` | `double`
collapse all
Gamma Function
The `gamma` function is defined for real `x > 0` by the integral:
`$\Gamma \left(x\right)={\int }_{0}^{\infty }{e}^{-t}{t}^{x-1}dt$`
The `gamma` function interpolates the `factorial` function. For integer `n`:
`gamma(n+1) = factorial(n) = prod(1:n)`
The domain of the `gamma` function extends to negative real numbers by analytic continuation, with simple poles at the negative integers. This extension arises from repeated application of the recursion relation
`$\Gamma \left(n-1\right)=\frac{\Gamma \left(n\right)}{n-1}\text{\hspace{0.17em}}.$`
Algorithms
The computation of `gamma` is based on algorithms outlined in [1]. Several different minimax rational approximations are used depending upon the value of `A`.
References
[1] Cody, J., An Overview of Software Development for Special Functions, Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.
[2] Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8679729104042053, "perplexity": 1234.573725632956}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806620.63/warc/CC-MAIN-20171122175744-20171122195744-00286.warc.gz"}
|
http://openstudy.com/updates/4ea61de2e4b05519bdb3da0b
|
## Got Homework?
### Connect with other students for help. It's a free community.
• across
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
55 members online
• 0 viewing
## LagrangeSon678 Group Title derivative of secx derivative of secx @Mathematics 2 years ago 2 years ago Edit Question Delete Cancel Submit
• This Question is Closed
1. LagrangeSon678 Group Title
Best Response
You've already chosen the best response.
0
anybody can help me?
• 2 years ago
2. becca18 Group Title
Best Response
You've already chosen the best response.
0
What's that supposed to mean?
• 2 years ago
3. LagrangeSon678 Group Title
Best Response
You've already chosen the best response.
0
a derivative?
• 2 years ago
4. agreene Group Title
Best Response
You've already chosen the best response.
0
tan(x)sec(x) This are all very common derivatives... your book should have a table of them somewhere... and I would suggest just memorizing all of the trig derivatives and integrals, it will come in handy when you get to trig substitution integration.
• 2 years ago
5. Tyler1992 Group Title
Best Response
You've already chosen the best response.
0
ok.. sec(x) is the same as $\frac{1}{\cos(x)}$ So use the quotient rule to find the derivative... $\frac{\cos(x)(0) - 1(-\sin(x))}{\cos^2(x)}$ Simplify and you get $\frac{\sin(x)}{\cos^2(x)}$ This can be written as $\frac{1}{\cos(x)} * \frac{\sin(x)}{\cos(x)}$ Which is sec(x)tan(x)
• 2 years ago
• Attachments:
## See more questions >>>
##### spraguer (Moderator) 5→ View Detailed Profile
23
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967140555381775, "perplexity": 10716.223259517288}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500821666.77/warc/CC-MAIN-20140820021341-00134-ip-10-180-136-8.ec2.internal.warc.gz"}
|
http://www.q-chem.com/qchem-website/manual/qchem51_manual/sec-ElectricProps.html
|
Q-Chem 5.1 User’s Manual
# 11.12 Linear-Scaling Computation of Electric Properties
The search for new optical devices is a major field of materials sciences. Here, polarizabilities and hyperpolarizabilities provide particularly important information on molecular systems. The response of the molecular systems in the presence of an external, monochromatic, oscillatory electric field is determined by the solution of the time-dependent SCF (TDSCF) equations. Within the dipole approximation, the perturbation is represented as the interaction of the molecule with a single Fourier component of the external field, :
(11.67)
with
(11.68)
Here, is the field frequency and is the dipole moment operator. The TDSCF equations can be solved via standard techniques of perturbation theory. As a solution, one obtains the first-order perturbed density matrix [] and the second-order perturbed density matrices []. From these quantities, the following properties can be calculated:
• Static polarizability:
• Dynamic polarizability:
• Static hyperpolarizability:
• Second harmonic generation:
• Electro-optical Pockels effect:
• Optical rectification:
Here, is the matrix representation of the component of the dipole moment.
Note that third-order properties () can be computed either with the equations above, which is based on a second-order TDSCF calculation (for ), or alternatively from first-order properties using Wigner’s rule. The second-order approach corresponds to MOPROP job numbers 101 and 102 (see below) whereas use of the rule corresponds to job numbers 103 and 104. Solution of the second-order TDSCF equations depends upon first-order results and therefore convergence can be more problematic as compared to the first-order calculation. For this reason, we recommend job numbers 103 and 104 for the calculation of first hyperpolarizabilities.
The TDSCF calculation is more time-consuming than the SCF calculation that precedes it (where the field-free, unperturbed ground state of the molecule is obtained). Q-Chem’s implementation of the TDSCF equations is MO based and the cost therefore formally scales asymptotically as . The prefactor of the cubic-scaling step is rather small, however, and in practice (over a wide range of molecular sizes) the calculation is dominated by the cost of contractions with two-electron integrals, which is formally scaling but with a very large prefactor. The cost of these integral contractions can be reduced from quadratic to using LinK/CFMM methods (Section 4.6). All derivatives are computed analytically.
The TDSCF module in Q-Chem is know as “MOProp", since it corresponds (formally) to time propagation of the molecular orbitals. (For actual time propagation of the MOs, see Section 7.11.) The MOProp module has the following features:
• LinK and CFMM support to evaluate Coulomb- and exchange-like matrices
• Analytic derivatives
• DIIS acceleration
• Both restricted and unrestricted implementations of CPSCF and TDSCF equations are available, for both Hartree-Fock and Kohn-Sham DFT.
• Support for LDA, GGA, and global hybrid functionals. Meta-GGA and range-separated functionals are not yet supported, nor are functionals that contain non-local correlation (e.g., those containing VV10).
## 11.12.1 $fdpfreq Input Section For dynamic response properties (i.e., ), various values of might be of interest, and it is considerably cheaper to compute properties for multiple values of in a single calculation than it is to run several calculations for one frequency each. The$fdpfreq input section is used to specify the frequencies of interest. The format is:
$fdpfreq property frequencies units$end
The first line is only required for third-order properties, to specify the flavor of first hyperpolarizability. The options are
• StaticHyper (static hyperpolarizability)
• SHG (second harmonic generation)
• EOPockels (electro-optical Pockels effect)
• OptRect (optical rectification)
The second line in the $fdpfreq section contains floating-point values representing the frequencies of interest. Alternatively, for dynamic polarizabilities an equidistant sequence of frequencies can be specified by the keyword WALK (see example below). The last line specifies the units of the input frequencies. Options are: • au (atomic units of frequency) • eV (frequency units, expressed in electron volts) • Hz (frequency units, expressed in Hertz) • nm (wavelength units, in nanometers) • cmInv (wavenumber units, ) Example 11.259 Static and dynamic polarizabilities, atomic units: $fdpfreq
0.0 0.03 0.05
au
$end Example 11.260 Series of dynamic polarizabilities, starting with 0.00 incremented by 0.01 up to 0.10: $fdpfreq
walk 0.00 0.10 0.01
au
$end Example 11.261 Static first hyperpolarizability, second harmonic generation and electro-optical Pockels effect, wavelength in nm: $fdpfreq
StaticHyper SHG EOPockels
1064
nm
$end ## 11.12.2 Job Control for the MOProp Module The MOProp module is invoked by specifying a job number using the MOPROP$rem variable. In addition to electric properties, this module can also compute NMR chemical shifts (MOPROP = 1); this functionality is described in Section 11.13.
MOPROP
Specifies the job number for MOProp module.
TYPE:
INTEGER
DEFAULT:
0 Do not run the MOProp module.
OPTIONS:
1 NMR chemical shielding tensors. 2 Static polarizability. 3 Indirect nuclear spin–spin coupling tensors. 100 Dynamic polarizability. 101 First hyperpolarizability. 102 First hyperpolarizability, reading First order results from disk. 103 First hyperpolarizability using Wigner’s rule. 104 First hyperpolarizability using Wigner’s rule, reading first order results from disk.
RECOMMENDATION:
None
MOPROP_PERTNUM
Set the number of perturbed densities that will to be treated together.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0 All at once. Treat the perturbed densities batch-wise.
RECOMMENDATION:
Use the default. For large systems, limiting this number may be required to avoid memory exhaustion.
MOPROP_CONV_1ST
Sets the convergence criteria for CPSCF and 1st order TDSCF.
TYPE:
INTEGER
DEFAULT:
6
OPTIONS:
Convergence threshold set to .
RECOMMENDATION:
None
MOPROP_CONV_2ND
Sets the convergence criterion for second-order TDSCF.
TYPE:
INTEGER
DEFAULT:
6
OPTIONS:
Convergence threshold set to .
RECOMMENDATION:
None
MOPROP_MAXITER_1ST
The maximum number of iterations for CPSCF and first-order TDSCF.
TYPE:
INTEGER
DEFAULT:
50
OPTIONS:
Set maximum number of iterations to .
RECOMMENDATION:
Use the default.
MOPROP_MAXITER_2ND
The maximum number of iterations for second-order TDSCF.
TYPE:
INTEGER
DEFAULT:
50
OPTIONS:
Set maximum number of iterations to .
RECOMMENDATION:
Use the default.
MOPROP_ISSC_PRINT_REDUCED
Specifies whether the isotope-independent reduced coupling tensor should be printed in addition to the isotope-dependent -tensor when calculating indirect nuclear spin-spin couplings.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Do not print . TRUE Print .
RECOMMENDATION:
None
MOPROP_ISSC_SKIP_FC
Specifies whether to skip the calculation of the Fermi contact contribution to the indirect nuclear spin-spin coupling tensor.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Calculate Fermi contact contribution. TRUE Skip Fermi contact contribution.
RECOMMENDATION:
None
MOPROP_ISSC_SKIP_SD
Specifies whether to skip the calculation of the spin-dipole contribution to the indirect nuclear spin-spin coupling tensor.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Calculate spin-dipole contribution. TRUE Skip spin-dipole contribution.
RECOMMENDATION:
None
MOPROP_ISSC_SKIP_PSO
Specifies whether to skip the calculation of the paramagnetic spin-orbit contribution to the indirect nuclear spin-spin coupling tensor.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Calculate paramagnetic spin-orbit contribution. TRUE Skip paramagnetic spin-orbit contribution.
RECOMMENDATION:
None
MOPROP_ISSC_SKIP_DSO
Specifies whether to skip the calculation of the diamagnetic spin-orbit contribution to the indirect nuclear spin-spin coupling tensor.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Calculate diamagnetic spin-orbit contribution. TRUE Skip diamagnetic spin-orbit contribution.
RECOMMENDATION:
None
MOPROP_DIIS
Controls the use of Pulay’s DIIS in solving the CPSCF equations.
TYPE:
INTEGER
DEFAULT:
5
OPTIONS:
0 Turn off DIIS. 5 Turn on DIIS.
RECOMMENDATION:
None
MOPROP_DIIS_DIM_SS
Specified the DIIS subspace dimension.
TYPE:
INTEGER
DEFAULT:
20
OPTIONS:
0 No DIIS. Use a subspace of dimension .
RECOMMENDATION:
None
SAVE_LAST_GPX
Save the last when calculating dynamic polarizabilities in order to call the MOProp code in a second run, via MOPROP = 102.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0 False 1 True
RECOMMENDATION:
None
MOPROP_RESTART
Specifies the option for restarting MOProp calculations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0 Not a restart calculation. 1 Restart from a previous calculation using the same scratch directory.
RECOMMENDATION:
Need to also include "SCF_GUESS READ" and "SKIP_SCFMAN TRUE" to ensure the same set of MOs.
## 11.12.3 Examples
Example 11.262 B97X-D/def2-SVPD static polarizability calculation for water cation, computed analytically using the MOProp module
$rem method hf basis def2-svpd scf_convergence 11 thresh 14 symmetry false sym_ignore true moprop 2 moprop_conv_1st 8 moprop_maxiter_1st 200$end
$molecule 1 2 O 0.003 1.517 0.000 H 0.913 1.819 0.000 H 0.081 0.555 0.000$end
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.772236168384552, "perplexity": 6863.389275290491}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867417.71/warc/CC-MAIN-20180526112331-20180526132331-00171.warc.gz"}
|
https://www.lmfdb.org/GaloisGroup/16T34
|
# Properties
Label 16T34 Order $$32$$ n $$16$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group Yes Group: $C_2^2:D_4$
# Related objects
## Group action invariants
Degree $n$ : $16$ Transitive number $t$ : $34$ Group : $C_2^2:D_4$ Parity: $1$ Primitive: No Nilpotency class: $2$ Generators: (1,11,16,13)(2,12,15,14)(3,9,5,7)(4,10,6,8), (1,15)(2,16)(3,5)(4,6)(7,8)(9,10), (1,10,16,8)(2,9,15,7)(3,12,5,14)(4,11,6,13) $|\Aut(F/K)|$: $4$
## Low degree resolvents
|G/N|Galois groups for stem field(s)
2: $C_2$ x 7
4: $C_2^2$ x 7
8: $D_{4}$ x 4, $C_2^3$
16: $D_4\times C_2$ x 2, $Q_8:C_2$
Resolvents shown for degrees $\leq 47$
## Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$, $D_{4}$ x 4
Degree 8: $D_4\times C_2$ x 2, $Q_8:C_2$
## Low degree siblings
16T34, 16T43 x 2, 32T20
Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
## Conjugacy Classes
Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 2, 2, 2, 2, 1, 1, 1, 1$ $4$ $2$ $( 3, 4)( 5, 6)( 7, 9)( 8,10)(11,14)(12,13)$ $2, 2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)$ $2, 2, 2, 2, 2, 2, 2, 2$ $2$ $2$ $( 1, 3)( 2, 4)( 5,16)( 6,15)( 7,13)( 8,14)( 9,11)(10,12)$ $4, 4, 4, 4$ $4$ $4$ $( 1, 3, 2, 4)( 5,15, 6,16)( 7,11, 8,12)( 9,13,10,14)$ $2, 2, 2, 2, 2, 2, 2, 2$ $2$ $2$ $( 1, 5)( 2, 6)( 3,16)( 4,15)( 7,11)( 8,12)( 9,13)(10,14)$ $4, 4, 4, 4$ $2$ $4$ $( 1, 7,16, 9)( 2, 8,15,10)( 3,13, 5,11)( 4,14, 6,12)$ $2, 2, 2, 2, 2, 2, 2, 2$ $4$ $2$ $( 1, 7)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 9,16)(10,15)$ $4, 4, 4, 4$ $2$ $4$ $( 1, 8,16,10)( 2, 7,15, 9)( 3,14, 5,12)( 4,13, 6,11)$ $4, 4, 4, 4$ $2$ $4$ $( 1,11,16,13)( 2,12,15,14)( 3, 9, 5, 7)( 4,10, 6, 8)$ $4, 4, 4, 4$ $4$ $4$ $( 1,11, 2,12)( 3,10, 4, 9)( 5, 8, 6, 7)(13,15,14,16)$ $4, 4, 4, 4$ $2$ $4$ $( 1,12,16,14)( 2,11,15,13)( 3,10, 5, 8)( 4, 9, 6, 7)$ $2, 2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1,15)( 2,16)( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)$ $2, 2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1,16)( 2,15)( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)$
## Group invariants
Order: $32=2^{5}$ Cyclic: No Abelian: No Solvable: Yes GAP id: [32, 28]
Character table: 2 5 3 5 4 3 4 4 3 4 4 3 4 5 5 1a 2a 2b 2c 4a 2d 4b 2e 4c 4d 4e 4f 2f 2g 2P 1a 1a 1a 1a 2b 1a 2g 1a 2g 2g 2b 2g 1a 1a 3P 1a 2a 2b 2c 4a 2d 4b 2e 4c 4f 4e 4d 2f 2g X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 1 1 X.3 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 X.4 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 1 X.5 1 -1 1 1 -1 1 1 -1 1 1 -1 1 1 1 X.6 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 X.7 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 X.8 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 X.9 2 . 2 2 . -2 . . . . . . -2 -2 X.10 2 . 2 -2 . 2 . . . . . . -2 -2 X.11 2 . -2 . . . -2 . 2 . . . -2 2 X.12 2 . -2 . . . 2 . -2 . . . -2 2 X.13 2 . -2 . . . . . . A . -A 2 -2 X.14 2 . -2 . . . . . . -A . A 2 -2 A = -2*E(4) = -2*Sqrt(-1) = -2i
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9210391640663147, "perplexity": 264.9483214643797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145708.59/warc/CC-MAIN-20200222150029-20200222180029-00460.warc.gz"}
|
https://space.stackexchange.com/questions/31511/what-happens-to-the-acoustic-energy-removed-by-a-sound-suppression-system/31516
|
# What happens to the acoustic energy removed by a sound suppression system?
I was just watching this video of a launchpad sound suppression system, and realized if it removes acoustic energy from the air, the energy has to go somewhere.
Does the water heat up? Will any of it get hot enough to boil? Maybe evaporate a little?
• If there is no sound suppression system, acoustic energy will be (partially) transformed to heat. Why should that be different when water is used for sound supression? – Uwe Oct 22 '18 at 9:43
• I guess a lot of the acoustic energy would be absorbed by the water in the deluge system being torn into tiny droplets (by doing work against surface tension) – JCRM Oct 22 '18 at 10:29
• but undoubtedly some of the kinetic energy will be absorbed as heat. – JCRM Oct 22 '18 at 10:35
• I'll need time to go look at sources, but last time I checked the energy does get converted into heat, but it is a negligible source of energy compared to the other sources (i.e. the giant pillar of fire coming out of the space chariot!) – Cort Ammon Oct 22 '18 at 19:20
Yes, the water heats up. Lots of it evaporates. There is a system to catch and filter the remainder, which is polluted with combustion products of the SRBs.
Those massive clouds in the foreground are water vapor mixed with combustion products of the SRBs.
For the Shuttle, this report states that 166 tonnes of water is evaporated, out of 1135 tonnes supplied by the suppression system. But that's an incomplete number.
Another source has these numbers for the the deluge water:
_ 200 000 litres sont vaporisées ;
_ 10 000 litres sont atomisées ;
_ le reste est éparpillé ;
• 200 tons is vaporized
• 10 tons is atomized
• the rest is scattered (blasted away by the exhaust, ending up all over the vicinity of the flame trenches)
The mechanism seems to be that air bubbles in the water are compressed by the sound waves passing through, this compression generates heat. See this related question.
• Are the clouds (condensed) water vapour, or are they "atomised" water droplets? – JCRM Oct 22 '18 at 9:59
• Page 66 of the report states the 166 tonnes of water is vaporised due to the exhaust heat. Page 65 states "For this application the kinetic energy should not be included" - so, while extremely useful and interesting, it doesn't answer the question. – JCRM Oct 22 '18 at 10:16
• Page 66 also includes "The cloud must also contain a considerable quantity of liquid water atomized from the excess deluge water " and page 96 goes on to state "Since a substantial fraction of each deposition drop comes from the deluge water without an intervening phase transition" – JCRM Oct 22 '18 at 10:33
• found another number. – Hobbes Oct 22 '18 at 10:56
• I'm not sure how the (french) source gives a 70/30 split? It seems to be using single digit precision, 200 tonnes evaporated, 10 tonnes atomised and the rest scattered(?). Perhaps that refers to the three states the Nasa report notes when describing the interplay between vapour, atomised and small droplets as complex. However, If we take the 30% ending up in the pond as accurately applying to the 365 tonnes used in the 7.5 seconds, that's around 110 tonnes. No more than 166 tonnes is evaporated by the heat from the engines, so around 70 tonnes of water is put into the air by the kinetics – JCRM Oct 22 '18 at 11:54
tl;dr: water droplets scatter the sound keeping it more localized, and also absorb some of it, while some is also absorbed in all the other surfaces the sound strikes. There's no where near enough power to boil this much water.
Sound in the air at these (audio and sub-sonic) frequencies pretty much always ends up as mostly heat.
Ultrasonic sound can be use do work on the surface tension of water (ultrasonic atomizers, humidifiers, etc) but when that's used in a practical way the wavelength is usually millimeters and the corresponding frequency in MHz so the sound pressure can be focused to a small, high-intensity area for more efficient disruption of the surface into droplets.
But that's not what's going to happen here.
For audible and sub-sonic rocket launch sound, the deep sub-wavelength but high density droplet dispersion will diffusely scatter the sound waves, decreasing their mean free path and therefore increase the time for the sound energy to be mechanically absorbed, both by the droplets and by any other local surfaces the sound reaches.
How much energy and therefore heat are we talking about here?
Until dB levels with their corresponding distances and measurement conditions can be found, here is a walkthrough of the conversion process and are some rough estimates:
So far I found a sound level of about 160 dB at 125 feet in this answer and 180 dB in the payload bay of the Space Shuttle in this answer but these are not helpful; the first one is with the sound suppression in place, and the second is in a confined, closed space.
But I'll show how to do the estimating calculation here in hopes we can get better numbers.
In this excellent answer to my question How much power and energy is (actually) in a 230 dB “click” from a whale? the equation was derived as follows:
Intensity (or specifically sound intensity) of a linear sound wave is related to sound pressure, $$P$$, through: $$I = \frac{ P^{2} }{ \rho_{o} \ C_{s} }$$ where $$\rho_{o}$$ is the mass density and $$C_{s}$$ is the speed of sound in the medium. One can look up the properties of water to find that $$\rho_{o}$$ ~ 999.972 kg/m3 and $$C_{s}$$ ~ 1484 m/s. We can also look up the reference pressure level for water (or at NOAA) finding $$P_{H2O}$$ ~ 1 $$\mu$$Pa (compared to $$P_{air}$$ ~ 10 $$\mu$$Pa) at 1 meter from source. This corresponds to a reference intensity of $$I_{o} \sim 6.74 \times 10^{-19}$$ W/m2.
$$I = I_{o} \ 10^{L/10}$$
where $$I$$ is intensity (in W/m2) and $$L$$ is intensity (in dB).
So for example, 160 dB at 125 feet (38 meters) would be 7 mW/m^2 or about 15 Watts integrated over one hemisphere.
The largest number I saw was in this answer
The Saturn V predated this suppression system. Early engine tests reached as high as 211 decibels.
If we were to try to use the same 38 meters distance, 50 dB is 10^5 means 1.5 megaWatts, and that could potentially boil a few kilograms of water per second if it were concentrated on a few kilograms. But that's not the case, the sound is dispersed over many tons per second of water and the ground and other surfaces.
There are more dB values in this answer but they don't have a clear geometry description.
Nonetheless:
No, no water was harmed boiled in the making of this film orbit.
• youtu.be/THUMdTohWkI?t=192 Are you sure it's only ultrasound that can disperse water? – JCRM Oct 22 '18 at 11:39
• Then your third paragraph needs clarification. It appears to talk about ultrasound, separating it from "audible and sub-sonic rocket launch sound" by the use of the "but that's when the wavelength is millimeters and the corresponding frequency in MHz" clause. – JCRM Oct 22 '18 at 13:18
• @JCRM edited; I'll revisit this again in the morning. Thanks for the helpful comment! – uhoh Oct 22 '18 at 14:18
• Are you sure that 211dB "at the base of the test stand" are comparable to 160 dB in 38m distance? What was the size of the F-1 test stand? – asdfex Oct 23 '18 at 22:27
• @uhoh This suggests something in the order of 10m - if we take "bottom" as "ground floor" - they won't put the microphones into the water pit below. en.wikipedia.org/wiki/Rocketdyne_F-1#/media/… – asdfex Oct 24 '18 at 8:34
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 14, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6282197833061218, "perplexity": 1173.0239821062953}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107879673.14/warc/CC-MAIN-20201022141106-20201022171106-00450.warc.gz"}
|
http://link.springer.com/article/10.1134%2FS1061934811040071
|
, Volume 66, Issue 6, pp 618-622
Date: 10 Jun 2011
# Study on the interaction of DNA with resveratrol by resonance light scattering technique and its analytical application
Rent the article at a discount
Rent now
* Final gross prices may vary according to local VAT.
## Abstract
The interaction between resveratrol and DNA has been studied by resonance light scattering (RLS) technique. In strongly acidic solution, resveratrol has a maximum peak at 368 nm and the RLS intensity is remarkably enhanced by trace amounts of DNA due to its interaction with resveratrol. Based on this, a novel assay for nucleic acids has been developed. The characteristics of RLS, fluorescence and UV-VIS absorption spectra, the influential factors and optimum conditions of the reaction have been studied. The enhanced RLS intensity at 368 nm is proportional to the concentration of DNA within the range of 0–1600 μg/L for calf thymus DNA. The determination limit (3σ) is 5.2 ng/mL. The study of foreign substance effect on the determination of DNA indicates that most of metal ions have little effect on the determination of DNA. Three synthetic samples of DNA were analysed with satisfactory results. The results show that the proposed method is very sensitive, convenient, rapid and reproducible.
The article is published in the original.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8324615955352783, "perplexity": 2077.297319877004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936460577.67/warc/CC-MAIN-20150226074100-00102-ip-10-28-5-156.ec2.internal.warc.gz"}
|
http://www.lahey.com/docs/lfpro75help/gfortran/acosh.html
|
Lahey/GNU Fortran
Next: , Previous: ACOS, Up: Intrinsic Procedures
### 8.7 ACOSH — Inverse hyperbolic cosine function
Description:
ACOSH(X) computes the inverse hyperbolic cosine of X.
Standard:
Fortran 2008 and later
Class:
Elemental function
Syntax:
RESULT = ACOSH(X)
Arguments:
X The type shall be REAL or COMPLEX.
Return value:
The return value has the same type and kind as X. If X is complex, the imaginary part of the result is in radians and lies between 0 \leq \Im \acosh(x) \leq \pi.
Example:
PROGRAM test_acosh
REAL(8), DIMENSION(3) :: x = (/ 1.0, 2.0, 3.0 /)
WRITE (*,*) ACOSH(x)
END PROGRAM
Specific names:
Name Argument Return type Standard DACOSH(X) REAL(8) X REAL(8) GNU extension
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9904208183288574, "perplexity": 8493.815975297033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645264370.66/warc/CC-MAIN-20150827031424-00344-ip-10-171-96-226.ec2.internal.warc.gz"}
|
https://cstheory.stackexchange.com/questions/34877/complexity-of-the-homomorphism-problem-parameterized-by-treewidth
|
# Complexity of the homomorphism problem parameterized by treewidth
The homomorphism problem $\text{Hom}(\mathcal{G}, \mathcal{H})$ for two classes $\mathcal{G}$ and $\mathcal{H}$ of graphs is defined as follows:
Input: a graph $G$ in $\mathcal{G}$, a graph $H$ in $\mathcal{H}$
Output: decide if there is a homomorphism from $G$ to $H$, i.e., a mapping $h$ from the vertices of $G$ to those of $H$ such that, for any edge $\{x, y\}$ of $G$, $\{h(x), h(y)\}$ is an edge of $H$.
For each $k \in \mathbb{N}$, I will call $\mathcal{T}_k$ the class of the graphs of treewidth at most $k$. I'm interested in the problem $\text{Hom}(\mathcal{T}_k, \mathcal{T}_k)$, which I see as a parameterized problem (by the treewidth bound $k$). My question is: what is the complexity of this parameterized problem? Is it known to be FPT? or is it W[1]-hard?
Here are some things that I found about the $\text{Hom}$ problem, but which do not help me answer the question. (I write $-$ for the class of all graphs.)
• http://www.sciencedirect.com/science/article/pii/009589569090132J: If $\mathcal{H}$ is bipartite then $\text{Hom}(-, \mathcal{H})$ is in PTIME, otherwise it is NP-complete, but of course the NP-hardness relies on allowing arbitrary $G$.
• http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.9013&rep=rep1&type=pdf: If the treewidth of $\mathcal{G}$ (modulo homomorphic equivalence) is bounded by a constant then $\text{Hom}(\mathcal{G}, -)$ is in PTIME (and otherwise it isn't, assuming FPT != W[1]). Hence, in particular my problem $\text{Hom}(\mathcal{T}_k, \mathcal{T}_k)$ is in PTIME for fixed $k$, but this doesn't tell me what is the dependency on the parameter.
• From Flum and Grohe's book Parameterized Complexity Theory, Corollary 13.17: The problem $\text{Hom}(\mathcal{T}_k, -)$ is FPT when parameterized by the size of $G$ (but I am parameterizing by the treewidth)
• http://users.uoa.gr/~sedthilk/papers/homo.pdf, Corollary 3.2: When fixing a specific graph $H$, the problem $\text{Hom}(\mathcal{T}_k, \{H\})$, parameterized by k, is FPT (this even holds for more complicated counting variants), but I do not want to restrict to fixed $H$.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9749955534934998, "perplexity": 239.73415479599578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038083007.51/warc/CC-MAIN-20210415035637-20210415065637-00326.warc.gz"}
|
https://boolean.h.uib.no/mediawiki/index.php?title=Classification_of_Quadratic_APN_Trinomials,_Quadrinomials,_Pentanomials,_Hexanomials_(CCZ-inequivalent_with_infinite_monomial_families)_in_Small_Dimensions_with_all_Coefficients_equal_to_1&diff=prev&oldid=304
|
# Difference between revisions of "Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1"
The following tables list CCZ-inequivalent representatives found by systematically searching for APN functions among all trinomials, quadrinomials, pentanomials and hexanomials with coefficients in ${\displaystyle \mathbb {F} _{2}}$ over ${\displaystyle \mathbb {F} _{2^{n}}}$ with ${\displaystyle 6\leq n\leq 11}$ [1]. The tables also list which equivalence class from [2] the functions belong to. Only polynomials inequivalent to power functions are considered. If the polynomial is equivalent to a family from the table of infinite families, this is also listed.
## Trinomials
Dimension ${\displaystyle N^{\circ }}$ Functions Familiy Relation to [2]
${\displaystyle 6}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 7}$ ${\displaystyle 7.1}$ ${\displaystyle x^{20}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 8.1
${\displaystyle 7.2}$ ${\displaystyle x^{34}+x^{18}+x^{5}}$ ${\displaystyle -}$ Table 7: № 2.1
${\displaystyle 8}$ ${\displaystyle 8.1}$ ${\displaystyle x^{72}+x^{6}+x^{3}}$ ${\displaystyle N^{\circ }5}$ Table 9: № 1.3
${\displaystyle 8.2}$ ${\displaystyle x^{72}+x^{36}+x^{3}}$ ${\displaystyle -}$ Table 9: № 1.4
${\displaystyle 9}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 10}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 11}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
Dimension ${\displaystyle N^{\circ }}$ Functions Families Relation to [2]
${\displaystyle 6}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 7}$ ${\displaystyle 7.1}$ ${\displaystyle x^{72}+x^{40}+x^{12}+x^{3}}$ ${\displaystyle -}$ Table 7: № 12.1
${\displaystyle 7.2}$ ${\displaystyle x^{33}+x^{17}+x^{12}+x^{3}}$ ${\displaystyle -}$ Table 7: № 2.2
${\displaystyle 7.3}$ ${\displaystyle x^{34}+x^{33}+x^{10}+x^{3}}$ ${\displaystyle -}$ Table 7: № 10.1
${\displaystyle 7.4}$ ${\displaystyle x^{66}+x^{34}+x^{20}+x^{3}}$ ${\displaystyle -}$ Table 7: № 11.1
${\displaystyle 7.5}$ ${\displaystyle x^{68}+x^{18}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 8.1
${\displaystyle 7.6}$ ${\displaystyle x^{66}+x^{18}+x^{9}+x^{3}}$ ${\displaystyle -}$ Table 7: № 9.1
${\displaystyle 8}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 9}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 10}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 11}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
## Pentanomials
Dimension ${\displaystyle N^{\circ }}$ Functions Families Relation to [2]
${\displaystyle 6}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 7}$ ${\displaystyle 7.1}$ ${\displaystyle x^{68}+x^{40}+x^{24}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 13.1
${\displaystyle 7.2}$ ${\displaystyle x^{65}+x^{20}+x^{18}+x^{6}+x^{3}}$ ${\displaystyle N^{\circ }5}$ Table 7: № 1.2
${\displaystyle 7.3}$ ${\displaystyle x^{40}+x^{34}+x^{18}+x^{10}+x^{3}}$ ${\displaystyle -}$ Table 7: № 12.1
${\displaystyle 7.4}$ ${\displaystyle x^{48}+x^{40}+x^{10}+x^{9}+x^{3}}$ ${\displaystyle -}$ Table 7: № 1.2
${\displaystyle 7.5}$ ${\displaystyle x^{33}+x^{9}+x^{6}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 11.1
${\displaystyle 7.6}$ ${\displaystyle x^{40}+x^{36}+x^{34}+x^{24}+x^{3}}$ ${\displaystyle -}$ Table 7: № 10.1
${\displaystyle 7.7}$ ${\displaystyle x^{24}+x^{10}+x^{9}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 2.1
${\displaystyle 7.8}$ ${\displaystyle x^{65}+x^{36}+x^{20}+x^{17}+x^{3}}$ ${\displaystyle -}$ Table 7: № 14.1
${\displaystyle 7.9}$ ${\displaystyle x^{40}+x^{33}+x^{17}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 8.1
${\displaystyle 7.10}$ ${\displaystyle x^{36}+x^{33}+x^{18}+x^{9}+x^{5}}$ ${\displaystyle -}$ Table 7: № 10.1
${\displaystyle 8}$ ${\displaystyle 8.1}$ ${\displaystyle x^{36}+x^{33}+x^{9}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 9: № 1.4
${\displaystyle 8.2}$ ${\displaystyle x^{72}+x^{66}+x^{12}+x^{6}+x^{3}}$ ${\displaystyle N^{\circ }5}$ Table 9: № 1.3
${\displaystyle 8.3}$ ${\displaystyle x^{130}+x^{66}+x^{40}+x^{12}+x^{3}}$ ${\displaystyle -}$ Table 9: № 6.1
${\displaystyle 8.4}$ ${\displaystyle x^{66}+x^{40}+x^{18}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 9: № 5.1
${\displaystyle 9}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 10}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 11}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
## Hexanomials
Dimension ${\displaystyle N^{\circ }}$ Functions Families Relation to [2]
${\displaystyle 6}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 7}$ ${\displaystyle 7.1}$ ${\displaystyle x^{34}+x^{33}+x^{12}+x^{6}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 14.2
${\displaystyle 7.2}$ ${\displaystyle x^{40}+x^{24}+x^{20}+x^{9}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 14.1
${\displaystyle 7.3}$ ${\displaystyle x^{33}+x^{24}+x^{20}+x^{18}+x^{12}+x^{3}}$ ${\displaystyle -}$ Table 7: № 12.1
${\displaystyle 7.4}$ ${\displaystyle x^{24}+x^{17}+x^{12}+x^{10}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 2.1
${\displaystyle 7.5}$ ${\displaystyle x^{40}+x^{34}+x^{18}+x^{17}+x^{5}+x^{3}}$ ${\displaystyle N^{\circ }5}$ Table 7: № 1.2
${\displaystyle 7.6}$ ${\displaystyle x^{48}+x^{40}+x^{18}+x^{10}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 11.1
${\displaystyle 7.7}$ ${\displaystyle x^{40}+x^{12}+x^{10}+x^{9}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 2.2
${\displaystyle 7.8}$ ${\displaystyle x^{34}+x^{24}+x^{10}+x^{9}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 9.1
${\displaystyle 7.9}$ ${\displaystyle x^{34}+x^{33}+x^{20}+x^{17}+x^{10}+x^{3}}$ ${\displaystyle -}$ Table 7: № 13.1
${\displaystyle 7.10}$ ${\displaystyle x^{36}+x^{33}+x^{24}+x^{9}+x^{6}+x^{3}}$ ${\displaystyle -}$ Table 7: № 10.1
${\displaystyle 7.11}$ ${\displaystyle x^{40}+x^{36}+x^{20}+x^{10}+x^{5}+x^{3}}$ ${\displaystyle -}$ Table 7: № 10.2
${\displaystyle 7.12}$ ${\displaystyle x^{36}+x^{34}+x^{20}+x^{10}+x^{9}+x^{3}}$ ${\displaystyle -}$ Table 7: № 8.1
${\displaystyle 8}$ ${\displaystyle 8.1}$ ${\displaystyle x^{68}+x^{34}+x^{17}+x^{12}+x^{9}+x^{3}}$ ${\displaystyle -}$ Table 9: № 5.1
${\displaystyle 8.2}$ ${\displaystyle x^{72}+x^{40}+x^{34}+x^{20}+x^{12}+x^{3}}$ ${\displaystyle N^{\circ }5}$ Table 9: № 6.1
${\displaystyle 8.3}$ ${\displaystyle x^{72}+x^{66}+x^{34}+x^{18}+x^{10}+x^{5}}$ ${\displaystyle -}$ Table 9: № 4.1
${\displaystyle 9}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 10}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
${\displaystyle 11}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
1. Sun B. On Classification and Some Properties of APN Functions.
2. Edel Y, Pott A. A new almost perfect nonlinear function which is not quadratic. Adv. in Math. of Comm.. 2009 Mar;3(1):59-81.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 216, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23404522240161896, "perplexity": 3163.7954224396644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662647086.91/warc/CC-MAIN-20220527112418-20220527142418-00303.warc.gz"}
|
http://mathhelpforum.com/calculus/12542-application-2-a.html
|
1. ## application 2
problem: Two posts, one 3 meters high and the other 6 meters high, stand 10 meters apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the tops of the posts. Where should the stake be placed to use the least amount of wire?
2. Hello, cazimi!
This is one of the more unpleasant problems . . .
Two posts, one 3m high and the other 6m high, stand 10m apart.
They are to be stayed by wires attached to a single stake at ground level,
the wires running to the tops of the posts.
Where should the stake be placed to use the least amount of wire?
Code:
*C
* |
* |
* |
A* * | 6
| * * |
3 | * * |
| * * |
B* - - - - - * - - - - - - - *D
: x P 10-x :
AB is the 3-meter pole; CD is the 6-meter pole.
They are 10 meters apart: BD = 10.
The wire runs from A to a point P on the ground, then up to C.
Let x = BP, then PD = 10 - x.
From the right triangles (and Pythagorus), we have:
. . . . . . . . ______ . . . . . . . .___________
. . AP .= .√x² + 3², . CP .= .√(10 - x)² + 6²
The length of the wire is: .L .= .[x² + 9]^½ + [(10 - x)² + 36]^½
And that is the function you must minimize.
I'll wait in the car . . .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
There is a very clever geometric approach to this problem
. . which eliminates the need for all that Calculus.
I'll let someone else explain it.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8779435157775879, "perplexity": 1080.684474273215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867217.1/warc/CC-MAIN-20180525200131-20180525220131-00059.warc.gz"}
|
https://asmedigitalcollection.asme.org/appliedmechanics/article-abstract/68/2/199/458606/Bifurcations-of-Eigenvalues-of-Gyroscopic-Systems?redirectedFrom=fulltext
|
This paper deals with stability problems of linear gyroscopic systems $Mx¨+Gx˙+Kx=0$ with finite or infinite degrees-of-freedom, where the system matrices or operators depend smoothly on several real parameters. Explicit formulas for the behavior of eigenvalues under a change of parameters are obtained. It is shown that the bifurcation (splitting) of double eigenvalues is closely related to the stability, flutter, and divergence boundaries in the parameter space. Normal vectors to these boundaries are derived using only information at a boundary point: eigenvalues, eigenvectors, and generalized eigenvectors, as well as first derivatives of the system matrices (or operators) with respect to parameters. These results provide simple and constructive stability and instability criteria. The presented theory is exemplified by two mechanical problems: a rotating elastic shaft carrying a disk, and an axially moving tensioned beam.
1.
Thomson, W., and Tait, P. G., 1879, Treatise on Natural Philosophy, Vol. I, Part I, Cambridge University Press, Cambridge, U.K.
2.
Hagedorn
,
P.
,
1975
, “
U¨ber die Instabilita¨t konservativer Systeme mit gyroskopischen Kra¨ften
,”
Arch. Ration. Mech. Anal.
,
58
, No.
1
, pp.
1
9
.
3.
Huseyin
,
K.
,
Hagedorn
,
P.
, and
Teschner
,
W.
,
1983
, “
On the Stability of Linear Conservative Gyroscopic Systems
,”
Z. Angew. Math. Phys.
,
34
, No.
6
, pp.
807
815
.
4.
Walker
,
J. A.
,
1991
, “
Stability of Linear Conservative Gyroscopic Systems
,”
ASME J. Appl. Mech.
,
58
, pp.
229
232
.
5.
Barkwell
,
L.
, and
Lancaster
,
P.
,
1992
, “
Overdamped and Gyroscopic Vibrating Systems
,”
ASME J. Appl. Mech.
,
59
, pp.
176
181
.
6.
Seyranian
,
A. P.
,
1993
, “
Interaction of Vibrational Frequencies of a Gyroscopic System
,”
Mech. Solids
,
28
, No.
4
, pp.
33
41
.
7.
Veselic
,
K.
,
1995
, “
On the Stability of Rotating Systems
,”
Z. Angew. Math. Mech.
,
75
, No.
4
, pp.
325
328
.
8.
Seyranian
,
A. P.
,
Stoustrup
,
J.
, and
Kliem
,
W.
,
1995
, “
On Gyroscopic Stabilization
,”
Z. Angew. Math. Phys.
,
46
, pp.
255
267
.
9.
Lancaster
,
P.
, and
Zizler
,
P.
,
1998
, “
On the Stability of Gyroscopic Systems
,”
ASME J. Appl. Mech.
,
65
, pp.
519
522
.
10.
Kliem
,
W.
, and
Seyranian
,
A. P.
,
1997
, “
Analysis of the Gyroscopic Stabilization of a System of Rigid Bodies
,”
Z. Angew. Math. Phys.
,
48
, No.
5
, pp.
840
847
.
11.
Mailybaev
,
A. A.
, and
Seyranian
,
A. P.
,
1999
, “
The Stability Domains of Hamiltonian Systems
,”
J. Appl. Math. Mech.
,
63
, No.
4
, pp.
545
555
.
12.
Mu¨ller, P. C., 1977, Stabilita¨t und Matrizen, Springer-Verlag, Berlin.
13.
Huseyin, K., 1978, Vibrations and Stability of Multiple Parameter Systems, Noordhoff International Publishing, Alphen aan den Rijn.
14.
Merkin, D. R., 1987, Introduction to the Theory of Stability of Motion, Nauka, Moscow.
15.
Vishik
,
M. I.
, and
Lyusternik
,
L. A.
,
1960
, “
The Solution of Some Perturbation Problems for Matrices and Selfadjoint or Non-Selfadjoint Differential Equations I
,”
Russ. Math. Surv.
,
15
, pp.
1
74
.
16.
Lidskii
,
V. B.
,
1966
, “
Perturbation Theory of Non-Conjugate Operators
,”
USSR Comput. Math. Math. Phys.
,
6
, No.
1
, pp.
73
85
.
17.
Moro
,
J.
,
Burke
,
J. V.
, and
Overton
,
M. L.
,
1997
, “
On the Lidskii-Vishik-Lyusternik Perturbation Theory for Eigenvalues of Matrices With Arbitrary Jordan Structure
,”
SIAM J. Matrix Anal. Appl.
,
18
, No.
4
, pp.
793
817
.
18.
Seyranian
,
A. P.
,
1993
, “
Sensitivity Analysis of Multiple Eigenvalues
,”
Mech. Struct. Mach.
,
21
, No.
2
, pp.
261
284
.
19.
Renshaw
,
A. A.
, and
Mote
, Jr.,
C. D.
,
1996
, “
Local Stability of Gyroscopic Systems Near Vanishing Eigenvalues
,”
ASME J. Appl. Mech.
,
63
, pp.
116
120
.
20.
Lancaster
,
P.
, and
Kliem
,
W.
,
1999
, “
Comments on Stability Properties of Conservative Gyroscopic Systems
,”
ASME J. Appl. Mech.
,
66
, pp.
272
273
.
21.
Renshaw
,
A. A.
,
1998
, “
Stability of Gyroscopic Systems Near Vanishing Eigenvalues
,”
ASME J. Appl. Mech.
,
65
, pp.
1062
1064
.
22.
Hryniv
,
R. O.
,
Lancaster
,
P.
, and
Renshaw
,
A. A.
,
1999
, “
A Stability Criterion for Parameter Dependent Gyroscopic Systems
,”
ASME J. Appl. Mech.
,
66
, pp.
660
664
.
23.
Parker
,
R. G.
,
1998
, “
On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua
,”
ASME J. Appl. Mech.
,
65
, pp.
134
140
.
24.
Ziegler, H., 1968, Principles of Structural Stability, Blaisdell, Waltham, MA.
25.
Gohberg, I., Lancaster, P., and Rodman, L., 1982, Matrix Polynomials, Academic Press, San Diego, CA.
26.
Horn, R., and Johnson, C. A., 1985, Matrix Analysis, Cambridge University Press, Cambridge, UK.
27.
Wickert
,
J. A.
, and
Mote
, Jr.,
C. D.
,
1991
, “
Response and Discretization Methods for Axially Moving Materials
,”
ASME J. Appl. Mech.
,
44
, pp.
S279–S284
S279–S284
.
You do not currently have access to this content.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.686739981174469, "perplexity": 15535.710858558883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00535.warc.gz"}
|
https://en.wikipedia.org/wiki/Vo2_max
|
# VO2 max
(Redirected from Vo2 max)
VO2 max (also maximal oxygen consumption, maximal oxygen uptake, peak oxygen uptake or maximal aerobic capacity) is the maximum rate of oxygen consumption measured during incremental exercise; that is, exercise of increasing intensity.[1][2] The name is derived from three abbreviations: "V" for volume, "O2" for oxygen, and "max" for maximum. Maximal oxygen consumption reflects cardiorespiratory fitness and endurance capacity in exercise performance.
## Relationship to cardiovascular disease and life expectancy
VO2 max is widely used as an indicator of cardiorespiratory fitness. In 2016, the American Heart Association published a scientific statement[3] recommending that cardiorespiratory fitness (CRF), quantifiable as VO2 max, be regularly assessed and used as a clinical vital sign. This statement was based on mounting evidence that lower fitness levels are associated with high risk of cardiovascular disease, all-cause mortality, and mortality rates stemming from various types of cancers. In addition to risk assessment, the AHA recommendation cited the value measuring fitness for validating exercise prescription, physical activity counseling, and improving both patient management and patient health.
## Expression
VO2 max is expressed either as an absolute rate in (for example) litres of oxygen per minute (L/min) or as a relative rate in (for example) millilitres of oxygen per kilogram of body mass per minute (e.g., mL/(kg·min)). The latter expression is often used to compare the performance of endurance sports athletes. However, VO2 max generally does not vary linearly with body mass, either among individuals within a species or among species, so comparisons of the performance capacities of individuals or species that differ in body size must be done with appropriate statistical procedures, such as analysis of covariance.[2]
## Measurement and calculation
### Measurement
VO2 max measurement using instruments on a modern metabolic cart during a graded treadmill exercise test
Gas exchange of VO2 and VCO2 during max test. Begin for 3 mins at 60 watts and add 35 watts every 3 minutes until exhaustion
Accurately measuring VO2 max involves a physical effort sufficient in duration and intensity to fully tax the aerobic energy system. In general clinical and athletic testing, this usually involves a graded exercise test (either on a treadmill or on a cycle ergometer) in which exercise intensity is progressively increased while measuring:
• ventilation and
• oxygen and carbon dioxide concentration of the inhaled and exhaled air.
VO2 max is reached when oxygen consumption remains at a steady state despite an increase in workload.
### Calculation: the Fick equation
VO2 max is properly defined by the Fick equation:
${\displaystyle \mathrm {VO_{2}\;max} =Q\times \ (\mathrm {C_{a}O_{2}} -\mathrm {C_{v}O_{2}} )}$, when these values are obtained during an exertion at a maximal effort.
where Q is the cardiac output of the heart, CaO2 is the arterial oxygen content, and CvO2 is the venous oxygen content.
(CaO2 – CvO2) is also known as the arteriovenous oxygen difference.[4]
## Estimation using submaximal exercise testing
The necessity for a subject to exert maximum effort in order to accurately measure VO2 max can be dangerous in those with compromised respiratory or cardiovascular systems; thus, sub-maximal tests for estimating VO2 max have been developed.
### The heart rate ratio method
An estimate of VO2 max is based on maximum and resting heart rates.[5] It is given by:
${\displaystyle {\text{V}}{\ce {O2}}{\text{ max}}\approx {\frac {{\text{HR}}_{\text{max}}}{{\text{HR}}_{\text{rest}}}}\times 15.3{\text{ mL}}/({\text{kg·minute}}).}$
This equation uses the ratio of maximum heart rate (HRmax) to resting heart rate (HRrest) to predict VO2 max. The researchers cautioned that the conversion rule was based on measurements on well-trained men aged 21 to 51 only, and may not be reliable when applied to other sub-groups. They also advised that the formula is most reliable when based on actual measurement of maximum heart rate, rather than an age-related estimate.
### Cooper test
Kenneth H. Cooper conducted a study for the United States Air Force in the late 1960s. One of the results of this was the Cooper test in which the distance covered running in 12 minutes is measured. Based on the measured distance, an estimate of VO2 max [in mL/(kg·min)] is:[6]
${\displaystyle \mathrm {VO_{2}\;max} \approx {d_{12}-504.9 \over 44.73}}$
where d12 is distance (in metres) covered in 12 minutes.
An alternative equation is:
${\displaystyle \mathrm {VO_{2}\;max} \approx {(35.97*d'_{12})-11.29}}$
where d'12 is distance (in miles) covered in 12 minutes.
### Multi-stage fitness test
There are several other reliable tests and VO2 max calculators to estimate VO2 max, most notably the multi-stage fitness test (or beep test).[7]
### Rockport fitness walking test
Estimation of VO2 max from a timed one-mile track walk incorporating duration in minutes and seconds (${\displaystyle t}$, e.g.: 20:35 would be specified as 20.58), gender, age, body weight in pounds (${\displaystyle BW}$), and heart rate (${\displaystyle HR}$) at the end of the mile.[8] The constant x is 6.3150 for males, 0 for females. BW is in lbs, time is in minutes.
${\displaystyle \mathrm {VO_{2}\;max} \approx 132.853-0.0769BW-0.3877{\text{age}}-3.2649t-0.1565HR+x}$
## Effect of training
### Non-athletes
The average untrained healthy male has a VO2 max of approximately 35–40 mL/(kg·min).[9][10] The average untrained healthy female has a VO2 max of approximately 27–31 mL/(kg·min).[9] These scores can improve with training and decrease with age, though the degree of trainability also varies very widely: conditioning may double VO2 max in some individuals, and will never improve it in others.
### Athletes
In sports where endurance is an important component in performance, such as cycling, rowing, cross-country skiing, swimming and running, world-class athletes typically have high VO2 maxima. Elite male runners can consume up to 85 mL/(kg·min), and female elite runners can consume about 77 mL/(kg·min).[11] Five time Tour de France winner Miguel Indurain is reported to have had a VO2 max of 88.0 at his peak, while cross-country skier Bjørn Dæhlie measured at 96 mL/(kg·min).[12] Dæhlie's result was achieved out of season, and physiologist Erlend Hem who was responsible for the testing stated that he would not discount the possibility of the skier passing 100 mL/(kg·min) at his absolute peak. Norwegian cyclist Oskar Svendsen is thought to have recorded the highest VO2 max of 97.5 mL/(kg·min), when aged 18.[13]
The highest values in absolute terms for humans are often found in rowers, as their much greater bulk makes up for a slightly lower VO2 max per kg. Elite oarsmen measured in 1984 had VO2 max values of 6.1±0.6 L/min and oarswomen 4.1±0.4 L/min.[14] Rowers are interested in both absolute values of VO2 max and in lung capacity, and the fact that they are measured in similar units means that the two are often confused. British rower Sir Matthew Pinsent is reported to have had a VO2 of 7.5 L/min[15] . He also had a lung capacity of 8.5 litres.[16] New Zealand sculler Rob Waddell has one of the highest absolute VO2 max levels ever tested.[17] These VO2max figures are absolute figures (ie the total amount of oxygen metabolised in a minute). Rowers tend to be more interested in absolute VO2max whereas runners are generally more interested in relative VO2 max (ie the total amount of oxygen metabolised per minute per kilogram of body weight)[18].
### Animals
VO2 max has been measured in other animal species. During loaded swimming, mice had a VO2 max of around 140 mL/(kg·min),[19] Thoroughbred horses had a VO2 max of around 193 mL/(kg·min) after 18 weeks of high-intensity training.[20] Alaskan huskies running in the Iditarod Trail Sled Dog Race had VO2 max values as high as 240 mL/(kg·min).[21] Estimated VO2 max for pronghorn antelope was as high as 300 mL/(kg·min).[22]
## Limiting factors
The factors affecting VO2 are often divided into supply and demand.[23] Supply is the transport of oxygen from the lungs to the mitochondria (including lung diffusion, stroke volume, blood volume, and capillary density of the skeletal muscle) while demand is the rate at which the mitochondria can reduce oxygen in the process of oxidative phosphorylation.[23] Of these, the supply factor is often considered to be the limiting one.[23][24] However, it has also been argued that while trained subjects probably are supply limited, untrained subjects can indeed have a demand limitation.[25]
Factors that affect VO2 max are: age, gender, fitness and training, altitude, among others. VO2 max can be a poor predictor of performance in runners due to variations in running economy and fatigue resistance during prolonged exercise. Cardiac output, pulmonary diffusion capacity, oxygen carrying capacity, and the peripheral limitations of muscle diffusion capacity, mitochondrial enzymes, and capillary density are all examples of VO2 max determinants. The body works as a system. If one of these factor is sub-par, then the whole system loses its normal capacity to function properly.[25]
The drug erythropoietin (EPO) can boost VO2 max by a significant amount in both humans and other mammals.[26] This makes EPO attractive to athletes in endurance sports, such as professional cycling. EPO has been banned since the 1990s as an illicit performance-enhancing substance. But by 1998 it had become widespread in cycling and led to the Festina affair[27][28] as well as being mentioned ubiquitously in the USADA 2012 report on the U.S. Postal Service Pro Cycling Team.[29] Greg LeMond has suggested establishing a baseline for riders' VO2 max (and other attributes) to detect abnormal performance increases.[30]
## History
British physiologist Archibald Hill introduced the concepts of maximal oxygen uptake and oxygen debt in 1922.[31][24] Hill and German physician Otto Meyerhof shared the 1922 Nobel Prize in Physiology or Medicine for their independent work related to muscle energy metabolism.[32] Building on this work, scientists began measuring oxygen consumption during exercise. Notable contributions were made by Henry Taylor at the University of Minnesota, Scandinavian scientists Per-Olof Åstrand and Bengt Saltin in the 1950s and 60s, the Harvard Fatigue Laboratory, German universities, and the Copenhagen Muscle Research Centre among others.[33][34]
## References
1. ^ Clemente C. J.; Withers P. C.; Thompson G. G. (2009). "Metabolic rate and endurance capacity in Australian varanid lizards (Squamata; Varanidae; Varanus)". Biological Journal of the Linnean Society. 97 (3): 664–676. doi:10.1111/j.1095-8312.2009.01207.x.
2. ^ a b Dlugosz E. M., Chappell M. A., Meek T. H., Szafrañska P., Zub K., Konarzewski M., Jones J. H., Bicudo J. E. P. W., Careau V., Garland T., Jr (2013). "Phylogenetic analysis of mammalian maximal oxygen consumption during exercise" (PDF). Journal of Experimental Biology. 216 (24): 4712–4721. doi:10.1242/jeb.088914. PMID 24031059.CS1 maint: multiple names: authors list (link)
3. ^ Ross, Robert; Blair, Steven N.; Arena, Ross; Church, Timothy S.; Després, Jean-Pierre; Franklin, Barry A.; Haskell, William L.; Kaminsky, Leonard A.; Levine, Benjamin D. (2016-01-01). "Importance of Assessing Cardiorespiratory Fitness in Clinical Practice: A Case for Fitness as a Clinical Vital Sign: A Scientific Statement From the American Heart Association". Circulation. 134 (24): e653–e699. doi:10.1161/CIR.0000000000000461. ISSN 0009-7322. PMID 27881567.
4. ^ "Arteriovenous oxygen difference". Sports Medicine, Sports Science and Kinesiology. Net Industries and its Licensors. 2011. Archived from the original on 12 June 2011. Retrieved 30 April 2011.
5. ^ Uth, Niels; Henrik Sørensen; Kristian Overgaard; Preben K. Pedersen (January 2004). "Estimation of VO2max from the ratio between HRmax and HRrest--the Heart Rate Ratio Method" (PDF). Eur J Appl Physiol. 91 (1): 111–5. doi:10.1007/s00421-003-0988-y. PMID 14624296.
6. ^
7. ^ [Leger, Luc A., and J_ Lambert. "A maximal multistage 20-m shuttle run test to predict\ dot VO2 max." European journal of applied physiology and occupational physiology 49.1 (1982): 1-12.]
8. ^ Kilne G, et al. (1987). "Estimation of VO2 max from a one mile track walk, gender, age and body weight". Med. Sci. Sports Exerc. 19: 253–259.
9. ^ a b Heyward, V (1998). "Advance Fitness Assessment & Exercise Prescription, 3rd Ed". p. 48.
10. ^ Guyton, A.; Hall, J.E. (2011). "Textbook of Medical Physiology, 12th Ed". pp. 1035–1036.
11. ^ Noakes, Tim (2001). The Lore of Running. (3rd edition) Oxford University Press ISBN 978-0-88011-438-7
12. ^ VO2 max faq
13. ^ If all goes to plan, big future predicted for junior world champion Oskar Svendsen
14. ^ Hagerman, FC (Jul–Aug 1984). "Applied physiology of rowing". Sports Med. 1 (4): 303–26. doi:10.2165/00007256-198401040-00005. PMID 6390606.
15. ^ Bailey, James. "Intensity (3 of 6)". Q-power indoor rowing team.
16. ^ "What happens in a VO2 max test?". BBC Sport. 2009. - see an example here [1], which suggests that although British rower Pete Reed has recorded a lung capacity of 11.68 litres,(Hounslow Chronicle) Pinsent still regards his VO2 record as safe. A large lung capacity appears to be a particular advantage for rowing as it allows a rower to row more strokes at one breath per stroke.
17. ^ Gough, Martin (17 June 2009). "Monsters wanted". BBC. Archived from the original on 2010-11-01.
18. ^ Bailey, James. "Intensity (3 of 6)". Q-power indoor rowing team.
19. ^ Glaser, R. M.; Gross, P. M.; Weiss, H. S. (1972). "Maximal aerobic metabolism of mice during swimming". Experimental Biology and Medicine. 140 (1): 230–233. doi:10.3181/00379727-140-36431. PMID 5033099.
20. ^ Kitaoka, Y.; Masuda, H.; Mukai, K.; Hiraga, A.; Takemasa, T.; Hatta, H. (2011). "Effect of training and detraining on monocarboxylate transporter (MCT) 1 and MCT4 in Thoroughbred horses". Experimental Physiology. 96 (3): 348–55. doi:10.1113/expphysiol.2010.055483. PMID 21148623.
21. ^ Roger Segelke (9 December 1996). "Winterize Rover for cold-weather fitness, Cornell veterinarian advises". Cornell University Chronicle. Retrieved 7 December 2018.
22. ^ Lindstedt, S. L.; Hokanson, J. F.; Wells, D. J.; Swain, S. D.; Hoppeler, H.; Navarro, V. (1991). "Running energetics in the pronghorn antelope". Nature. 353 (6346): 748–50. doi:10.1038/353748a0. PMID 1944533.
23. ^ a b c Bassett D.R Jr.; Howley E.T. (2000). "Limiting factors for maximum oxygen uptake and determinants of endurance performance". Med Sci Sports Exerc. 32 (1): 70–84. doi:10.1097/00005768-200001000-00012. PMID 10647532.
24. ^ a b Bassett, D. R.; Howley, E. T. (1997). "Maximal oxygen uptake: "classical" versus "contemporary" viewpoints". Medicine and Science in Sports and Exercise. 29 (5): 591–603. doi:10.1097/00005768-199705000-00002. ISSN 0195-9131. PMID 9140894.
25. ^ a b Wagner P.D. (2000). "New ideas on limitations to VO2max". Exercise and Sport Sciences Reviews. 28 (1): 10–4. PMID 11131681.
26. ^ Kolb E. M. (2010). "Erythropoietin elevates V.O2, max but not voluntary wheel running in mice". Journal of Experimental Biology. 213 (3): 510–519. doi:10.1242/jeb.029074. PMID 20086137.
27. ^ Lundby C.; Robach P.; Boushel R.; Thomsen J. J.; Rasmussen P.; Koskolou M.; Calbet J. A. L. (2008). "Does recombinant human Epo increase exercise capacity by means other than augmenting oxygen transport?". Journal of Applied Physiology. 105 (2): 581–7. doi:10.1152/japplphysiol.90484.2008. hdl:10553/6534. PMID 18535134.
28. ^ Lodewijkx Hein F.M.; Brouwer Bram (2011). "EPO EPIDEMIC IN CYCLING: Some Empirical Notes on the ‗Epo Epidemic' in Professional Cycling". Open University. 82 (4): 740–754. doi:10.5641/027013611X13275192112069. PMID 22276416.
29. ^ USADA U.S. Postal Service Pro Cycling Team Investigation, Oct 2012, retr 2012 10 20 from usada.org
30. ^ Greg LeMond’s suggestions for a credible future for cycling Conal Andrews, July 28, 2010, Velo Nation, retr 2012 10 20
31. ^ Hale, Tudor (2008-02-15). "History of developments in sport and exercise physiology: A. V. Hill, maximal oxygen uptake, and oxygen debt". Journal of Sports Sciences. 26 (4): 365–400. doi:10.1080/02640410701701016. ISSN 0264-0414. PMID 18228167.
32. ^ "The Nobel Prize in Physiology or Medicine 1922". NobelPrize.org. Retrieved 2018-10-11.
33. ^ Seiler, Stephen (2011). "A Brief History of Endurance Testing in Athletes" (PDF). SportScience. 15 (5).
34. ^ "History of Exercise Physiology". Human Kinetics Europe. Retrieved 2018-10-11.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49272438883781433, "perplexity": 15184.099567962248}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146485.15/warc/CC-MAIN-20200226181001-20200226211001-00182.warc.gz"}
|
https://www.zbmath.org/?q=an%3A1385.53020
|
×
## On static three-manifolds with positive scalar curvature.(English)Zbl 1385.53020
Summary: We compute a Bochner type formula for static three-manifolds and deduce some applications in the case of positive scalar curvature. We also explain in details the known general construction of the (Riemannian) Einstein $$(n + 1)$$-manifold associated to a maximal domain of a static $$n$$-manifold where the static potential is positive. There are examples where this construction inevitably produces an Einstein metric with conical singularities along a codimension-two submanifold. By proving versions of classical results for Einstein four-manifolds for the singular spaces thus obtained, we deduce some classification results for compact static three-manifolds with positive scalar curvature.
### MSC:
53C20 Global Riemannian geometry, including pinching 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
### Keywords:
Bochner-type formula; Einstein metric; singular spaces
Full Text:
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.485442191362381, "perplexity": 1205.4675319227938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00638.warc.gz"}
|
https://tex.stackexchange.com/questions/216212/how-may-i-align-the-following-set-of-equations-as-represented-in-the-image
|
# How may I align the following set of equations as represented in the image?
If IEEEeqnarray environment is not best-suited for this particular alignment, what could be the best environment to be used?
\documentclass[11pt,a4paper]{article}
\usepackage{blindtext}
\usepackage{mathtools}
\usepackage{IEEEtrantools}
\begin{document}
\begin{IEEEeqnarray*}{rCl}
(x-a)(x-2a)(x-3a)(x-4a)=x^{4}-P_{1}x^{3}+P_{2}x^{2}-P_{3}x+P_{4}.\\
\shortintertext{Here}
P_{1}&=&a+2a+3a+4a=10a,\\
P_{2}&=&1\times 2a^{2}+1\times 3a^{2}+1\times 4a^{2}+2\times 4a^{2}+3\times 4a^{2}=35a^{2},\\
P_{3}&=&2\times 3\times 4a^{3}+1\times 3\times 4a^{2}+1\times 2\times 4a^{3}+1\times 2\times 3a^{3}=50a^{3},\\
P_{4}&=&1\times 2\times 3\times 4a^{4}=24a^{4}.
\shortintertext{so that}
(x-a)(x-2a)(x-3a)(x-4a)=x^{4}-10ax^{3}+35a^{2}x^{2}-50a^{3}x+24a^{4}.
\end{IEEEeqnarray*}
\end{document}
The presentation of your alignment is not really that accurate. So, I assume the following will be sufficient:
\documentclass{article}
\usepackage{array}
\begin{document}
$(x - a)(x - 2a)(x - 3a)(x - 4a) = x^4 - P_1 x^3 + P_2 x^2 - P_3 x + P_4.$
Here
$\renewcommand{\arraystretch}{1.3} \begin{array}{r@{}>{{}}l@{}r@{}>{{}}l} P_1 &= a+2a+3a+4a &&= 10a, \\ P_2 & \multicolumn{3}{@{}l}{{}= 1 \times 2a^2 + 1 \times 3a^2 + 1 \times 4a^2 + 2 \times 4a^2 + 3 \times 4a^2} \\ &&&= 35a^2,\\ P_3 & \multicolumn{3}{@{}l}{{}= 2 \times 3 \times 4a^3 + 1 \times 3 \times 4a^2 + 1 \times 2\times 4a^3 + 1 \times 2 \times 3a^3} \\ &&&= 50a^3,\\ P_4 &= 1 \times 2 \times 3 \times 4a^4 &&= 24a^4, \\ \end{array}$
so that
$(x - a)(x - 2a)(x - 3a)(x - 4a) = x^4 - 10ax^3 + 35a^2 x^{2} - 50a^3 x + 24a^4.$
\end{document}
Multiple alignments that's not strictly adhered to (some lines use the alignment points and some don't) is difficult to do with standard align and friends. Using an array may circumvent this difficulty with the aid of \multicolumn.
The use of the array package above is not really needed, but I've used it anyway.
• This is the exact alignment I wanted to have. I apologise for the inconvenience I caused by not making my set up inaccurate. Thank you very much for dedicating your precious time in looking to this matter. Dec 9, 2014 at 20:17
Why not this simple way?
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\noindent We have
\begin{align*}
\MoveEqLeft (x - a)(x - 2a)(x - 3a)(x - 4a)
= x^{4} - P_{1}x^{3} + P_{2}x^{2} - P_{3}x + P_{4}\\
\intertext{where}
P_{1} &= a + 2a + 3a + 4a = 10a,\\
P_{2} &= 1 \cdot 2a^{2} + 1 \cdot 3a^{2} + 1 \cdot 4a^{2} + 2 \cdot 4a^{2} + 3 \cdot 4a^{2} = 35a^{2},\\
P_{3} &= 2 \cdot 3 \cdot 4a^{3} + 1 \cdot 3 \cdot 4a^{2} + 1 \cdot 2 \cdot 4a^{3} + 1 \cdot 2 \cdot 3a^{3}= 50a^{3},\\
P_{4} &= 1 \cdot 2 \cdot 3 \cdot 4a^{4} = 24a^{4},
\intertext{so that}
\MoveEqLeft (x - a)(x - 2a)(x - 3a)(x - 4a)
= x^{4} - 10ax^{3} + 35a^{2}x^{2} - 50a^{3}x + 24a^{4}.
\end{align*}
\end{document}
• I honestly did not know the \MoveEqLeft-command, and also I seldom used the align-environment. Your set-up allowed me to understand how to use the align-environment coherently. Thank you very much, Bernard! Dec 10, 2014 at 3:41
Here is how I would do it:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\noindent We have
\begin{equation*}
(x - a)(x - 2a)(x - 3a)(x - 4a)
= x^{4} - P_{1}x^{3} + P_{2}x^{2} - P_{3}x + P_{4}
\end{equation*}
where
\begin{align*}
P_{1} &= a + 2a + 3a + 4a\\
&= 10a,\\
P_{2} &= 1 \cdot 2a^{2} + 1 \cdot 3a^{2} + 1 \cdot 4a^{2} + 2 \cdot 4a^{2} + 3 \cdot 4a^{2}\\
&= 35a^{2},\\
P_{3} &= 2 \cdot 3 \cdot 4a^{3} + 1 \cdot 3 \cdot 4a^{2} + 1 \cdot 2 \cdot 4a^{3} + 1 \cdot 2 \cdot 3a^{3}\\
&= 50a^{3},\\
P_{4} &= 1 \cdot 2 \cdot 3 \cdot 4a^{4}\\
&= 24a^{4},
\end{align*}
so that
\begin{equation*}
(x - a)(x - 2a)(x - 3a)(x - 4a)
= x^{4} - 10ax^{3} + 35a^{2}x^{2} - 50a^{3}x + 24a^{4}.
\end{equation*}
\end{document}
• Thank you very much for all the corrections you made. I could use the aforementioned set up for my work for it is more organised than the set up I had in mind. Dec 9, 2014 at 20:11
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000081062316895, "perplexity": 2280.5212167108684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103850139.45/warc/CC-MAIN-20220630153307-20220630183307-00601.warc.gz"}
|
http://mathhelpforum.com/algebra/40241-homework-due-tomoz-had-total-blankk-most-simple-thing.html
|
# Math Help - homework due tomoz!!! and had a total BLANKK on the most simple thing!!
1. ## homework due tomoz!!! and had a total BLANKK on the most simple thing!!
fractions; i suck at them and i just had a total blank on the most simple fraction sum.
1 - 1/9 = ?? plz help
1/5 of ?? = 6
and i have a kinda word prob,
if 5 * 3 = 4
2 * 8 = 2
6 * 3 = 3
find the value of
1 * 7 ??
im so stupid i know you think i am lol
please get back to me ASAP!!
thanks xoxo
2. Originally Posted by emm
fractions; i suck at them and i just had a total blank on the most simple fraction sum.
1 - 1/9 = ?? plz help
1/5 of ?? = 6
$1 - \frac{1}{9} = \frac{9}{9} - \frac{1}{9}$ = ?
$\frac{1}{5} \cdot x = 6$
$5 \cdot \frac{1}{5} \cdot x = 5 \cdot 6$
-Dan
3. Originally Posted by emm
im so stupid i know you think i am lol
Stop demeaning yourself. Everyone needs help every now and again.
-Dan
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9034205079078674, "perplexity": 2256.2704790934154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678704059/warc/CC-MAIN-20140313024504-00079-ip-10-183-142-35.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/help-with-solving-a-cauchy-euler-differential-equation.387581/
|
# Homework Help: Help with Solving a Cauchy-Euler Differential Equation
1. Mar 17, 2010
### Jim4592
1. The problem statement, all variables and given/known data
x2 y'' + x y' + 4 y = 0
2. Relevant equations
y = xr
y' = r xr-1
y'' = (r2-r)xr-2
3. The attempt at a solution
x2{(r2-r)xr-1} + x{r xr-1} + 4xr
r2 - r + r + 4
r2 + 4 = 0
r = +- 2i
y = C1x2i + c2x-2i
My question is how can i remove the imaginary number with cos[] and sin[]
If you could be as descriptive as possible i'd really appreciate it!
2. Mar 18, 2010
### vela
Staff Emeritus
Use the definition of exponentiation: xa=ea log x.
3. Mar 18, 2010
### HallsofIvy
In fact, the substitution y= ln(x) will change any "Cauchy-Euler" equation into an equation with constant coefficients with the same characteristic equation. An equation with constant coefficients, with $\pm 2$ as characteristic roots, has general solution C cos(2y)+ D sin(2y).
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9004661440849304, "perplexity": 2612.8195509035827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865250.0/warc/CC-MAIN-20180623210406-20180623230406-00119.warc.gz"}
|
https://www.cfd-online.com/Forums/fluent/88612-2nd-order-upwind-scheme-fluent-cfx-print.html
|
CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
- FLUENT (https://www.cfd-online.com/Forums/fluent/)
- - 2nd order upwind scheme (Fluent and CFX) (https://www.cfd-online.com/Forums/fluent/88612-2nd-order-upwind-scheme-fluent-cfx.html)
Far May 22, 2011 01:50
2nd order upwind scheme (Fluent and CFX)
It is stated in the CFX theory (above link) that when one selects the high resolution scheme as below
is the value at the upwind node.
On the other hand when user selects the specified blend factor for (between 0 and 1), is equal to the average of the adjacent nodal gradients. I wanna know, this scheme is the upwind or central differencing scheme?
http://my.fit.edu/itresources/manual...ug/node992.htm
Where as in fluent user guide (above link) 2nd order upwind scheme is given by following formula
is the gradient of in the upwind cell
Both high resolution (CFX) and 2nd order upwind scheme (Fluent) are based on the principles by Barth and Jespersen [1] so that no new extrema is introduced in the solution, therfore monotonic behavior is preserved.
1. Does it mean that the high resolution scheme of CFX and 2nd order upwind scheme of fluent are equivalent.
2. Does it mean that the CFX 2nd order scheme is more like a baised 2nd order scheme with one term of upwind and 2nd term (anti diffusive term) is central differencing type?
3. Will 2nd order upwind (CFX definition) will make the solution worst than even 1st order upwind scheme?
References:
[1]
Barth and Jespersen "The design and application of upwind schemes on unstructured meshes" .
Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.
All times are GMT -4. The time now is 21:06.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8517034649848938, "perplexity": 4071.3899436941024}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280761.39/warc/CC-MAIN-20170116095120-00471-ip-10-171-10-70.ec2.internal.warc.gz"}
|
https://mechanismsrobotics.asmedigitalcollection.asme.org/biomechanical/article-abstract/127/6/934/465674/A-Light-Weight-Compliant-Hand-Mechanism-With-High?redirectedFrom=fulltext
|
This paper presents the design and prototyping of an inherently compliant lightweight hand mechanism. The hand mechanism itself has 15 degrees of freedom and five fingers. Although the degrees of freedom in each finger are coupled, reducing the number of independent degrees of freedom to 5, the 15 degrees of freedom of the hand could potentially be individually actuated. Each joint consists of a novel flexing mechanism that is based on the loading of a compression spring in the axial and transverse direction via a cable and conduit system. Currently, a bench top version of the prototype is being developed; the three joints of each finger are coupled together to simplify the control system. The current control scheme under investigation simulates a control scheme where myoelectric signals in the wrist flexor and extensor muscles are converted in to $x$ and $y$ coordinates on a control scheme chart. Static load-deformation analysis of finger segments is studied based on a 3-dimensional model without taking the stiffener into account, and the experiment validates the simulation.
1.
Atkins
,
D.
,
Heard
,
D.
, and
Donovan
,
W.
, 1996, “
Epidemiologic Overview of Individuals with Upper Limb Loss and Their Reported Research Priorities
,”
Journal of Prosthetics and Orthotics
, Vol.
8
, No.
1
,
2
11
.
2.
Schulz
,
C.
,
Pylatiuk
,
G.
, and
Bretthauer
,
A.
, 2001, “
A New Ultralight Anthropomorphic Hand
,”
IEEE Conference on Robotics and Automation
, pp.
2437
2441
.
3.
Massa
,
B.
,
Roccella
,
S.
,
Carrozza
,
M. C.
, and
Dario
,
P.
, 2002, “
Design and Development of an Underactuated Prosthetic Hand
,”
Proceeding of the 2002 IEEE International Conference on Robotics & Automation
, Washington, DC.
4.
Hirose
,
S.
,
,
T.
, and
Umetani
,
Y.
, 1983, “
Tensor Actuated Elastic Manipulator
,”
Proceedings of the 6th IFToMM World Congress
, New Delhi, Vol.
2
, pp.
978
981
.
5.
Kyberd
,
P.
,
Chappell
,
P.
, and
Gow
,
D.
, 2003, “
Advances in the Control of Prosthetic Arms
,”
Technology & Disability
;
15
(
2
), pp.
57
61
.
6.
Butterfass
,
J.
,
Hirzinger
,
G.
,
Knoch
,
S.
and
Liu
,
H.
, 1998, “
DLR’s Multisensory Articulated Hand. Part I: Hard- and Software Architecture
,”
Proceedings of the 1998 IEEE International Conference on Robotics & Automation
,
Leuven
, Belgium.
7.
Kyberd
,
P.
and
Chappell
,
P.
, (1994), “
The Southampton Hand: An Intelligent Myoelectric Prosthesis
,”
J. Rehabil. R. D
0742-3241, Vol.
31
, Issue
4
,
326
334
.
8.
Kyberd
P.
,
Light
,
C.
,
Chappell
,
P.
,
Nightingale
,
J.
,
Whatley
,
D.
, and
Evans
,
M.
, 2001, “
The Design of Anthropomorphic Prosthetic Hands: A Study of the Southampton Hand
,”
Robotica
0263-5747,
19
, pp.
593
600
.
9.
Tura
,
A.
,
Lamberti
,
C.
,
Davalli
,
A.
, and
Sacchetti
,
R.
, 1998, “
Experimental Development of a Sensory Control System for an Upper Limb Myoelectric Prosthesis with Cosmetic Covering
,”
J. Rehabil. R. D
0742-3241,
35
(
1
), pp.
14
26
.
10.
Carrozza
,
M. C.
,
Dario
,
P.
,
Vecchi
,
F.
,
Roccella
,
S.
,
Zecca
,
M.
, and
Sebastiani
,
F.
, 2003, “
The CyberHand: On the Design of a Cybernetic Prosthetic Hand Intended To Be Interfaced To the Peripheral Nervous System
,”
Proceedings, 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems
.
11.
Zecca
,
M.
,
Cappiello
,
G.
,
Sebastiani
,
F.
,
Roccella
,
S.
,
Vecchi
,
F.
,
Carrozza
,
M. C.
, and
Dario
,
P.
, 2003 “
Experimental Analysis of the Proprioceptive and Exteroceptive Sensors of an Underactuated Prosthetic Hand
,”
Proceeding of the ICORR 2003 (The Eighth International Conference on Rehabilitation Robotics)
.
12.
Carrozza
,
M. C.
,
Suppo
,
C.
,
Sebastiani
,
F.
,
Massa
,
B.
,
Vecchi
,
F.
,
Lazzarini
,
R.
,
Cutkosky
,
M. R.
, and
Dario
,
P.
, 2004, “
The SPRING Hand: Development of a Self-Adaptive Prosthesis for Restoring Natural Grasping
,”
Auton. Rob.
0929-5593,
16
(
2
), pp.
125
141
.
13.
Pons
,
J. L.
,
Rocon
,
E.
,
Ceres
,
R.
,
Reynaerts
,
D.
,
Saro
,
B.
,
Levin
,
S.
, and
Van Moorleghem
,
W.
, 2004, “
The MANUS-HAND Dextrous Robotics Upper Limb Prosthesis: Mechanical and Manipulation Aspects
,”
Auton. Rob.
0929-5593,
16
(
2
), pp.
143
163
.
14.
Yang
,
J.
,
Abdel-Malek
,
K.
, and
Potratz
,
J.
, 2005, “
Design and Prototyping of an Active Hand Prosthetic Device
,”
Ind. Robot
0143-991X,
32
(
1
), pp.
71
78
.
15.
Peña Pitarch
,
E.
,
Yang
,
J.
, and
Abdel-Malek
,
K.
, 2003, “
Santos™ Hand: A 25-Degree-of-Freedom Model
,”
Proceedings of SAE Digital Human Modeling for Design and Engineering
, 14–16 June, 2005, Iowa City, IA.
16.
Lindkvist
,
L.
, 1995,
,
Chalmers University of Technology
, Goteborg, Sweden.
17.
Knutson
,
J.
,
Hoyen
,
H.
,
Kilgore
,
K.
, and
Peckham
P.
, 2004, “
Simulated Neuroprosthesis State Activation and Hand-Position Control Using Myoelectric Signals from Wrist Muscles
,”
J. Rehabil. R. D
0742-3241,
41
(
3B
), pp.
461
472
.
18.
Savescu
,
A.
,
Cheze
,
L.
,
Wang
,
X.
,
Beurier
,
G.
, and
Verriest
,
J.
, 2004, “
A 25 Degrees of Freedom Hand Geometrical Model for Better Hand Attitude Simulation
,”
Proceedings of the Digital Human Modeling for Design and Engineering Symposium
, Rochester, MI.
19.
Yang
,
J.
,
Peña Pitarch
,
E.
,
Abdel-Malek
,
K.
,
Patrick
,
A.
, and
Lindkvist
,
L.
, 2004, “
A Multi-Finger Hand Prosthesis
,”
Mech. Mach. Theory
0094-114X,
39
(
6
), pp.
555
581
.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29784759879112244, "perplexity": 16251.163001478131}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710902.80/warc/CC-MAIN-20221202114800-20221202144800-00046.warc.gz"}
|
http://math.stackexchange.com/questions/869652/a-field-having-an-automorphism-of-order-2
|
# A field having an automorphism of order 2
The following fact is used in the Unitary space.
If $F$ is a field having an automorphism $\alpha$ of order 2. Let $F_0=\{a\in F: \alpha(a)=a\}$. Then $|F:F_0|=2$.
## Is there any easy proof (or reference) for this fact?
Let $Char F \ne 2$, and write $\bar{a}$ for $\alpha(a)$. Note $x=1/2(x+\bar{x})+1/2(x-\bar{x})\ \ \ (*)$ and $\overline{x-\bar{x}}=-(x-\bar{x})$ and $x+\bar{x} \in F_0$. So there exists $a$ such that $\bar{a}=-a$ and $a \not \in F_0$. By (*), we just need to proof the elements $b$ such that $\bar{b}=-b$ is in the space $K$ generated by 1 and $a$ over $F_0$ (Clearly, $|K:F_0|=2$).
Since $\bar{a}=-a$, we get $k=a^2\in F_0$, and $a^{-1}=k^{-1}a \in K$. Now $\overline{ab}=\bar{a}\bar{b}=(-a)(-b)=ab$, we get $l=ab\in F_0$, and $b=la^{-1} \in K$. Hence $K=F$ and then $|F:F_0|=2$.
But I can not prove the case that $Char K=2$. Any idea about this case?
-
This is a special case of Artin's theorem from Galois theory. The field $F_0$ is strictly smaller than $F$ (not all elements are fixed by $\alpha$). If $a, b \in F \setminus F_0$ then
$$a - \frac{a-\alpha(a)}{b-\alpha(b)} b + \frac{a \, \alpha(b)-b\,\alpha(a)}{b-\alpha(b)} =0$$
which shows that $1, a, b$ are linearly dependent over $F_0$. Therefore $|F:F_0|=2$.
-
Sweet! Artin's book is a gem, isn't it! +1! – Robert Lewis Jul 17 '14 at 6:58
Thanks. A beautiful proof. I have think about this for a long time. – Wei Zhou Jul 17 '14 at 8:03
Here's a different demonstration which, like Wei Zhou's argument, works in the case $\text{char} F \ne 2$, although I admit part of it was inspired by WimC's most excellent answer. But, based upon that inspiration (and exactly what that is will shortly become manifest), we have a self-contained proof as follows:
First of all, we note that, unless $\alpha$ is the trivial automorphism, i.e., unless $\alpha$ fixes all of $F$, that there must exist $\aleph \in F$ with $\alpha(\aleph) \ne \aleph$; by definition, such an $\aleph \notin F_0$, and $\alpha(\aleph) \notin F_0$ either, lest we have $\aleph = \alpha(\alpha(\aleph)) = \alpha(\aleph) \in F_0$. Choosing such an $\aleph$, consider the field elements $\aleph + \alpha(\aleph), \aleph \alpha(\aleph) \in F$; we see they are both fixed by $\alpha$, for
$\alpha(\aleph + \alpha(\aleph)) = \alpha(\aleph) + \alpha^2(\aleph) = \aleph + \alpha(\aleph) \tag{1}$
since $\alpha^2 = 1$, and likewise
$\alpha(\aleph \alpha(\aleph)) = \alpha(\aleph) \alpha^2(\aleph) = \aleph \alpha(\aleph), \tag{2}$
again since $\alpha^2 = 1$. Thus we see that both $\aleph + \alpha(\aleph), \aleph \alpha(\aleph) \in F_0$, since $F_0$ is the fixed field of $\alpha$. Next consider the polynomial
$p_\aleph(x) = x^2 - (\aleph +\alpha(\aleph))x + \aleph \alpha(\aleph) \in F_0[x]; \tag{3}$
we have $p_\aleph(x) \in F_0[x]$ since its coefficients, as has been seen, are all fixed by $\alpha$. The roots of $p_\aleph(x)$ are easily seen to be $\aleph$ and $\alpha(\aleph)$; indeed we have
$p_\aleph(\aleph) = \aleph^2 - (\aleph + \alpha(\aleph)) \aleph + \aleph \alpha(\aleph) = \aleph^2 -\aleph^2 - \alpha(\aleph) \aleph + \aleph \alpha(\aleph) = 0, \tag{4}$
with a similar calculation showing that
$p_\aleph(\alpha(\aleph)) = 0 \tag{5}$
as well; alternatively, it may be observed that $p_\aleph(x)$ splits in $F$ as
$p_\aleph(x) = x^2 - (\aleph +\alpha(\aleph))x + \aleph \alpha(\aleph) = (x - \aleph)(x - \alpha(\aleph)), \tag{6}$
which also shows the roots are $\aleph$, $\alpha(\aleph)$. Based on these considerations, we may conclude that (i) $p_\aleph(x)$ is irreducible over $F_0$, since $\aleph, \alpha(\aleph) \notin F_0$; (ii.) $F_0(\aleph) \subset F$ is the splitting field of $p_\aleph(x)$ over $F_0$, since $\alpha(\aleph) = \aleph^{-1}(\aleph \alpha(\aleph)) \in F_0(\aleph)$ by virtue of $\aleph \in F_0(\aleph)$, $\aleph \alpha(\aleph) \in F_0 \subset F(\aleph)$; (iii.) $[F_0(\aleph):F_0] = 2$, since $\deg p_\aleph(x) = 2$.
Having $[F_0(\aleph):F_0] = 2$, we conclude by showing that $F = F_0(\aleph)$. Clearly $F_0(\aleph) \subset F$, so let $\beth \in F$ and consider the product $\gimel = (\beth - \alpha(\beth))(\aleph - \alpha(\aleph))$; we have
$\alpha((\beth - \alpha(\beth))(\aleph - \alpha(\aleph))) = (\alpha(\beth) - \beth)(\alpha(\aleph) - \aleph) = (\beth - \alpha(\beth))(\aleph - \alpha(\aleph)), \tag{7}$
that is, $\gimel = (\beth - \alpha(\beth))(\aleph - \alpha(\aleph))$ is fixed by $\alpha$, hence
$(\beth - \alpha(\beth))(\aleph - \alpha(\aleph)) = \gimel \in F_0. \tag{8}$
We now have
$\beth - \alpha(\beth) = (\aleph - \alpha(\aleph))^{-1} \gimel \in F_0(\aleph), \tag{9}$
and since
$\beth + \alpha(\beth) \in F_0, \tag{10}$
being fixed by $\alpha$ just as is $\aleph + \alpha(\aleph)$, we conclude that (and this is where we need the assumption $\text{char}F \ne 2$):
$2\beth = (\beth - \alpha(\beth)) + (\beth + \alpha(\beth)) \in F_0(\aleph), \tag{11}$
whence
$\beth \in F_0(\aleph) \tag{12}$
and hence $F \subset F_0(\aleph)$; thus in fact $F = F_0(\aleph)$ and finally
$[F:F_0] = [F_0(\aleph): F_0] = 2, \tag{13}$
the desired conclusion. QED.
Note: The inspiration I took from WimC's answer was to examine the quantity $\gimel = (\beth - \alpha(\beth))(\aleph - \alpha(\aleph))$; this originated in a careful scrutiny of the coefficient of $b$ in his equation
$a - \dfrac{a-\alpha(a)}{b-\alpha(b)} b + \dfrac{a \, \alpha(b)-b\,\alpha(a)}{b-\alpha(b)} =0, \tag{14}$
which is also invariant under $\alpha$. I too would like to see if and how the assumption $\text{char} F \ne 2$ could be circumvented in the context of the above argument. End of Note.
Hope this helps. Cheers,
and as always,
Fiat Lux!!!
-
Interesting answer. – Wei Zhou Jul 18 '14 at 0:49
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9974517822265625, "perplexity": 165.8250248762725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398449793.41/warc/CC-MAIN-20151124205409-00314-ip-10-71-132-137.ec2.internal.warc.gz"}
|
https://www.physicsforums.com/threads/hp-50g-expand-and-simplify.343199/
|
# Calculators Hp 50g expand and simplify
1. Oct 5, 2009
### graycolor
I remember setting my calculator so it would automatically use the expand function or simplify fractions for me in RPN mode.Since I did a reset I don't know how to put that function on again.
For example if I was to put 1 enter 3 divided, I would get 1/3 then if I were to multiply by 2 the calculator would give this 1/3*2
I want the calculator to automatically simplify the fraction to 2/3. This is done automatically in algebraic mode how can I do this with rpn.
Hp calculators are very confusing.
2. May 18, 2017
### LouisBRZ
Solving it is very easy. Press MODE, then press CAS and uncheck "Approx". I know it's been 8 years, but maybe someone could be interested.
3. Jan 20, 2018
i do. thanks
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9431252479553223, "perplexity": 1725.348212196602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676594790.48/warc/CC-MAIN-20180723012644-20180723032644-00190.warc.gz"}
|
https://code.adonline.id.au/applying-dates-to-normalised-data-in-excel/
|
Dear Internet Explorer user: Your browser is no longer supported
Please switch to a modern browser such as Microsoft Edge, Mozilla Firefox or Google Chrome to view this website's content.
Applying dates to normalised data in Excel
Use this formula to apply dates to all variables in a normalised linear list data set in Excel.
In order to create Pivot Tables in Excel (and conduct other analyses), I often restructure matrix data into a “linear list”. This is variously known as unpivoting, normalising or linearising data. (An excellent explanation of this can be found on ExcelCampus).
I recently linearised (normalised) a large data set, as per the example below. Unfortunately the script that linearised the data listed the date as another variable rather than attaching it to each instance. I needed a formula to assign the correct date to each variable.
Here’s an example of the linearised data output, which was converted from a matrix:
Barcode Variable Value
1000547 Time Stamp 12/02/2015 9:51
1000547 vissv1 1012.305
1000547 vissv2 1072.168
1000547 vissv3 1228.595
1000547 vistv 1384.012
1000548 Time Stamp 12/02/2015 9:52
1000548 vissv1 1172.659
1000548 vissv2 1209.106
1000548 vissv3 1003.14
1000548 vistv 1439.781
1000552 Time Stamp 12/02/2015 9:54
1000552 vissv1 1110.405
1000552 vissv2 1099.066
1000552 vissv3 1111.265
1000552 vistv 1505.061
As can be seen, in this format it’s not possible to determine which variable was measured on which date. It is inferred because of the order in which the data is entered, but this will be lost if the data is re-sorted.
This is what I needed to achieve: A date matched to each measured variable.
Barcode Variable Value Date
1000547 vissv1 1012.305 12/02/2015
1000547 vissv2 1072.168 12/02/2015
1000547 vissv3 1228.595 12/02/2015
1000547 vistv 1384.012 12/02/2015
1000548 vissv1 1172.659 12/02/2015
1000548 vissv2 1209.106 12/02/2015
1000548 vissv3 1003.14 12/02/2015
1000548 vistv 1439.781 12/02/2015
1000552 vissv1 1110.405 12/02/2015
1000552 vissv2 1099.066 12/02/2015
1000552 vissv3 1111.265 12/02/2015
1000552 vistv 1505.061 12/02/2015
With 5000+ rows of data, doing this manually is not an option.
Identifying dates from data
In order to extract the dates, I needed to format the list as a table.
Next, I added a column called “Date” (which is shown in the second table above).
Unfortunately the date data is not actually in date format. There are two spaces between the time and date and the cell format is “custom”.
In essence, the dates are text and do not actually translate to a date value.
Excel stores dates and times as a number representing the number of days since 1 January 1900, plus a fractional portion of a 24 hour day: ddddd.tttttt. This is called a serial date. Typically, machines that generate data sets (especially in CSV format) do not enter dates in serial format (as is the case here) and so Excel cannot read the date properly. To test whether a date is entered correctly, a DATEVALUE() can be used to test this. An error indicates that the date is stored as text. This is a problem.
The formula
To extract the dates for all the entries, I needed to apply the following logic for each line of data:
1. Is the number in the “Value” column meant to be read as a date? (eg: 12/02/2015 9:51:26 AM)
2. If so, what is the translation of that number into a serial date?
3. If the number in the “Value” column is not meant to be read as a date, what date should be matched to that row?
Two tests will be applied to see whether a number is a date:
• The serial date should start with a “4” (40000 = 6 July 2009 and all dates fall after this period)
• There should be a decimal point at the sixth position (eg: 12/02/2015 9:51:26AM = 42047.4107175926)
The chances that a number meets these criteria and isn’t a date is slim in this data set. Beware: Other data sets may require additional tests. Think carefully about this step.
The following formula will apply the test:
=IF(AND(FIND("4",[@Value],1)=1, FIND(".",[@Value],1)=6), SUM(DATEVALUE(TEXT([@Value], "dd/mm/yyyy"))+TIMEVALUE(TEXT([@Value], "hh:mm"))))
This formula applies the aforementioned test (using a combination of IF and AND functions) and extracts both the date (DATEVALUE) and time (TIMEVALUE) from the text string. A SUM function is used to add them together to derive the full serial date.
Unfortunately, the formula is not complete, because:
• If a number in the “Value” column contains a “4” anywhere in it but can’t be read as a date, the equation will return a FALSE value
• If a number in the “Value” column does not contain a “4” anywhere and can’t be read as a date, the equation will return a #VALUE! error
To fix these, we need to expand the equation so that under both scenarios, the equation will obtain the date from the cell above.
Here’s the final equation:
=IFERROR(IF(AND(FIND("4",[@Value],1)=1, FIND(".",[@Value],1)=6), SUM(DATEVALUE(TEXT([@Value], "dd/mm/yyyy"))+TIMEVALUE(TEXT([@Value], "hh:mm"))), INDIRECT("R[-1]", FALSE)), INDIRECT("R[-1]", FALSE))
The combination of IFERROR and IF helps deal with both scenarios. The instructions about where to get the date from are given by INDIRECT("R[-1]", FALSE) which says “get the date from the cell above” (refer to a previous blog post about INDIRECT). The INDIRECT function must be repeated twice within the formula in order to deal with both the FALSE and #VALUE! answers.
Finishing the job
The next step is to copy all of the dates and paste as values. That way, the dates and times will permanently be attached to each variable measurement.
Finally, re-sort the data and delete all the entries where “Time Stamp” appears in the “Variable” column.
<a href="" title=""> <b> <blockquote cite=""> <code> <em> <i> <q cite=""> <strike> <strong>
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18478213250637054, "perplexity": 3485.2308257051377}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499700.67/warc/CC-MAIN-20230129044527-20230129074527-00522.warc.gz"}
|
https://www.physicsforums.com/threads/need-help-with-entropy-question.49552/
|
# Need help with entropy question
• Start date
• #1
551
1
Can anyone help me with this, please?
1. 1 mol of an ideal gas is compressed slowly and isothermally at 400 K in a piston-cylinder arrangement. Initial pressure = 100 kPa, final pressure 1000 kPa. The system is surrounded by a resevoir at 300 K such that heat exchange can take place between the piston-cylinder arrangement and the resevoir. System is isolated, so no heat exchange with outside world.
Calculate the entropy change of the gas, resevoir and universe if:
i. the piston is frictionless.
I'm stuck trying to do the entropy change for the gas. If I manage to do it, I should be able to do the rest.
I know delta S = INT dQ/T (haven't used tex before)
Also, from the 1st law: delta U = Qin + Won
For an isothermal change, delta U = 0 (as U depends on T only)
=> Qin = -Won
=> Qin = INT P dV
I'm not sure where to go from there, cos I can't put dQ = P dV in the integral above, can I (then substitute P = nRT/V, obviously)?
Related Introductory Physics Homework Help News on Phys.org
• #2
17
0
Sure. It says in the excersize that the gas is compressed slowly and isothermally, so there always is an equilibrium. nRT/V can be put into the integral, making Q = nRT * INT (dV/V) from V1 to V2. (Which makes Q = nRT *ln(V2/V1).
Using relative volumes is enough here. Good luck!
• #3
551
1
Ok, thanks :).
• #4
551
1
I'm stuck again. How do I calculate the entropy change for the resevoir now?
1st law: delta U = Qin + Won
Won = 0, right? So delta U = Qin and I'm stuck :/.
• #5
17
0
Alright, you already showed us that delta U = 0, since it's an ideal gas. So Qin = -Won. In this case the Work on the gas is positive, the piston has to do work on the gas to compress it, so heat has to be removed from the gas, which follows fromthe formula.
Won = - INT P dV ---> so Qin = INT P dV = nRT * INT dV/V
So not Won = 0 but delta U = 0. This is because it's an isothermal process, which already suggests no change of internal energy (in the case of an ideal gas that is).
Now solve the integral and put relative values for V2 and V1 into it. There you go!
• Last Post
Replies
3
Views
7K
• Last Post
Replies
1
Views
1K
• Last Post
Replies
0
Views
3K
• Last Post
Replies
1
Views
7K
• Last Post
Replies
3
Views
2K
• Last Post
Replies
2
Views
5K
• Last Post
Replies
2
Views
902
• Last Post
Replies
3
Views
5K
• Last Post
Replies
5
Views
2K
• Last Post
Replies
1
Views
2K
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9089689254760742, "perplexity": 1738.2537901201015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107889173.38/warc/CC-MAIN-20201025125131-20201025155131-00188.warc.gz"}
|
https://tug.org/pipermail/texworks/2009q1/000603.html
|
# [texworks] commands
Hans Hagen pragma at wxs.nl
Thu Mar 19 13:21:49 CET 2009
Joseph Wright wrote:
> Hans Hagen wrote:
>> Hi
>>
>> A few questions ...
>>
>> - I want to add a 'typesetting command' that does not need a file at all
>> (it just runs). In that case I need an option not to ask for an input
>> file or save or whatever. Maybe check if the command has an argument
>> that specifies a file will do. Or otherwise a checkbox like the one that
>> can be used not to open a pdf afterwards.
>
> I'm intrigued as to what this is!
things like updating, help info and more
>> - I think that the 'cleanup aux' files in the menu is too specific for a
>> macro package, so it should either be configurable or be made
>> typesetting command dependent or whatever. I can even imagine that there
>> is an extra menu with options that change depending on the typesetting
>> command being selected.
>
> You can customise it in ~/TeXworks/configuration/texworks-config.txt, at
> least in the sense of altering what is on the list.
i think that there should be a config per typesetting command, as most
of what is in this file does not make sense for context (we have no
\include and \includegraphics but different commands and there cleanup
suffixes are also different and could even lead to unwanted cleanup)
>> - The open file menu can have a context entry as well. Valid suffixes
>> are: .tex .mkii .mkiv .xml .ctx (and maybe a few more in the future)
>
> I guess that the assumption was that ConTeXt only uses .tex (this would
> have been my guess, for example).
actualy there are a few more but the average user will not use them
i'm playing with coloring xml and wondering if it makes sense to add an
option to associate file suffixes with specific syntax patterns
another thing that comes to mind (when testing) is a quick way to open
the most recent file(s) [esp handy when testing changes in the
configuration, the multistep menu choice involved too many steps or
maybe there's already a magic key combination that does that]
Hans
-----------------------------------------------------------------
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.883709728717804, "perplexity": 3686.916616725484}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572934.73/warc/CC-MAIN-20190916200355-20190916222355-00133.warc.gz"}
|
http://www.latex-community.org/forum/viewtopic.php?f=5&t=6906&start=0
|
## LaTeX forum ⇒ General ⇒ Tcilatex
LaTeX specific issues not fitting into one of the other forums of this category.
bazman
Posts: 78
Joined: Mon Jan 26, 2009 3:24 am
### Tcilatex
\documentclass{article}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\usepackage{amsmath} %TCIDATA{OutputFilter=LATEX.DLL}%TCIDATA{Created=Friday, September 22, 2006 08:26:57}%TCIDATA{LastRevised=Saturday, September 30, 2006 18:37:59}%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}%TCIDATA{<META NAME="DocumentShell" CONTENT="Articles\SW\Standard LaTeX Article">}%TCIDATA{CSTFile=LaTeX article (bright).cst} \newtheorem{theorem}{Theorem}\newtheorem{acknowledgement}[theorem]{Acknowledgement}\newtheorem{algorithm}[theorem]{Algorithm}\newtheorem{axiom}[theorem]{Axiom}\newtheorem{case}[theorem]{Case}\newtheorem{claim}[theorem]{Claim}\newtheorem{conclusion}[theorem]{Conclusion}\newtheorem{condition}[theorem]{Condition}\newtheorem{conjecture}[theorem]{Conjecture}\newtheorem{corollary}[theorem]{Corollary}\newtheorem{criterion}[theorem]{Criterion}\newtheorem{definition}[theorem]{Definition}\newtheorem{example}[theorem]{Example}\newtheorem{exercise}[theorem]{Exercise}\newtheorem{lemma}[theorem]{Lemma}\newtheorem{notation}[theorem]{Notation}\newtheorem{problem}[theorem]{Problem}\newtheorem{proposition}[theorem]{Proposition}\newtheorem{remark}[theorem]{Remark}\newtheorem{solution}[theorem]{Solution}\newtheorem{summary}[theorem]{Summary}\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}\input{tcilatex} \begin{document}
when I try to run the above document I get the error:
I as using someone else's file here so I have no idea what tcilatex does?
Kind Regards
Baz
localghost
Site Moderator
Posts: 9206
Joined: Fri Feb 02, 2007 12:06 pm
Location: Braunschweig, Germany
bazman wrote:[...] I as using someone else's file here so I have no idea what tcilatex does? [...]
Ask the person you've got the file from.
Best regards
Thorsten
LaTeX Community Moderator
¹ System: openSUSE 13.1 (Linux 3.11.10), TeX Live 2013 (vanilla), TeXworks 0.5 (r1351)
² Posting stopped indefinitely due to offenses
lalop
Posts: 63
Joined: Fri Sep 11, 2009 11:25 pm
There seems to be some copies of tcilatex.tex on google. No promises they are the one you want, however.
Apparently, it's a macro collection.
sitex
Posts: 70
Joined: Sat May 09, 2009 12:37 pm
Hello,
I think the person who created the file is using Scientific WorkPlace or Scientific Word. Depending on what the file contains, you may be able to compile the it by simply removing the tcilatex command. If this does not work ask the creator to save the file as a Portable Latex File and send you a copy.
If all this fails and the file is not too big, you can post it and I can try to fix it for you.
Tom
daleif
Posts: 199
Joined: Wed Nov 19, 2008 12:46 am
best thing to do is to ask the person using Scientific Workplace to save the Document as Portable LaTeX, it is in the dropdown under the file name when use uses the 'Save as' feature.
This will remove the tcilatex from the document.
ticlatex is only found in Scientific Workplace and the firm for some reason does not share their stuff with the rest of us.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8494266867637634, "perplexity": 4720.4470986310835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542213.61/warc/CC-MAIN-20161202170902-00181-ip-10-31-129-80.ec2.internal.warc.gz"}
|
https://ask.wireshark.org/question/18832/how-can-i-differentiate-rtp-and-srtp-packets/?sort=latest
|
Ask Your Question
# How can I differentiate RTP and SRTP packets? edit
Hi there,
I have 2 camera's both streaming video. One should be streaming SRTP and the other RTP.
But when I wireshark the packets, both streams (RTP packets) look the same. They both are listed as RTP (in the protocol column)
Though I get RTSP packets from the one camera, it seems to me the RTP packets are not encrypted at all. I can see the RTP fields and even the payload.
How do I know if SRTP is used? Shouldn't I see SRTP in the protocol column? I'm really confused.
edit retag close merge delete
## Comments
Add a column for rtp.setup-method
Description: [Setup Method: ZRTP]
Field Name: rtp.setup-method
Value: ZRTP
Can you share a packet capture?
If not, there is a Asterisk_ZFONE_XLITE.pcap Sample SIP call with ZRTP protected media. on the Wireshark wiki which has an example of SRTP.
( 2020-09-11 15:47:42 +0000 )edit
## 1 Answer
Sort by » oldest newest most voted
First thing would be to have access to the media session setup protocol (e.g., SDP in SIP). This can tell the parameters of the media stream, carried by RTP, and the encryption parameters.This will then show up in the related RTP stream, being shown as SRTP.
When this is not available in the capture (e.g., the media session setup protocol is encrypted itself) there's nothing really the RTP dissector can do but to show the packets as if they where RTP. There are some telltale signs you can spot to see if this is SRTP after all. Usually the SRTP packets have a HMAC at the end, increasing the payload beyond what is expected from the media encoder. Sometimes you can spot recognisable patterns in the data (e.g. PCM encoded silence in audio packets). When these are missing it may be SRTP after all. As said, it's not trivial to distinguish the two.
more
## Comments
I used RTSPS (encrypted RTSP) to start the RTP stream, so I can't see the parameters in those packets, but I do know they both use h.264 codec for the videostream.
Now because of this, I am able to dissect the RTP packets (for both streams) as h.264 packets. I did this by filling in the RTP dynamic payload type in the H.264 protocol in Wireshark. The value I put in, is the value in the RTP packets headers I already was able to see. link text
Now both stream are detected as h.264 streams and I can even see some h.264 headers. Does this mean both streams are unencrypted?
I really want to create an image/video of this payload to see if one makes a correct/recognizable image/video and the other... guess noise (if it is truly encrypted).
I can't ...(more)
( 2020-09-12 15:50:25 +0000 )edit
## Your Answer
Please start posting anonymously - your entry will be published after you log in or create a new account.
Add Answer
## Stats
Asked: 2020-09-11 15:32:29 +0000
Seen: 1,483 times
Last updated: Sep 11 '20
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20853236317634583, "perplexity": 5250.559594083496}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585353.52/warc/CC-MAIN-20211020214358-20211021004358-00453.warc.gz"}
|
https://www.physicsforums.com/threads/where-does-the-energy-come-from.130816/
|
# Where does the energy come from?
1. Sep 5, 2006
### goodboy
put a iron beside a magnet,then we konw the iron would be attracted toward the magnet.but where does the kinetic energy of the iron come from?
2. Sep 5, 2006
### Tomsk
The iron is in a magnetic field, hence it has potential energy due to its position. This becomes KE when the iron is released. The total energy, KE+PE, is conserved.
3. Sep 5, 2006
4. Sep 5, 2006
### Meir Achuz
You are now wrong. You were right the first time. For a permanent magnet and ferromagnetic iron, the energy considerations do work just as they would in electrostatics with a charge attractilng a polarizable object.
Similar Discussions: Where does the energy come from?
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9319864511489868, "perplexity": 1694.4832051380274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607120.76/warc/CC-MAIN-20170522211031-20170522231031-00187.warc.gz"}
|
http://mathhelpforum.com/calculus/10857-large-derivative.html
|
# Math Help - large derivative
1. ## large derivative
Can someone give the derivative of the equation below.
Joram
Attached Thumbnails
2. The trouble I am having with this is that your derivative isn't picking out a specific value of "i."
-Dan
3. ## Thanks...
Yes the derivative when i=k is easily obtained. However I need the complete system of solutions. I forgot to mention though that the derivative needs to be zero. To be precise the vector of derivatives need to equal a empty vector, see below.
Joram
Attached Thumbnails
4. Originally Posted by Patek
Yes the derivative when i=k is easily obtained. However I need the complete system of solutions. I forgot to mention though that the derivative needs to be zero. To be precise the vector of derivatives need to equal a empty vector, see below.
Joram
If I'm understanding you correctly then what you need to do is take the derivative for i = k, where k is at the moment undefined. Then your vector components will be in terms of the index k as k runs from 1 to m.
-Dan
5. ## Thanks...
Thanks, your hint helped me solve it.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.973152756690979, "perplexity": 512.3940185830938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115869647.75/warc/CC-MAIN-20150124161109-00160-ip-10-180-212-252.ec2.internal.warc.gz"}
|
http://scripts.epicsol.org/input?rev=1157135570&do=diff
|
input
# Differences
This shows you the differences between two versions of the page.
— input [2006/09/01 18:32] (current) Go Go Line 1: Line 1: + ======Synopsis:====== + __input__ "<prompt>" <command> [<arguments>] \\ + __input_char__ "<prompt>" <command> [<arguments>] + + ======Description:====== + This command is primarily for use inside scripts. It allows the client + to present the user with a visible prompt for specific commands. This + can be used for interactive commands, for command confirmation, etc. + Multiple commands may be specified if surrounded with curly braces. + + The variant __INPUT_CHAR__ words the same as __INPUT__, except it only takes a + single character. The primary difference is that it does not require + that a carriage return be entered before executing the command; the first + keystroke will trigger it. + + ======Options:====== + |-noecho |stops the echoing of characters as they are typed | + + ======Examples:====== + To let a command ask for confirmation: + input "Are you REALLY sure you want to do this? (y/n) " { + if ( [\$0] == [y] ) exec rm -rf * + } + + The basis for a simple paging mechanism: + input_char "Press 'q' to quit, any other key to continue: " { + unless ( [\$0] == [q] ) { + /* do whatever */ + } + } + + ======Aliases:====== + These commands are functionally equivalent to the \$"..." expando. In + truth, they supersede \$"...".
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9127844572067261, "perplexity": 6607.754471064225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250591431.4/warc/CC-MAIN-20200117234621-20200118022621-00018.warc.gz"}
|
https://soffer801.wordpress.com/blog/
|
## Maximum modulus principle
Here’s a fact you probably never noticed: Holomoprhic functions have no local maxima. Okay, constant functions do, but those are lame.
Theorem 1 (Maximum modulus principle) Let ${f\in{\mathcal H}(U)}$. Then if ${z_0\in U}$ has ${|f(z_0)|\ge|f(z)|}$ for every ${z\in U}$, then ${f}$ is constant.
Proof: If ${|f|}$ has a local maximum at ${z_0}$, then in a small ball around ${z_0}$, consider the image of ${|f|}$. It looks something like ${(f(z_0)-\varepsilon, f(z_0)]}$. We don’t really care about the lower bound. The important point is that the upper bound is attained. This tells us that, the image of the small ball ${B_r(z_0)}$ under ${f}$ is completely contained in ${\overline{B_{f(z_0)}(0)}}$, and that it touches the boundary. Thus, the image of this ball has a boundary and thus cannot be an open set. But by the open mapping theorem, this is only possible if ${f}$ were in fact constant. $\Box$
## Open mapping theorem
Today we’ll prove the open mapping theorem:
Theorem 1 (Open mapping Theorem) Let ${f\in{\mathcal H}(U)}$, for some open set ${U}$ in ${{\mathbb C}}$. Then ${f(U)}$, the set of all possible images of ${f}$ is either constant, or is open in ${{\mathbb C}}$.
Let ${z_0\in f(U)}$, and let ${w_0}$ be a preimage. That is, ${f(w_0)=z_0}$. Since ${U}$ is open, there must be a small closed ball around ${w_0}$ completely contained in ${U}$. Let ${r}$ be it’s radius. Then ${\overline{B_r(w_0)}\subseteq U}$. Let ${g(z)=f(z)-z_0}$. What do we know about ${g}$?
We know that the roots of ${g}$ are isolated points. After all, if not, we would have a convergent sequence of roots, contradiction one of the theorems we proved here. So we can choose ${r}$ to be even smaller so that the only root of ${g}$ in ${\overline{B_r(w_0)}}$ is ${w_0}$. Since the boundary of ${\overline{B_r(w_0)}}$ is a circle, and hence compact, and ${|g(z)|}$ is continuous it attains its minimum when restricted to the boundary. Let ${m}$ be the minimum value of ${|g(z)|}$ for ${z}$ on the boundary of ${\overline{B_r(w_0)}}$.
Now, by Rouché’s theorem, ${g}$ will have the same number of roots in in ${B_r(w_0)}$ as ${f(z)-z_1}$ for any ${z_1}$ in ${B_m(z_0)}$. (Application of Rouché’s theorem is left as an exercise.)
In particular, this means that for every complex number in ${z_1\in B_m(z_0)}$, the function ${f(z)-z_1}$ has at least one root in ${B_r(w_0)}$, and so ${B_m(z_0)}$ is contained in ${f(U)}$, meaning our arbitrarily chosen point ${z_0}$ is in the interior of ${f(U)}$. Thus ${f(U)}$ is open.
## Rouche’s Theorem
Today we prove Rouché’s theorem. The gist is that it helps us count the number of roots of a holomorphic function, given some bounds on its values.
Theorem 1 Suppose ${f}$ and ${g}$ are holomorphic functions inside and on the boundary of some closed contour ${\gamma}$. If
$\displaystyle |g(z)|<|f(z)|$
on ${\gamma}$, then ${f}$ and ${f+g}$ have the same number of zeros on the interior of ${\gamma}$.
Before we begin proving this, it should be emphasized that we count with multiplicity. We would count the number 1 as a root of ${x^2-2x+1}$ twice. Most root counting we every do will be done this way. I feel confident in saying that it is the correct way to count roots, even if at first it is unintuitive.
Proof: By hypothesis, ${f}$ has no roots on the boundary ${\gamma}$. Define ${F(z)=\frac{f(z)+g(z)}{f(z)}}$. The roots of ${F}$ are the roots of ${f+g}$. The poles of ${F}$ are the roots of ${f}$. So it suffices to use the argument principal to show that ${N(F)=P(F)}$. That is, we need to show that
$\displaystyle \displaystyle\frac1{2\pi i}\int_\gamma\frac{F'}{F}=N(F)-P(F)$
is zero.
But from our hypotheses, we can conclude that
$\displaystyle |F(z)-1|=\left|\frac{f(z)+g(z)}{f(z)}-1\right|=\left|\frac{f(z)}{g(z)}\right|<1.$
That is, ${F}$ never takes on values more than ${1}$ away from ${1}$. Imagine a dog tethered by a leash of length less than ${1}$ to the point ${1\in{\mathbb C}}$. That dog can’s reach the origin, but more importantly, he can’t walk a loop around the origin. So computing the winding number about the origin must give us zero. This proves the theorem. $\Box$
## Argument Principle
Let ${z_0}$ be a zero of a meromorphic ${f}$ with multiplicity ${m}$. Then we can write ${f(z)=(z-z_0)^m\cdot g(z)}$ where ${g(z_0)\ne0}$. Taking derivatives yields
$\displaystyle f'(z)=m(z-z_0)^{m-1}\cdot g(z)+(z-z_0)^m\cdot g'(z).$
Hence, for ${f'/f}$, we get
$\displaystyle \displaystyle\frac{f'(z)}{f(z)}=\frac{m}{z-z_0}+\frac{g'(z)}{g(z)}.$
The residue of this sum is simply the sum of the residues of the two parts. The first term has residue ${m}$ at ${z_0}$. The second part has no pole at ${z_0}$, and hence zero residue. Thus, the residue of ${f'/f}$ at ${z_0}$ is ${m}$.
What if we pick a pole of ${z_p}$ of ${f}$? Then by a similar construction, if ${z_p}$ is an order ${q}$ pole, we can write ${f(z)=(z-z_p)^{-q}\cdot h(z)}$ and compute
$\displaystyle \displaystyle\frac{f'(z)}{f(z)}=\frac{-q}{z-z_p}+\frac{h'(z)}{h(z)},$
yielding a total residue of ${-q}$.
If a point ${z}$ is neither a pole nor a zero, then ${f'/f}$ is holomorphic at ${z}$, and has residue zero at ${z}$.
If we take a big contour around all of these points, then the integral will be the sum of the residues inside the contour, which we have just shown is the number of roots minus the number of poles (counted with multiplicity and order, respectively).
That is, if ${N_\gamma(f)}$ denotes the number of zeros counted with multiplicity inside a contour ${\gamma}$, and ${P_\gamma(f)}$ denotes the number of poles counted with order, then
$\displaystyle \displaystyle\frac{1}{2\pi i}\int_\gamma \frac{f'(z)}{f(z)}dz=N_\gamma(f)-P_\gamma(f)$
This result is known as the argument principle.
## A joke
Today, a definition, then a joke.
I defined poles of meromorphic functions, but we can be a bit more descriptive. Suppose we have a meromorphic function $f$ which is is undefined at some point $z_0$. We can expand it as a Laurent series, and get something like:
$\displaystyle\sum_{-\infty}^\infty a_n(z-z_0)^n$
It may be that we can make $n$ arbitrarily negative and still have $a_n$ be nonzero. This is basically the worst situation possible. We don’t in fact call it a pole. We say that it is an essential singularity at $z_0$
In a better situation, it might be that $a_{-17}$ is nonzero, but with any smaller (more negative) index, $a_n$ is zero. Then, we would say that $f$ has a pole at $z_0$ of order $17$. Of course there’s nothing special about seventeen.
If a pole has order 1, we say that it is a simple pole.
Now for a joke.
An airplane is on its way out of Warsaw, and the pilot suffers a heart attack and dies. A passenger is asked to navigate the plane to safety. He looks worried, so the stewardess asks “what’s wrong?” He responds “I’m just a simple Pole in a complex plane!”
Laugh, damn it!
## Residue calculus
There’s a neat trick we can use to integrate real integrals using complex analysis. These can be made arbitrarily complicated, but I’ll give you a simple example. Compute the integral:
$\displaystyle \displaystyle\int_{-\infty}^\infty\frac1{(1+x^2)^3}dx$
This is another way to write down
$\displaystyle \displaystyle\lim_{a\rightarrow\infty}\int_{-a}^a\frac1{(1+x^2)^2}dx.$
Let’s change all the ${x}$s to ${z}$s, and pretend we’re integrating along the path ${[-a,a]}$ in the complex plane. Our notion of integrating in ${{\mathbb C}}$ is defined in such a way that this makes sense. Okay, but we normally integrate loops, not paths, so let’s complete a full loop ${\gamma_a}$ is the semi-circle in the upper half-plane with base ${[-a,a]}$ and radius ${a}$. Then we can break the path into two pieces:
$\displaystyle\int_{\gamma_a}\frac1{(1+z^2)^{2}}dz=\int_{-a}^a\frac1{(1+x^2)^{2}}dx+\int_0^\pi\frac1{(1+(ae^{i\theta})^2)^{2}}d\theta.$
The first piece is the integral we want to compute, and the second is the curved part of the semi-circle. Together they make a closed loop whose integral we can actually calculate using the residue theorem. Since our function is meromorphic on all of ${{\mathbb C}}$, we need to simply figure out which poles are inside the semicircle ${\gamma_a}$, and find their residues. We can tell that the only poles are at ${i}$ and ${-i}$, of which only ${i}$ is in the semicircle ${\gamma_a}$ (for every ${a>1}$). It’s residue we compute as $-i/4$.
Thus, the left hand side, via the residue theorem, must be ${2\pi i\cdot (-i/4)=\pi/2}$.
Now we just need to show that the semi-circular arc’s contiribution is neglibible for large ${a}$. Then, taking ${a\rightarrow\infty}$ yields
$\displaystyle \displaystyle\lim_{a\rightarrow\infty}\int_{-a}^a\frac1{(1+x^2)^2}dx=\pi/2.$
Indeed,
$\displaystyle \begin{array}{rcl} \left|\displaystyle\int_0^\pi\frac1{(1+(ae^{i\theta})^2)^{2}}d\theta\right| &\le& \displaystyle\int_0^\pi\left|\frac1{(1+(ae^{i\theta})^2)^{2}}\right|d\theta\\ &=& \displaystyle\int_0^\pi\frac1{(1+a^2)^{2}}d\theta\\ &=& \frac{\pi}{(1+a^2)^2} \end{array}$
which decreases to zero as ${a\rightarrow\infty}$.
I’m awful at integration in general, so I’m not sure if this integral can be done using integration by parts, or a tricky ${u}$-substitution. There are definitely some integrals though, for which those standard methods just don’t cut it.
## Meromorphic functions and residues
Last time, we discussed Laurent series, which are essentially two-way power series. They are almost as nice as holomorphic functions, but not quite. Maybe we can recoup some of the lost beauty of holomorphicity by imposing a reasonable condition.
We want to allow ourselves to have points where the function isn’t defined, but let’s limit these points. Let’s require them to be isolated points. We say that a function ${f}$ is meromorphic on an open set ${U\subseteq {\mathbb C}}$ if ${f}$ is holomorphic on ${U}$, except at some number of isolated points. We write ${f\in{\mathcal M}(U)}$. These isolated points are called poles. We obviously shouldn’t expect ${f}$ to have a power series centered at one of these poles, but it does have a Laurent series.
Let ${f\in{\mathcal M}(U)}$ and let ${z_0\in U}$ be a pole of ${f}$. Then as we saw last time, ${f}$ has a Laurent series centered at ${z_0}$:
$\displaystyle f(z)=\cdots+a_{-2}(z-z_0)^{-2}+a_{-1}(z-z_0)^{-1}+a_0+a_1(z-z_0)+a_2(z-z_0)^2+\cdots$
Moreover, the series has inner radius of convergence 0, so this representation is valid for all ${z}$ close enough to ${z_0}$.
Now if we take a loop ${\gamma}$ in ${U}$, and integrate, if ${f}$ has no poles on the interior of ${\gamma}$, then the integral is zero. This is the Cauchy integral theorem. What if it does have a pole? We can use the generalized Cauchy integral formula we saw last time:
Theorem 1 (Residue theorem) Let ${f\in{\mathcal M}(U)}$ and let ${z_0}$ be a pole of ${f}$ in ${U}$. Expand ${f}$ as a Laurent series as above. Let ${\gamma}$ be a small counter-clockwise circle about ${z_0}$ such that the only pole in its interior is ${z_0}$. Then
$\displaystyle \displaystyle\frac{1}{2\pi i}\int_\gamma f(z)dz=a_{-1}.$
Proof:The generalized Cauchy integral formula we saw last time said that
$\displaystyle a_n=\displaystyle\frac{1}{2\pi i}\int_\gamma\frac{f(z)}{(z-z_0)^{n+1}}dz.$
Let ${n=-1}$.
$\Box$
If we take a loop that goes around several poles, the integral must be the sum of the integrals, as we can build a homotopy as shown in the images below (click to blow up).
The value ${a_{-1}}$ (for an expansion about ${z_0}$) is called the residue of ${f}$ at the pole ${z_0}$. In other words, the theorem states that the value of an integral about a contour is the sum of the residues of the poles inside.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 179, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9882963299751282, "perplexity": 120.08084500373258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891546.92/warc/CC-MAIN-20180122232843-20180123012843-00188.warc.gz"}
|
http://hal.in2p3.fr/view_by_stamp.php?label=IN2P3&langue=fr&action_todo=view&id=in2p3-00115973&version=1&view=extended_view
|
HAL : in2p3-00115973, version 1
Structural and nuclear characterizations of defects created by noble gas implantation in silicon oxideAssaf H., Ntsoenzok E., Barthe M.-F., Ruault M.-O., Sauvage T. et alDans Nuclear Instruments and Methods in Physics Research B - E-MRS IUMRS ICEM 2006 Spring Meeting - Symposium U: Si-based Materials for Advanced Microelectronic Devices: Synthesis, Defects and Diffusion, Nice : France - http://hal.in2p3.fr/in2p3-00115973
Chimie/Cristallographie Physique/Matière Condensée/Autre
Structural and nuclear characterizations of defects created by noble gas implantation in silicon oxide
H. Assaf1, E. Ntsoenzok1, 2, M.-F. Barthe1, M.-O. Ruault3, T. Sauvage1, S. Ashok4
1 : CERI - Centre d'Études et de Recherches par Irradiation http:///web.cnrs-orleans.fr/~ceri CNRS : UPR33 3A, rue de la Férollerie 45071 ORLEANS cedex 2 France 2 : LESI - Laboratoire d' Électronique, Signaux, Images http://www.univ-orleans.fr/lesi/ Université d'Orléans – Institut Universitaire de Technologie de Chartres – Ecole Polytechnique de l'Université d'Orléans 21 rue de Loigny la bataille 28000 Chartres France 3 : CSNSM - Centre de Spectrométrie Nucléaire et de Spectrométrie de Masse http://www-csnsm.in2p3.fr/ CNRS : UMR8609 – IN2P3 – Université Paris XI - Paris Sud batiments 104 et 108 - 91405 Orsay Campus France 4 : DEPARTMENT OF ENGINEERING SCIENCE - Department of Engineering Science The Pennsylvania State University 212 Earth and Engineering Science Building University Park PA 16802 États-Unis
Thermally grown silicon oxide layer was implanted at room temperature with 300keV Xe at fluences ranging from 0.5 to 5x10$^16$Xe/cm$^2$. Bubbles created after Xe-implantation provided a low-k silicon oxide that has potential use as a dielectric material for interconnects in Si integrated circuits. Transmission Electron Microscopy (TEM), Rutherford Backscattering Spectrometry (RBS) and Positron Annihilation Spectroscopy (PAS) were used to provide a comprehensive characterization of defects (bubbles, vacancy, gas atoms and other types of defects) created by Xe implantation in $SiO_2$ layer. These measurements suggest that the bubbles observed with TEM for all fluences were a consequence of the interaction between Xe and vacancies (V), with $V_nXe_m$ complexes created in the zone where V and Xe profiles overlap. Negatively charged defects such as ($Si-O^-$, $Si-O-O^-$ and $O_2^-$) are also created after implantation.
Communications avec actes
2006
Nuclear Instruments and Methods in Physics Research B
253
Enrico Napolitani, Andrej Kuznetsov, Wolfgang Skorupa and Majeed Foad
222-226
E-MRS IUMRS ICEM 2006 Spring Meeting - Symposium U: Si-based Materials for Advanced Microelectronic Devices: Synthesis, Defects and Diffusion
Nice
France
29/05/2006
02/06/2006
77.55.+f; 78.55.Mb; 78.66.Nk; 61.72.Ji; 61.72.Qq; 61.80.Jh; 71.60.+z
Low-k SiO2 – Defects – Bubbles – Xe implantation – Positron annihilation spectroscopy – Rutherford Backscattering – Transmission electron microscopy
Liste des fichiers attachés à ce document :
DOC
e-MRS-ASSAF_Hanan.doc(3.1 MB)
PDF
e-MRS-ASSAF_Hanan.pdf(3 MB)
in2p3-00115973, version 1 http://hal.in2p3.fr/in2p3-00115973 oai:hal.in2p3.fr:in2p3-00115973 Contributeur : Dominique Girod <> Soumis le : Vendredi 24 Novembre 2006, 12:00:41 Dernière modification le : Mercredi 29 Novembre 2006, 13:13:13
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4490301311016083, "perplexity": 16084.399217932492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510273350.41/warc/CC-MAIN-20140728011753-00160-ip-10-146-231-18.ec2.internal.warc.gz"}
|
http://math.stackexchange.com/questions/684770/homology-isomorphism-of-h-nsd-times-x-and-h-n-1sd-1-times-x
|
# Homology isomorphism of $H_n(S^d\times X)$ and $H_{n-1}(S^{d-1}\times X)$
$X$ is an arbitrary space, $d\geq 1$.
The existence of such isomorphism in the title supposedly follows from the Mayer-Vietoris sequence of $(S^d\times X,S^d_{+}\times X,S^d_{-}\times X)$:
$..\rightarrow H_n(S^d_+\times X)\oplus H_n(S^d_-\times X) \rightarrow H_n(S^d\times X)\rightarrow H_{n-1}(S^{d-1}\times X)\rightarrow H_{n-1}(S^d_+\times X)\oplus H_{n-1}(S^d_-\times X)\rightarrow ..$
This is an exact sequence and the homomorphism in the middle should be an isomorphism. But $S^d_+ \times X$ and $S^d_-\times X$ are homotopy equivalent to $X$, so the corresponding homology groups need not be zero. So how can I show this?
-
Since $H_n(S^d\times X)\cong H_n(X)\oplus H_{n-d}(X)$, the statement is generally false. – Carsten S Feb 21 '14 at 11:39
Thanks. Maybe I made a mistake copying the statement. – user35359 Feb 21 '14 at 11:45
One way to fix it is to consider the kernel of the map $H_n(S^d\times X)\to H_n(X)$ induced by the projection map instead. – Carsten S Feb 21 '14 at 12:07
The spaces $S^d_+\times X$ and $X$ are homotopy equivalent, thus the map you are considering is an isomorphism in reduced homology if, and only if $X$ is acyclic. – Daniel Robert-Nicoud Feb 22 '14 at 0:36
Let $X = S^1$ and $d = n = 2$, then $H_2(S^2 \times S^1) = \mathbb{Z}$ but $H_1(S^1 \times S^1) = \mathbb{Z} \oplus \mathbb{Z}$ so you might want to prove something else.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9931527376174927, "perplexity": 156.9233918491054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049279525.46/warc/CC-MAIN-20160524002119-00086-ip-10-185-217-139.ec2.internal.warc.gz"}
|
http://www.ndsl.kr/ndsl/search/detail/article/articleSearchResultDetail.do?cn=JAKO201215053141800
|
HOME> 논문 > 논문 검색상세
## 논문 상세정보
### 일반화된 직교 매칭 퍼슛 알고리듬 Generalized Orthogonal Matching Pursuit
권석법 (고려대학교 컴퓨터.전파통신공학과 ); 심병효 (고려대학교 컴퓨터.전파통신공학과 );
• #### 초록
Compressive sensing 분야에서 orthogonal matching pursuit (OMP) 알고리듬은 underdetermined 시스템의 스파스 (sparse) 신호를 복구하는 대표적인 greedy 알고리듬으로 많은 관심을 받고 있다. 본 논문에서는 OMP 알고리듬의 반복과정에서 하나 이상의 support들을 선택할 수 있도록 하는 OMP 알고리듬의 일반화된 형태의 generalized orthogonal matching pursuit (gOMP)기법을 제안한다. gOMP가 완벽한 신호 복원을 보장하기 위해 restricted isometry property (RIP)를 이용한 충분조건, ${\delta}_{NK}$ $\frac{\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$ 을 제시한다. 실험을 통해 gOMP는 매 반복과정에서 하나 이상의 support들를 선택함으로써 높은 복원 성능과 낮은 복잡도를 가짐을 확인하였다.
As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N) columns are identified per step. Using the restricted isometry property (RIP), we derive the condition for gOMP to recover the sparse signal exactly. The gOMP guarantees to reconstruct sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{NK}$ $\frac{\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$ . In addition, we show recovery performance and the reduced number of iteration required to recover the sparse signal.
• #### 주제어
orthogonal matching pursuit (OMP) . compressive sensing (CS) . restricted isometry property (RIP).
• #### 참고문헌 (13)
1. D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM Journal on Applied Mathematics, Vol. 49, no. 3, pp. 906-931, 1989.
2. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approximation, Vol. 28, no. 3, pp. 253-263, Dec. 2008.
3. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Information Theory, Vol. 52, no. 2, pp. 489-509, Feb. 2006.
4. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, Vol. 51, no. 12, pp. 4203-4215, Dec. 2005.
5. R. Giryes and M. Elad, "RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT," IEEE Trans. on Signal Processing, Vol. PP, no. 99, Nov. 2011.
6. J. A. Tropp and A. C. Gilbery, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. on Information Theory, Vol. 53, no. 12, pp. 4655-4666, Dec. 2007.
7. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, Vol. 26, no. 3, pp. 301-321, Mar. 2009.
8. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. on Information Theory, Vol. 55, no. 5, pp. 2230-2249, May. 2009.
9. D. Needell and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE J. Sel. Topics Signal Processing, Vol. 4, no. 2, pp. 310-316, Apr. 2010.
10. D. L. Donoho and I. Drori and Y. Tsaig and J. L. Starck,, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," Mar. 2006.
11. M. A. Davenport and M. B. Wakin, "Analysis of Orthogonal Matching Pursuit using the restricted isometry property," IEEE Trans. on Information Theory, Vol. 56, no. 9, pp. 4395-4401, Sep. 2010.
12. E. J. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, Vol. 346, no. 9-10, pp. 589-592, May. 2008.
13. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. on Information Theory, Vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
• #### 이 논문을 인용한 문헌 (3)
1. Kim, Seehyun 2013. "Probabilistic Exclusion Based Orthogonal Matching Pursuit Algorithm for Sparse Signal Reconstruction" 전기전자학회논문지 = Journal of IKEEE, 17(3): 339~345
2. 2016. "" Journal of communications and networks, 18(5): 699~712
3. Sim, Byeong-Hyo ; Kim, Jin-Hong ; Kim, Won-Jun 2016. "" 정보와 통신 : 한국통신학회지 = Information & communications magazine, 33(6): 34~44
활용도 분석
amChart 영역
amChart 영역
#### 원문보기
• NDSL :
##### 유료다운로드
유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.
원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.
NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.
이 논문과 함께 출판된 논문 + 더보기
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.902639627456665, "perplexity": 16764.772724856935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145774.75/warc/CC-MAIN-20200223123852-20200223153852-00267.warc.gz"}
|
https://www.physicsforums.com/threads/dirac-gamma-matrices.49915/
|
Dirac Gamma Matrices
1. Oct 27, 2004
Kane O'Donnell
Hi everyone,
From the condition:
$$\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu} = 2g_{\mu\nu}$$
how does one formally proceed to show that the objects $$\gamma_{\mu}$$ must be 4x4 matrices? I unfortunately know very little about Clifford algebras, and for this special relativity project of mine I'd much rather not need brute force!
Cheerio!
Kane
PS: I'm using the signature (+---) for the metric tensor, although this should only change the content of the matrices, not the proof itself, I suspect.
PPS: I quite realise that it probably cannot be shown that the gamma matrices *must* be 4x4 matrices, what I want to know is if the anticommutator conditions are precisely the defining relations for a R(1,3) Clifford algebra or something like that, and how we eliminate the possibility of lower-dimensional 'isomorphisms' (don't know the correct algebra mapping term) existing.
Last edited: Oct 27, 2004
2. Oct 27, 2004
nrqed
I don't know any sophisticated demonstration with a lot of jargon, but I know the simple, dumb approach.
From $\gamma_0^2 =1$ one sees that the eigenvalues are $\pm 1$ (and $\pm i$ for the other gamma matrices). Also it's easy to show from the anticommutation relations that the matrices must be traceless. From those two conditions, a representation must be even dimensional. Since we need 4 linearly independent matrices, 2 dimensions is not enough (there's only the 3 Pauli matrices available). So the next possibility is 4 dimensions.
Pat
3. Oct 28, 2004
pat_connell
I could be wrong here, forgive me if I am. I haven't really gotten around to calculating specifically Dirac's gamma matrices. however, note that the metric tensor g is symmetric under interchange of indices, maybe proceed from there.
Last edited: Oct 28, 2004
4. Oct 28, 2004
Kane O'Donnell
No it's fine , I am really just trying to understand how to justify the selections step by step other than just guessing the things.
Thanks,
Kane
5. Oct 28, 2004
Kane O'Donnell
I get all of it now except why the matrices must be of even dimension. I've read on the net about a hundred times that it is because the eigenvalues are so and so and the matrices are traceless, but I can't see it - why can't you have a traceless odd-dimension square matrix with eigenvalues of say plus or minus 1?
Cheers,
Kane
6. Oct 28, 2004
dextercioby
You can find a good proof in the case D=4 in the article written by Wolfgang Pauli:"Contributions mathématiques à la théorie des matrices de Dirac"Ann.Inst.Henri Poincaré 6,109-136(1936).You can find this article in the book :"Wolfgang Pauli Collected Scientific Papers" edited by R.Kronig & V.F.Weisskopf,Interscience Publishers,a division of John Wiley & Sons,Inc.,1964,volume 2,page 753.
He uses $$\displaystyle{x_{4} = x^4 = ict}$$ so be careful with the transcription to coordinates with $$\displaystyle{\eta_{\mu\nu} = diag (+1\-1\-1\-1)}$$.
Good luck in all!!
7. Oct 28, 2004
Staff Emeritus
Umm, so the eigenvalues are all $$\pm 1 and \pm i$$. We assume the matrices are of full rank (to check the case dim=n) and that they are diagonal in the eigenvalue basis. So the trace is the sum of the elements on the diagonal, i.e. the eigenvalues. Now if there are an even number of elements, you can arrange the 1's and i's to cancel out, but in an odd number of dimensions, you can't, there will always be an unmatched term, and the trace in an odd dimension cannot therefore be 0.
8. Oct 28, 2004
nrqed
Because (as SelfAdjoint already mentioned) if you go to a basis where the gamma are diagonal, the trace is the sum of the eigenvalues. If the eigenvalues are $\pm 1$ and the sum of the eigenvalues is 0, therefore....
Pat
9. Oct 28, 2004
dextercioby
That's the simplest explanation,but it's got so much mathematics in it.In order to go to a basis in which those $$\gamma$$ matrices are diagonal,you've got to use a theorem which enables passing from one to another irreductible representation of the Clifford algebra.This theorem (proved in many QFT books for the case D=4;e.g.Jauch,Rohrlich,Appendix A2,but also the article by Wolfgang Pauli (see above))
states that if $$\gamma_{\mu}$$ and $$\gamma_{\mu}\prime$$ are 2 irreductible representations of the Clifford algebra (and hence satisfy the anticommutation relations),then there is a NONSINGULAR MATRIX "S" such that
$$\gamma_{\mu}\prime = S\gamma_{\mu}S^-1$$,and that this matrix is unique,except for an arbitrary multiplicative factor.
To quote Jauch,Rohrlich,Appendix A2:
"The proof of the main theorem is greatly facilitated by the powerful lemma of Schur (I.Schur,<<Neue Begruendung der Theorie der Gruppencharaktere",Sitzungsber.Preuss.Akad.,1905,p.406) which,for our purpose,may be formulated as follows:Let $$\gamma_{r}$$ and $$\gamma_{r}\prime$$ two irreductible representations of degree n,n' ($$n\leq n\prime$$) and let S be a matrix with n' rows and n columns which connects the two representations by
$$\gamma_{r}\prime S = S\gamma_{r}$$.Then S is either the null matrix (the matrix which consists only of zeros) or it is nonsingular.In the latter case,n=n'"
And then a demonstration of Schur's lemma is given.
It's also the Schur's lemma that enebles us to prove Burnside's theorem:"The matrices of an irreductible n-dimensional representation of any group contain $$n^2$$ LINIARLY INDEPENDENT MATRICES".I quoted from Francis D.Murnaghan's book:" The theory of group representations",The John Hopkins Press,Baltimore,1938,p51 (for a reference to Schur's lemma,v p.47).
To conclude:irreductible matrix representations of the Clifford algebra constructed as the liniar space of complex n*n matrices together with the anticommutation relation cannot have odd number of lines and columns.It follows that n can be only even.For n=2 you find the Pauli matrices+unit matrix.For n=4,you have the Dirac matrices,etc.
The anticommutation relation enebles us to find EXACTLY 16 liniarly independent elements of the Clifford algebra,and hence,using Burnsides theorem to find that for Clifford algebra given by $$\gamma_{(\mu} \gamma_{(\nu} = 2g_{\mu\nu} I_n$$ "n" MUST be 4.
10. Oct 28, 2004
dextercioby
sorry
that should have been of course:
$$\gamma_{(\mu} \gamma_{\nu)} = 2g_{\mu\nu} I_n$$
I'm still a novice in editing TEX :tongue2:
11. Oct 28, 2004
Staff Emeritus
Sure, Shur. Shur's lemma is ordinarily taught as a part of modern undergraduate courses in linear algebra. Not always proved, but stated and used.
12. Oct 28, 2004
Kane O'Donnell
Thankyou to everyone that replied! This quote above is precisely what I was after, as I realised that if we could pass to a diagonal matrix we wouldn't have a problem - the problem of course is that since the gamma matrices are not self-adjoint they don't have a basis of eigenvectors and hence there was (to my knowledge) no diagonal representation of each of the gammas as linear transformations. If there *is* a way to pass to a diagonal form, then my issue is resolved
Thanks again,
Kane
13. Nov 2, 2004
Kane O'Donnell
Ok. I have been looking at this problem quite a bit in order to find a good balance between simplicity and rigour in making this argument. So, my question is - is the following correct?
1. The operators $$\gamma_{\mu}$$ together with their anticommuting property have the structure of a Clifford algebra. We assume the Clifford algebra is finite dimensional and over some complex space (can't justify it, don't know enough about Clifford algebras - help?). Hence it is isomorphic to a matrix algebra over R, C or H, and we have a matrix representation. For each gamma operator it's matrix must be traceless (sum of eigenvalues is zero).
2. From the four operators you can (by multiplication) construct exactly 16 operators. Using the traceless property one can show the 16 operators are linearly independent. As such the dimension of the Clifford algebra is 16. This implies the underlying vector space has dimension 4 (16 = 2^4). Therefore our Clifford algebra is over a 4D vector space and (since n is even) is isomorphic to the 4x4 complex matrix algebra.
The reason I've taken this approach is that I still can't justify to myself that the gammas are diagonalisable directly, hence I can't use the simple trace/eigenvalue pair argument.
Kane
Last edited: Nov 2, 2004
14. Nov 3, 2004
dextercioby
Actually Burnside's theorem implies:$$4=\sqrt{16}$$.Of course,u don't need Bunside's theorem to tell u that $$4=\sqrt{16}$$,it's just that it makes the connection between the dimension of an irreductible representation and the number of (linearly independent) generators of the Clifford algebra.
15. Nov 3, 2004
Kane O'Donnell
http://en.wikipedia.org/wiki/Clifford_algebra
Under Bases and Dimension it gives the dimension of a Clifford algebra to be 2^n, where n is the basis of the underlying vector space.
Of course, wiki isn't the greatest source in the world. The point is, to use Burnside's theorem convincingly (to myself) I would have to know a lot more about the underlying maths, which unfortunately I don't (although that will be fixed over the Dec/Feb summer hols).
Cheerio,
Kane
Similar Discussions: Dirac Gamma Matrices
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9613913893699646, "perplexity": 724.7336190749357}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805708.41/warc/CC-MAIN-20171119172232-20171119192232-00663.warc.gz"}
|
https://www.physicsforums.com/threads/need-help-applying-kirchhoffs-voltage-law.673709/
|
# Need help applying Kirchhoff's voltage law
1. Feb 22, 2013
### InvalidID
I made a circuit that matches the attached figure. Then, I measured values of voltage and current and I ended up with the attached table. Now I'm applying KVL to both loops.
For the first loop:
$$-23.9+13.981+10.120≅0\\ 0.201≅0$$
For the second loop:
$$10.120+4.118+6≅0$$
What am I doing wrong for the second loop?
#### Attached Files:
File size:
27.4 KB
Views:
178
• ###### Data.png
File size:
3.4 KB
Views:
153
2. Feb 22, 2013
### Staff: Mentor
Mark the polarities of the voltages you measured on the circuit diagram. When you do a "KVL walk" around a loop, take into account these polarities; does the potential drop or rise when you "walk over" a given component along your path?
3. Feb 22, 2013
### tiny-tim
Hi InvalidID!
You haven't drawn any arrows on your diagram, to show the direction of the current.
So how do you know whether to use plus or minus for the voltage drops across each resistor?
Apply KCL to node 2
4. Feb 22, 2013
### InvalidID
I thought resistors don't have polarities?
I assumed that the current flows in clockwise direction.
KCL applied to node 2:
0.601+4.594=5.195
5.195=5.195
Edit: I think I might be mixing up mesh analysis with KVL. You can only apply KVL to the large loop, right? You can't apply it to the individual meshes, correct?
Last edited: Feb 22, 2013
5. Feb 22, 2013
### tiny-tim
Hi InvalidID!
You can apply KVL to any loop.
In this case, you can apply KVL to all three loops (the outside one, and the two small ones), but the KVL equation for the two small ones will add up to the KVL equation for the large one, so you only have two independent KVL equations.
ok, now do KVL for two loops, and draw in those arrows!!
6. Feb 22, 2013
### Staff: Mentor
Resistors themselves do not have polarities. However, when a current flows through a resistor, the potential drops in the direction of current flow. You may have noticed when you were measuring voltages across the resistors that you would see a positive value with the meter leads placed in one orientation, and a negative value (same magnitude) if the leads were reversed. So when you measure the voltage across a resistor, you should take note of the polarity you see since that will also tell you the direction that the current is flowing.
KVL can be applied around any closed path.
7. Feb 23, 2013
### InvalidID
I've applied KVL to all 3 loops but the equations of the smaller loops don't add up to the the equation of the larger loop.
#### Attached Files:
• ###### Untitled.png
File size:
30.3 KB
Views:
107
8. Feb 23, 2013
### Staff: Mentor
KVL states that the sum of the potential changes around a closed path (a loop) is zero. It doesn't say anything about a sum of the equations derived from this property.
9. Feb 23, 2013
### InvalidID
So I suppose you are disagreeing with tiny-tim? Did I setup the equations correctly?
10. Feb 23, 2013
### Staff: Mentor
I don't think I'm disagreeing with tiny-tim; the circuit admits two independent loops, since two loops (chosen appropriately) are sufficient to include every component of the circuit at least once. This means that if you use a third loop, its equation will be linearly dependent (mathematically speaking) on the other two. A straight sum of terms from two of the equations usually will not result in the third equation; Some scaling of the equations might be required (multiplication by constant values).
Last edited: Feb 23, 2013
11. Feb 23, 2013
### InvalidID
Alright, but if I input the values into the KVL equation for the loop on the right, I get:
$$10.120+4.118+6≅0$$
which isn't correct. :S
12. Feb 23, 2013
### Staff: Mentor
Then you have a sign issue with the terms. Did you mark in the polarities of the potential drops due to the currents and take them into account when you wrote the KVL expression?
13. Feb 23, 2013
### tiny-tim
Hi InvalidID!
No you haven't, you've written equations like E - R1 - R2 = 0.
Sorry, but that is nothing like Kirchhoff's law.
KVL requires you to add the potential drops across all the components in the loop (and the emf).
The potential drop is IR, not R, and you multiply it by 1 or -1 depending on the direction of the current.
Write i1 i2 and i3 on your diagram, with arrows specifying a direction for each current, then write out the three loop equations.
With 3 loops, the sum or difference of 2 KVL equations will always equal the third.
(so long as you don't multiply one by a factor for no particular reason)
14. Feb 23, 2013
### InvalidID
I think I got it now. Is this correct?
#### Attached Files:
• ###### Untitled.png
File size:
17.2 KB
Views:
101
15. Feb 23, 2013
### tiny-tim
yes, that looks ok now
always draw the arrows for KVL like that!
(i think you were getting confused with mesh analysis, where there's one circular arrow for the whole of each loop)
16. Feb 23, 2013
### InvalidID
Kind of embarrassing question, but I forget why VE is negative in the main loop.
17. Feb 23, 2013
### tiny-tim
why shouldn't it be?
if you go clockwise round both the left and the main loop, why would you make the two VEs different?
18. Feb 23, 2013
### InvalidID
Well, we would want to be consistent so they would either both be positive or negative. We're going from the negative end to the positive end of the battery but why does that give negative voltage? Because the positive end is 15V higher than the negative end? So going from negative to positive, it would be -15V?
Also, VR2 is negative in the right loop because we're going in the clockwise direction when doing KVL which is in the opposite direction of i2, right?
19. Feb 23, 2013
### tiny-tim
i can never remember which way round the battery works!
but i'm not taking the exams, so i don't need to!
you'll just have to remember it
(btw, you can use the X2 button twice: VR2: isn't that cute? )
yes, i2 is positive in one loop but negative in the other loop, because the arrows go opposite ways
(you get the same thing in mesh analysis: the arrows always go different ways for any section that's in two loops)
Similar Discussions: Need help applying Kirchhoff's voltage law
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8539584875106812, "perplexity": 1285.6260058724497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823839.40/warc/CC-MAIN-20171020063725-20171020083725-00844.warc.gz"}
|
http://cerco.cs.unibo.it/changeset/1786
|
# Changeset 1786
Ignore:
Timestamp:
Feb 27, 2012, 6:40:46 PM (8 years ago)
Message:
...
File:
1 edited
Unmodified
Removed
• ## Deliverables/D1.2/CompilerProofOutline/outline.tex
r1785 \label{subsect.rtlabs.rtl.translation} \subsubsection*{Translation of values and memory} The RTLabs to RTL translation pass marks the frontier between the two memory models used in the CerCo project. As a result, we require some method of translating between the values that the two memory models permit. property of $\sigma$ to be proved. \subsubsection*{Translation of RTLabs states} RTLabs states come in three flavours: \begin{displaymath} \end{figure} \subsubsection*{The forward simulation proof} The forward simulation proof for all steps that do not involve function calls are lengthy, but routine. They consist of simulating a front-end operation on front-end pseudo-registers and the front-end memory with sequences of back-end operations on the back-end pseudo-registers and back-end memory. We sketch here what happens on the source code and on its translation. \subparagraph{Function call/return in RTLabs} \begin{displaymath} \begin{array}{rcl} \mathtt{Call(id,\ args,\ dst,\ pc),\ State(Frame^*, Frame)} & \longrightarrow & \mathtt{Call(M(args), dst)}, \\ & & \mathtt{PUSH(Frame[PC := after\_return])} \mathtt{Call(id,\ args,\ dst,\ pc) \in State(Frame^*, Frame)} & \longrightarrow & \mathtt{Call(M(args), dst)}, \\ & & \mathtt{PUSH(Frame[pc := after\_return])} \end{array} \end{displaymath} \begin{array}{rcl} \mathtt{Call(M(args), dst)}, & \stackrel{\mathtt{ret\_val = f(M(args))}}{\longrightarrow} & \mathtt{Return(ret\_val,\ dst,\ PUSH(...))} \\ \mathtt{PUSH(current\_frame[PC := after\_return])} & & \mathtt{PUSH(current\_frame[pc := after\_return])} & & \end{array} \end{displaymath} \begin{displaymath} \begin{array}{rcl} \mathtt{Call(M(args), dst)} & \longrightarrow & \mathtt{SP = alloc,\ regs = \emptyset[- := params]} \\ \mathtt{PUSH(current\_frame[PC := after\_return])} & & \mathtt{State(regs,\ sp,\ pc_\emptyset,\ dst)} \mathtt{Call(M(args), dst)} & \longrightarrow & \mathtt{sp = alloc,\ regs = \emptyset[- := params]} \\ \mathtt{PUSH(current\_frame[pc := after\_return])} & & \mathtt{State(regs,\ sp,\ pc_\emptyset,\ dst)} \end{array} \end{displaymath} Here, execution of the \texttt{Call} state first pushes the current frame with the program counter set to the address following the function call. The stack pointer allocates more space, the register map is initialized first to the empty map, assigning an undefined value to all register, before the value of the parameters is inserted into the map into the argument registers, and a new \texttt{State} follows. After this, the stack pointer is freed and a \texttt{Return} state is entered: A new stack frame is allocated and its address is stored in the stack pointer. The register map is initialized first to the empty map, assigning an undefined value to all register, before the value of the parameters is inserted into the map into the argument registers, and a new \texttt{State} follows. Eventually, a Return instruction is faced, the return value is fetched from the registers map, the stack frame is deallocated and a Return state is entered: \begin{displaymath} \begin{array}{rcl} \mathtt{sp = alloc,\ regs = \emptyset[- := PARAMS]} & \longrightarrow & \mathtt{free(sp)} \\ \mathtt{State(regs,\ sp,\ pc_\emptyset,\ dst)} & & \mathtt{Return(M(ret\_val), dst, Frames)} \mathtt{Return(id,\ args,\ dst,\ pc) \in State(Frame^*, Frame)} & \longrightarrow & \mathtt{free(sp)} \\ & & \mathtt{Return(M(ret\_val), dst, Frames)} \end{array} \end{displaymath} Then the return state restores the program counter by popping the stack, and execution proceeds in a new \texttt{State}, like the case for external functions: \begin{displaymath} \end{displaymath} Translation from RTLabs to RTL states proceeds as follows. Return states are translated as is: \subparagraph{The RTLabs to RTL translation for function calls} Return instructions are translated to return instructions: \begin{displaymath} \mathtt{Return} \longrightarrow \mathtt{Return} \end{displaymath} \texttt{Call} states are translated to \texttt{Call\_ID} states: \begin{displaymath} \mathtt{Call(id,\ args,\ dst,\ pc)} \longrightarrow \mathtt{Call\_ID(id,\ \sigma'(args),\ \sigma(dst),\ pc)} \end{displaymath} Here, $\sigma$ and $\sigma'$ are two maps to be defined between pseudo-registers and lists of pseudo-registers, of the type: \begin{displaymath} \sigma: \mathtt{register} \rightarrow \mathtt{list\ register} \end{displaymath} and: \begin{displaymath} \sigma': \mathtt{list\ register} \rightarrow \mathtt{list\ register} \end{displaymath} where $\sigma'$ is implemented as: \begin{displaymath} \sigma' = \mathtt{flatten} \circ \sigma \end{displaymath} \texttt{Call} instructions are translated to \texttt{Call\_ID} instructions: \begin{displaymath} \mathtt{Call(id,\ args,\ dst,\ pc)} \longrightarrow \mathtt{CALL\_ID(id,\ \Sigma'(args),\ \Sigma(dst),\ pc)} \end{displaymath} Here $\Sigma$ is the map, computed by the compiler, that translate pseudo-registers holding front-end values to list of pseudo-registers holding the chunks for the front-end values. The specification for $\Sigma$ is that for every state $s$, $$\sigma(s(r)) = (\sigma(s))(\Sigma(r))$$ \subparagraph{Function call/return in RTL} In the case of RTL, execution proceeds as follows. Then a case split occurs depending on whether we are executing an internal or an external function, as in the RTLabs case: \begin{displaymath} \hspace{-3.5cm} \begin{diagram} & & \llbracket \mathtt{CALL\_ID}(\mathtt{id}, \mathtt{args}, \mathtt{dst}, \mathtt{pc})\rrbracket & & \\ & \ldTo^{\text{external}} & & \rdTo^{\text{internal}} & \\ \skull & & & & \mathtt{regs} = [\mathtt{params}/-] \\ & & & & \mathtt{sp} = \mathtt{ALLOC} \\ & & & & \mathtt{PUSH}(\mathtt{carry}, \mathtt{regs}, \mathtt{dst}, \mathtt{return\_addr}), \mathtt{pc}_{0}, \mathtt{regs}, \mathtt{sp} \\ \skull & & & & \begin{array}{l} \mathtt{sp = alloc,\ regs = \emptyset[- := params]} \\ \mathtt{PUSH}(\mathtt{carry}, \mathtt{regs}, \mathtt{dst}, \mathtt{return\_addr}), \mathtt{pc}_{0}, \mathtt{regs}, \mathtt{sp} \end{array} \end{diagram} \end{displaymath} Note, in particular, that this final act of pushing a frame on the stack leaves us in an identical state to the RTLabs case, where the instruction \begin{displaymath} \mathtt{PUSH(current\_frame[PC := after\_return])} \end{displaymath} was executed. \mathtt{PUSH(current\_frame[pc := after\_return])} \end{displaymath} was executed. To summarize, up to the different numer of transitions required to do the job, the RTL code for internal function calls closely simulates the RTLabs code. The execution of \texttt{Return} in RTL is similarly straightforward, with the return address, stack pointer, and so on, being computed by popping off the top of the stack, and the return value computed by the function being retrieved from memory: \begin{align*} \mathtt{return\_addr} & := \mathtt{top}(\mathtt{stack}) \\ v* & := M(\mathtt{rv\_regs}) \\ v^* & := M(\mathtt{rv\_regs}) \\ \mathtt{dst}, \mathtt{sp}, \mathtt{carry}, \mathtt{regs} & := \mathtt{pop} \\ \mathtt{regs}[v* / \mathtt{dst}] \\ \mathtt{regs}[v^* / \mathtt{dst}] \\ \end{align*} To summarize, the forward simulation diagrams for function call/return XXX Translation and execution must satisfy a pair of commutation properties for the \texttt{Return} and \texttt{Call} cases. \subsection{The ERTL to LTL translation} \label{subsect.ertl.ltl.translation} During the ERTL to LTL translation pseudo-registers are stored in hardware registers or spilled on to the stack frame. The decision is based on liveness analysis of the ERTL code to determine what pair of pseudoregisters are live at the same time at a given location. A coloring algorithm is then used to choose where to store the pseudo-registers, allowing pseudo-registers that are never live at the same time to share the same location. We will not certify any coloring algorithm or control flow analysis. Instead, we axiomatically assume the existence of solutions to the coloring and liveness problems. In a later phase we plan to validate the solutions by writing and certifying the code of a validator. We describe the liveness analysis and colouring analysis first and then the ERTL to LTL translation. Throughout this section, we denote pseudoregisters with the type $\mathtt{register}$ and hardware ones with $\mathtt{hdwregister}$. \subsubsection{Liveness analysis} \newcommand{\declsf}[1]{\expandafter\newcommand\expandafter{\csname #1\endcsname}{\mathop{\mathsf{#1}}\nolimits}} \declsf{Livebefore} \declsf{Eliminable} \declsf{StatementSem} Throughout this section, we denote pseudoregisters with the type $\mathtt{register}$ and hardware ones with $\mathtt{hdwregister}$. For the liveness analysis, we aim at a map is the type of sets of registers\footnote{More precisely, it is the lattice of pairs of sets of pseudo-registers and sets of hardware registers, with pointwise operations.}, we also have have the following with pointwise operations.}), we also have have the following predicates: We mark a certain colouring with a subscript if we want to specify in which internal function it is taken. \subsubsection{The translation} For example: (with appropriate cost-labelled trace preservation which we omit). We will call $S\mathrel \sigma T$ the inductive hypothsis, as it will be such in the complete proof by induction on the trace of the program. As usual, this step be done by cases As usual, this step is done by cases on the statement at $\ell(S)$ and how it is translated. We carry out in some detail a single case, the one of a binary operation on registers. Total & 14630 & 3.75 \permil & 49.30 & 54.0 \\ \end{tabular} \caption{\label{table}Estimated effort} \caption{\label{table} Estimated effort} \end{table} are relative to an early version of CompCert) we computed the ratio between men months and lines of code in CompCert for each CerCo pass. This is shown in the third column of Table~\ref{wildguess}. For those CerCo passes that in the third column of Table~\ref{table}. For those CerCo passes that have no correspondence in CompCert (like the optimizing assembler) or where we have insufficient data, we have used the average of the ratios computed
Note: See TracChangeset for help on using the changeset viewer.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9910369515419006, "perplexity": 7727.594876613316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668334.27/warc/CC-MAIN-20191114081021-20191114105021-00041.warc.gz"}
|
http://donghao.org/2018/03/02/compute-gradients-of-different-part-of-model-in-tensorflow/
|
# Compute gradients of different part of model in Tensorflow
In Tensorflow, we could use Optimizer to train model:
But sometimes, model need to be split to two parts and trained separately, so we need to compute gradients and apply them by two steps:
Then how could we delivery gradients from first part to second part? Here is the equation to answer:
The means ‘intermediate vector’, which is the interface vector between first-part and second-part and it is belong to both first-part and second-part. The is the weights of second part of model. Therefore we could use tf.gradients() to connect gradients of two parts:
This site uses Akismet to reduce spam. Learn how your comment data is processed.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 3, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3968830406665802, "perplexity": 2327.3418484055032}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156780.2/warc/CC-MAIN-20180921033529-20180921053929-00039.warc.gz"}
|
https://www.rdocumentation.org/packages/vcd/versions/1.4-7/topics/agreementplot
|
vcd (version 1.4-7)
# agreementplot: Bangdiwala's Observer Agreement Chart
## Description
Representation of a $$k \times k$$ confusion matrix, where the observed and expected diagonal elements are represented by superposed black and white rectangles, respectively. The function also computes a statistic measuring the strength of agreement (relation of respective area sums).
## Usage
# S3 method for default
agreementplot(x, reverse_y = TRUE, main = NULL,
weights = c(1, 1 - 1/(ncol(x) - 1)^2), margins = par("mar"),
newpage = TRUE, pop = TRUE,
xlab = names(dimnames(x))[2],
ylab = names(dimnames(x))[1],
xlab_rot = 0, xlab_just = "center",
ylab_rot = 90, ylab_just = "center",
fill_col = function(j) gray((1 - (weights[j]) ^ 2) ^ 0.5),
line_col = "red", xscale = TRUE, yscale = TRUE,
return_grob = FALSE,
prefix = "", …)
# S3 method for formula
agreementplot(formula, data = NULL, ..., subset)
## Arguments
x
a confusion matrix, i.e., a table with equal-sized dimensions.
reverse_y
if TRUE, the y axis is reversed (i.e., the rectangles' positions correspond to the contingency table).
main
user-specified main title.
weights
vector of weights for successive larger observed areas, used in the agreement strength statistic, and also for the shading. The first element should be 1.
margins
vector of margins (see par).
newpage
logical; if TRUE, the plot is drawn on a new page.
pop
logical; if TRUE, all newly generated viewports are popped after plotting.
return_grob
logical. Should a snapshot of the display be returned as a grid grob?
xlab, ylab
labels of x- and y-axis.
xlab_rot, ylab_rot
rotation angle for the category labels.
xlab_just, ylab_just
justification for the category labels.
fill_col
a function, giving the fill colors used for exact and partial agreement
line_col
color used for the diagonal reference line
formula
a formula, such as y ~ x. For details, see xtabs.
data
a data frame (or list), or a contingency table from which the variables in formula should be taken.
subset
an optional vector specifying a subset of the rows in the data frame to be used for plotting.
xscale, yscale
logicals indicating whether the marginals should be added on the x-axis/y-axis, respectively.
prefix
character string used as prefix for the viewport name
further graphics parameters (see par).
## Value
Invisibly returned, a list with components
Bangdiwala
the unweighted agreement strength statistic.
Bangdiwala_Weighted
the weighted statistic.
weights
the weight vector used.
## Details
Weights can be specified to allow for partial agreement, taking into account contributions from off-diagonal cells. Partial agreement is typically represented in the display by lighter shading, as given by fill_col(j), corresponding to weights[j].
A weight vector of length 1 means strict agreement only, each additional element increases the maximum number of disagreement steps.
cotabplot can be used for stratified analyses (see examples).
## References
Bangdiwala, S. I. (1988). The Agreement Chart. Department of Biostatistics, University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 1859, https://repository.lib.ncsu.edu/bitstream/handle/1840.4/3827/ISMS_1988_1859.pdf
Bangdiwala, S. I., Ana S. Haedo, Marcela L. Natal, and Andres Villaveces. The agreement chart as an alternative to the receiver-operating characteristic curve for diagnostic tests. Journal of Clinical Epidemiology, 61 (9), 866-874.
Michael Friendly (2000), Visualizing Categorical Data. SAS Institute, Cary, NC.
## Examples
Run this code
# NOT RUN {
data("SexualFun")
agreementplot(t(SexualFun))
data("MSPatients")
# }
# NOT RUN {
## best visualized using a resized device, e.g. using:
## get(getOption("device"))(width = 12)
pushViewport(viewport(layout = grid.layout(ncol = 2)))
pushViewport(viewport(layout.pos.col = 1))
agreementplot(t(MSPatients[,,1]), main = "Winnipeg Patients",
newpage = FALSE)
popViewport()
pushViewport(viewport(layout.pos.col = 2))
agreementplot(t(MSPatients[,,2]), main = "New Orleans Patients",
newpage = FALSE)
popViewport(2)
dev.off()
# }
# NOT RUN {
## alternatively, use cotabplot:
cotabplot(MSPatients, panel = cotab_agreementplot)
# }
Run the code above in your browser using DataCamp Workspace
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4121266007423401, "perplexity": 10936.211462229157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948951.4/warc/CC-MAIN-20230329054547-20230329084547-00370.warc.gz"}
|
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/251/2/112795/a-strictly-ergodic-positive-entropy-subshift-uniformly-uncorrelated-to-the-mobius-function
|
JEDNOSTKA NAUKOWA KATEGORII A+
Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty
Studia Mathematica
Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).
A strictly ergodic, positive entropy subshift uniformly uncorrelated to the Möbius function
Tom 251 / 2020
Studia Mathematica 251 (2020), 195-206 MSC: Primary 37B05; Secondary 37B10, 37A35, 11Y35. DOI: 10.4064/sm180719-13-12 Opublikowany online: 23 August 2019
Streszczenie
A recent result of Downarowicz and Serafin (2019) shows that there exist positive entropy subshifts satisfying the assertion of Sarnak’s conjecture. More precisely, it is proved that if $y=(y_n)_{n\ge 1}$ is a bounded sequence with zero average along every infinite arithmetic progression (the Möbius function is an example of such a sequence $y$) then for every $N\ge 2$ there exists a subshift $\varSigma$ over $N$ symbols, with entropy arbitrarily close to $\log N$, uncorrelated to $y$.
In the present note, we improve the above result. First of all, we observe that the uncorrelation is uniform, i.e., for any continuous function $f:\varSigma \to \mathbb R$ and every $\epsilon \gt 0$ there exists $n_0$ such that for any $n\ge n_0$ and any $x\in \varSigma$ we have $$\bigg |\frac 1n\sum _{i=1}^{n}f(T^ix)\,y_i\bigg | \lt \epsilon .$$ More importantly, by a fine-tuned modification of the construction we create a strictly ergodic subshift with the desired properties (uniformly uncorrelated to $y$ and with entropy arbitrarily close to $\log N$).
The question about these two additional properties (uniformity of uncorrelation and strict ergodicity) has been posed by Mariusz Lemańczyk in the context of the so-called strong MOMO (Möbius Orthogonality on Moving Orbits) property. Our result shows, among other things, that strong MOMO is essentially stronger than uniform uncorrelation, even for strictly ergodic systems.
Autorzy
• Tomasz DownarowiczFaculty of Pure and Applied Mathematics
Wrocław University of Science and Technology
Wybrzeże Wyspiańskiego 27
50-370 Wrocław, Poland
e-mail
• Jacek SerafinFaculty of Pure and Applied Mathematics
Wrocław University of Science and Technology
Wybrzeże Wyspiańskiego 27
50-370 Wrocław, Poland
e-mail
Przeszukaj wydawnictwa IMPAN
Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.
Odśwież obrazek
Odśwież obrazek
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7736853361129761, "perplexity": 2989.7950877407084}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499891.42/warc/CC-MAIN-20230131222253-20230201012253-00818.warc.gz"}
|
https://www.physicsforums.com/threads/newtonian-mechanics-question.166982/
|
# Newtonian Mechanics Question
1. Apr 22, 2007
### robhlee
Hello,
Say you have a frictionless setting. In this setting are two skateboards. One has a waterwheel (or any wheel with fins) propped up on beams so that it is on the skateboard and can freely turn. On the other skateboard is a person standing on it. If the skateboards are one behind the other (like train carts) and the person punches the wheel on a fin so that the wheel spins, what will happen?
In the instant of physical interaction (when the person punches the wheel) the fist/person is exerting a force on the fin, and, according to Newton's Third Law, the fin is exerting a force on the fist/person.
Correct?
If so, since the fin is part of a wheel, the force exerted by the person turns into centripetal acceleration and there is no net force on the waterwheel-skateboard apparatus. Meanwhile, there is a net force being exerted toward the person.
Correct?
If so, the person will be moved and the waterwheel-skateboard will remain stationary relative to its environment, but the water wheel will spin.
Please post any flaws or fallacies in theory you see in this situation.
:rofl: :rofl: :surprised :tongue2: :tongue:
2. Apr 22, 2007
### Staff: Mentor
No. You are missing the force that the skateboard exerts on the person to keep the person from moving. The skateboard does not move.
3. Apr 22, 2007
### robhlee
The only force the skateboard could exert would be friction. This is frictionless. Unless you meant inertia, but thats not force. Force overcomes inertia.
Last edited: Apr 22, 2007
4. Apr 22, 2007
### robhlee
so, russ_watters, your saying if someone flatout pushes you, you wont move because the skateboard is exerting a force back? is that what youre saying?
As far as the situation above is concerned, the person and the skateboard are one thing. If you dont agree, then say a mutant human with wheels on their feet replaces the person on the skateboard.
5. Apr 22, 2007
### Staff: Mentor
By "frictionless" I assume you mean no friction between wheels and floor.
Right! They both accelerate in opposite directions.
Huh? You just pushed on the waterwheel-skateboard--of course there's a net force on it.
The same net force is exerted on both.
Nope.
The tricky thing is that it will be difficult to exert a force on that spinning wheel, but if you do, it will accelerate.
6. Apr 22, 2007
### Crosson
I guess that:
is the crux of your discussion. It sounds similar to various (fallacious) "get rid of the force" ideas I used to have before getting formal training in physics.
I think the misunderstanding occurs in the difference between force and energy; energy is conserved and force is not. If somehow all of the energy of the punch went into the wheel, there would be no kinetic energy to move the person, but the punch is a net force and so it has to move the COM of the person attached to the flywheel.
7. Apr 22, 2007
### robhlee
Crosson, what do you mean by "COM"?
8. Apr 22, 2007
### robhlee
Hey guys,
What I meant by "no net force on the waterwheel-skateboard apparatus" was that there is no net force relative to environment. There is a force, but it is converted to centripetal force, since the fin is part of a wheel, I think.
Doc Al, I know there is a net force exerted on the fin and the fist, HOWEVER, the fin is part of a wheel and thus centripetal acceleration occurs when force is applied to the fin, so looking at the waterwheel/skateboard AS A WHOLE, there is no net DIRECTIONAL force.
Last edited: Apr 22, 2007
9. Apr 22, 2007
### robhlee
Doc Al, the punch is nearly instantaneous, just one punch. (In response to your last comment on your last post)
10. Apr 22, 2007
### robhlee
Wait, wait: "PERSON ATTACHED TO FLYWHEEL"? What do you mean Crosson?
11. Apr 22, 2007
### robhlee
Oh and Crosson, there is no force disappearing. Opposite and equal reactions on fin and person. The main question is, is the reaction onto the fin "converted" into a non-directional centripetal force?
12. Apr 22, 2007
### robhlee
Doc Al, by "frictionless", I mean "frictionless".
13. Apr 22, 2007
### robhlee
By "accelerate", do you mean the wheel's spinning or the movement of the waterwheel-skateboard?
14. Apr 22, 2007
### robhlee
sorry for the numerous posts, guys. Also I appreciate all your help.
15. Apr 22, 2007
### Staff: Mentor
Sure there's a net horizontal force on both. And forces don't "convert". True, if the wheel spins there'll be a centripetal force acting on all parts of it--but that's not the force that you hit it with.
Nope. Did you exert a horizontal force on it? Yes. Then there's a net force on it AS A WHOLE. Regardless of whether the wheel spins or not.
So?
16. Apr 22, 2007
### Staff: Mentor
I mean that the center of mass (COM) of the system will accelerate--the whole waterwheel-skateboard system.
17. Apr 22, 2007
### robhlee
Doc Al,
I know forces dont "convert", I felt iffy typing that word :), but the centripetal force is the result of the force on the fin.
Say the wheel was locked, it didnt spin. Comparing locked wheel punching and unlocked wheel punching, would you get the same result?
Oh, I said the punch was instantaneous just for your clarification. It seemed my first description was not clear enough.
18. Apr 22, 2007
### Staff: Mentor
The spinning is the result of the impulse you delivered with your punch.
Sure, if you delivered the same impulse--the same force for the same time. But you'd most likely be able to exert more force on the locked wheel.
Regardless: However you did it, if you delivered a horizontal impulse to the waterwheel-skateboard system, its total momentum will change--it's center of mass will move. No way around it.
19. Apr 22, 2007
### robhlee
Hey thanks. I dont wanna waste your time anymore, so could you tell me where I can get more information related to this on center of mass?
20. Apr 22, 2007
### robhlee
Wait one second...if you say the horizontal force of a locked and unlocked wheel would result in the same effect, in the unlocked wheel at any instant of movement there is an opposite side with equal momentum acting the opposite direction..so is there a net momentum?
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8863489627838135, "perplexity": 1837.6865545587596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542765.40/warc/CC-MAIN-20161202170902-00253-ip-10-31-129-80.ec2.internal.warc.gz"}
|
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-8-section-8-4-circumference-and-area-of-a-circle-exercises-page-374/36
|
## Elementary Geometry for College Students (6th Edition)
Given A track is to be constructed around the football field at a junior high school. If the straightaways are 100 yd in length, The total length around the track is 440yd The total length of the track = 100 +100 + 2*Circumference of the two semi circles = 100 + 100 + 2$\frac{2\pi r}{2}$ 440 yd = 200 + 2($\pi$ r) 2($\pi$ r) = 440 -200 2($\pi$ r) = 240 $\pi$ r = $\frac{240}{2}$ r = $\frac{120}{\pi}$ = 38.19 yd
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3483844995498657, "perplexity": 1457.7108419010924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986657586.16/warc/CC-MAIN-20191015055525-20191015083025-00033.warc.gz"}
|
https://cdn-macroaxis.netdna-ssl.com/invest/technicalIndicator/QADB.BE/Standard-Deviation
|
# Standard Deviation
The Standard Deviation is a measure of how spread out the prices or returns of an asset are on average. It is the most widely used risk indicator in the field of investing and finance. Standard Deviation is commonly used to measure confidence in statistical conclusions regarding certain equity instruments or portfolios of equities.
## Standard Deviation = SQRT(V)
Standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected market volatility. A large standard deviation usually indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
## Standard Deviation In A Nutshell
The more volatile a given equity instrumet, the larger its standard deviation. Standard deviation helps money managers to capture volatility of the portfolio into a single number. For most traded equities, future monthly returns are usually destributed within one standard deviation of its average return (68% of the time), and within two standard deviations 95% of the time.
The standard deviation is one of the main statistical indicators commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. In finance and investing Standard Deviation is usually used to measure risk.
## Closer Look at Standard Deviation
Other deviation levels to watch out for are the 1.5 and 2 standard deviation level. At 2 standard deviations, the likely hood that your data point occurs within 2 standard deviations increases to roughly 95%. Again, just like any tool, this may not be 100% accurate, but it certainly have proven true more times than not. Using standard deviation is simple statistics and it takes emotion out of the picture. Another way people use standard deviation is to incorporate volume, which takes a little time to master the equation, but is certainly possible. Identifying what tools to use for you investing needs can take time, but a standard deviation tool is one to keep your eye on. It is reliable compared to the others and has proven to be one of the more useful out of the many that exist.
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8596211671829224, "perplexity": 643.6037054973323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711475.44/warc/CC-MAIN-20221209181231-20221209211231-00354.warc.gz"}
|
https://mathematica.stackexchange.com/questions/86505/ubuntu-dynamics-are-not-working-after-suspending-system
|
# Ubuntu: Dynamics are not working after suspending system
I'm working on Ubuntu 14.04 LTS 64-bit and I'm running Mathematica 10.1. Usually, I don't turn my computer completely off but I'm using the Suspend function which is AFAIK a suspend to RAM.
After waking the computer, everything is normal except that I cannot use any dynamic content inside Mathematica. Specifically, this means I see e.g. Manipulate regions normally, but I cannot move any slider. Let me clear this further. For this simple example
Manipulate[Plot[Sin[x (1 + a x)], {x, 0, 6}], {a, 0, 2}]
• I cannot move the slider a
• I can press the + signs and the slider controls open. There
• I can input a value manually and it is applied to the graphic
• I cannot press any buttons, although the buttons are highlighted when I move the mouse over them.
• I can "hide the controls" on the + sign in the very top right corner and all other things like "Autorun" seems to work too.
• During the autorun, I can pause the animation but I'm not able to start it again. The "close" button works. All other buttons don't.
The problem is fixed by restarting Mathematica (a Kernel quit is not enough).
The question is: Does someone have the same problem? Is it possible to fix this problem?
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17068445682525635, "perplexity": 1736.2005651793725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737039.58/warc/CC-MAIN-20200806210649-20200807000649-00107.warc.gz"}
|
https://blog.mbedded.ninja/programming/embedded-linux/yocto-project/premade-recipes/
|
YOCTO PROJECT
A SSH server can be a very useful thing to have in a embedded Linux build. It enables things such as scp (secure copy, allowing you to copy files between the embedded device to a development computer over the internet).
You should be able to add a SSH server by adding the following line to your build/conf/local.conf file.
EXTRA_IMAGE_FEATURES += "ssh-server-openssh"
## Add Python To A Build
Add the following line of code to your build/conf/local.conf file:
IMAGE_INSTALL_append = " python-core"
## Add Boost To A Build
Add the following line of code to your build/conf/local.conf file:
IMAGE_INSTALL_append = " boost"
When adding boost, it is work recreating the SDK so that you have the available libraries for cross-compiling.
Valgrind is provided under meta/recipes-devtools/valgrind. As of Nov 2017, Valgrind v3.12.0 is supported. Valgrind can be added to your Yocto image by adding the following line of code to your build/conf/local.conf file:
IMAGE_INSTALL += " valgrind"
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3410428464412689, "perplexity": 5348.918888428866}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594391.21/warc/CC-MAIN-20200119093733-20200119121733-00498.warc.gz"}
|
https://www.actuaries.digital/2015/04/24/bitcoins-banking-and-the-blockchain/
|
Throughout history, money has taken on many different forms, such as gold and other precious metals, salt, cattle, slaves, cocoa beans, alcohol, cigarettes, coins, paper notes, and certificates of deposit. Money derives its value purely from the confidence and trust that everyone else places in it. The recent innovation of bitcoins has pushed the boundaries by allowing money to evolve into the ethereal form of digital 0s and 1s.
At a recent Sydney Financial Mathematics Workshop, Sean Carmody (Head of Credit Risk at Westpac) delivered a seminar on the history, mechanics and implications of bitcoin technology on the banking industry and society.
# Why bitcoins?
Ever since the internet has formed a global marketplace, the desire for a universal decentralised currency arose to facilitate international payments, reduce transaction costs and provide anonymity and privacy. But the simple idea of digital money, free from the control of governments and printing-press-happy central bankers, requires a mechanism to stop fraudsters from counterfeiting or “double-spending” the currency, which might appear to be as easily duplicated as movies and music are pirated online. Early efforts in the 1990s, such as Ecash, bit gold and b-money, failed because they depended on the existing infrastructures of banks and credit card companies.[1]
The eureka moment came on 31 October 2008 when a mysterious person(s) known as Satoshi Nakamoto published an ingenious system that proposed a Peer-to-Peer network to maintain the “blockchain” which is a publicly distributed encrypted ledger of every bitcoin transaction.[2] Such a system would no longer rely on a centralised authority to verify each transaction, but instead uses innovative cryptographic protocols to protect both the integrity of the currency and the anonymity of every party. Strangely enough, the true identity of the inventor is yet to be uncovered, but many have speculated it may be Julian Assange or even possibly a team of researchers at Google or the National Security Agency. [3]
The aftermath of the 2007/08 Global Financial Crisis catalysed a libertarian movement which lost faith in Wall Street bankers and politicians to rescue the banking system with “quantitative easing”, essentially printing money to jump-start the economy. Nakamoto argued that “The root problem with conventional currency is all the trust that’s required to make it work. The central bank must be trusted not to debase the currency, but the history of fiat currencies is full of breaches of that trust. Banks must be trusted to hold our money and transfer it electronically, but they lend it out in waves of credit bubbles with barely a fraction in reserve.
# How does it work?
Bitcoins are stored in virtual wallets, which are protected with a private key known only to the owner. Transactions allow bitcoins to be transferred from one wallet to another (e.g. “payer X sends Y bitcoins to payee Z”), which are validated and broadcast into the network. Bitcoin miners bundle transactions into blocks through a computational brute force process, rewarding the lucky miner with newly created bitcoins, which acts as an incentive to support the network. The chronological history of all blocks is linked together into the blockchain (currently over 30GB and growing). Figure 1 provides an illustration of the bitcoin payment process.
The very first block of 50 bitcoins, known as the genesis block, was mined by Nakatomo himself on 3 January 2009, in which he permanently embedded the Times of London newspaper headline “Chancellor on brink of a second bailout for banks[4]. The supply of bitcoins has been designed to increase steadily at 25 bitcoins per block mined (about every 10 minutes), then halving to 12.5 bitcoins per block and so on halving every 4 years. This will continue until the ultimate limit of 21 million bitcoins is reached by 2140 and miners will be rewarded for their computationally intensive record keeping services solely through transaction fees.
Figure 1: Operation of the P2P network in keeping the blockchain up to date with the latest transactions
Bitcoins are able to be transferred in almost any amount, with one bitcoin able to be divided into 100 million satoshis, the smallest unit. As at April 2015, there are 14 million bitcoins in circulation worth about $US3.6 billion, with increasingly formidable computing power needed to stand any chance at mining new bitcoins. Proponents argue that such a fixed money supply will eliminate inflation and provide a competitive alternative to the typical 2-3% credit card payment processing fees.[5] Figure 2: Dedicated bitcoin mining hardware underground in northern Sweden # Why does it work? The bitcoin scheme is based on the mathematics of public key cryptography, a pioneering invention from the 1970s, which allows two parties to communicate securely over an insecure channel, allowing for the fact that a malicious eavesdropper may intercept and deliberately alter messages to mislead either party. This technology is critical to the functioning of e-commerce and the secure operation of the internet. Such a cryptographic scheme requires a pair of mathematically linked keys for each user: a public key published for everyone to see and a private key to keep secret, analogous to a padlock and key, which are used together for: • Confidentiality through encryption / decryption (to stop an eavesdropper from reading your messages) and • Authentication with a digital signature (to prove that the messages actually come from the sender) Security is ensured through the use of cryptographic hash functions, which are easy to compute for a given input, but are very difficult to reverse engineer for a given output (also known as a type of trapdoor function). As a simple analogy, adding up the letters in the name of an animal (assuming A=1, B=2, C=3 etc.) might give HORSE as 8+15+18+19+5=65. This function is easy to compute for any given animal, but it is very time-consuming to find out the animal for a given sum. Figure 3: The chain of ownership of a bitcoin. A bitcoin can be represented as a series of transactions between successive owners such that only the current owner can “spend” it by digitally signing the next transaction and anyone can verify who the coin currently belongs to. The bitcoin protocol uses the current state-of-the-art algorithms, such as SHA-256 (Secure Hash Algorithm) and the Elliptic Curve Digital Signature Algorithm known as secp256k1. In a similar fashion, bitcoin miners use dedicated computer hardware to solve these complex hash functions, generating a “proof-of-work” for each block that verifies the authenticity and irreversibility of each transaction. # Attacking the system Can bitcoins be stolen by modifying the blockchain? Many currencies are protected by advanced security measures such as Australian polymer banknotes with microprinting and clear plastic windows. In contrast, the integrity of the blockchain is demonstrated with a simple probabilistic argument. As the consensus rule for the network is to always accept the longest blockchain starting with the genesis block as the official one, it is proven that the only way for an attacker (counterfeiter) to publish an alternate longer blockchain of fake transactions is to control more than 50% of the total CPU processing power of the entire network (known as the 51% attack). As Nakamoto explains, “If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. We will show that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added.” Thus, the system is designed to take advantage of the fact that information is easy to spread, but hard to stifle. The race between the honest chain and an attacker’s chain can be modelled as a Binomial Random Walk. The probability of an attacker ever catching up from a given deficit is reminiscent of the classic actuarial problem of Gambler’s Ruin, which can be applied to give the following result:[6] Similarly, we can determine how long the recipient of a new transaction needs to wait before being sufficiently certain the sender can’t change the transaction. As a block moves deeper into the blockchain, the probability of it being invalid shrinks exponentially. The current market convention is to wait for 6 blocks to confirm a transaction, which gives a probability of 0.02428% of fraud for an attacker with 10% of the total computing power in the network, as seen in Figure 4. Figure 4: The probability of fraud (P) after confirmation of various numbers of blocks, assuming an attacker’s computing power (q) is 10% of the total network. # The challenges The anonymity of bitcoin makes it the currency of choice for the online black market with websites such as The Silk Road, Black Market Reloaded and Utopia where users can purchase child pornography, illicit drugs, stolen credit cards, weapons and even murder-for-hire services. Such websites on the Dark Web can only be accessed through special anonymity software such as ToR (The Onion Router), which directs Internet traffic through a worldwide network of more than six thousand relays to conceal the user’s identity and location. The currency has also posed challenges for authorities to monitor Anti-Money Laundering, Counter-Terrorism Financing and tax evasion, which is ironic given that all transactions are broadcast publicly in the blockchain (even though the identities of each party are kept secret). Some bitcoin startups have complained that, “banks are scared to deal with bitcoin companies, even if they really want to”[8], due to the reputational risks of being linked to illicit activities, such as NAB and HSBC in 2014 refusing to serve clients with ties to bitcoin.[9] Some skeptics have labelled bitcoin as ‘BitCon’[10], or simply the “21st century Ponzi scheme”, with the whole mythical anonymous founder story as a sexy marketing trick. It is all the more suspicious that Nakamoto himself is believed to be in possession of about one million bitcoins ($US300 million).[11] However, as University of Chicago law professor Eric Posner pointed out “A real Ponzi scheme takes fraud; bitcoin, by contrast, seems more like a collective delusion.”[12]
However, some evangelists are much more optimistic about the role of bitcoin as a global currency. It may have the potential to help the developing world’s 2.5 billion unbanked to connect to the formal financial system, with stories like that of an Afghan woman who gets paid in bitcoin for the articles she writes for an American website.[13] Another author has suggested that bitcoin will be a “force for peace” because governments will be unable to raise money for long wars if the universal currency is widely adopted.[14]
The price of the startup currency has gone through a rollercoaster ride, with annual volatility about 7 times greater than gold and 18 times greater than the US dollar[15], which reflects the uncertainty of its long-term value. Figure 5 shows the extreme price reactions to various historical events.
Figure 5: Selected events in bitcoin price history
(A) 10-Apr-2013: The 2012-13 Cypriot Financial Crisis causes the price of bitcoin to soar to over $260, before crashing to$50. Bitcoin purchases in Cyprus rise due to fears that savings accounts would be confiscated or taxed.
(B) 1-Oct-2013: The Silk Road is shut down by the FBI, causing a flash crash from $133 to$110. The owner Ross Ulbricht (aka Dread Pirate Roberts) is arrested with 174,000 bitcoins seized. Former administrators launch Silk Road 2.0 afterwards, but it is also eventually shut down.
(C) 20-Nov-2013: Price almost doubles to $1200 as People’s Bank of China gives bitcoin the green light. Yi Gang, deputy governor, says that “people are free to participate in the Bitcoin market”. (D) 5-Dec-2013: Price plummets as People’s Bank of China reverses previous sentiment and decides to ban financial institutions from dealing in Bitcoin with guidelines specifying that “it is not considered a currency”. Buying real-world goods with any virtual currency is ruled illegal in China. (E) 24-Feb-2014: A major bitcoin exchange, Mt. Gox (short for “Magic The Gathering Online eXchange”) finally closes down, losing its customers over 744,000 bitcoins ($US400 million). The exchange had suffered through previous controversies such as being hacked, being subject to seizure warrants by the US Department of Homeland Security and being the target of Denial of Service attacks.
# Beyond bitcoin…?
The blockchain of bitcoins has proven its potential to be a real disruption to the financial system which will inspire further innovation. The idea of “crowd-sourced” publicly maintained record-keeping can be applied beyond the banking system and to decentralised exchanges of equities holdings, bonds, derivatives, land titles, and passports. Some more exotic examples include storing digital car keys, betting transactions, patents, copyrights, weapon unlock codes and even nuclear launch codes on the “Blockchain 2.0”. [17]
IBM has started experimenting with a blockchain for payment settlements between the world’s central banks[18], as well as applying the blockchain concept to the “Internet of Things”, which allows consumer devices to be remotely controlled and autonomously maintained e.g. self-driving self-owned taxis which are owned and repaired by the blockchain itself![19]
Regardless of whoever or wherever Satoshi Nakamoto is, at the moment only six years ago that he uploaded a nine page research paper along with 30,000 lines of open-source code, he created a billion dollar market out of thin air and an idea with a life of its own.
[1] Benjamin Wallace, “The Rise and Fall of Bitcoin” from Wired Magazine
http://www.wired.com/2011/11/mf_bitcoin/all/
[2] Satoshi Nakamoto (2008) “Bitcoin: A Peer-to-Peer Electronic Cash System” https://bitcoin.org/bitcoin.pdf
[3] Nakamoto is considered unlikely to be Japanese or living in Japan given his flawless English, the timing of his forum posts and emails imply his time zone lies in the Americas and the fact that the bitcoin system seems too well designed for one person to figure out. However, he tends to use British spellings e.g. optimise, colour
[4] https://en.bitcoin.it/wiki/Genesis_block
[5] http://www.nytimes.com/2013/10/31/technology/bitcoin-pursues-the-mainstream.html?_r=0
[6] William Feller (1957), “An introduction to probability theory and its applications”
[7] Satoshi Nakamoto (2008) “Bitcoin: A Peer-to-Peer Electronic Cash System” https://bitcoin.org/bitcoin.pdf
[8] http://www.bloomberg.com/news/articles/2013-12-05/bitcoin-skepticism-by-bankers-from-china-to-u-s-hinders-growth
[9] http://www.theguardian.com/world/2014/apr/10/bitcoin-dumped-by-national-australia-bank-as-too-risky
[10] Jeffrey Robinson, “BitCon: The naked Truth About Bitcoin”
[11] http://motherboard.vice.com/blog/bitcoin-mints-its-first-billionaire-satoshi-nakamoto
[12] http://www.slate.com/articles/news_and_politics/view_from_chicago/2013/04/bitcoin_is_a_ponzi_scheme_the_internet_currency_will_collapse.html
[14] Dominic Frisby, “Bitcoin: The Future of Money”
[15] http://www.bu.edu/questrom/files/2014/10/Wlliams-World-Bank-10-21-2014.pdf
[16] https://bitcoinhelp.net/know/more/price-chart-history
[17] http://ledracapital.com/blog/2014/3/11/bitcoin-series-24-the-mega-master-blockchain-list
[18] http://www.reuters.com/article/2015/03/12/us-bitcoin-ibm-idUSKBN0M82KB20150312
[19] http://www.marketwatch.com/story/how-bitcoin-technology-could-power-driverless-cars-2015-03-03
CPD: Actuaries Institute Members can claim two CPD points for every hour of reading articles on Actuaries Digital.
### Comment on the article (Be kind)
Your comment will be revised by the site if needed.
Previous
Next
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18686708807945251, "perplexity": 5110.180437153956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402124756.81/warc/CC-MAIN-20201001062039-20201001092039-00208.warc.gz"}
|
https://simonshine.dk/
|
# Simon Shine's Page
$\{\cdot$ Home $\cdot$ Blog $\cdot$ 中文 $\cdot$ GitHub $\cdot$ StackOverflow $\cdot$ $\}$
## Welcome!
You have landed on the personal homepage of Simon Shine. I am a cellular automaton from Copenhagen, Denmark. My favorite prime is
$$2^{64} - 2^{32} + 1$$
because it allows for efficient prime field arithmetic. It is similar to the Goldilocks prime, $2^{448} - 2^{224} - 1$, as the golden ratio is a root of $\phi^2 - \phi - 1$ with $\phi ≡ 2^{224}$, but due to the small offset, this prime is Goldilock-ish.
I'm currently fixated on making Neptune.
I believe that imagination is stronger than knowledge. That myth is more potent than history. That dreams are more powerful than facts. That hope always triumphs over experience. That laughter is the only cure for grief. And I believe that love is stronger than death.
– Robert Fulghum
## Creative writing
Of my available online writing, I consider only Hvorfor må jeg ikke eje en svensker? and Getting recursively drunk with monoids well-written, but you can read a bunch of other small texts on blog.
## Cellular automata and non-square tilings
I sometimes wonder what life is like for other cellular automata. It seems that most hexagonal Game of Life adaptations reduces the complexity rather fast; perhaps hexagonal tiles are better suited for creating order rather than chaos, like Uber's H3. Then how about Penrose tilings, can they sustain life? I wanted to create a browser game using hexagons, but I didn't get very far. Here's a small demo that renders hexagons and reacts when you hover:
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20071324706077576, "perplexity": 3619.8560809510814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104597905.85/warc/CC-MAIN-20220705174927-20220705204927-00351.warc.gz"}
|
http://sportmondo-sportsportal.blogspot.com/2012/08/business-news-garmins-outdoor-and.html
|
02/08/2012
Business news :Garmin's Outdoor and Fitness Segments Set the Pace in Q2
Garmin Ltd. reported that revenue at its Outdoor segment increased 24 percent to $100 million, while Fitness revenues increased 5 percent to$82 million in the second quarter. The company, which also operates Aviation and Marine segments, reported overall sales increase 7 percent to $718 million. In the Outdoor segment growth was driven by golf, dog tracking and training products and Garmin's recently refreshed eTrex series. During the quarter, the company introduced its latest outdoor product, the f¨¥nix wristwatch, which offers both a feature-rich experience for the outdoorsman and also a classic style for everyday use. The fitness segment posted revenue growth of 5 percent in the quarter compared against strong performance in 2011 driven by promotional activity on the Forerunner 305 and the launch of the Forerunner 610. In the current quarter, new products such as the high-end Forerunner 910XT sold well and drove margin expansion for the fitness segment. "In late June, we introduced the Garmin Swim ¨C targeting a new niche for us in the fitness market," said Dr. Min Kao, chairman and chief executive officer of Garmin Ltd. "The product has already been well-received in the swimming community. We anticipate growth rates will improve in the second half of 2012 as we launch new products for the holiday season to drive further market penetration." Garmin's revenue in the Americas reached$392 million, up 9 percent; $269 million in Europe, the Middle East and Africa, up 6 percent; and$57 million in the Asia Pacific, down 9 percent.
Year©\to©\Date Outdoor segment revenue increased 20 percent to $178 million, while Fitness segment revenue increased 14 percent to$153 million. That compared to a 4 percent increase in Aviation segment to $149 million, a 5 percent increase in the Marine segment to$124 million.
In the second quarter of 2012 we again posted strong revenue, unit volumes, and operating income even though the global economy is still difficult,¡± said Kao. ¡°We have had a great first half; yet, we remain cautious given the macroeconomic dynamics facing each of our segments. Based on our first half performance, we are narrowing our full year revenue guidance to $2.75 -$2.80 billion. This represents the high end of our prior range with improvement in auto/mobile and outdoor offset by the remaining segments. We are increasing our EPS guidance to $2.70 -$2.85 due to the outstanding margins in the first half. Overall, we believe we are executing well in both the current environment and in preparation for long-term sustained growth.
(SportsOneSource Media )
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1722533255815506, "perplexity": 5450.290838636075}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413558066265.80/warc/CC-MAIN-20141017150106-00250-ip-10-16-133-185.ec2.internal.warc.gz"}
|
https://www.coursehero.com/subjects/marginal-propensity-to-consume/
|
• ### Marginal Propensity To Consume Q&A
##### Marginal Propensity To Consume Study Resources Q&A View all
• ###### Q. if, C= 120 + 0.9Y, YD= Y + TR - T, T= 100 + 0.1Y, I= 500, G= 600, TR= 200, X= 700 and IM= 300 + 0.2Y a) What is the value of marginal propensity to...
• Not Rated Yet
• ###### Q. Suppose an economy is experiencing a recessionary gap equal to $10 billion. a) If the government does nothing then use the AD/AS model to... • Answer Rating: • 1 file(s) attached • View Answer • ###### Q. Assuming that the economy’s MPC is 2/3 and that the government spending increases by$20 billion, what would be the impact on the equilibrium level...
• Not Rated Yet
• ###### Q. Please fully explain why the answer is what it is in detail (the reason for your answer) *For both bullet points* Bayou Sans Espoir, LA, has been...
• 1 file(s) attached
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7131802439689636, "perplexity": 17053.92758299996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347394756.31/warc/CC-MAIN-20200527141855-20200527171855-00483.warc.gz"}
|
https://www.thejournal.club/c/paper/354372/
|
#### Fast and More Powerful Selective Inference for Sparse High-order Interaction Model
##### Diptesh Das, Vo Nguyen Le Duy, Hiroyuki Hanada, Koji Tsuda, Ichiro Takeuchi
Automated high-stake decision-making such as medical diagnosis requires models with high interpretability and reliability. As one of the interpretable and reliable models with good prediction ability, we consider Sparse High-order Interaction Model (SHIM) in this study. However, finding statistically significant high-order interactions is challenging due to the intrinsic high dimensionality of the combinatorial effects. Another problem in data-driven modeling is the effect of "cherry-picking" a.k.a. selection bias. Our main contribution is to extend the recently developed parametric programming approach for selective inference to high-order interaction models. Exhaustive search over the cherry tree (all possible interactions) can be daunting and impractical even for a small-sized problem. We introduced an efficient pruning strategy and demonstrated the computational efficiency and statistical power of the proposed method using both synthetic and real data.
arrow_drop_up
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9159969091415405, "perplexity": 2592.6103285845584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00124.warc.gz"}
|
https://www.iaa.es/seminars/so-iaa-colloquium-neutral-and-molecular-gas-outflows-tracers-impact-radio-jets
|
# SO-IAA Colloquium: Neutral and molecular gas outflows as tracers of the impact of radio jets
Our view of the gas and its physical conditions in the central region of AGN has been enriched by the discover of fast and massive outflows of HI and molecular gas. These outflows can be driven by radiation/winds but also by the interaction of the radio plasma with the ISM. Understanding the origin and quantifying their impact requires to trace their location and derive their physical conditions (density of the gas, mass, mass outflow rate and kinetic energy of the outflow etc.). Particularly interesting has been the finding that in the first phase of their life, jet in radio galaxies can be particularly effective in driving such outflows. This crucial phase is at the heart of the idea of feedback, therefore particularly relevant for studying feedback in action.
In this talk, I will present some of the results we have obtained to trace jet-driven HI and molecular gas outflows down to scales ranging from hundred to tens of pc. The impact of low-power radio jets will be discussed and the comparison with the predictions from numerical simulations will also be presented.
Outflows of up to few hundred Msun/yr have been found in molecular gas using ALMA while the HI observed with VLBI is showing that the outflowing gas is clumpy as also predicted from numerical simulations. I will describe the kinematics of the gas and its conditions and the relevance they may have for feedback.
Fecha:
31/10/2019 - 12:30
Conferenciante:
Dr. Raffaella Morganti
Filiación:
ASTRON, the Netherlands Institute for Radio Astronomy and Kapteyn Astronomical Institute, University of Groningen
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8290959000587463, "perplexity": 1214.595475654493}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534669.47/warc/CC-MAIN-20220520191810-20220520221810-00537.warc.gz"}
|
https://no.overleaf.com/articles/fsu-math2400-project4/yhrwhphsdpdg
|
# FSU-MATH2400-Project4
Author
Sarah Wright
AbstractThis is the fourth project in Calculus 2 at Fitchburg State. Spring 2017.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.937981903553009, "perplexity": 18784.676096404757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733120.84/warc/CC-MAIN-20201204010410-20201204040410-00033.warc.gz"}
|
http://hal.in2p3.fr/in2p3-00730853
|
# Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) and the direct CP asymmetry in B0 -> K*0 gamma
Abstract : The ratio of branching fractions of the radiative B decays B0 -> K*0 gamma and Bs0 phi gamma has been measured using an integrated luminosity of 1.0 fb-1 of pp collision data collected by the LHCb experiment at a centre-of-mass energy of sqrt(s)=7 TeV. The value obtained is BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) = 1.23 +/- 0.06(stat.) +/- 0.04(syst.) +/- 0.10(fs/fd), where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is associated with the ratio of fragmentation fractions fs/fd. Using the world average value for BR(B0 -> K*0 gamma), the branching fraction BR(Bs0 -> phi gamma) is measured to be (3.5 +/- 0.4) x 10^{-5}. The direct CP asymmetry in B0 -> K*0 gamma decays has also been measured with the same data and found to be A(CP)(B0 -> K*0 gamma) = (0.8 +/- 1.7(stat.) +/- 0.9(syst.))%. Both measurements are the most precise to date and are in agreement with the previous experimental results and theoretical expectations.
Type de document :
Article dans une revue
Nuclear Physics B, Elsevier, 2013, 867, pp.1-18. 〈10.1016/j.nuclphysb.2012.09.013〉
http://hal.in2p3.fr/in2p3-00730853
Contributeur : Claudine Bombar <>
Soumis le : mardi 11 septembre 2012 - 12:05:52
Dernière modification le : jeudi 18 janvier 2018 - 01:49:04
### Citation
R. Aaij, C. Abellan Beteta, A. Adametz, B. Adeva, M. Adinolfi, et al.. Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) and the direct CP asymmetry in B0 -> K*0 gamma. Nuclear Physics B, Elsevier, 2013, 867, pp.1-18. 〈10.1016/j.nuclphysb.2012.09.013〉. 〈in2p3-00730853〉
### Métriques
Consultations de la notice
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9750382900238037, "perplexity": 11750.573718053478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646875.28/warc/CC-MAIN-20180319101207-20180319121207-00696.warc.gz"}
|
https://www.ncbi.nlm.nih.gov/pubmed/10505065
|
Format
Choose Destination
J Reprod Fertil. 1999 May;116(1):143-56.
# Cytoplasmic maturation for activation of pig follicular oocytes cultured and arrested at metaphase I.
### Author information
1
Department of Genetic Resources II, National Institute of Agrobiological Resources, Ibaraki, Japan.
### Abstract
A large population (62-90%) of pig follicular oocytes can mature to metaphase II after culture for 48 h. However, a proportion (6-22%) remain in an immature stage at metaphase I (metaphase I-arrested). The main objective of this study was to determine whether the cytoplasm of metaphase I-arrested pig oocytes is capable of being activated by sperm penetration or parthenogenetic stimulation. After culture for 48 h, oocytes without a polar body (73% were shown to be at metaphase I after staining) and those with a polar body (94% were at metaphase II) were fertilized in vitro. A total of 69% and 62% of the oocytes were activated to form a female pronucleus, respectively, and the rate of polar body extrusion induced by fertilization in the activated oocytes was 90% (the first polar body) and 95% (the second polar body), respectively. When oocytes without and with a polar body were stimulated with an electric pulse, 53% and 81% of the oocytes were activated, respectively. The rate of polar body extrusion in the activated oocytes was 73% (the first polar body) and 79% (the second polar body), respectively. In contrast, young metaphase I oocytes cultured for 24 h had low (6%) or zero activation rate after in vitro fertilization or electric pulse stimulation. However, about one-third of the young metaphase I oocytes penetrated by spermatozoa after in vitro fertilization responded to electric pulse 12 h after insemination, and almost all (93%) were activated when they were stimulated 24 h after insemination. Patterns of polypeptide synthesis and histone H1 kinase activity were similar in metaphase I-arrested and metaphase II oocytes, and were characterized by increase in a 25 kDa polypeptide and by decrease in kinase activity. Although the first step of meiotic division is impaired, these results indicate that metaphase I-arrested oocytes are mature cytoplasmically.
PMID:
10505065
[Indexed for MEDLINE]
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.897894024848938, "perplexity": 14630.648773912864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202872.8/warc/CC-MAIN-20190323141433-20190323163433-00312.warc.gz"}
|
http://clay6.com/qa/7684/find-the-magnitude-of-overrightarrow-times-overrightarrow-if-overrightarrow
|
# Find the magnitude of $\overrightarrow{a} \times \overrightarrow{b}$ if $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{b}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$
Toolbox:
• If $\overrightarrow a = a_1\overrightarrow i+a_2\overrightarrow j+a_3\overrightarrow k, \: \overrightarrow b = b_1\overrightarrow i+b_2\overrightarrow j+b_3\overrightarrow k$ then $\overrightarrow a$ x $\overrightarrow b = \begin{vmatrix} \overrightarrow i & \overrightarrow j & \overrightarrow k \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$
$\overrightarrow a$ x $\overrightarrow b = \begin{vmatrix} \overrightarrow i & \overrightarrow j & \overrightarrow k \\ 2 & 0 & 1 \\ 1 & 1 & 1 \end{vmatrix} = (0-1)\overrightarrow i-(2-1)\overrightarrow j+(2-0)\overrightarrow k$
$= -\overrightarrow i-\overrightarrow j+2\overrightarrow k$
$|\overrightarrow a$ x $\overrightarrow b| = \sqrt{1+1+4}= \sqrt 6$
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9834139943122864, "perplexity": 894.6024073801566}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863570.21/warc/CC-MAIN-20180520131723-20180520151723-00258.warc.gz"}
|
https://www.physicsforums.com/threads/dirac-proves-0-1.122063/
|
# Dirac Proves 0 =1
1. May 26, 2006
### George Jones
Staff Emeritus
Dirac Proves 0 = 1
Suppose $A$ is an observable, i.e., a self-adjoint operator, with real eigenvalue $a$ and normalized eigenket $\left| a \right>$. In other words,
$$A \left| a \right> = a \left| a \right>, \hspace{.5 in} \left< a | a \right> = 1.$$
Suppose further that $A$ and $B$ are canonically conjugate observables, so
$$\left[ A , B \right] = i \hbar I,$$
where $I$ is the identity operator. Compute, with respect to $\left| a \right>$, the matrix elements of this equation divided by $i \hbar$:
$$\begin{equation*} \begin{split} \frac{1}{i \hbar} \left< a | \left[ A , B \right] | a \right> &= \left< a | I | a \right>\\ \frac{1}{i \hbar} \left( \left< a | AB | a \right> - \left<a | BA | a \right> \right) &= <a|a>. \end{split} \end{equation*}$$
In the first term, let $A$ act on the bra; in the second, let $A$ act on the ket:
$$\frac{1}{i \hbar} \left( a \left< a | B | a \right> - a \left<a | B | a \right> \right)= <a|a>.$$
Thus,
$$0 = 1.$$
This is my favourite "proof" of the well-known equation $0 = 1$.
What gives?
In order not spoil other people's fun, it might be best to put "spoiler" at the top of any post that explains what's happening.
Regards,
George
Last edited: Feb 28, 2012
2. May 26, 2006
I don't think you can do that because A and B don't commute?
3. May 26, 2006
### George Jones
Staff Emeritus
That step is OK.
One way to see this is to take |b> = A|a> and |c> = B|a>, and then to consider <b|c>.
Any is to to look at (AB)^* = B^* A^* = B A, which takes care of the order of the operators.
Regards,
George
4. May 26, 2006
Staff Emeritus
Isn't this the one about the domains of the operators?
5. May 26, 2006
### George Jones
Staff Emeritus
I don't think the problem is with domains. I think it is possible for the intersection of the domains of A, B, and [A , B] to be dense, and to still have the proof be "true".
Regards,
George
6. May 26, 2006
### waht
Interesting, but the proof is based on an assumption that A and B are canonically conjugate observables. Therefore 0=1 is constrained to that condition.
how does <a|[A,B]|a> = <a|AB|a> - <a|BA|a>
btw?
7. May 26, 2006
### Physics Monkey
Spoiler Below!
What a wonderful proof! I have never seen this one before, George. My discussion is below.
***SPOILER***
Think about the real line where we can represent the algebra by the usual quantum mechanical operators X and P. The key is to realize that X and P have no normalizable eigenvectors! The usual "normalization" for position "eigenstates" (lots of scare quotes) is $$\langle x | x' \rangle = \delta(x-x')$$, so let's have some fun with this formula. Since X and P are canonically conjugate we have that $$[X,P] = i \hbar$$, and we can take matrix elements of both sides. The right side is $$\langle x | i \hbar | x' \rangle = i \hbar \delta(x-x')$$. The left side is $$(x - x')( - i \hbar \frac{d}{dx} \delta(x-x'))$$ where I have used $$\langle x | P = - i \hbar \frac{d}{dx} \langle x |$$. Thus we appear to have stumbled onto the rather cute identity $$- x \frac{d}{dx} \delta(x) = \delta(x)$$. Go ahead, try it under an integral, it actually works! I love such silly little formulae between wildly singular objects.
A further amusing challenge:
It isn't always true that the derivative operator has no eigenstates. Suppose you look at the derivative operator on a finite interval. It turns out that the Neumann indices are (1,1), and thus self adjoint extensions exist which are parameterized by a phase (the boundary condition). One can now find proper eigenfunctions and eigenvalues for a given self adjoint extension of the derivative operator. Are we therefore back to proving that 0 = 1 or what?
Last edited: May 26, 2006
8. May 26, 2006
### mikeu
Except you can always find such A and B, so you can always find 0=1..... :)
It's just the definition of the commutator and linearity of the inner product:
$$\langle a | [A,B] | a\rangle = \langle a | (AB-BA) | a \rangle = \langle a | AB | a \rangle - \langle a | BA | a \rangle$$.
*** SPOILER cont. ***
I suspected (based on X and P ) that delta distributions would enter into it, since we end up with $$\frac{1}{i\hbar}(a-a)\langle a|B|a\rangle=1$$ so it is clear that $$\langle a|B|a\rangle$$ must be ill-defined (i.e. infinite) to get something like "$$0\cdot\infty=1$$." Recovering the definition of the derivative of the delta was neat. What I still don't see though is what the flaw in the proof is in the case of discrete operators...?
George, I thought of another 'interpretation' of the 'proof' too: you could prove 0=ih => h=0 => things aren't quantized
9. May 26, 2006
### George Jones
Staff Emeritus
So, you want to take A = P and B = X for the Hilbert space of square-integrable functions on the closed interval [0 , 1], say.
SPOILER for Physic Monkey's Challenge.
It looks like, appropriately, selfAdjoint was right - domains are important. For the operator PX, operating by X on an eigenfunction of P results in a function that is not in the domain of selfadjointness for P, so P cannot be moved left while remaining to be P.
Easy direct calculations in this example reveal a lot.
As I said in another thread, if A and B satisfy [A , B] = ihbar, then at least one of A and B must be unbounded. In example of functions on the whole real line, both X and P are unbounded, while for functions on [0 ,1], X is bounded and P is unbounded.
Regards,
George
10. May 27, 2006
### George Jones
Staff Emeritus
Time to come clean!
I lifted (and addded a liitle elaboration) this example from the Chris Isham's nice little book Lectures on Quantum Theory: Mathematical and Structural Foundations.
Very interesting discussion!
Regards,
George
11. May 28, 2006
### Physics Monkey
Very good, George. The commutator is indeed ill defined on the momentum eigenstates.
Well then, I think I might have to take a look at Isham's book.
Thanks for the interesting post!
P.S. To all you readers out there, I can't resist telling about some nice physical applications of such ideas. It turns out that the self adjoint extensions of the momentum operator on a finite interval describe physically the problem of a particle on a ring with a magnetic field through the ring. This is in turn equivalent to imposing a 'twisted' boundary condition $$\psi(x+L) = e^{i \alpha} \psi(x)$$ on the wavefunction for a particle on a ring with no magnetic field. But there's more! Impurities in a metal can localize electronic states and cause a metal to become an insulator. One way to tell if you have localized states is to look at how sensitive such states are to the boundary conditions of your sample. The above ideas can then be applied, and you can relate the question of localization to the behavior of the system under an applied magnetic field (a problem which can be attacked with perturbation theory). And you thought self adjoint extensions were dull! Shame on you. :tongue:
12. May 30, 2006
### reilly
First, if "0 = 1" is true then QM completely falls apart, sorta like proof by contradiction, and "0=1" is certainly a contradiction. That tells me that the various proofs must be incorrect, or most physicists have been living like Alice in Wonderland.
The problem is that P X | x> is not equal to P|x> x. As in, go to an x position representation in which P = -i d/dx. That is,
P X |x> = -i d/dx x |x> = (-i + {-i x d/dx})|x>
Delta functions and domaines are not at issue
Sometimes abstraction can lead even the best astray.
Think about Wick's Thrm, which would not hold if "0 =1" were true, nor would many standard manipulations of creation and destruction operators be legitimate. .
(For the abstract truth about momentum operators see Hille and Phillips, Functional Analysis and Semi Groups, Chap XIX, which discusses translation operators (d/dx) in great and highly rigorous detail. The authors demonstrate that there really is not a problem with such operators.
Again, if "0=1" then QM is inherently mathematically trustworthy, which seems to me to be a completely absurd idea.
Regards,
Reilly Atkinson
13. May 30, 2006
### Hurkyl
Staff Emeritus
Any notation can lead people astray. But abstraction has the advantage that there are fewer messy details, which means less opportunities to make mistakes, and less possibility for those mistakes to be obscured.
Avoiding abstraction certainly doesn't prevent one from making mistakes...
such as overworking your variables. The x in d/dx is not the same as the x as in |x>; the former is the coordinate variable of the position representation, and the latter is a constant denoting which position eigenstate we've selected.
If I relabel the variables so x is no longer being overworked, we're looking at -i d/dx x |a>. (And don't forget that x |a> = a |a>)
You could rewrite George's entire post in the A-representation (so that A = x, and B = -ih d/dx), but that doesn't resolve the paradox: you still wind up with 0 = 1.
That's not accurate: if 0=1 were true, then everything is true. (And simultaneously false)
I'm completely confused by this.
Last edited: May 30, 2006
14. May 31, 2006
### Gokul43201
Staff Emeritus
Can we go over this again, slowly ? This is something that has bothered me for a little while.
Is L the circumference of the ring ? Does this not destroy the single-valuedness of $\psi(x)$? Or is that what is being probed ?
I think I've drunk too deep from the cup of Periodic BCs, what with all the goodies like flux quantization in SCs and Brillouin zones in crystals that it has thrown up like so many marshmallows!
Let's start with a simple case : the Anderson hamiltonian for non-interacting electrons in a cubic lattice.
The Hamiltonian consists of your favorite on-site disorder potential and the usual hopping term (nn, say). You then apply the above boundary condition to the single-particle eigenfunction in one or more directions. Ignoring what this means for now, this allows you to Taylor expand the eigenvalues $E_i(\alpha)$ and look at the coefficients of higher order terms in $\alpha$. The deviations from 0 of these coefficients is what you call the phase sensitivity? If that's true, how exactly is this a "measure" of localization? Is the point to extract a dimensionless number (like T/U) and looking for a scaling law? And if not, what happens next?
Last edited: May 31, 2006
15. May 31, 2006
### lalbatros
George Jones,
Physics Monkey,
Would that "0=1" contradiction be a proof that no finite-dimentional matrix could satisfy the commutation relation $$\left[ A , B \right] = i \hbar I$$ ?
Would it possible to see that easily for two-dimentional matrices?
Michel
16. May 31, 2006
### Haelfix
The problem is indeed one of domains of definition, its the last step in the sequence that is erroneous. Ask yourselves, what *is* the operator AB or BA and where and what are they defined on?
Most of this is easily demystified if you recall the spectral theorem. For general operators, you usually are confronted not just with discrete or continous spectra, but instead you have that + a bunch of other stuff, often called the residual spectrum. All bets are off when confronted with this, you can't just use naive physicist language of functional analysis in those cases.
17. May 31, 2006
### mikeu
It does appear to be a proof by contradiction, at least for observables. If A is not Hermitean then $$\langle a|A=(A^\dagger|a\rangle)^\dagger\neq (A|a\rangle)^\dagger$$, so acting A to the left in the term $$\langle a|AB|a\rangle$$ doesn't yield $$a\langle a|B|a\rangle$$, as required to obtain the contradiction 0=1. Your conclusion is correct anyway, it's just not proven by this example (unless I missed something else, it is late...).
For 2D matrices, if A and B are completely arbitrary then
$$A=\left(\begin{array}{cc} a & b \\ c & d\end{array}\right),\ B=\left(\begin{array}{cc} w & x \\ y & z\end{array}\right),\ AB-BA=\left(\begin{array}{cc} bz-cy & b(w-x)+y(a-d) \\ c(x-w)+z(d-a) & -(bz-cy)\end{array}\right).$$
Since the 1-1 entry is the negative of the 2-2 entry, this can never be proportional to the identity matrix.
18. May 31, 2006
### Physics Monkey
The proofs that 0 = 1 are certainly incorrect!
I'm afraid this isn't true. It doesn't matter what P is, if X hits the state $$|x\rangle$$ first, then you can replace X with x.
No, these things really are the relevant issues.
19. May 31, 2006
### Physics Monkey
Hi Gokul,
Do you want to hear just the story about the application to localization, or the whole story including the explanation of the paradox? I'm just gonna talk about localization for the moment, but I'm happy to say something else if you want.
To start with, the physical system is a piece of material in d dimensions of typical size L. I'll talk in one dimensional terms because this is easiest to understand, but the theory generalizes easily. The physical geometry is not periodic, although what we will eventually imagine is putting lots of these intervals of length L next to each other. As I indicated above, it is a technical fact that the momentum operator $$P = - i \frac{d}{dx}$$ is not self adjoint on such a finite interval. This is easy to understand from the fact that the equations $$P \psi = \pm i k \psi$$ have perfectly good solutions in the Hilbert space. As an aside, notice how this situation is modified if the interval is infinite $$(-\infty, \infty)$$. In this case, neither equation has a solution in the Hilbert space (of square integrable functions), and the momentum operator on the real line is called essentially self adjoint.
There is then some mathematical procedure for fixing the momentum operator up by defining what is called a self adjoint extension. This extension is characterized by a phase which can be identified with the boundary condition of your sample $$\psi(x+L) = e^{i \alpha} \psi(x)$$. In other words, your new fixed up momentum operator only makes sense on functions that satisfy this property. The physical geometry isn't periodic so there really aren't any issues about multivaluedness here. My original description is somewhat confusing on this point, so sorry about that. You can think of this phase as more like the Bloch factor $$e^{i k a}$$ that obtains from translating a Bloch state by one lattice spacing. The important physical realization is that this weird phase factor can be mapped via a gauge transformation to the problem of a particle on a ring with periodic boundary conditions and a magnetic field. The wavefunction can be thought of as being multivalued, with branches labeled by the winding number, but you are protected from unpleasantness by gauge invariance. Mmmmm marshmallows.
Now for some physics. The Anderson model is a good place to start, and your understanding is quite right. This twisted boundary condition is imposed with the physical idea that somehow sensitivity to boundary conditions will tell you whether states are extended or localized. You then map the problem to the equivalent system on a ring with a magnetic field. The vector potential is propotional to $$\alpha$$, and it makes sense to do perturbation theory in order to understand how the twisted boundary condition effects states. You would be interested in comparing something like the variance of $$\frac{\partial^2 E_i(\alpha)}{\partial \alpha^2}$$ to the typical level spacing $$\Delta$$. For a given realization of disorder, you can work out something like $$\frac{\partial^2 E_i(\alpha)}{\partial \alpha^2} \sim \sum_{j \neq i} \frac{1}{L^2} \frac{|\langle i | P/m | j \rangle|^2}{E_i - E_j}$$ plus some constant term you don't really care about.
To estimate the variance we can replace the energy denominator with the level spacing and the velocity matrix elements with some kind of typical velocity scale. Such matrix elements also enter into the Kubo formula for conductivity, so you can use the conductivity to estimate the typical matrix element. The Einstein formula for conductivity is $$\sigma = 2 e^2 N(0) D / \Omega$$ where D is the diffusion constant, and with the help of the Kubo formula you can easily estimate $$v^2 \sim D / N(0) = D \Delta$$ where $$N(0)$$ is the density of states per unit energy at the Fermi surface. The variance is then simply $$D/L^2$$ which is called the Thouless energy $$E_T$$. The sensitivity to boundary conditions is given in terms of the ratio $$\frac{E_T}{\Delta}$$.
Actually, this ratio has a very direct physical meaning. Go back to the Einstein formula for the conductivity. Freshman physics says the conductance is related to the conductivity by $$G(L) = \sigma L^{d-2}$$. We can define a dimensionless conductance $$g(L)$$ by multiplying the conductance by the resistance quantum $$\sim 1/e^2$$. The result is that the dimensionless conductance is given by $$g(L) \sim \frac{N(0)}{L^d} D L^{d-2} = \frac{D}{L^2} \frac{1}{\Delta} = \frac{E_T}{\Delta}$$. So the sensitivity to boundary conditions is just determined by the dimensionless conductance $$g$$! The physical picture is now quite nice. If we have localized states then the system is an insulator and g should be very small which we interpret as saying the states are insensitive to boundary conditions. If we have extended states then the system is a metal and g should be large which we interpret as pronounced sensitivity to boundary conditions.
With the understanding that localized and extended states can be characterized in terms of the dimensionless conductance, we can now build our scaling theory and get all the usual fun results. The added bonus here is that you can solve the Anderson model easily enough and directly compute the Thouless energy and level spacing. It's especially easy in d = 1, and you can verify the prediction of the scaling theory that g always goes to zero as L grows large. And all this can be phrased in the language of self adjoint extensions!
Refs:
Thouless has a number of papers on this sensitivity to boundary conditions idea. The book by Imry also has something about this in it as I recall.
Last edited: May 31, 2006
20. Jun 1, 2006
### Gokul43201
Staff Emeritus
Thanks for the response, PM.
I've only gotten half-way through it, and won't likely find more time until later tonight, but I wanted to let you know that I've seen this.
I'll reply later. And if this is distracting (for others) from the rest of the thread, I could request that it be split off into a new thread.
PS : Most everything Thouless has written in this field involves the RG!
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.912422776222229, "perplexity": 568.4899331565404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171706.94/warc/CC-MAIN-20170219104611-00393-ip-10-171-10-108.ec2.internal.warc.gz"}
|
https://artofproblemsolving.com/wiki/index.php?title=1955_AHSME_Problems&oldid=121999
|
1955 AHSME Problems
1955 AHSC (Answer Key)Printable version: Wiki | AoPS Resources • PDF Instructions This is a 50-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. You will receive ? points for each correct answer, ? points for each problem left unanswered, and ? points for each incorrect answer. No aids are permitted other than scratch paper, graph paper, ruler, compass, protractor and erasers. Figures are not necessarily drawn to scale. You will have ? minutes working time to complete the test. 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
Problem 1
Which one of the following is not equivalent to ?
Problem 2
The smaller angle between the hands of a clock at p.m. is:
Problem 3
If each number in a set of ten numbers is increased by , the arithmetic mean (average) of the ten numbers:
Problem 4
The equality is satisfied by:
Problem 5
varies inversely as the square of . When . When equals:
Problem 6
A merchant buys a number of oranges at for cents and an equal number at for cents. To "break even" he must sell all at:
Problem 7
If a worker receives a % cut in wages, he may regain his original pay exactly by obtaining a raise of:
The graph of :
Problem 9
A circle is inscribed in a triangle with sides , and . The radius of the circle is:
Problem 10
How many hours does it take a train traveling at an average rate of 40 mph between stops to travel a miles it makes n stops of m minutes each?
Problem 11
The negation of the statement "No slow learners attend this school" is:
Problem 12
The solution of is:
Problem 13
The fraction is equal to:
Problem 14
The length of rectangle is % more than the side of square . The width of the rectangle is % less than the side of the square. The ratio of the areas, , is:
Problem 15
The ratio of the areas of two concentric circles is . If the radius of the smaller is , then the difference between the radii is best approximated by:
Problem 16
The value of when and is:
Problem 17
If , then equals:
Problem 18
The discriminant of the equation is zero. Hence, its roots are:
Problem 19
Two numbers whose sum is and the absolute value of whose difference is are roots of the equation:
Problem 20
The expression equals zero for:
Problem 21
Represent the hypotenuse of a right triangle by and the area by . The altitude on the hypotenuse is:
Problem 22
On a \textdollar{10000} order a merchant has a choice between three successive discounts of %, %, and % and three successive discounts of %, %, and %. By choosing the better offer, he can save:
Problem 23
In checking the petty cash a clerk counts quarters, dimes, nickels, and cents. Later he discovers that of the nickels were counted as quarters and of the dimes were counted as cents. To correct the total obtained the clerk must:
The function :
Problem 25
One of the factors of is:
Problem 26
Mr. A owns a house worth . He sells it to Mr. at % profit. Mr. sells the house back to Mr. at a % loss. Then:
Problem 27
If and are the roots of , then equals:
Problem 28
On the same set of axes are drawn the graph of and the graph of the equation obtained by replacing by in the given equation. If and these two graphs intersect:
Problem 29
In the figure, is tangent to semicircle ; is tangent to semicircle ; is a straight line; the arcs are indicated in the figure. is measured by:
Problem 30
Each of the equations has:
Problem 31
An equilateral triangle whose side is is divided into a triangle and a trapezoid by a line drawn parallel to one of its sides. If the area of the trapezoid equals one-half of the area of the original triangle, the length of the median of the trapezoid is:
Problem 32
If the discriminant of is zero, then another true statement about , and is that:
Problem 33
Henry starts a trip when the hands of the clock are together between a.m. and a.m. He arrives at his destination between p.m. and p.m. when the hands of the clock are exactly apart. The trip takes:
Problem 34
A -inch and -inch diameter pole are placed together and bound together with wire. The length of the shortest wire that will go around them is:
Problem 35
Three boys agree to divide a bag of marbles in the following manner. The first boy takes one more than half the marbles. The second takes a third of the number remaining. The third boy finds that he is left with twice as many marbles as the second boy. The original number of marbles:
Problem 36
A cylindrical oil tank, lying horizontally, has an interior length of feet and an interior diameter of feet. If the rectangular surface of the oil has an area of square feet, the depth of the oil is:
Problem 37
A three-digit number has, from left to right, the digits , and , with . When the number with the digits reversed is subtracted from the original number, the units' digit in the difference of r. The next two digits, from right to left, are:
Problem 38
Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers , and are obtained. One of the original integers is:
Problem 39
If , then if the least possible value of is zero is equal to:
Problem 40
The fractions and are unequal if:
Problem 41
A train traveling from Aytown to Beetown meets with an accident after hr. It is stopped for hr., after which it proceeds at four-fifths of its usual rate, arriving at Beetown hr. late. If the train had covered miles more before the accident, it would have been just hr. late. The usual rate of the train is:
Problem 42
If , and are positive integers, the radicals and are equal when and only when:
Problem 43
The pairs of values of and that are the common solutions of the equations and are:
Problem 44
In circle chord is produced so that equals a radius of the circle. is drawn and extended to . is drawn. Which of the following expresses the relationship between and ?
Problem 45
Given a geometric sequence with the first term and and an arithmetic sequence with the first term . A third sequence is formed by adding corresponding terms of the two given sequences. The sum of the first ten terms of the third sequence is:
Problem 46
The graphs of , and intersect in:
Problem 47
The expressions and are:
Problem 48
Given with medians ; parallel and equal to ; are drawn; extended meets in . Which one of the following statements is not necessarily correct?
Problem 49
The graphs of and intersect in:
Problem 50
In order to pass going mph on a two-lane highway, , going mph, must gain feet. Meantime, feet from , is headed toward him at mph. If and maintain their speeds, then, in order to pass safely, must increase his speed by:
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8239964842796326, "perplexity": 1382.7308906057795}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056752.16/warc/CC-MAIN-20210919065755-20210919095755-00150.warc.gz"}
|
https://www.thieme-connect.com/products/ejournals/abstract/10.1055/s-0034-1380231
|
Synlett 2015; 26(04): 563-564
DOI: 10.1055/s-0034-1380231
spotlight
© Georg Thieme Verlag Stuttgart · New York
# Trimethylsilyl Cyanide (TMSCN)
› Author Affiliations
Further Information
### Publication History
Publication Date:
06 February 2015 (online)
### Introduction
Trimethylsilyl cyanide (TMSCN) is a commercial reagent used as cyanide source for nucleophilic reactions. It is a colorless liquid, moisture sensitive, with a boiling point of 114–117 °C, which was first synthetized by the reaction of trimethylsilicon halides TMSX and AgCN in 1952.[1] TMSCN is a versatile reagent that can be used in several different reactions, but it is generally used in nucleophilic additions to aldehydes, ketones and imines to form cyanohydrin silyl ethers[2] (Scheme [1a]) and α-aminonitriles[3] in Strecker-type reactions (Scheme [1b]).
### Table 1 Use of TMSCN
(A) The direct substitution of benzylic and allylic alcohols by cyanide using TMSCN and Brønsted acid Montmorillonite catalysts was developed by Wang et al. After optimizing the reaction conditions, the compounds were obtained with moderate to excellent yields and high regioselectivity.[4]
(B) The thiocyanate group is a useful moiety for the synthesis of various heterocycles[5] and it is an important function which has shown biological activity in a series of derivatives.[6] Recently, Yamaguchi et al. reported the synthesis of alkyl and aryl thiocyanates by nucleophilic cyanation of thiols using TMSCN, manganese oxide octahedral molecular sieves (OMS-2), KF and O2 to afford the products with excellent yields (>90%).[7]
(C) A novel stereospecific synthesis of acyl cyanides from propargyl aldehydes was described by Choi et al. The procedure involves the use of Et3N as dual catalyst, acting as a Lewis base in the cyanosilylation process and then as a Brønsted base in the umpolung step. The final hydrolysis and tautomerization of the resulting allene gave the (E)-isomers with moderate to good yields.[8]
(D) Arai et al. reported the dicyanation of alkynes using TMSCN, Pd(CN)2 as the catalyst and atmospheric O2. The mechanism begins with the π-complex formation and subsequent nucleophilic attack of the cyano group (syn or anti) to one carbon of the alkyne. The reductive elimination afforded the dicyanated products with good diastereoisomeric excess depending on the substrates.[9]
(E) A variety of aryl nitriles has been synthetized by Ye et al. by a cross-coupling reaction under mild and simple conditions. The reaction involves the use of aryl boronic acids or esters as starting materials, TMSCN as the cyanide source, Cu2O as the catalyst and DMEDA as a ligand under an O2 atmosphere.[10]
(F) TMSCN was used in the second step of an oxidative Michael addition of cyanide anion to Baylis–Hillman adducts. The importance of the addition of cyanide to α,β-unsaturated carbonyl derivatives is that the products can be converted into a variety of compounds including γ-aminobutyric acids. The reaction took place in a liquid ionic medium ([bmim]Br), which was reused several times without losing its activity. The β-cyano carbonyl compounds were obtained with high regioselectivity and yields (>79%).[11]
(G) Xu et al. described the α-azidocyanation of aryl alkenes using TMSN3 and TMSCN in the presence of an oxidative agent and a copper catalyst. The difunctionalization of alkenes with these versatile groups allows the transformation into many derivatives such as amino acids. The mechanism is believed to start by the formation of an azide radical that reacts with the alkene; the oxidation of the resulting radical leads to a carbocation which is finally trapped by the cyanide anion. The azidocyano derivatives were achieved with low to moderate yields depending on the substituents.[12]
(H) The regioselective cyanation of allylic derivatives was reported by Munemori et al. The best results were obtained using CuI, CuCN or CuCl2 as catalysts. The experiment in the presence of the free radical TEMPO showed that the cyanation proceeds through a radical pathway. The compounds were obtained with low to moderate yields.[13]
• ### References
• 1 McBride Jr JJ, Beachell HC. J. Am. Chem. Soc. 1952; 74: 5247
• 2 Kikukawa Y, Suzuki K, Sugawa M, Hirano T, Kamata K, Yamaguchi K, Mizuno N. Angew. Chem. Int. Ed. 2012; 51: 3686
• 3 Dekamin MG, Mokhtari Z. Tetrahedron 2012; 68: 922
• 4 Wang J, Masui Y, Onaka M. ACS Catal. 2011; 1: 446
• 5 Langi BP, Mulwad VV, Chaskar AC. Acta Pol. Pharm. 2011; 68: 441
• 6 Silveira GP, Ferreira M, Fernandes L, Moraski GC, Cho S, Hwang C, Franzblau SG, Sá MM. Bioorg. Med. Chem. Lett. 2012; 22: 6486
• 7 Yamaguchi K, Sakagami K, Miyamoto Y, Jin X, Mizuno N. Org. Biomol. Chem. 2014; DOI: 10.1039/C4OB01655F.
• 8 Choi HH, Son YH, Jung MS, Kang EJ. Tetrahedron Lett. 2011; 52: 2312
• 9 Arai S, Sato T, Koike Y, Hayashi M, Nishida A. Angew. Chem. Int. Ed. 2009; 48: 4528
• 10 Ye Y, Wang Y, Liu P, Han F. Chin. J. Chem. 2013; 31: 27
• 11 Yadav LD. S, Awasthi C, Rai A. Tetrahedron Lett. 2008; 49: 6360
• 12 Xu L, Mou X.-Q, Chen Z.-M, Wang S.-H. Chem. Commun. 2014; 50: 10676
• 13 Munemori D, Tsuji H, Uchida K, Suzuki T, Isa K, Minakawa M, Kawatsura M. Synthesis 2014; 46: 2747
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8379174470901489, "perplexity": 28620.56931126626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400206763.24/warc/CC-MAIN-20200922192512-20200922222512-00745.warc.gz"}
|
http://www.perimeterinstitute.ca/fr/seminar/black-hole-accretion-flows
|
Black Hole Accretion Flows
Two nearby, slowly accreting
black holes have angular size large enough to be resolved by submillimeter wavelength interferometry. This motivated our development of ab initio
dynamical and radiative models of the plasma surrounding the event horizon. I will describe the state of the art in these models, and in particular what is known about tilted disks, in which the black hole spin angular momentum is misaligned with the orbital angular momentum of the accreting plasma.
Collection/Series:
Event Type:
Seminar
Scientific Area(s):
Speaker(s):
Event Date:
Jeudi, Novembre 29, 2012 - 13:00 to 14:30
Location:
The Space Room (400)
Room #:
400
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8449894785881042, "perplexity": 1876.9062749355871}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867364.94/warc/CC-MAIN-20180625014226-20180625034226-00575.warc.gz"}
|
https://codereview.stackexchange.com/questions/122116/interactive-command-line-youtube-downloader-with-option-to-burn-subtitles-into-v
|
EDIT: This code is now public on GitHub with more focused purpose in case anyone is interested. Thanks for the help!
This is only used on Mac machines. I know that there is a Python implementation of youtube-dl and several for ffmpeg, however I chose to use subprocess so that I can see the real-time stdout/stderr of them while videos are downloading/encoding.
# The goal
Easy to use (for non-programmers) interactive command line interface that can:
2. Optionally burn subtitles into the video.
• Either subtitles that the uploader entered or YouTube auto-generated subtitles (if they exist).
This is not meant to be an all-encompassing program for youtube-dl and ffmpeg and their many options, it is simply intended to perform the above 2 tasks easily.
# My main concerns
1. Ensuring that if this program fails on a particular video (or for any reason), it fails elegantly such that the lamen user doesn't have to do anything magical to get back on track and try another video.
2. In the long run I would like to build a GUI for this but I have no experience doing that yet. I'm hoping that I'm programming this in a way that is relatively easy to turn into a program with a GUI later, so any advice in that area will be greatly appreciated.
# The Code
#!/usr/bin/python
import shutil
import os
import urllib2
import subprocess
# Set paths
HOME = os.path.expanduser("~")
SUPPORTED_SUBS = ['.srt', '.sbv', '.sub', '.mpsub', '.lrc', '.cap', '.smi',
'.sami', '.rt', '.vtt', '.ttml', '.dfxp', '.scc', '.stl',
'.tds', '.cin', '.asc']
# Clear terminal window
def clear():
p = subprocess.Popen(['clear'])
p.communicate()
def intro_message():
print '-----------------------------------------------------------------'
print '-----------------------------------------------------------------\n'
# Create necessary directories
def make_dirs():
if not os.path.exists(folder):
os.mkdir(folder)
def get_url():
if not check_url(url):
print 'Something went wrong, please ensure you entered a valid URL.'
get_url()
return url
# Check if URL is valid
def check_url(url):
try:
urllib2.urlopen(url)
return True
except:
return False
def get_captions():
user_input = raw_input('Burn subtitles into video? (yes/no): ')
if not user_input[0].lower() == 'y':
return False
return True
# If user wants captions, ask if they want them auto-generated by YouTube
# This is not available for all videos
def get_auto_captions():
user_input = raw_input('Auto-generated subtitles? (yes/no): ')
if not user_input[0].lower() == 'y':
return False
return True
# Return tuple of filepaths to use for encoding/burning/moving
def get_files():
vid = subs = None
for f in files:
if f.startswith('.'):
continue
if os.path.splitext(f)[1] in SUPPORTED_SUBS:
subs = f
if os.path.splitext(f)[1] == '.mp4':
vid = f
# Burn in subs with FFMPEG
def burn_captions(VIDPATH, SUBSPATH):
filename = os.path.basename(VIDPATH)
# Prepend filename with "CC_" to indicate that it has captions
OUTPATH = os.path.join(ENCODING, 'CC_' + filename)
p = subprocess.Popen(['ffmpeg', '-i', VIDPATH, '-vf',
'subtitles={0}'.format(SUBSPATH),
OUTPATH])
p.communicate()
return [OUTPATH]
if not captions:
dl_with_no_cc(url)
elif auto_captions:
dl_with_auto_cc(url)
elif captions:
dl_with_cc(url)
def dl_with_no_cc(url):
'-f bestvideo[ext=mp4]+bestaudio[ext=m4a]/best '
'--merge-output-format mp4 '
'--restrict-filenames '
'--prefer-ffmpeg '
'-o "{path}%(title)s.%(ext)s" '
shell=True)
p.communicate()
def dl_with_cc(url):
'-f "bestvideo[ext=mp4]+bestaudio[ext=m4a]/best" '
'--merge-output-format mp4 '
'--write-srt '
'--sub-lang en '
'--restrict-filenames '
'--prefer-ffmpeg '
'-o "{path}%(title)s.%(ext)s" {url}'.format(
url=url)),
shell=True)
p.communicate()
def dl_with_auto_cc(url):
'-f "bestvideo[ext=mp4]+bestaudio[ext=m4a]/best" '
'--merge-output-format mp4 '
'--write-auto-sub '
'--sub-lang en '
'--restrict-filenames '
'--prefer-ffmpeg '
'-o "{path}%(title)s.%(ext)s" {url}'.format(
url=url)),
shell=True)
p.communicate()
def move_file(filepath):
def cleanup():
try:
shutil.rmtree(ENCODING)
except OSError:
pass
def main():
while True:
cleanup()
clear()
intro_message()
url = get_url()
captions = get_captions()
auto_captions = get_auto_captions() if captions else False
make_dirs()
files = get_files()
if captions:
files = burn_captions(*files)
move_file(filepath=files[0])
cleanup()
if __name__ == '__main__':
main()
From a first glance it looks okay, but there many things that can be written in a nicer / more idiomatic way.
The choice of using subprocess is completely fine - for the reason you mentioned, but also since libraries depending on their interface can also be much harder to use than their command line counterparts. Note that you don't seem to use the more complex features of subprocess, so perhaps os.system will suffice for you (at the moment) to save the reader some time.
• Python 3 compatibility would be good; in particular using print() as a function instead of a statement springs to mind.
• The comments above the functions are almost docstrings, they just have to be put into the functions - docstrings are a good idea to have documentation easily available in the REPL.
• Instead of the os.path.join call I'd probably do the expansion inline as the path with the ~ included is more amenable to putting it into a configuration file or exposing as a command line argument. Btw. though the calls as they are work thanks to how the join function works, joining HOME over and over again looks wrong, it should be:
DOWNLOAD_LOCATION = os.path.expanduser('~/Desktop/YT_Downloads/')
If that's not what you meant replace the DOWNLOAD_LOCATION with HOME of course.
• The SUPPORTED_SUBS list can be a set, that rarely matters though.
• For the clear function there are probably better ways (using escape codes) but it's probably alright here.
• In make_dirs it should be most likely os.makedirs as not every user might have ~/Desktop in the first place.
• AFAIK the CPython interpreter doesn't optimise tail recursion, so calling the function itself like in get_url is bad and in this case also wrong as no value is returned, respectively the first wrong value is returned. Consider using a loop, e.g.:
def get_url():
while True:
if check_url(url):
return url
print('Something went wrong, please ensure you entered a valid URL.')
• In get_captions and get_auto_captions the return value should be the value from the test immediately. The current code reads almost like if True == True:, it's just unnecessary complexity. Also consider moving this into a function like yes_or_no('<prompt here>').
• The dl_... functions are mostly duplicated code, better to have common arguments somewhere in a constant and then just add the additional things with format.
• I don't quite get the calling convention for burn_captions - if you have just two values, write it that way. The whole block in main looks like it can fail at any moment given the right filenames or something - if get_files doesn't match anything there will be an exception raised just because of the None values, thus terminating the whole program.
2. So as long as you have modular functions and keep in mind that you have separate processes running and you have a plan to pass in user input in some other way than by querying like get_url/get_captions/get_auto_captions currently do, then it should be relatively easy to adapt.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3055656850337982, "perplexity": 5424.985952439877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00712.warc.gz"}
|
http://math.stackexchange.com/users/17688/wendelin?tab=reputation
|
# Wendelin
Unregistered less info
reputation
2
bio website location age member for 3 years, 3 months seen Oct 24 '11 at 17:43 profile views 9
# 25 Reputation
5 Apr 6 '14
+5 16:52 upvote Projective Spectrum of $K[X,Y]$
2 Oct 24 '11
+2 17:22 accept Factoring polynomials in several variables over algebraically closed fields
5 Oct 23 '11
+5 16:04 upvote Factoring polynomials in several variables over algebraically closed fields
12 Oct 15 '11
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19630655646324158, "perplexity": 5109.692298483217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121744242.57/warc/CC-MAIN-20150124174904-00232-ip-10-180-212-252.ec2.internal.warc.gz"}
|
https://math.stackexchange.com/questions/1770414/are-all-normal-subgroups-abelian
|
# Are all normal subgroups Abelian?
If $H \subset G$ is a normal subgroup of G,
=> $xHx^{-1} = H$ or $xH = Hx$ for all $x \epsilon G$
=> $xH = Hx$ for all $x \epsilon H$
Hence, all normal subgroups of a group are themselves Abelian?
Also, does that mean that all normal towers of subgroups are also Abelian?
• An easy counterexample is $A_4 \trianglelefteq S_4$ but $A_4$ is not abelian. – lokodiz May 3 '16 at 21:27
• One thing it think about is that H is a set, so it may be confusing if you are thinking of elements in G or H. – wesssg May 4 '16 at 3:26
It is quite a common misunderstanding that $xH=Hx$ means that $xh=hx$ for any $h\in H$. This is generally false.
The assertion $xH=Hx$ means that
1. for every $h\in H$, there exists $h_1\in H$ with $xh=h_1x$
2. for every $h\in H$, there exists $h_2\in H$ with $hx=xh_2$
Consider the group $G=S_4$ and its normal subgroup $H=A_4$ (the even permutations). Since $[S_4:A_4]=2$, the subgroup $A_4$ is normal. However, taking $x=(12)$ and $h=(123)$, we have $$(12)(123)=(23)\ne(123)(12)=(13)$$ However, $(132)(12)=(23)$, so in this case $h_1=(132)\ne h$.
We can also find two elements in $A_4$ that don't commute: $$(123)(124)=(13)(24) \\ (124)(123)=(14)(23)$$
Note: the convention about function composition is the standard functional one, that is, on the left (think to $\circ$ between two cycles).
• That is exactly what I thought, but then realized that $xyx^{-1} = z$ for $y,z \epsilon H$ does not imply $y = z$, rather $xyx^{-1} \epsilon H$ – ixaxaar May 3 '16 at 21:42
• What notation is that? It doesn't seem to work if it's permutation cycle notation. – Mateen Ulhaq Jun 22 '17 at 8:39
• @MateenUlhaq I use composition in the standard direction, so $f=(123)$, $g=(124)$ and $f\circ g(1)=f(2)=3$ and so on. – egreg Jun 22 '17 at 8:42
• @egreg Ah OK, thanks. Is that a typical convention in group theory? – Mateen Ulhaq Jun 22 '17 at 8:48
• @MateenUlhaq Depending on the textbook it can be reversed. – egreg Jun 22 '17 at 8:49
No. $G$ is a normal subgroup of itself for any group $G$. Commutativity is a local property of a group (all the way down to the elements), whereas normality is more of a mid-scale property of a group (collections of elements, but not necessarily the whole group). Just because you permute the elements around the same way if you multiply on the left and right (in regards to normality) does not mean it is abelian.
• Got it, thanks! – ixaxaar May 3 '16 at 21:33
To get other counterexamples, $A$ and $B$ are normal subgroups in the direct product $A \times B$.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9192066788673401, "perplexity": 309.12517466331354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540569146.17/warc/CC-MAIN-20191213202639-20191213230639-00084.warc.gz"}
|
https://fredrikj.net/arb/doc.html
|
# Arb documentation
Last updated: 2012-09-29 01:27:03 CET
## Introduction
Arb is an experimental C library implementing arbitrary-precision floating-point ball arithmetic, written by Fredrik Johansson <[email protected]>. The git repository is https://github.com/fredrik-johansson/arb/
Ball arithmetic, also known as mid-rad interval arithmetic, is an extension of floating-point arithmetic in which an error bound is attached to each variable. This allows doing rigorous computations over the real numbers, while avoiding the overhead of traditional (inf-sup) interval arithmetic at high precision, and eliminating much of the need for time-consuming and bug-prone manual error analysis.
At the moment, Arb contains:
• A module (fmpr) for correctly rounded arbitrary-precision floating-point arithmetic. Arb numbers have a few special features, such as arbitrary-size exponents (useful for combinatorics and asymptotics) and dynamic allocation (facilitating implementation of hybrid integer/floating-point and mixed-precision algorithms).
• A module (fmprb) for real ball arithmetic, where a ball is implemented as a pair of fmpr numbers.
• Functions for fast high-precision computation of some mathematical constants, based on ball arithmetic.
• A module (fmprb_poly) for polynomials or power series over the real numbers, implemented using balls as coefficients, with fast polynomial multiplication.
• A rudimentary module (fmprb_mat) for matrices over the real numbers, implemented using balls as coefficients.
Planned features include: transcendental functions, more extensive polynomial and matrix functionality, and complex balls (and polynomials and matrices thereof).
Arb uses MPIR and FLINT for the underlying integer arithmetic. The code conventions borrow from FLINT, and the project might get merged back into FLINT when the code stabilizes in the future. Arb also uses MPFR for some fallback code and for testing purposes.
The current version of Arb implements most of its floating-point arithmetic naively using high-level FLINT types. The speed at low precision is far from optimal, and the memory management can sometimes be wasteful. The internals will be rewritten in the future to fix the inefficiencies, which eventually should make Arb ball arithmetic about as fast as mpz or mpfr arithmetic at any precision.
Warning: as this is an early version, any part of the interface is subject to change! Also be aware that there are known and unknown bugs.
## Setup
To compile, test and install Arb, do:
./configure <options>
make
make check
make install
Arb requires recent versions of MPIR, MPFR and FLINT. Currently a source checkout of FLINT from https://github.com/fredrik-johansson/flint2 is required. If MPIR, MPFR or FLINT is installed in some other location than the default path /usr/local, pass the flag --with-mpir=... --with-mpfr=... or --with-flint=... with the correct path to configure (type ./configure --help to show more options).
Here is a simple sample program to get started using Arb:
#include "fmprb.h"
int main()
{
fmprb_t x;
fmprb_init(x);
fmprb_const_pi(x, 50 * 3.33);
fmprb_printd(x, 50); printf("\n");
fmprb_clear(x);
}
The output should be something like the following:
3.1415926535897932384626433832795028841971693993751 +/- 4.2764e-50
## fmpr.h (floating-point arithmetic)
A variable of type fmpr_t holds an arbitrary-precision binary floating-point number, i.e. a rational number of the form $x \times 2^y$ where $x, y \in \mathbb{Z}$ and $x$ is odd; or one of the special values zero, plus infinity, minus infinity, or NaN (not-a-number).
The component $x$ is called the mantissa, and $y$ is called the exponent. Note that this is just one among many possible conventions: the mantissa (alternatively significand) is sometimes viewed as a fraction in the interval $[1/2, 1)$, with the exponent pointing to the position above the top bit rather than the position of the bottom bit, and with a separate sign.
The conventions for special values largely follow those of the IEEE floating-point standard. At the moment, there is no support for negative zero, unsigned infinity, or a NaN with a payload, though some these might be added in the future.
An fmpr number is exact and has no inherent "accuracy". We use the term precision to denote either the target precision of an operation, or the bit size of a mantissa (which in general is unrelated to the "accuracy" of the number: for example, the floating-point value 1 has a precision of 1 bit in this sense and is simultaneously an infinitely accurate approximation of the integer 1 and a 2-bit accurate approximation of $\sqrt 2 = 1.011010100\ldots_2$).
Except where otherwise noted, the output of an operation is the floating-point number obtained by taking the inputs as exact numbers, in principle carrying out the operation exactly, and rounding the resulting real number to the nearest representable floating-point number whose mantissa has at most the specified number of bits, in the specified direction of rounding. Some operations are always or optionally done exactly.
### Types, macros and constants
fmpr_struct
An fmpr_struct holds a mantissa and an exponent. If the mantissa and exponent are sufficiently small, their values are stored as immediate values in the fmpr_struct; large values are represented by pointers to heap-allocated arbitrary-precision integers. Currently, both the mantissa and exponent are implemented using the FLINT fmpz type. Special values are currently encoded by the mantissa being set to zero.
fmpr_t
An fmpr_t is defined as an array of length one of type fmpr_struct, permitting an fmpr_t to be passed by reference.
fmpr_rnd_t
Specifies the rounding mode for the result of an approximate operation.
FMPR_RND_NEAREST
Specifies that the result of an operation should be rounded to the nearest representable number, rounding to an odd mantissa if there is a tie between two values. Note: the code for this rounding mode is currently not implemented.
FMPR_RND_DOWN
Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards zero.
FMPR_RND_UP
Specifies that the result of an operation should be rounded to the nearest representable number in the direction away from zero.
FMPR_RND_FLOOR
Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards minus infinity.
FMPR_RND_CEIL
Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards plus infinity.
FMPR_PREC_EXACT
If passed as the precision parameter to a function, indicates that no rounding is to be performed. This must only be used when it is known that the result of the operation can be represented exactly and fits in memory (the typical use case is working with values small integers). Note that, for example, adding two numbers whose exponents are far apart can easily produce an exact result that is far too large to store in memory.
### Memory management
void fmpr_init(fmpr_t x)
Initializes the variable x for use. Its value is set to zero.
void fmpr_clear(fmpr_t x)
Clears the variable x, freeing or recycling its allocated memory.
### Special values
void fmpr_zero(fmpr_t x)
void fmpr_one(fmpr_t x)
void fmpr_pos_inf(fmpr_t x)
void fmpr_neg_inf(fmpr_t x)
void fmpr_nan(fmpr_t x)
Sets x respectively to 0, 1, $+\infty$, $-\infty$, NaN.
int fmpr_is_zero(const fmpr_t x)
int fmpr_is_one(const fmpr_t x)
int fmpr_is_pos_inf(const fmpr_t x)
int fmpr_is_neg_inf(const fmpr_t x)
int fmpr_is_nan(const fmpr_t x)
Returns nonzero iff x respectively equals 0, 1, $+\infty$, $-\infty$, NaN.
int fmpr_is_inf(const fmpr_t x)
Returns nonzero iff x equals either $+\infty$ or $-\infty$.
int fmpr_is_normal(const fmpr_t x)
Returns nonzero iff x is a finite, nonzero floating-point value, i.e. not one of the special values 0, $+\infty$, $-\infty$, NaN.
int fmpr_is_special(const fmpr_t x)
Returns nonzero iff x is one of the special values 0, $+\infty$, $-\infty$, NaN, i.e. not a finite, nonzero floating-point value.
### Assignment and rounding
long _fmpr_normalise(fmpz_t man, fmpz_t exp, long prec, fmpr_rnd_t rnd)
Rounds the mantissa and exponent in-place.
void fmpr_set(fmpr_t y, const fmpr_t x)
Sets y to a copy of x.
long fmpr_set_round(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets y to a copy of x rounded in the direction specified by rnd to the number of bits specified by prec.
void fmpr_set_error_result(fmpr_t err, const fmpr_t result, long rret)
Given the return value rret and output variable result from a function performing a rounding (e.g. fmpr_set_round or fmpr_add), sets err to a bound for the absolute error.
void fmpr_add_error_result(fmpr_t err, const fmpr_t err_in, const fmpr_t result, long rret, long prec, fmpr_rnd_t rnd)
Like fmpr_set_error_result, but adds err_in to the error.
### Comparisons
int fmpr_equal(const fmpr_t x, const fmpr_t y)
Returns nonzero iff x and y are exactly equal. This function does not treat NaN specially, i.e. NaN compares as equal to itself.
int fmpr_cmp(const fmpr_t x, const fmpr_t y)
Returns negative, zero, or positive, depending on whether x is respectively smaller, equal, or greater compared to y. Comparison with NaN is undefined.
int fmpr_cmpabs(const fmpr_t x, const fmpr_t y)
Compares the absolute values of x and y.
int fmpr_sgn(const fmpr_t x)
Returns $-1$, $0$ or $+1$ according to the sign of x. The sign of NaN is undefined.
### Random number generation
void fmpr_randtest(fmpr_t x, flint_rand_t state, long bits, long mag_bits)
Generates a finite random number whose mantissa has precision at most bits and whose exponent has at most mag_bits bits. The values are distributed non-uniformly: special bit patterns are generated with high probability in order to allow the test code to exercise corner cases.
void fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, long bits, long mag_bits)
Identical to fmpr_randtest, except that zero is never produced as an output.
void fmpr_randtest_special(fmpr_t x, flint_rand_t state, long bits, long mag_bits)
Indentical to fmpr_randtest, except that the output occasionally is set to an infinity or NaN.
### Conversions
int fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd)
Sets the MPFR variable x to the value of y. If the precision of x is too small to allow y to be represented exactly, it is rounded in the specified MPFR rounding mode. The return value indicates the direction of rounding, following the standard convention of the MPFR library.
void fmpr_set_mpfr(fmpr_t x, const mpfr_t y)
Sets x to the exact value of the MPFR variable y.
void fmpr_set_ui(fmpr_t x, ulong c)
void fmpr_set_si(fmpr_t x, long c)
void fmpr_set_fmpz(fmpr_t x, const fmpz_t c)
Sets x exactly to the integer c.
void fmpr_get_fmpq(fmpq_t y, const fmpr_t x);
Sets y to the exact value of x. The result is undefined if x is not a finite fraction.
long fmpr_set_fmpq(fmpr_t x, const fmpq_t y, long prec, fmpr_rnd_t rnd);
Sets x to the value of y, rounded according to prec and rnd.
void fmpr_set_fmpz_2exp(fmpr_t x, const fmpz_t man, const fmpz_t exp);
void fmpr_set_si_2exp_si(fmpr_t x, long man, long exp)
void fmpr_set_ui_2exp_si(fmpr_t x, ulong man, long exp)
Sets x to $\mathrm{man} \times 2^{\mathrm{exp}}$.
void fmpr_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const fmpr_t x);
Sets man and exp to the unique integers such that $x = \mathrm{man} \times 2^{\mathrm{exp}}$ and man is odd, provided that x is a nonzero finite fraction. If x is zero, both man and exp are set to zero. If x is infinite or NaN, the result is undefined.
int fmpr_get_fmpz_fixed_fmpz(fmpz_t y, const fmpr_t x, const fmpz_t e)
int fmpr_get_fmpz_fixed_si(fmpz_t y, const fmpr_t x, long e)
Converts x to a mantissa with predetermined exponent, i.e. computes an integer y such that $y \times 2^e \approx x$, truncating if necessary. Returns 0 if exact and 1 if truncation occurred.
### Input and output
void fmpr_print(const fmpr_t x)
Prints the mantissa and exponent of x as integers, precisely showing the internal representation.
void fmpr_printd(const fmpr_t x, long digits)
Prints x as a decimal floating-point number, rounding to the specified number of digits. This function is currently implemented using MPFR, and does not support large exponents.
### Arithmetic
void fmpr_neg(fmpr_t y, const fmpr_t x)
Sets y to the negation of x.
long fmpr_neg_round(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets y to the negation of x, rounding the result.
void fmpr_abs(fmpr_t y, const fmpr_t x)
Sets y to the absolute value of x.
long fmpr_add(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_add_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_add_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_add_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = x + y$, rounded according to prec and rnd. The precision can be FMPR_PREC_EXACT to perform an exact addition, provided that the result fits in memory.
long _fmpr_add_eps(fmpr_t z, const fmpr_t x, int sign, long prec, fmpr_rnd_t rnd)
Sets z to the value that results by adding an infinitesimal quantity of the given sign to x, and rounding. The result is undefined if x is zero.
long fmpr_sub(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_sub_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_sub_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_sub_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = x - y$, rounded according to prec and rnd. The precision can be FMPR_PREC_EXACT to perform an exact addition, provided that the result fits in memory.
long fmpr_mul(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_mul_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_mul_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_mul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = x \times y$, rounded according to prec and rnd. The precision can be FMPR_PREC_EXACT to perform an exact multiplication, provided that the result fits in memory.
void fmpr_mul_2exp_si(fmpr_t y, const fmpr_t x, long e)
void fmpr_mul_2exp_fmpz(fmpr_t y, const fmpr_t x, const fmpz_t e)
Sets y to x multiplied by $2^e$ without rounding.
long fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_div_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_ui_div(fmpr_t z, ulong x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_div_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_si_div(fmpr_t z, long x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_div_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
long fmpr_fmpz_div(fmpr_t z, const fmpz_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_fmpz_div_fmpz(fmpr_t z, const fmpz_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = x / y$, rounded according to prec and rnd. If $y$ is zero, $z$ is set to NaN.
long fmpr_addmul(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_addmul_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_addmul_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_addmul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = z + x \times y$, rounded according to prec and rnd. The intermediate multiplication is always performed without roundoff. The precision can be FMPR_PREC_EXACT to perform an exact addition, provided that the result fits in memory.
long fmpr_submul(fmpr_t z, const fmpr_t x, const fmpr_t y, long prec, fmpr_rnd_t rnd)
long fmpr_submul_ui(fmpr_t z, const fmpr_t x, ulong y, long prec, fmpr_rnd_t rnd)
long fmpr_submul_si(fmpr_t z, const fmpr_t x, long y, long prec, fmpr_rnd_t rnd)
long fmpr_submul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, long prec, fmpr_rnd_t rnd)
Sets $z = z - x \times y$, rounded according to prec and rnd. The intermediate multiplication is always performed without roundoff. The precision can be FMPR_PREC_EXACT to perform an exact subtraction, provided that the result fits in memory.
long fmpr_sqrt(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
long fmpr_sqrt_ui(fmpr_t z, ulong x, long prec, fmpr_rnd_t rnd)
long fmpr_sqrt_fmpz(fmpr_t z, const fmpz_t x, long prec, fmpr_rnd_t rnd)
Sets $z$ to the square root of $x$, rounded according to prec and rnd. The result is NaN if $x$ is negative.
void fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e, long prec, fmpr_rnd_t rnd)
void fmpr_pow_sloppy_ui(fmpr_t y, const fmpr_t b, ulong e, long prec, fmpr_rnd_t rnd)
void fmpr_pow_sloppy_si(fmpr_t y, const fmpr_t b, long e, long prec, fmpr_rnd_t rnd)
Sets $y = b^e$, computed using without guaranteeing correct (optimal) rounding, but guaranteeing that the result is a correct upper or lower bound if the rounding is directional. Currently requires $b \ge 0$.
### Special functions
long fmpr_log(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets $z$ to $\log(x)$, rounded according to prec and rnd. The result is NaN if $x$ is negative. This function is currently implemented using MPFR and does not support large exponents.
long fmpr_log1p(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets $z$ to $\log(1+x)$, rounded according to prec and rnd. This function computes an accurate value when $x$ is small. The result is NaN if $1+x$ is negative. This function is currently implemented using MPFR and does not support large exponents.
long fmpr_exp(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets $z$ to $\exp(x)$, rounded according to prec and rnd. This function is currently implemented using MPFR and does not support large exponents.
long fmpr_expm1(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
Sets $z$ to $\exp(x)-1$, rounded according to prec and rnd. This function computes an accurate value when $x$ is small. This function is currently implemented using MPFR and does not support large exponents.
## fmprb.h (real ball arithmetic)
An fmprb_t represents a ball over the real numbers, that is, an interval $[m-r, m+r]$ where the midpoint $m$ and the radius $r$ are (extended) real numbers and $r$ is nonnegative. The result of an (approximate) operation done on fmprb_t variables is a ball which contains the result of the (mathematically exact) operation applied to any choice of points in the input balls. In general, the output ball is not the smallest possible.
The precision parameter passed to each function roughly indicates the precision to which calculations on the midpoint are carried out (operations on the radius are always done using a fixed, small precision.)
For arithmetic operations, the precision parameter currently simply specifies the precision of the corresponding fmpr operation. In the future, the arithmetic might be made faster by incorporating sloppy rounding (typically equivalent to a loss of 1-2 bits of effective working precision) when the result is known to be inexact (while still propagating errors rigorously, of course). Arithmetic operations done on exact input with exactly representable output are always guaranteed to produce exact output.
For more complex operations, the precision parameter indicates a minimum working precision (algorithms might allocate extra internal precision to attempt to produce an output accurate to the requested number of bits, especially when the required precision can be estimated easily, but this is not generally required).
If the precision is increased and the inputs either are exact or are computed with increased accuracy as well, the output should converge proportionally, absent any bugs. The general intended strategy for using ball arithmetic is to add a few guard bits, and then repeat the calculation as necessary with an exponentially increasing number of guard bits (Ziv's strategy) until the result is exact enough for one's purposes (typically the first attempt will be successful). There are some caveats: in general, ball arithmetic only makes sense for (Lipschitz) continuous functions, and trying to approximate functions close to singularities might result in slow convergence, or failure to converge.
Warning: some methods for transcendental functions and constants currently perform the error propagation in a non-rigorous way, due to the implementation being incomplete (in some cases, a rigorous error bound for the algorithm or function might not be known at all). This should be indicated in the documentation for each function.
### Types, macros and constants
fmprb_struct
fmprb_t
An fmprb_struct consists of a pair of fmpr_struct:s. An fmprb_t is defined as an array of length one of type fmprb_struct, permitting an fmprb_t to be passed by reference.
The precision used for operations on the radius. This is small enough to fit in a single word, currently 30 bits.
fmprb_midref(x)
Macro returning a pointer to the midpoint of x as an fmpr_t.
Macro returning a pointer to the radius of x as an fmpr_t.
### Memory management
void fmprb_init(fmprb_t x)
Initializes the variable x for use. Its midpoint and radius are both set to zero.
void fmprb_clear(fmprb_t x)
Clears the variable x, freeing or recycling its allocated memory.
fmprb_struct * _fmprb_vec_init(long n)
Returns a pointer to an array of n initialized fmprb_struct:s.
void _fmprb_vec_clear(fmprb_struct * v, long n)
Clears an array of n initialized fmprb_struct:s.
### Basic manipulation
int fmprb_is_exact(const fmprb_t x)
Returns nonzero iff the radius of x is zero.
int fmprb_equal(const fmprb_t x, const fmprb_t y)
Returns nonzero iff x and y are equal as balls, i.e. have both the same midpoint and radius.
void fmprb_zero(fmprb_t x)
Sets x to zero.
fmprb_is_zero(const fmprb_t x)
Returns nonzero iff the midpoint and radius of x are both zero.
void fmprb_set(fmprb_t y, const fmprb_t x)
Sets y to a copy of x.
void fmprb_set_round(fmprb_t y, const fmprb_t x, long prec)
Sets y to a copy of x, rounded to prec bits.
fmprb_neg(fmprb_t y, const fmprb_t x)
Sets y to the negation of x.
fmprb_abs(fmprb_t y, const fmprb_t x)
Sets y to the absolute value of x. No attempt is made to improve the interval represented by x if it contains zero.
void fmprb_set_fmpr(fmprb_t y, const fmpr_t x)
void fmprb_set_si(fmprb_t y, long x)
void fmprb_set_ui(fmprb_t y, ulong x)
void fmprb_set_fmpz(fmprb_t y, const fmpz_t x)
Sets y exactly to x.
void fmprb_set_fmpq(fmprb_t y, const fmpq_t x, long prec)
Sets y to the rational number x, rounded to prec bits.
int fmprb_is_one(const fmprb_t x)
Returns nonzero iff x is exactly 1.
void fmprb_one(fmprb_t x)
Sets x to the exact integer 1.
### Input and output
void fmprb_print(const fmprb_t x)
Prints the internal representation of x.
void fmprb_printd(const fmprb_t x, long digits)
Prints x in decimal. The printed value of the radius is not adjusted to compensate for the fact that the binary-to-decimal conversion of both the midpoint and the radius introduces additional error.
### Random number generation
void fmprb_randtest(fmprb_t x, flint_rand_t state, long prec, long mag_bits)
Generates a random ball. The midpoint and radius will both be finite.
void fmprb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const fmprb_t x, long bits)
Sets q to a random rational number from the interval represented by x. A denominator is chosen by multiplying the binary denominator of x by a random integer up to size bits.
The outcome is undefined if the midpoint or radius of x is non-finite, or if the exponent of the midpoint or radius is so large or small that representing the endpoints as exact rational numbers would cause overflows.
### Precision and comparisons
void fmprb_add_error_fmpr(fmprb_t x, const fmpr_t err)
Adds err, which is assumed to be nonnegative, to the radius of x.
Adds $2^e$ to the radius of x.
void fmprb_add_error(fmprb_t x, const fmprb_t err)
Adds the supremum of err, which is assumed to be nonnegative, to the radius of x.
int fmprb_contains_fmpr(const fmprb_t x, const fmpr_t y)
int fmprb_contains_fmpq(const fmprb_t x, const fmpq_t y)
int fmprb_contains_fmpz(const fmprb_t x, const fmpz_t y)
int fmprb_contains_mpfr(const fmprb_t x, const mpfr_t y)
int fmprb_contains_zero(const fmprb_t x)
Returns nonzero iff the given number is contained in the interval represented by x.
void fmprb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const fmprb_t x)
Computes the exact interval represented by x, in the form of an integer interval multiplied by a power of two, i.e. $x = [a, b] \times 2^{\mathrm{exp}}$.
The outcome is undefined if the midpoint or radius of x is non-finite, or if the difference in magnitude between the midpoint and radius is so large that representing the endpoints exactly would cause overflows.
long fmprb_rel_error_bits(const fmprb_t x)
Returns the effective relative error of self measured in bits, defined as the difference between the position of the top bit in the radius and the top bit in the midpoint, plus one. The result is clamped between plus/minus FMPR_PREC_EXACT.
long fmprb_rel_accuracy_bits(const fmprb_t x)
Returns the effective relative accuracy of x measured in bits, equal to the negative of the return value from fmprb_rel_error_bits.
### Arithmetic
void fmprb_add(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_add_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_add_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_add_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
void fmprb_add_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, long prec)
Sets $z = x + y$, rounded to prec bits. The precision can be FMPR_PREC_EXACT provided that the result fits in memory.
void fmprb_sub(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_sub_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_sub_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_sub_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
Sets $z = x - y$, rounded to prec bits. The precision can be FMPR_PREC_EXACT provided that the result fits in memory.
void fmprb_mul(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_mul_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_mul_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_mul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
Sets $z = x \times y$, rounded to prec bits. The precision can be FMPR_PREC_EXACT provided that the result fits in memory.
void fmprb_mul_2exp_si(fmprb_t y, const fmprb_t x, long e)
Sets $y$ to $x$ multiplied by $2^e$.
void fmprb_div(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_div_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_div_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_div_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
void fmprb_fmpz_div_fmpz(fmprb_t y, const fmpz_t num, const fmpz_t den, long prec)
void fmprb_ui_div(fmprb_t z, ulong x, const fmprb_t y, long prec);
Sets $z = x / y$, rounded to prec bits. If $y$ contains zero, $z$ is set to $0 \pm \infty$. Otherwise, error propagation uses the rule $$\left| \frac{x}{y} - \frac{x+\xi_1 a}{y+\xi_2 b} \right| = \left|\frac{x \xi_2 b - y \xi_1 a}{y (y+\xi_2 b)}\right| \le \frac{|xb|+|ya|}{|y| (|y|-b)}$$ where $-1 \le \xi_1, \xi_2 \le 1$, and where the triangle inequality has been applied to the numerator and the reverse triangle inequality has been applied to the denominator.
void fmprb_div_2expm1_ui(fmprb_t y, const fmprb_t x, ulong n, long prec);
Sets $y = x / (2^n - 1)$, rounded to prec bits.
void fmprb_addmul(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_addmul_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_addmul_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_addmul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
Sets $z = z + x \times y$, rounded to prec bits. The precision can be FMPR_PREC_EXACT provided that the result fits in memory.
void fmprb_submul(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec)
void fmprb_submul_ui(fmprb_t z, const fmprb_t x, ulong y, long prec)
void fmprb_submul_si(fmprb_t z, const fmprb_t x, long y, long prec)
void fmprb_submul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, long prec)
Sets $z = z - x \times y$, rounded to prec bits. The precision can be FMPR_PREC_EXACT provided that the result fits in memory.
void fmprb_sqrt(fmprb_t z, const fmprb_t x, long prec)
void fmprb_sqrt_ui(fmprb_t z, ulong x, long prec)
void fmprb_sqrt_fmpz(fmprb_t z, const fmpz_t x, long prec)
Sets $z$ to the square root of $x$, rounded to prec bits. Error propagation is done using the following rule: assuming $m > r \ge 0$, the error is largest at $m - r$, and we have $\sqrt{m} - \sqrt{m-r} \le r / (2 \sqrt{m-r})$.
void fmprb_pow_fmpz(fmprb_t y, const fmprb_t b, const fmpz_t e, long prec)
void fmprb_pow_ui(fmprb_t y, const fmprb_t b, ulong e, long prec)
void fmprb_ui_pow_ui(fmprb_t y, ulong b, ulong e, long prec)
void fmprb_si_pow_ui(fmprb_t y, long b, ulong e, long prec)
Sets $y = b^e$ using binary exponentiation. Provided that $b$ and $e$ are small enough and the exponent is positive, the exact power can be computed using FMPR_PREC_EXACT.
### Special functions
void fmprb_log(fmprb_t z, const fmprb_t x, long prec)
void fmprb_log_ui(fmprb_t z, ulong x, long prec)
void fmprb_log_fmpz(fmprb_t z, const fmpz_t x, long prec)
Sets $z = \log(x)$. Error propagation is done using the following rule: assuming $m > r \ge 0$, the error is largest at $m - r$, and we have $\log(m) - \log(m-r) = \log(1 + r/(m-r))$. The last expression is calculated accurately for small radii via fmpr_log1p. An input containing zero currently raises an exception.
void fmprb_exp(fmprb_t z, const fmprb_t x, long prec)
Sets $z = \exp(x)$. Error propagation is done using the following rule: the error is largest at $m + r$, and we have $\exp(m+r) - \exp(m) = \exp(m) (\exp(r)-1)$. The last expression is calculated accurately for small radii via fmpr_expm1.
void fmprb_sin(fmprb_t s, const fmprb_t x, long prec)
void fmprb_cos(fmprb_t c, const fmprb_t x, long prec)
void fmprb_sin_cos(fmprb_t s, fmprb_t c, const fmprb_t x, long prec)
Sets $s = \sin x$, $c = \cos x$. Error propagation uses the rule $|\sin(m \pm r) - \sin(m)| \le r$ (this could be tightened to $\min(r,2)$).
void fmprb_atan(fmprb_t z, const fmprb_t x, long prec)
Sets $z = \tan^{-1} x$. Letting $d = \max(0, |m| - r)$, the propagated error is bounded by $r / (1 + d^2)$ (this could be tightened).
void fmprb_fac_ui(fmprb_t x, ulong n, long prec)
Sets x to n factorial, computed using binary splitting. Provided that $n$ is small enough, the exact factorial can be computed using FMPR_PREC_EXACT.
void fmprb_rfac_ui_bsplit(fmprb_t y, const fmprb_t x, ulong n, long prec)
Sets x to the rising factorial $x (x+1) (x+2) \cdots (x+n-1)$, computed using binary splitting. The basecase processes eight factors at a time using the formula $x(x+1)\cdots(x+7) = (28 + 98x + 63x^2 + 14x^3 + x^4)^2 - 16 (7+2x)^2$, replacing 7 full-precision multiplications with 4 squarings and 1 multiplication [1]. Empirically, this is about twice as fast at high precision. Numerical stability is slightly worse.
[1] R. Crandall and C. Pomerance, "Prime Numbers: A Computational Perspective", second edition, Springer (2005), p. 316.
void fmprb_rfac_ui_multipoint(fmprb_t y, const fmprb_t x, ulong n, long prec)
Sets x to the rising factorial $x (x+1) (x+2) \cdots (x+n-1)$, computed using fast multipoint evaluation. This only requires $O(n^{1/2+\varepsilon})$ multiplications, but has high overhead and poor numerical stability (adding $O(n)$ guard bits to the input might be necessary to achieve full accuracy). It can be expected to be faster than the binary splitting algorithm if the input is a full-precision number, the precision is at least 100000 bits, and $n$ is of the same order of magnitude as (perhaps slightly smaller than) the number of bits.
void fmprb_bin_ui(fmprb_t x, const fmprb_t n, ulong k, long prec)
void fmprb_bin_uiui(fmprb_t x, ulong n, ulong k, long prec)
Sets x to the binomial coefficient ${n \choose k}$, computed using binary splitting. Provided that $n$ and $k$ are small enough, an exact binomial coefficient can be computed using FMPR_PREC_EXACT.
void fmprb_fib_fmpz(fmprb_t f, const fmpz_t n, long prec)
void fmprb_fib_ui(fmprb_t f, ulong n, long prec)
Sets x to the Fibonacci number $F_n$. Uses the binary squaring algorithm described in D. Takahashi, "A fast algorithm for computing large Fibonacci numbers", Information Processing Letters 75 (2000) 243-246 Provided that $n$ is small enough, an exact Fibonacci number can be computed using FMPR_PREC_EXACT.
void fmprb_const_pi_chudnovsky(fmprb_t x, long prec)
Sets x to $\pi$, computed using the Chudnovsky algorithm. Letting $A = 13591409$, $B = 545140134$, $C = 640320$, we have $\pi \approx 1 / s_N$ where $$s_N = 12 \sum_{k=0}^N \frac{(-1)^k (6k)! (A+Bk)} {(3k)! (k!)^3 C^{3k+3/2}}$$
The implementation computes an approximation for the algebraic number $1/s_N$ using binary splitting, bounding the rounding error automatically. The hypergeometric term ratio is asymptotically $R = C^3 / (2^6 \times 3^3) \approx 1.5 \times 10^{14}$, and in fact we have $|\pi - 1/s_N| < 1/R^N$ (with a more detailed calculation, the truncation error could be bounded closer to $1/R^{N+1}$).
void fmprb_const_pi(fmprb_t x, long prec)
Sets x to $\pi$. The value is cached for repeated use.
void fmprb_const_log_sqrt2pi(fmprb_t x, long prec)
Sets x to $\log \sqrt{2 \pi}$. The value is cached for repeated use.
void fmprb_const_euler_brent_mcmillan(fmprb_t res, long prec)
Sets x to Euler's constant $\gamma$, computed using the second Bessel function formula of Brent and McMillan. Brent and McMillan conjectured that the error depending on the internal parameter $n$ is of order $O(e^{-8n})$. Brent has recently proved that this bound is correct, but without determining an explicit big-O factor.
[1] R. P. Brent and E. M. McMillan, "Some new algorithms for high-precision computation of Euler's constant", Mathematics of Computation 34 (1980), 305-312.
[2] R. P. Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf
[3] The MPFR team (2012), "MPFR Algorithms", http://www.mpfr.org/algo.html
void fmprb_const_zeta3_bsplit(fmprb_t x, long prec)
Sets x to Apery's constant $\zeta(3)$, computed by applying binary splitting to a hypergeometric series.
void fmprb_zeta_ui_asymp(fmprb_t z, ulong s, long prec)
Assuming $s \ge 2$, approximates $\zeta(s)$ by $1 + 2^{-s}$ along with a correct error bound. We use the following bounds: for $s > b$, $\zeta(s) - 1 < 2^{-b}$, and generally, $\zeta(s) - (1 + 2^{-s}) < 2^{2-\lfloor 3 s/2 \rfloor}$.
void fmprb_zeta_ui_euler_product(fmprb_t z, ulong s, long prec)
Computes $\zeta(s)$ using the Euler product. This is fast only if s is large compared to the precision.
Writing $P(a,b) = \prod_{a \le p \le b} (1 - p^{-s})$, we have $1/\zeta(s) = P(a,M) P(M+1,\infty)$.
To bound the error caused by truncating the product at $M$, we write $P(M+1,\infty) = 1 - \epsilon(s,M)$. Since $0 < P(a,M) \le 1$, the absolute error for $\zeta(s)$ is bounded by $\epsilon(s,M)$.
According to the analysis in [1], it holds for all $s \ge 6$ and $M \ge 1$ that $1/P(M+1,\infty) - 1 \le f(s,M) \equiv 2 M^{1-s} / (s/2 - 1)$. Thus, we have $1/(1-\epsilon(s,M)) - 1 \le f(s,M)$, and expanding the geometric series allows us to conclude that $\epsilon(M) \le f(s,M)$.
[1] S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13, 431-445 (1992)
void fmprb_zeta_ui_bernoulli(fmprb_t x, ulong n, long prec)
Computes $\zeta(n)$ for even $n$ via the corresponding Bernoulli number, which is generated using FLINT.
void fmprb_zeta_ui_vec_borwein(fmprb_struct * z, ulong start, long num, ulong step, long prec)
Evaluates $\zeta(s)$ at $\mathrm{num}$ consecutive integers $s$ beginning with $\mathrm{start}$ and proceeding in increments of $\mathrm{step}$. Uses Borwein's formula [1], implemented to support fast multi-evaluation (but also works well for a single $s$).
Requires $\mathrm{start} \ge 2$. For efficiency, the largest $s$ should be at most about as large as $\mathrm{prec}$. Arguments approaching LONG_MAX will cause overflows. One should therefore only use this function for s up to about prec, and then switch to the Euler product.
The algorithm for single $s$ is basically identical to the one used in MPFR (see [2] for a detailed description). In particular, we evaluate the sum backwards to avoid storing more than one $d_k$ coefficient, and use integer arithmetic throughout since it is convenient and the terms turn out to be slightly larger than $2^\mathrm{prec}$. The only numerical error in the main loop comes from the division by $k^s$, which adds less than 1 unit of error per term. For fast multi-evaluation, we repeatedly divide by $k^{\mathrm{step}}$. Each division reduces the input error and adds at most 1 unit of additional rounding error, so by induction, the error per term is always smaller than 2 units.
References:
[1] P. Borwein, "An Efficient Algorithm for the Riemann Zeta Function", Constructive experimental and nonlinear analysis, CMS Conference Proc. 27 (2000), 29-34 http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
[2] The MPFR team (2012), "MPFR Algorithms", http://www.mpfr.org/algo.html
[3] X. Gourdon and P. Sebah (2003), "Numerical evaluation of the Riemann Zeta-function" http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf
void fmprb_zeta_ui_bsplit(fmprb_t x, ulong s, long prec)
Computes $\zeta(s)$ for arbitrary $s \ge 2$ using a binary splitting implementation of Borwein's formula. The algorithm has quasilinear complexity with respect to the precision.
void fmprb_zeta_ui(fmprb_t x, ulong s, long prec)
Computes $\zeta(s)$ for nonnegative integer $s \ne 1$, automatically choosing an appropriate algorithm.
void fmprb_zeta_ui_vec(fmprb_struct * x, ulong start, long num, long prec)
void fmprb_zeta_ui_vec_even(fmprb_struct * x, ulong start, long num, long prec)
void fmprb_zeta_ui_vec_odd(fmprb_struct * x, ulong start, long num, long prec)
Computes $\zeta(s)$ at num consecutive integers (respectively num even or num odd integers) beginning with $s = \mathrm{start} \ge 2$, automatically choosing an appropriate algorithm.
void fmprb_gamma_fmpq_karatsuba(fmprb_struct * v, const fmpq_t a, long num, long prec)
Uses Karatsuba's algorithm [1] to compute num coefficients in the Taylor series of $\Gamma(a+x)$ for rational $0 < a ≤ 1$, i.e. computes $\Gamma(a), \Gamma'(a) ... \Gamma^{(\mathrm{num}-1)}(a) / (\mathrm{num}-1)!$ This algorithm is most efficient at high precision, for num much smaller than the number of bits, and with small denominators of $a$. In particular, with num = 1, this algorithm computes $\Gamma(a)$ efficiently for small rational $a$.
Let $s = \max(2, \mathrm{num}-1)$. With parameters $r$ and $n$ chosen such that $r \ge n$ and $n \ge 2 s \log 2 s$, Karatsuba shows that $$\Gamma^{(j)}(a) = \sum_{k=0}^r \frac{(-1)^k}{k!} \frac{n^{k+a}}{k+a} \sum_{m=0}^j (-1)^m \frac{j! \, \log^{j-m} n}{(j-m)! (k+a)^m} + \theta_j$$
where $$|\theta_j| \le \frac{5}{3} e^{-n} \log^s n + \left(\frac{e}{r+2}\right)^{r+2} (1 + n^{r+2} \log^s n).$$
We choose the parameters $n$ and $r$ heuristically to be nearly optimal, and then evaluate the above formula to bound $\theta_j$ rigorously.
Karatsuba claims that choosing $r \ge 3n$ gives $|\theta_j| \le 2^{-n-1}$. This is, unfortunately, incorrect. Setting $r = n \alpha$ and expanding the error term around $n = \infty$, one finds that $\alpha$ asymptotically should be $1/W(1/e) \approx 3.59112147666862$ where $W(x)$ is the Lambert W-function. We also optimize the selection of $n$ by choosing $n \approx b \log 2$ where $b$ is the desired number of bits, rather than $n \approx b$, and round $n$ so that it has a short binary expansion (this gives smaller numbers in the binary splitting stage).
Finally, if $s$ is small, we perform binary splitting to a working precision of about $2.2$ times the target precision rather than exactly. This factor was tested to give full accuracy up to at least one million digits when $s \approx 1$. A more careful analysis should be done here so that a working precision is selected which always is sufficient and also nearly optimal.
[1] E. A. Karatsuba, "Fast evaluation of the Hurwitz zeta function and Dirichlet L-series", Problems of Information Transmission, Vol. 34, No. 4, 1998.
void fmprb_gamma_log(fmprb_t y, const fmprb_t x, long prec)
Sets $y = \log \Gamma(x)$, assuming that $x > 0$.
For large $x$, uses Stirling's expansion $$\log \Gamma(x) = \left(x-\frac{1}{2}\right)\log x - x + \frac{\ln {2 \pi}}{2} + \sum_{k=1}^{n-1} t_k + R(n,x)$$ where $$t_k = \frac{B_{2k}}{2k(2k-1)x^{2k-1}}$$ and $|R(n,x)| < t_n$.
If $x$ is too small for the asymptotic expansion to give sufficient accuracy directly, we translate to $x + r$ using the formula $\log \Gamma(x) = \log \Gamma(x+r) - \log(x (x+1) (x+2) \cdots (x+r-1))$. To obtain a remainder smaller than $2^{-b}$, we must choose an $r$ such that $x + r > \beta b$, where $\beta > \log(2) / (2 \pi) \approx 0.11$. We use a slightly larger factor $\beta \approx 0.2$ to more closely balance $n$ and $r$. A much larger $\beta$ (e.g. $\beta = 1$) could be used to reduce the number of Bernoulli numbers that have to be precomputed, at the expense of slower repeated evaluation.
## fmprb_poly.h (polynomials of real balls)
An fmprb_poly_t represents a polynomial over the real numbers, implemented as an array of coefficients of type fmprb_struct.
Most functions are provided in two versions: an underscore method which operates directly on pre-allocated arrays of coefficients and generally has some restrictions (such as requiring the lengths to be nonzero and not supporting aliasing of the input and output arrays), and a non-underscore method which performs automatic memory management and handles degenerate cases.
### Types, macros and constants
fmprb_poly_struct
fmprb_poly_t
Contains a pointer to an array of coefficients (coeffs), the used length (length), and the allocated size of the array (alloc).
An fmprb_poly_t is defined as an array of length one of type fmprb_poly_struct, permitting an fmprb_poly_t to be passed by reference.
### Memory management
void fmprb_poly_init(fmprb_poly_t poly)
Initializes the polynomial for use, setting it to the zero polynomial.
void fmprb_poly_clear(fmprb_poly_t poly)
Clears the polynomial, deallocating all coefficients and the coefficient array.
void fmprb_poly_fit_length(fmprb_poly_t poly, long len)
Makes sures that the coefficient array of the polynomial contains at least len initialized coefficients.
void _fmprb_poly_set_length(fmprb_poly_t poly, long len)
Directly changes the length of the polynomial, without allocating or deallocating coefficients. The value shold not exceed the allocation length.
void _fmprb_poly_normalise(fmprb_poly_t poly)
Strips any trailing coefficients which are identical to zero. The output
void fmprb_poly_zero(fmprb_poly_t poly)
void fmprb_poly_one(fmprb_poly_t poly)
Sets poly to the constant 0 respectively 1.
### Conversions
void fmprb_poly_set_fmpz_poly(fmprb_poly_t poly, const fmpz_poly_t src, long prec)
void fmprb_poly_set_fmpq_poly(fmprb_poly_t poly, const fmpq_poly_t src, long prec)
Sets poly to src.
### Input and output
void fmprb_poly_printd(const fmprb_poly_t poly, long digits)
Prints the polynomial as an array of coefficients, printing each coefficient using fmprb_printd.
### Comparisons
int fmprb_poly_contains_fmpq_poly(const fmprb_poly_t poly1, const fmpq_poly_t poly2)
Returns nonzero iff poly1 contains poly2.
int fmprb_poly_equal(const fmprb_t A, const fmprb_t B)
Returns nonzero iff A and B are equal as polynomial balls, i.e. all coefficients have equal midpoint and radius.
### Arithmetic
void _fmprb_poly_add(fmprb_struct * C, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long prec)
Sets {C, max(lenA, lenB)} to the sum of {A, lenA} and {B, lenB}. Allows aliasing of the input and output operands.
void fmprb_poly_add(fmprb_poly_t C, const fmprb_poly_t A, const fmprb_poly_t B, long prec)
Sets C to the sum of A and B.
void _fmprb_poly_mullow(fmprb_struct * C, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long n, long prec)
Sets {C, n} to the product of {A, lenA} and {B, lenB}, truncated to length n. The output is not allowed to be aliased with either of the inputs. We require lenA ≥ lenB > 0, n > 0, lenA + lenB - 1 ≥ n.
As currently implemented, this function puts each input polynomial on a common exponent, truncates to prec bits, and multiplies exactly over the integers. The output error is computed by cross-multiplying the max norms.
void fmprb_poly_mullow(fmprb_poly_t C, const fmprb_poly_t A, const fmprb_poly_t B, long n, long prec)
Sets C to the product of A and B, truncated to length n.
void _fmprb_poly_mul(fmprb_struct * C, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long prec)
Sets {C, n} to the product of {A, lenA} and {B, lenB}, truncated to length n. The output is not allowed to be aliased with either of the inputs. We require lenA ≥ lenB > 0, n > 0. This function currently calls _fmprb_poly_mullow.
void fmprb_poly_mul(fmprb_poly_t C, const fmprb_poly_t A, const fmprb_poly_t B, long prec)
Sets C to the product of A and B.
void _fmprb_poly_inv_series(fmprb_struct * Qinv, const fmprb_struct * Q, long len, long prec)
Sets {Qinv, len} to the power series inverse of {Q, len}. Uses Newton iteration.
void fmprb_poly_inv_series(fmprb_poly_t Qinv, const fmprb_poly_t Q, long n, long prec)
Sets Qinv to the power series inverse of Q.
void _fmprb_poly_div(fmprb_struct * Q, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long prec)
void _fmprb_poly_rem(fmprb_struct * R, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long prec)
void _fmprb_poly_divrem(fmprb_struct * Q, fmprb_struct * R, const fmprb_struct * A, long lenA, const fmprb_struct * B, long lenB, long prec)
void fmprb_poly_divrem(fmprb_poly_t Q, fmprb_poly_t R, const fmprb_poly_t A, const fmprb_poly_t B, long prec)
Performs polynomial division with remainder, computing a quotient $Q$ and a remainder $R$ such that $A = BQ + R$. The leading coefficient of $B$ must not contain zero. The implementation reverses the inputs and performs power series division.
void _fmprb_poly_div_root(fmprb_struct * Q, fmprb_t R, const fmprb_struct * A, long len, const fmprb_t c, long prec)
Divides $A$ by the polynomial $x - c$, computing the quotient $Q$ as well as the remainder $R = f(c)$.
### Product trees
void _fmprb_poly_product_roots(fmprb_struct * poly, const fmprb_struct * xs, long n, long prec)
void fmprb_poly_product_roots(fmprb_poly_t poly, fmprb_struct * xs, long n, long prec)
Generates the polynomial $(x-x_0)(x-x_1)\cdots(x-x_{n-1})$.
fmprb_struct ** _fmprb_poly_tree_alloc(long len)
Returns an initialized data structured capable of representing a remainder tree (product tree) of the given number of roots.
void _fmprb_poly_tree_free(fmprb_struct ** tree, long len)
Deallocates a tree structure as allocated using _fmprb_poly_tree_alloc.
void _fmprb_poly_tree_build(fmprb_struct ** tree, const fmprb_struct * roots, long len, long prec)
Constructs a product tree from a given array of roots. The tree structure must be pre-allocated to the specified length using _fmprb_poly_tree_alloc.
### Composition
void _fmprb_poly_compose_horner(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long prec)
void fmprb_poly_compose_horner(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec)
void _fmprb_poly_compose_divconquer(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long prec);
void fmprb_poly_compose_divconquer(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec)
void _fmprb_poly_compose(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long prec)
void fmprb_poly_compose(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long prec)
Sets res to the composition $h(x) = f(g(x))$ where $f$ is given by poly1 and $g$ is given by poly2, respectively using Horner's rule, divide-and-conquer, and an automatic choice between the two algorithms. The underscore methods do not support aliasing of the output with either input polynomial.
void _fmprb_poly_compose_series_horner(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long n, long prec)
void fmprb_poly_compose_series_horner(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long n, long prec)
void _fmprb_poly_compose_series_brent_kung(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long n, long prec)
void fmprb_poly_compose_series_brent_kung(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long n, long prec)
void _fmprb_poly_compose_series(fmprb_struct * res, const fmprb_struct * poly1, long len1, const fmprb_struct * poly2, long len2, long n, long prec)
void fmprb_poly_compose_series(fmprb_poly_t res, const fmprb_poly_t poly1, const fmprb_poly_t poly2, long n, long prec)
Sets res to the power series composition $h(x) = f(g(x))$ truncated to order $O(x^n)$ where $f$ is given by poly1 and $g$ is given by poly2, respectively using Horner's rule, the Brent-Kung baby step-giant step algorithm, and an automatic choice between the two algorithms. We require that the constant term in $g(x)$ is exactly zero. The underscore methods do not support aliasing of the output with either input polynomial.
### Evaluation and interpolation
void _fmprb_poly_evaluate(fmprb_t res, const fmprb_struct * f, long len, const fmprb_t a, long prec)
void fmprb_poly_evaluate(fmprb_t res, const fmprb_poly_t f, const fmprb_t a, long prec)
Sets res to $f(a)$, evaluated using Horner's rule.
void _fmprb_poly_evaluate_vec_iter(fmprb_struct * ys, const fmprb_struct * poly, long plen, const fmprb_struct * xs, long n, long prec)
void fmprb_poly_evaluate_vec_iter(fmprb_struct * ys, const fmprb_poly_t poly, const fmprb_struct * xs, long n, long prec)
Evaluates the polynomial simultaneously at n given points, calling _fmprb_poly_evaluate repeatedly.
void _fmprb_poly_evaluate_vec_fast_precomp(fmprb_struct * vs, const fmprb_struct * poly, long plen, fmprb_struct ** tree, long len, long prec)
void _fmprb_poly_evaluate_vec_fast(fmprb_struct * ys, const fmprb_struct * poly, long plen, const fmprb_struct * xs, long n, long prec)
void fmprb_poly_evaluate_vec_fast(fmprb_struct * ys, const fmprb_poly_t poly, const fmprb_struct * xs, long n, long prec)
Evaluates the polynomial simultaneously at n given points, using fast multipoint evaluation.
void _fmprb_poly_interpolate_newton(fmprb_struct * poly, const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec)
void fmprb_poly_interpolate_newton(fmprb_poly_t poly, const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec)
Recovers the unique polynomial of length at most n that interpolates the given x and y values. This implementation first interpolates in the Newton basis and then converts back to the monomial basis.
void _fmprb_poly_interpolate_barycentric(fmprb_struct * poly, const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec)
void fmprb_poly_interpolate_barycentric(fmprb_poly_t poly, const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec)
Recovers the unique polynomial of length at most n that interpolates the given x and y values. This implementation uses the barycentric form of Lagrange interpolation.
void _fmprb_poly_interpolation_weights(fmprb_struct * w, fmprb_struct ** tree, long len, long prec)
void _fmprb_poly_interpolate_fast_precomp(fmprb_struct * poly, const fmprb_struct * ys, fmprb_struct ** tree, const fmprb_struct * weights, long len, long prec)
void _fmprb_poly_interpolate_fast(fmprb_struct * poly, const fmprb_struct * xs, const fmprb_struct * ys, long len, long prec)
void fmprb_poly_interpolate_fast(fmprb_poly_t poly, const fmprb_struct * xs, const fmprb_struct * ys, long n, long prec)
Recovers the unique polynomial of length at most n that interpolates the given x and y values, using fast Lagrange interpolation. The precomp function takes a precomputed product tree over the x values and a vector of interpolation weights as additional inputs.
### Differentiation
void _fmprb_poly_derivative(fmprb_struct * res, const fmprb_struct * poly, long len, long prec)
Sets {res, len - 1} to the derivative of {poly, len}. Allows aliasing of the input and output.
void fmprb_poly_derivative(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
Sets res to the derivative of poly.
void _fmprb_poly_integral(fmprb_struct * res, const fmprb_struct * poly, long len, long prec)
Sets {res, len} to the integral of {poly, len - 1}. Allows aliasing of the input and output.
void fmprb_poly_integral(fmprb_poly_t res, const fmprb_poly_t poly, long prec)
Sets res to the integral of poly.
### Special functions
void _fmprb_poly_log_series(fmprb_struct * f, fmprb_struct * h, long n, long prec)
void fmprb_poly_log_series(fmprb_poly_t f, const fmprb_poly_t h, long n, long prec)
Sets $f$ to the power series logarithm of $h$, truncated to length $n$. Uses the formula $\log f = \int f' / f$, adding the logarithm of the constant term in $h$ as the constant of integration. The underscore method does not support aliasing of the input and output arrays.
void _fmprb_poly_exp_series_basecase(fmprb_struct * f, const fmprb_struct * h, long hlen, long n, long prec)
void fmprb_poly_exp_series_basecase(fmprb_poly_t f, const fmprb_poly_t h, long n, long prec)
void _fmprb_poly_exp_series(fmprb_struct * f, const fmprb_struct * h, long hlen, long n, long prec)
void fmprb_poly_exp_series(fmprb_poly_t f, const fmprb_poly_t h, long n, long prec)
Sets $f$ to the power series exponential of $h$, truncated to length $n$.
The basecase version uses a simple recurrence for the coefficients, requiring $O(nm)$ operations where $m$ is the length of $h$.
The main implementation uses Newton iteration, starting from a small number of terms given by the basecase algorithm. The complexity is $O(M(n))$. Redundant operations in the Newton iteration are avoided by using the scheme described in [1].
The underscore methods support aliasing and allow the input to be shorter than the output, but require the lengths to be nonzero.
[1] G. Hanrot and P. Zimmermann, "Newton Iteration Revisited", http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz (2004 preprint)
void fmprb_poly_log_gamma_series(fmprb_poly_t f, long n, long prec)
Sets $f$ to the series expansion of $\log(\Gamma(1-x))$, truncated to length $n$.
## fmprb_mat.h (matrices of real balls)
An fmprb_mat_t represents a dense matrix over the real numbers, implemented as an array of entries of type fmprb_struct.
The dimension (number of rows and columns) of a matrix is fixed at initialization, and the user must ensure that inputs and outputs to an operation have compatible dimensions. The number of rows or columns in a matrix can be zero.
### Types, macros and constants
fmprb_mat_struct
fmprb_mat_t
Contains a pointer to a flat array of the entries (entries), an array of pointers to the start of each row (rows), and the number of rows (r) and columns (c).
An fmprb_mat_t is defined as an array of length one of type fmprb_mat_struct, permitting an fmprb_mat_t to be passed by reference.
fmprb_mat_entry(mat, i, j)
Macro giving a pointer to the entry at row i and column j.
fmprb_mat_nrows(mat)
Returns the number of rows of the matrix.
fmprb_mat_ncols(mat)
Returns the number of columns of the matrix.
### Memory management
void fmprb_mat_init(fmprb_mat_t mat, long r, long c)
Initializes the matrix, setting it to the zero matrix with the given number of rows and columns.
void fmprb_mat_clear(fmprb_mat_t mat)
Clears the matrix, deallocating all entries.
### Conversions
void fmprb_mat_set(fmprb_mat_t dest, const fmprb_mat_t src)
void fmprb_mat_set_fmpz_mat(fmprb_mat_t dest, const fmpz_mat_t src)
void fmprb_mat_set_fmpq_mat(fmprb_mat_t dest, const fmpq_mat_t src, long prec)
Sets dest to src. The operands must have identical dimensions.
### Input and output
void fmprb_mat_printd(const fmprb_mat_t mat, long digits)
Prints each entry in the matrix with the specified number of decimal digits.
### Comparisons
int fmprb_mat_equal(const fmprb_mat_t mat1, const fmprb_mat_t mat2)
Returns nonzero iff the matrices have the same dimensions and identical entries.
int fmprb_mat_contains_fmpq_mat(const fmprb_mat_t mat1, const fmpq_mat_t mat2)
Returns nonzero iff the matrices have the same dimensions and each entry in mat2 is contained in the corresponding entry in mat1.
### Special matrices
void fmprb_mat_zero(fmprb_mat_t mat)
Sets all entries in mat to zero.
void fmprb_mat_one(fmprb_mat_t mat)
Sets the entries on the main diagonal to ones, and all other entries to zero.
### Arithmetic
void fmprb_mat_neg(fmprb_mat_t dest, const fmprb_mat_t src)
Sets dest to the exact negation of src. The operands must have the same dimensions.
void fmprb_mat_add(fmprb_mat_t res, const fmprb_mat_t mat1, const fmprb_mat_t mat2, long prec)
Sets res to the sum of mat1 and mat2. The operands must have the same dimensions.
void fmprb_mat_sub(fmprb_mat_t res, const fmprb_mat_t mat1, const fmprb_mat_t mat2, long prec)
Sets res to the difference of mat1 and mat2. The operands must have the same dimensions.
void fmprb_mat_mul(fmprb_mat_t res, const fmprb_mat_t mat1, const fmprb_mat_t mat2, long prec)
Sets res to the matrix product of mat1 and mat2. The operands must have compatible dimensions for matrix multiplication.
### Solving
int fmprb_mat_lu(long * perm, fmprb_mat_t LU, const fmprb_mat_t A, long prec)
Given an $n \times n$ matrix $A$, computes an LU decomposition $PLU = A$ using Gaussian elimination with partial pivoting. The input and output matrices can be the same, performing the decomposition in-place.
Entry $i$ in the permutation vector perm is set to the row index in the input matrix corresponding to row $i$ in the output matrix.
The algorithm succeeds and returns nonzero if it can find $n$ invertible (i.e. not containing zero) pivot entries. This guarantees that the matrix is invertible.
The algorithm fails and returns zero, leaving the entries in $P$ and $LU$ undefined, if it cannot find $n$ invertible pivot elements. In this case, either the matrix is singular, the input matrix was computed to insufficient precision, or the LU decomposition was attempted at insufficient precision.
void fmprb_mat_solve_lu_precomp(fmprb_mat_t X, const long * perm, const fmprb_mat_t LU, const fmprb_mat_t B, long prec)
Solves $AX = B$ given the precomputed nonsingular LU decomposition $A = PLU$. The matrices $X$ and $B$ are allowed to be aliased with each other, but $X$ is not allowed to be aliased with $LU$.
int fmprb_mat_solve(fmprb_mat_t X, const fmprb_mat_t A, const fmprb_mat_t B, long prec)
Solves $AX = B$ where $A$ is a nonsingular $n \times n$ matrix and $X$ and $B$ are $n \times m$ matrices, using LU decomposition.
If $m > 0$ and $A$ cannot be inverted numerically (indicating either that $A$ is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that $A$ is invertible and that the exact solution matrix is contained in the output.
int fmprb_mat_inv(fmprb_mat_t X, const fmprb_mat_t A, long prec)
Sets $X = A^{-1}$ where $A$ is a square matrix, computed by solving the system $AX = I$.
If $A$ cannot be inverted numerically (indicating either that $A$ is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that the matrix is invertible and that the exact inverse is contained in the output.
void fmprb_mat_det(fmprb_t det, const fmprb_mat_t A, long prec)
Computes the determinant of the matrix, using Gaussian elimination with partial pivoting. If at some point an invertible pivot element cannot be found, the elimination is stopped and the magnitude of the determinant of the remaining submatrix is bounded using Hadamard's inequality.
## History
• 2012-09-29 - version 0.2
• code for computing the gamma function (Karatsuba, Stirling's series)
• rising factorials
• fast exp_series using Newton iteration
• improved multiplication of small polynomials by using classical multiplication
• implemented error propagation for square roots
• polynomial division (Newton-based)
• polynomial evaluation (Horner) and composition (divide-and-conquer)
• product trees, fast multipoint evaluation and interpolation (various algorithms)
• power series composition (Horner, Brent-Kung)
• added the fmprb_mat module for matrices of balls of real numbers
• matrix multiplication
• interval-aware LU decomposition, solving, inverse and determinant
• many helper functions and small bugfixes
• 2012-09-14 - version 0.1
• 2012-08-05 - began simplified rewrite
• 2012-04-05 - experimental ball and polynomial code
## Credits
Arb is licensed GNU General Public License version 2, or any later version.
Fredrik's work on Arb is supported by Austrian Science Fund FWF Grant Y464-N18 (Fast Computer Algebra for Special Functions).
Arb includes code written by Bill Hart and Sebastian Pancratz for FLINT (also licensed GPL 2.0+).
Wishes or bug reports? Send any comments to [email protected]
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7884736657142639, "perplexity": 6922.736959400564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572833.78/warc/CC-MAIN-20220817001643-20220817031643-00238.warc.gz"}
|
https://micro-manager.org/Projector-1.4
|
# Projector-1.4
The Projector plugin provides a single graphical user interface for controlling SLMs (spatial light modulators), such as DMDs (digital mirror devices), LCOS (liquid crystal on silicon) modulators or even digital computer projectors, and also for controlling steerable-mirror (e.g. galvo-based) phototargeting devices, including the Rapp UGA-40, the Andor MicroPoint, and the ASI scanner.
The Projector plugin’s interface shows three tabs: Point and Shoot, ROIs, and Setup. How to operate each tab is described in detail below.
## Setup tab
The Setup tab allows you to test the phototargeting device and perform initial calibration. Press On and Off buttons to turn the light on and off (in the case of a pulsed laser such as the MicroPoint, the On button will only turn the light on briefly). Press the “Show center spot” button to illuminate the center of the phototargeting device’s range. This Center Spot should be visible in the camera’s field of view – if it isn’t, the physical alignment of the camera and/or phototargeter will need to be adjusted.
The Calibrate button starts an automated calibration procedure, where the phototargeter’s internal coordinates are mapped to the pixel coordinates to the camera’s pixel coordinates. This calibration allows the Projector plugin to convert mouse clicks or ROIs drawn on the live camera image into precisely directed phototargeting events.
The calibration procedure starts by illuminating a few spots near the center of the phototargeter range. This gives the Projector plugin an estimate of the orientation and location of the camera field of view relative to the phototargeter range. Then, points in a square lattice are illuminated one by one, and imaged on the camera. The Projector plugin then uses the lattice measurements to compute a mapping of each pixel to phototargeter coordinates for future phototargeting. Mappings for each camera and phototargeting deviced are stored and will be remembered even after Micro-Manager is restarted. The relative orientation of the camera and phototargeting device does not matter; however they should be turned roughly square with each other (0, 90, 180, or 270 degrees) so that the square lattice isn’t cut off.
Obviously the calibration should be performed with the same objective and camera that will be used for actual phototargeting. Currently there is no way to store different calibration mappings, e.g. for two different objectives.
Setting Description
On / Off Toggles calibration mode.
Calibrate Creates calibration map of phototargeting device range to the camera pixel position.
Show center spot Illuminate center of SLM or galvo device.
Phototargeting channel Toggles to specified channel during phototargeting. You don’t need to set this unless some hardware needs to be moved during imaging, like a dichroic and/or a shutter. If you don’t see your channel listed, you must set the Core-ChannelGroup in the Property Browser to the Group containing this channel.
## Point and Shoot tab
Point and Shoot lets you phototarget a small region instantaneously, by clicking on a live image of the specimen. Galvo-based devices fire a single shot, while SLM devices will turn on in a small region around the clicked pixel. The procedure is very simple:
1. Under the Point and Shoot tab, set “Point and shoot mode” to “On.”
2. Turn on live mode.
3. Hold down the Control key (on the keyboard) and click anywhere in the live image window. You should immediately see a laser spot appear for a time at the clicked location.
## ROIs tab
The Regions of Interest (ROIs) tab lets you specify regions on the image to be phototargeted. Phototargeting of an ROI can be carried out instantly, or programmed into a Multi-Dimensional Acquisition.
1. Before running an ROI experiment, the calibration (described above under “Setup Tab”) must already have been carried out. Over time, the calibration may drift, so repeat calibration as needed. It’s also useful to try “Point and Shoot” first, to make sure the phototargeting hardware is working and the calibration is correct.
The procedure for illuminating a single ROI is as follows:
1. Select one of the ROI tools on the ImageJ toolbar. Possible ROIs tools can include Rectangular, Oval, Polygon, Freehand, or Point. (Note that some devices, such as the MicroPoint and ASI scanner, currently only support Point targeting.)
2. Press “Set ROI(s)”. The ROI will be uploaded to the phototargeting device.
3. Choose a value of 1 or more for “Loop”. If Loop is greater than 1, then for every phototargeting event, the phototargeter will loop through the set of ROIs multiple times.
4. Turn on Live mode (on the main Micro-Manager window).
5. Press “Run Rois now!” The ROI should be illuminated (rastered in the case of a galvo-based device).
It’s also possible to run multiple ROIs:
1. Click the ROI Manager button to display ImageJ’s ROI Manager.
2. Draw an ROI, and press “Add.” The ROI will be included in the list. This is further detailed in Drawing Multiple ImageJ ROIs.
3. Press “Set ROI(s)”, turn on Live mode, and then “Run Rois now!”
Pressing “Run ROIs now!” is a good way to phototarget the specimen during a Multi-Dimensional Acquisition. Just start the MDA, wait for the right moment, and then hit “Run Rois now!” to cause phototargeting to start, while acquisition continues simultaneously.
Alternatively, you can run ROIs at pre-determined time points in an acquisition sequence:
1. Check Run ROIs in Multi-Dimensional Acquisition
2. Enter a “Start Frame” index – that is, the first frame at which phototargeting should commence.
3. If further phototargeting events are desired, check “Repeat every” and specify how many frames should elapse before the next phototargeting event should occur (after the first).
Setting Description
Set ROI(s) Upload ROI(s) drawn on the selected image to the device.
ROI Manager Add multiple ROIs to the image.
Loop Number of times to target a group of ROIs.
Spot dwell time Stops photo illumination after a certain interval. (Does not affect pulsed lasers or the Rapp Optoelectronic UGA-40.)
Run ROIs now! Fires ROIs drawn on current image.
Run ROIs in Multi-Dimensional Acquisition Fires phototargeting device at a pre-determined time during MDA.
Start Frame Timepoint in MDA to fire sequence.
Repeat every __ frames Number of frames between successive phototargeting events in an MDA. Setup tab.
## Drawing Multiple ImageJ ROIs
If you are not as familiar with ImageJ ROIs and have been using ROIs in other software packages, some differences are:
1. Only a single ROI can be drawn at a time. Drawing another ROI erases the current drawing, and so one must click the Add[t] button in the ROI Manager before drawing another ROI.
2. To change a ROI that has already been added to the ROI Manager list:
• Select the ROI. The easiest way to select a ROI is clicking on the label as explained in the tips; alternatively, select the entry in the ROI Manager list.
• Reshape the ROI with the square white handles, or to change the type of ROI, draw the new ROI.
• Click Update.
### Tips
1. Delete all ROIs by double-clicking the ⌦ Delete button.
2. Visually select a ROI by clicking the ROI’s center label number in the image. You will need to enable both the “Show All” and “Labels” checkboxs in the ROI Manager to do this.
3. Move a ROI by dragging the ROI’s center label number in the image.
Also see the … ROI Manager section on the ImageJ User Guide.
## FAQ
Can one stop the device firing at any time?
Unfortunately there is no emergency “off” button at the moment.
What happens when I target something outside the device range?
It ignores those clicks.
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15012438595294952, "perplexity": 5505.687346993159}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303864.86/warc/CC-MAIN-20220122134127-20220122164127-00513.warc.gz"}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.