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Structural system Summary Structural_frame The term structural system or structural frame in structural engineering refers to the load-resisting sub-system of a building or object. The structural system transfers loads through interconnected elements or members. Commonly used structures can be classified into five major categories, depending on the type of primary stress that may arise in the members of the structures under major design loads. However any two or more of the basic structural types described in the following may be combined in a single structure, such as a building or a bridge in order to meet the structure's functional requirements.
Zero vector space Unital structures Trivial_module > Properties > Unital structures If mathematicians sometimes talk about a field with one element, this abstract and somewhat mysterious mathematical object is not a field. In categories where the multiplicative identity must be preserved by morphisms, but can equal to zero, the {0} object can exist. But not as initial object because identity-preserving morphisms from {0} to any object where 1 ≠ 0 do not exist. For example, in the category of rings Ring the ring of integers Z is the initial object, not {0}. If an algebraic structure requires the multiplicative identity, but neither its preservation by morphisms nor 1 ≠ 0, then zero morphisms exist and the situation is not different from non-unital structures considered in the previous section.
Boline Description Boline > Description Unlike the athame, which in most traditions is never used for actual physical cutting, the boline is used for cutting cords and herbs, carving candles, etc. It has a small, straight or crescent-shaped blade with, traditionally, a white handle.
Coherent diffractive imaging Imaging process Coherent_diffractive_imaging > Imaging process Image recovered by Inverse Fourier transform In CDI, the objective lens used in a traditional microscope is replaced with computational algorithms and software which are able to convert from the reciprocal space into the real space. The diffraction pattern picked up by the detector is in reciprocal space while the final image must be in real space to be of any use to the human eye. To begin, a highly coherent light source of x-rays, electrons, or other wavelike particles must be incident on an object.
Superior vena cava obstruction Signs and symptoms SVC_syndrome > Signs and symptoms Shortness of breath is the most common symptom, followed by face or arm swelling.Following are frequent symptoms: Difficulty breathing Headache Facial swelling Venous distention in the neck and distended veins in the upper chest and arms Migraines (especially if unusual to normal) Large decrease in lung capacity Facial swelling after bending/laying down Upper limb edema Lightheadedness Cough Edema (swelling) of the neck, called the collar of Stokes Pemberton's signSuperior vena cava syndrome usually presents more gradually with an increase in symptoms over time as malignancies increase in size or invasiveness.
Haloperidol Special cautions Haloperidol > Adverse effects > Special cautions The drug bears a boxed warning about this risk. Impaired liver function, as haloperidol is metabolized and eliminated mainly by the liver In patients with hyperthyroidism, the action of haloperidol is intensified and side effects are more likely. IV injections: risk of hypotension or orthostatic collapse Patients at special risk for the development of QT prolongation (hypokalemia, concomitant use of other drugs causing QT prolongation) Patients with a history of leukopenia: a complete blood count should be monitored frequently during the first few months of therapy and discontinuation of the drug should be considered at the first sign of a clinically significant decline in white blood cells. Pre-existing Parkinson's disease or dementia with Lewy bodies
Glossary of genetics (M–Z) M Glossary_of_genetics_(M–Z) > M mutator gene Any mutant gene or sequence that increases the spontaneous mutation rate of one or more other genes or sequences. Mutators are often transposable elements, or may be mutant housekeeping genes such as those that encode helicases or proteins involved in proofreading. mutein A mutant protein, i.e. a protein whose amino acid sequence differs from that of the normal because of a mutation. muton The smallest unit of a DNA molecule in which a physical or chemical change can result in a mutation (conventionally a single nucleotide).
Outline of algebraic structures Study of algebraic structures Outline_of_algebraic_structures > Study of algebraic structures Universal algebra studies algebraic structures abstractly, rather than specific types of structures. Varieties Category theory studies interrelationships between different structures, algebraic and non-algebraic. To study a non-algebraic object, it is often useful to use category theory to relate the object to an algebraic structure. Example: The fundamental group of a topological space gives information about the topological space.
Parallel algorithms Parallelizability Parallel_algorithms > Parallelizability Examples include many algorithms to solve Rubik's Cubes and find values which result in a given hash.Some problems cannot be split up into parallel portions, as they require the results from a preceding step to effectively carry on with the next step – these are called inherently serial problems. Examples include iterative numerical methods, such as Newton's method, iterative solutions to the three-body problem, and most of the available algorithms to compute pi (π). Some sequential algorithms can be converted into parallel algorithms using automatic parallelization.
Cell lineage tree Mapping the embryogenic tree Cell_lineage_tree > Mapping the embryogenic tree If cells of a particular line have been removed from the embryo and are growing alone in a Petri dish in the lab, and some cell signaling chemicals are put in the growth medium bathing the cells, this can induce the cells to differentiate into a different, “daughter” cell type, mimicking the differentiation process that occurs naturally in the developing embryo. Artificially inducing differentiation in this way can yield clues to the correct placement of a particular cell line in the embryogenic tree, by observing what kind of cell results from inducing the differentiation. In the laboratory, human embryonic stem cells growing in culture can be induced to differentiate into progenitor cells by exposing the hESCs to chemicals (e.g. protein growth and differentiation factors) present in the developing embryo. The progenitor cells so produced may then be isolated into pure colonies, grown in culture, and then classified according to type and assigned positions in the embryogenic tree. Such purified cultures of progenitor cells may be used in research to study disease processes in vitro, as diagnostic tools, or potentially developed for use in regenerative medicine therapies.
Organizational technoethics Technoethical challenges in medical organizations Organizational_technoethics > New ethical challenges > Technoethical challenges in medical organizations Another area of organizational technoethics that has been becoming increasingly popular is in the field of medicine. Medical ethics are based on values and judgments in a practical clinical placement where six values are portrayed the most: autonomy, beneficence, non-maleficence, justice, dignity, truthfulness and honesty. Many of the issues in medical ethics are due to a lack of communication between the patients, family members, and health care team. An asset to medical ethics that has brought attention to its advantages and disadvantages are electronic medical records.
Computer architecture simulator Cycle-accurate simulator Cycle-accurate_simulator > Categories > Cycle-accurate simulator A cycle-accurate simulator is a computer program that simulates a microarchitecture on a cycle-by-cycle basis. In contrast an instruction set simulator simulates an instruction set architecture usually faster but not cycle-accurate to a specific implementation of this architecture; they are often used when emulating older hardware, where time precision is important for legacy reasons. Often, a cycle-accurate simulator is used when designing new microprocessors – they can be tested, and benchmarked accurately (including running full operating system, or compilers) without actually building a physical chip, and easily change design many times to meet expected plan. Cycle-accurate simulators must ensure that all operations are executed in the proper virtual (or real if it is possible) time – branch prediction, cache misses, fetches, pipeline stalls, thread context switching, and many other subtle aspects of microprocessors.
Corecursion Factorial Corecursion > Examples > Factorial The recursive call does the same, unless the base case has been reached. Thus a call stack develops in the process. For example, to compute fac(3), this recursively calls in turn fac(2), fac(1), fac(0) ("winding up" the stack), at which point recursion terminates with fac(0) = 1, and then the stack unwinds in reverse order and the results are calculated on the way back along the call stack to the initial call frame fac(3) that uses the result of fac(2) = 2 to calculate the final result as 3 × 2 = 3 × fac(2) =: fac(3) and finally return fac(3) = 6.
Cadwork informatik AG Products and technical details Cadwork_informatik_AG > Products > Products and technical details cadwork is mainly known for its timber industry wood products, but in Switzerland, it is a leading software for civil engineers. In 2004, cadwork started the development of Lexocad, a BIM-level design-planning-construction software. cadwork 2D: The entry-level module to cadwork 2d, with two-dimensional lines and surfaces with different hatches. It is a '2.5D CAD system', in addition to two-dimensional editing, cadwork 2d also allows for height information.
Feynman diagram Path integral formulation Feynman_diagrams > Path integral formulation In a path integral, the field Lagrangian, integrated over all possible field histories, defines the probability amplitude to go from one field configuration to another. In order to make sense, the field theory should have a well-defined ground state, and the integral should be performed a little bit rotated into imaginary time, i.e. a Wick rotation. The path integral formalism is completely equivalent to the canonical operator formalism above.
S-duality Overview S-duality > Overview For certain theories, S-duality provides a way of doing computations at strong coupling by translating these computations into different computations in a weakly coupled theory. S-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way.
Ellsberg paradox Summary Ellsberg_paradox In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". John Maynard Keynes published a version of the paradox in 1921. It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks.
Sprocket Transportation Sprocket > Transportation In the case of bicycle chains, it is possible to modify the overall gear ratio of the chain drive by varying the diameter (and therefore, the tooth count) of the sprockets on each side of the chain. This is the basis of derailleur gears. A multi-speed bicycle, by providing two or three different-sized driving sprockets and up to 12 (as of 2018) different-sized driven sprockets, allows up to 36 different gear ratios.
Search Based Software Engineering Methods and techniques Search-based_software_engineering > Methods and techniques A number of methods and techniques are available, including: Profiling via instrumentation in order to monitor certain parts of a program as it is executed. Obtaining an abstract syntax tree associated with the program, which can be automatically examined to gain insights into its structure. Applications of program slicing relevant to SBSE include software maintenance, optimization and program analysis. Code coverage allows measuring how much of the code is executed with a given set of input data. Static program analysis
Epigenetic landscape Histone variants Epigenetic_theory > Mechanisms > Histone variants Different histone variants are incorporated into specific regions of the genome non-randomly. Their differential biochemical characteristics can affect genome functions via their roles in gene regulation, and maintenance of chromosome structures.
Solar thermal collector General Principles of Operation Evacuated_tube > General Principles of Operation A solar thermal collector functions as a heat exchanger that converts solar radiation into thermal energy. It differs from a conventional heat exchanger in several aspects. The solar energy flux (irradiance) incident on the Earth's surface has a variable and relatively low surface density, usually not exceeding 1100 W/m² without concentration systems. Moreover, the wavelength of incident solar radiation falls between 0.3 and 3 µm, which is significantly shorter than the wavelength of radiation emitted by most radiative surfaces.The collector absorbs the incoming solar radiation, converting it into thermal energy.
Glossary of genetics (M–Z) P Glossary_of_genetics_(M–Z) > P Position effects are a major focus of research in the field of epigenetic inheritance. positional cloning Also map-based cloning. A strategy for identifying and cloning a candidate gene based on knowledge of its locus or position alone and with little or no information about its products or function, in contrast to functional cloning.
Surf forecasting Wrapping and refraction Surf_forecasting > Using bathymetry to predict surf for a specific break > Wrapping and refraction One important fact about waves is that they focus more of their energy towards shallower water. Waves will always turn and refract towards shallower water. This is where swell period can drastically affect the conditions.
Load and Resistance Factor Design Serviceability limit state (SLS) Limit_state_design > Serviceability limit state (SLS) The aim is to prove that under the action of Characteristic design loads (un-factored), and/or whilst applying certain (un-factored) magnitudes of imposed deformations, settlements, or vibrations, or temperature gradients etc. the structural behavior complies with, and does not exceed, the SLS design criteria values, specified in the relevant standard in force. These criteria involve various stress limits, deformation limits (deflections, rotations and curvature), flexibility (or rigidity) limits, dynamic behavior limits, as well as crack control requirements (crack width) and other arrangements concerned with the durability of the structure and its level of everyday service level and human comfort achieved, and its abilities to fulfill its everyday functions. In view of non-structural issues it might also involve limits applied to acoustics and heat transmission that might also affect the structural design. This calculation check is performed at a point located at the lower half of the elastic zone, where characteristic (un-factored) actions are applied and the structural behavior is purely elastic.
Multiple correspondence analysis Multiple correspondence analysis and principal component analysis Multiple_correspondence_analysis > Multiple correspondence analysis and principal component analysis Let denote p k {\displaystyle p_{k}} , the proportion of individuals possessing the category k {\displaystyle k} . The transformed CDT (TCDT) has as general term: x i k = y i k / p k − 1 {\displaystyle x_{ik}=y_{ik}/p_{k}-1} The unstandardized PCA applied to TCDT, the column k {\displaystyle k} having the weight p k {\displaystyle p_{k}} , leads to the results of MCA. This equivalence is fully explained in a book by Jérôme Pagès.
Absorptive state Digestive hormones Chemical_digestion > Digestive hormones Connections to metabolic control (largely the glucose-insulin system) have been uncovered. Gastrin – is in the stomach and stimulates the gastric glands to secrete pepsinogen (an inactive form of the enzyme pepsin) and hydrochloric acid. Secretion of gastrin is stimulated by food arriving in stomach.
Viewing transformation Application Vertex_lighting > Structure > Application The application step is executed by the software on the main processor (CPU). During the application step, changes are made to the scene as required, for example, by user interaction by means of input devices or during an animation. The new scene with all its primitives, usually triangles, lines and points, is then passed on to the next step in the pipeline.
Sedimentary Rock Summary Sedimentary_rocks The geological detritus is transported to the place of deposition by water, wind, ice or mass movement, which are called agents of denudation. Biological detritus was formed by bodies and parts (mainly shells) of dead aquatic organisms, as well as their fecal mass, suspended in water and slowly piling up on the floor of water bodies (marine snow). Sedimentation may also occur as dissolved minerals precipitate from water solution.
Base-e logarithm Summary Base-e_logarithm The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural".
Multi-track Turing machine Summary Multi-track_Turing_machine A Multitrack Turing machine is a specific type of multi-tape Turing machine. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in an n-track Turing Machine contains n symbols from the tape alphabet. It is equivalent to the standard Turing machine and therefore accepts precisely the recursively enumerable languages.
Sensor based sorting Summary Sensor_based_sorting Sensor-based sorting, is an umbrella term for all applications in which particles are detected using a sensor technique and rejected by an amplified mechanical, hydraulic or pneumatic process. The technique is generally applied in mining, recycling and food processing and used in the particle size range between 0.5 and 300 mm (0.020 and 11.811 in). Since sensor-based sorting is a single particle separation technology, the throughput is proportional to the average particle size and weight fed onto the machine.
Slope of a line Statistics Slope_of_a_line > Statistics In statistics, the gradient of the least-squares regression best-fitting line for a given sample of data may be written as: m = r s y s x {\displaystyle m={\frac {rs_{y}}{s_{x}}}} ,This quantity m is called as the regression slope for the line y = m x + c {\displaystyle y=mx+c} . The quantity r {\displaystyle r} is Pearson's correlation coefficient, s y {\displaystyle s_{y}} is the standard deviation of the y-values and s x {\displaystyle s_{x}} is the standard deviation of the x-values. This may also be written as a ratio of covariances: m = cov ⁡ ( Y , X ) cov ⁡ ( X , X ) {\displaystyle m={\frac {\operatorname {cov} (Y,X)}{\operatorname {cov} (X,X)}}}
History of special relativity Electromagnetic mass History_of_special_relativity > Aether and electrodynamics of moving bodies > Electromagnetic mass Also for Lorentz (1899), the integration of the speed-dependence of masses recognized by Thomson was especially important. He noticed that the mass not only varied due to speed, but is also dependent on the direction, and he introduced what Abraham later called "longitudinal" and "transverse" mass. (The transverse mass corresponds to what later was called relativistic mass.)
Principle of least time Laplace, Young, Fresnel, and Lorentz Principle_of_least_time > History > Laplace, Young, Fresnel, and Lorentz On 30 January 1809, Pierre-Simon Laplace, reporting on the work of his protégé Étienne-Louis Malus, claimed that the extraordinary refraction of calcite could be explained under the corpuscular theory of light with the aid of Maupertuis's principle of least action: that the integral of speed with respect to distance was a minimum. The corpuscular speed that satisfied this principle was proportional to the reciprocal of the ray speed given by the radius of Huygens' spheroid. Laplace continued: According to Huygens, the velocity of the extraordinary ray, in the crystal, is simply expressed by the radius of the spheroid; consequently his hypothesis does not agree with the principle of the least action: but it is remarkable that it agrees with the principle of Fermat, which is, that light passes, from a given point without the crystal, to a given point within it, in the least possible time; for it is easy to see that this principle coincides with that of the least action, if we invert the expression of the velocity. Laplace's report was the subject of a wide-ranging rebuttal by Thomas Young, who wrote in part: The principle of Fermat, although it was assumed by that mathematician on hypothetical, or even imaginary grounds, is in fact a fundamental law with respect to undulatory motion, and is explicitly the basis of every determination in the Huygenian theory... Mr. Laplace seems to be unacquainted with this most essential principle of one of the two theories which he compares; for he says, that "it is remarkable," that the Huygenian law of extraordinary refraction agrees with the principle of Fermat; which he would scarcely have observed, if he had been aware that the law was an immediate consequence of the principle.
Steering ratio Summary Steering_ratio Steering ratio refers to the ratio between the turn of the steering wheel (in degrees) or handlebars and the turn of the wheels (in degrees).The steering ratio is the ratio of the number of degrees of turn of the steering wheel to the number of degrees the wheel(s) turn as a result. In motorcycles, delta tricycles and bicycles, the steering ratio is always 1:1, because the steering wheel is fixed to the front wheel. A steering ratio of x:y means that a turn of the steering wheel x degree(s) causes the wheel(s) to turn y degree(s). In most passenger cars, the ratio is between 12:1 and 20:1.
Tree automata Recognizability Nondeterministic_tree_automaton > Properties > Recognizability For a bottom-up automaton, a ground term t (that is, a tree) is accepted if there exists a reduction that starts from t and ends with q(t), where q is a final state. For a top-down automaton, a ground term t is accepted if there exists a reduction that starts from q(t) and ends with t, where q is an initial state. The tree language L(A) accepted, or recognized, by a tree automaton A is the set of all ground terms accepted by A. A set of ground terms is recognizable if there exists a tree automaton that accepts it. A linear (that is, arity-preserving) tree homomorphism preserves recognizability.
Desorption Thermal desorption Desorption > Desorption mechanisms > Thermal desorption An example of an Arrhenius plot can be seen in the figure on the right. The activation energy can be found from the gradient of this Arrhenius plot.
Resistance spot welding Characteristics Resistance_spot_welding > Characteristics The resistance presented to the welder is complicated. There is the resistance of secondary winding, the cables, and the welding electrodes. There is also the contact resistance between the welding electrodes and the workpiece.
Infrared countermeasures Principles Infrared_countermeasure > Principles The effectiveness of the IRCM is determined by the ratio of jamming intensity to the target (or signal) intensity. This ratio is usually called the J/S ratio. Another important factor is the modulation frequencies which should be close to the actual missile frequencies. For spin scan missiles the required J/S is quite low but for newer missiles the required J/S is quite high requiring a directional source of radiation (DIRCM).
Reductions with hydrosilanes Safety Reductions_with_hydrosilanes > Safety Trifluoroacetic acid, often used in these reductions, is a strong, corrosive acid. Some hydrosilanes are pyrophoric. == References ==
Boiling point elevation The equation for calculations at dilute concentration Boiling_point_elevation > The equation for calculations at dilute concentration bc is the colligative molality, calculated by taking dissociation into account since the boiling point elevation is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as bc = bsolute · i, where bsolute is the molality of the solution. The factor i accounts for the number of individual particles (typically ions) formed by a compound in solution.
Self-adjoint operators Spectral theorem Self-adjoint_operator > Spectral theorem In the physics literature, the spectral theorem is often stated by saying that a self-adjoint operator has an orthonormal basis of eigenvectors. Physicists are well aware, however, of the phenomenon of "continuous spectrum"; thus, when they speak of an "orthonormal basis" they mean either an orthonormal basis in the classic sense or some continuous analog thereof. In the case of the momentum operator P = − i d d x {\textstyle P=-i{\frac {d}{dx}}} , for example, physicists would say that the eigenvectors are the functions f p ( x ) := e i p x {\displaystyle f_{p}(x):=e^{ipx}} , which are clearly not in the Hilbert space L 2 ( R ) {\displaystyle L^{2}(\mathbb {R} )} . (Physicists would say that the eigenvectors are "non-normalizable.")
Premature aging Werner syndrome Premature_aging > Defects in DNA repair > RecQ-associated PS > Werner syndrome This leads to a reduction in DNA repair. Furthermore, mutated proteins are more likely to be degraded than normal WRNp. Apart from causing defects in DNA repair, its aberrant association with p53 down-regulates the function of p53, leading to a reduction in p53-dependent apoptosis and increase the survival of these dysfunctional cells.Cells of affected individuals have reduced lifespan in culture, more chromosome breaks and translocations and extensive deletions. These DNA damages, chromosome aberrations and mutations may in turn cause more RecQ-independent aging phenotypes.
Equilibrium fractionation Other types of fractionation Equilibrium_fractionation > Other types of fractionation Kinetic fractionation Mass-independent fractionation Transient kinetic isotope fractionation
Junction transistor Structure PNP_transistor > Structure BJTs can be thought of as voltage-controlled current sources, but are more simply characterized as current-controlled current sources, or current amplifiers, due to the low impedance at the base. Early transistors were made from germanium but most modern BJTs are made from silicon.
Differential form Applications in physics Exterior_form > Applications in physics Differential forms arise in some important physical contexts. For example, in Maxwell's theory of electromagnetism, the Faraday 2-form, or electromagnetic field strength, is F = 1 2 f a b d x a ∧ d x b , {\displaystyle {\textbf {F}}={\frac {1}{2}}f_{ab}\,dx^{a}\wedge dx^{b}\,,} where the fab are formed from the electromagnetic fields E → {\displaystyle {\vec {E}}} and B → {\displaystyle {\vec {B}}} ; e.g., f12 = Ez/c, f23 = −Bz, or equivalent definitions. This form is a special case of the curvature form on the U(1) principal bundle on which both electromagnetism and general gauge theories may be described. The connection form for the principal bundle is the vector potential, typically denoted by A, when represented in some gauge.
Disability access Education and accessibility for students Accessible_image > Education and accessibility for students Equal access to education for students with disabilities is supported in some countries by legislation. It is still challenging for some students with disabilities to fully participate in mainstream education settings, but many adaptive technologies and assistive programs are making improvements. In India, the Medical Council of India has now passed the directives to all the medical institutions to make them accessible to persons with disabilities. This happened due to a petition by Dr Satendra Singh founder of Infinite Ability.Students with a physical or mental impairment or learning disability may require note-taking assistance, which may be provided by a business offering such services, as with tutoring services.
Plasmon Surface plasmons Plasmon > Surface plasmons This is much more difficult and has only recently become possible to do in any reliable or available way. Recently, graphene has also been shown to accommodate surface plasmons, observed via near field infrared optical microscopy techniques and infrared spectroscopy. Potential applications of graphene plasmonics mainly addressed the terahertz to midinfrared frequencies, such as optical modulators, photodetectors, biosensors.
Ogden–Roxburgh model Summary Ogden–Roxburgh_model The basis of pseudo-elastic material models is a hyperelastic second Piola–Kirchhoff stress S 0 {\displaystyle {\boldsymbol {S}}_{0}} , which is derived from a suitable strain energy density function W ( C ) {\displaystyle W({\boldsymbol {C}})}: S = 2 ∂ W ∂ C . {\displaystyle {\boldsymbol {S}}=2{\frac {\partial W}{\partial {\boldsymbol {C}}}}\quad .} The key idea of pseudo-elastic material models is that the stress during the first loading process is equal to the basic stress S 0 {\displaystyle {\boldsymbol {S}}_{0}} .
Glossary of chemistry terms T Glossary_of_chemistry_terms > T trace element An element in a sample which has an average concentration of less than 100 parts per million atoms or less than 100 micrograms per gram. transactinides Also superheavy elements. In the periodic table, the set of chemical elements with an atomic number greater than 103, i.e. those heavier than the actinides.
Conjugate depth Mathematical derivation Conjugate_depth > Mathematical derivation {\displaystyle {\frac {q^{2}}{g}}\left({\frac {1}{y_{1}y_{2}}}\right)={\frac {1}{2}}(y_{2}+y_{1})\qquad {\text{where }}q_{1}^{2}=y_{1}^{2}v_{1}^{2}=y_{2}^{2}v_{2}^{2}.} Divide by y12 v 1 2 g ( 1 y 1 y 2 ) = 1 2 y 1 2 ( y 2 + y 1 ) recall F r 1 2 = v 1 2 g y 1 . {\displaystyle {\frac {v_{1}^{2}}{g}}\left({\frac {1}{y_{1}y_{2}}}\right)={\frac {1}{2y_{1}^{2}}}(y_{2}+y_{1})\qquad {\text{recall }}Fr_{1}^{2}={\frac {v_{1}^{2}}{gy_{1}}}.}
Polymer characterization Mechanical properties Polymer_characterization > Mechanical properties An oscillating force is applied to a polymer sample and the sample’s response is recorded. DMA documents the lag between force applied and deformation recovery in the sample. Viscoelastic samples exhibit a sinusoidal modulus called the dynamic modulus.
Value cache encoding Replacement Policy Value_cache_encoding > Replacement Policy LRU is used as replacement policy in both caches. It is implemented using reference bit and a n-bit time stamp for each value stored in cache. When a value appears in input, reference bit is set. At regular intervals, the reference bit is shifted right into the high-order bit position of the n-bit timestamp causing all bits in the timestamp also to be shifted right and the lowest-order bit in the timestamp being discarded.
Alpha adrenergic receptor History Alpha_adrenergic_receptor > History Although, if the animal had been exposed to ergotoxine, the blood pressure decreased. He proposed that the ergotoxine caused "selective paralysis of motor myoneural junctions" (i.e. those tending to increase the blood pressure) hence revealing that under normal conditions that there was a "mixed response", including a mechanism that would relax smooth muscle and cause a fall in blood pressure. This "mixed response", with the same compound causing either contraction or relaxation, was conceived of as the response of different types of junctions to the same compound.
Shape control in nanocrystal growth Thermodynamic versus kinetic control Shape_control_in_nanocrystal_growth > Thermodynamic versus kinetic control The addition of a monomer to the crystal happens at the highest energy facet of the crystal, since that is the most active site and the monomer deposition thus has the lowest activation energy there. Usually, this facet is situated at a corner of the nanoparticle. These facets however, as explained in the section above, are not the most energetically favorable position for the added monomer.
Cooperative principle Criticism Cooperative_principle > Criticism Grice's theory is often disputed by arguing that cooperative conversation, like most social behaviour, is culturally determined, and therefore the Gricean maxims and the cooperative principle do not universally apply because of cultural differences. Keenan (1976) claims, for example, that the Malagasy people follow a completely opposite cooperative principle to achieve conversational cooperation. In their culture, speakers are reluctant to share information and flout the maxim of quantity by evading direct questions and replying on incomplete answers because of the risk of losing face by committing oneself to the truth of the information, as well as the fact that having information is a form of prestige. To push back on this point, Harnish (1976) points out that Grice only claims his maxims hold in conversations where the cooperative principle is in effect.
Point-to-Point Tunneling Protocol Security Point-to-Point_Tunneling_Protocol > Security There is no method for authentication of the ciphertext stream and therefore the ciphertext is vulnerable to a bit-flipping attack. An attacker could modify the stream in transit and adjust single bits to change the output stream without possibility of detection. These bit flips may be detected by the protocols themselves through checksums or other means.EAP-TLS is seen as the superior authentication choice for PPTP; however, it requires implementation of a public-key infrastructure for both client and server certificates.
Fairness (machine learning) Adversarial debiasing Fairness_(machine_learning) > Bias Mitigation strategies > Inprocessing > Adversarial debiasing Then we update U {\textstyle U} to minimize L A {\textstyle L_{A}} at each training step according to the gradient ∇ U L A {\textstyle \nabla _{U}L_{A}} and we modify W {\textstyle W} according to the expression: where α \alpha is a tuneable hyperparameter that can vary at each time step. The intuitive idea is that we want the predictor to try to minimize L P {\textstyle L_{P}} (therefore the term ∇ W L P {\textstyle \nabla _{W}L_{P}} ) while, at the same time, maximize L A {\textstyle L_{A}} (therefore the term − α ∇ W L A {\textstyle -\alpha \nabla _{W}L_{A}} ), so that the adversary fails at predicting the sensitive variable from Y ^ {\textstyle {\hat {Y}}} . The term − p r o j ∇ W L A ∇ W L P {\textstyle -proj_{\nabla _{W}L_{A}}\nabla _{W}L_{P}} prevents the predictor from moving in a direction that helps the adversary decrease its loss function. It can be shown that training a predictor classification model with this algorithm improves demographic parity with respect to training it without the adversary.
Neuroesthetics Abstraction Neuroesthetics > Frameworks > Semir Zeki's laws of the visual brain > Abstraction This process refers to the hierarchical coordination where a general representation can be applied to many particulars, allowing the brain to efficiently process visual stimuli. The ability to abstract may have evolved as a necessity due to the limitations of memory. In a way, art externalizes the functions of abstraction in the brain. The process of abstraction is unknown to cognitive neurobiology. However, Zeki proposes an interesting question of whether there is a significant difference in the pattern of brain activity when viewing abstract art as opposed to representational art.
Continuum Mechanics Body forces Cauchy's_laws_of_motion > Forces in a continuum > Body forces Body forces are forces originating from sources outside of the body that act on the volume (or mass) of the body. Saying that body forces are due to outside sources implies that the interaction between different parts of the body (internal forces) are manifested through the contact forces alone. These forces arise from the presence of the body in force fields, e.g. gravitational field (gravitational forces) or electromagnetic field (electromagnetic forces), or from inertial forces when bodies are in motion. As the mass of a continuous body is assumed to be continuously distributed, any force originating from the mass is also continuously distributed.
Water key Summary Water_key A water key is a valve or tap used to allow the drainage of accumulated fluid from wind instruments. It is otherwise known as a water valve or spit valve. They are most often located where gravity assists the fluid collection, in such valved instruments such as trumpets, cornets and flugelhorns under the lowest bend of the main tuning slide and on valve slides. On the trombone, it is on the lower side of the bend in the hand slide.
Sigma Pi Executive Office and Executive Director Sigma_Pi > Government > Executive Office and Executive Director The Executive Office, located in Nashville, Tennessee, serves as an information and service center as well as being the primary record keeper of the fraternity. Information and assistance is available for all phases of chapter operations. All templates of forms and other materials are kept at the Executive Office. All of the Fraternity's publications are prepared and distributed at the Executive Offices.
DNA damage (naturally occurring) Summary DNA_damage_(naturally_occurring) (Also see DNA damage theory of aging.) In replicating cells, such as cells lining the colon, errors occur upon replication past damages in the template strand of DNA or during repair of DNA damages.
Dirichlet's ellipsoidal problem Summary Dirichlet's_ellipsoidal_problem In astrophysics, Dirichlet's ellipsoidal problem, named after Peter Gustav Lejeune Dirichlet, asks under what conditions there can exist an ellipsoidal configuration at all times of a homogeneous rotating fluid mass in which the motion, in an inertial frame, is a linear function of the coordinates. Dirichlet's basic idea was to reduce Euler equations to a system of ordinary differential equations such that the position of a fluid particle in a homogeneous ellipsoid at any time is a linear and homogeneous function of initial position of the fluid particle, using Lagrangian framework instead of the Eulerian framework.
Kepler-13b Planetary system Kepler-13 > Planetary system Kepler-13 was identified as one of 1235 planetary candidates with transit-like signatures in the first four months of Kepler data. It was confirmed as a planet by measuring the Doppler beaming effect on the Kepler light curve. The planet that has been confirmed, having a radius of between 1.5 and 2.6 RJ, is also one of the largest known exoplanets.
Voltage scaling Program execution speed Switching_power > Program execution speed The speed at which a digital circuit can switch states - that is, to go from "low" (VSS) to "high" (VDD) or vice versa - is proportional to the voltage differential in that circuit. Reducing the voltage means that circuits switch slower, reducing the maximum frequency at which that circuit can run. This, in turn, reduces the rate at which program instructions that can be issued, which may increase run time for program segments which are sufficiently CPU-bound. This again highlights why dynamic voltage scaling is generally done in conjunction with dynamic frequency scaling, at least for CPUs.
Viral meningitis Summary Viral_meningitis Viral meningitis, also known as aseptic meningitis, is a type of meningitis due to a viral infection. It results in inflammation of the meninges (the membranes covering the brain and spinal cord). Symptoms commonly include headache, fever, sensitivity to light and neck stiffness.Viruses are the most common cause of aseptic meningitis. Most cases of viral meningitis are caused by enteroviruses (common stomach viruses).
Metamorphic code Overview Metamorphic_code > Overview Metamorphism does not protect a virus against heuristic analysis.Metamorphic code can also mean that a virus is capable of infecting executables from two or more different operating systems (such as Windows and Linux) or even different computer architectures. Often, the virus does this by carrying several viruses within itself. The beginning of the virus is then coded so that it translates to correct machine-code for all of the platforms that it is supposed to execute in. This is used primarily in remote exploit injection code where the target platform is unknown.
Apache Parquet Features Apache_Parquet > Features Apache Parquet is implemented using the record-shredding and assembly algorithm, which accommodates the complex data structures that can be used to store data. The values in each column are stored in contiguous memory locations, providing the following benefits: Column-wise compression is efficient in storage space Encoding and compression techniques specific to the type of data in each column can be used Queries that fetch specific column values need not read the entire row, thus improving performanceApache Parquet is implemented using the Apache Thrift framework, which increases its flexibility; it can work with a number of programming languages like C++, Java, Python, PHP, etc.As of August 2015, Parquet supports the big-data-processing frameworks including Apache Hive, Apache Drill, Apache Impala, Apache Crunch, Apache Pig, Cascading, Presto and Apache Spark. It is one of external data formats used by pandas Python data manipulation and analysis library.
Protein S Structure Protein_S > Structure Protein S is partly homologous to other vitamin K-dependent plasma coagulation proteins, such as protein C and factors VII, IX, and X. Similar to them, it has a Gla domain and several EGF-like domains (four rather than two), but no serine protease domain. Instead, there is a large C-terminus domain that is homologous to plasma steroid hormone-binding proteins such as sex hormone-binding globulin and corticosteroid-binding globulin. It may play a role in the protein functions as either a cofactor for activated protein C (APC) or in binding C4BP.Additionally, protein S has a peptide between the Gla domain and the EGF-like domain, that is cleaved by thrombin. The Gla and EGF-like domains stay connected after the cleavage by a disulfide bond. However, protein S loses its function as an APC cofactor following either this cleavage or binding C4BP.
Local oxidation nanolithography Basic principle Local_oxidation_nanolithography > Basic principle When the liquid meniscus is created the applied voltage pulse causes an oxidation reaction by breaking the covalent bonds in the water molecules. The liquid bridge provides the oxyanions (OH−,O−) needed to form the oxide and confines the lateral extension of the region to be oxidized. The chemical reactions that govern the Local Oxidation in a metallic substrate (M) are the following: M + n H 2 O ⟶ MO n + 2 n H + + 2 n e − {\displaystyle {\ce {M}}+n{\ce {H2O -> MO}}_{n}+2n{\ce {H+}}+2n{\ce {e-}}} M n + 2 n H 2 O + 2 n e − ⟶ n H 2 + 2 n OH − + M {\displaystyle {\ce {M}}^{n}+2n{\ce {H2O}}+2n{\ce {e- ->}}\ n{\ce {H2}}+2n{\ce {OH- + M}}} while hydrogen gas is liberated at the AFM tip through the reduction reaction: 2 H + + 2 e − ⟶ H 2 {\displaystyle {\ce {2H+ + 2e- -> H2}}} When the voltage pulse is off the AFM feedback forces the cantilever to recover its original oscillation amplitude withdrawing the tip from the sample and breaking the liquid meniscus.
Non-measurable set Historical constructions Non-measurable_subset > Historical constructions While a finitely additive measure is sufficient for most intuition of area, and is analogous to Riemann integration, it is considered insufficient for probability, because conventional modern treatments of sequences of events or random variables demand countable additivity. In this respect, the plane is similar to the line; there is a finitely additive measure, extending Lebesgue measure, which is invariant under all isometries. For higher dimensions the picture gets worse. The Hausdorff paradox and Banach–Tarski paradox show that a three-dimensional ball of radius 1 can be dissected into 5 parts which can be reassembled to form two balls of radius 1.
Mars Oxygen ISRU Experiment Principle Mars_Oxygen_ISRU_Experiment > Principle Through a combination of thermal dissociation and electrocatalysis, an oxygen atom is liberated from the CO2 molecule and picks up two electrons from the cathode to become an oxide ion (O2–). Via oxygen ion vacancies in the crystal lattice of the electrolyte, the oxygen ion is transported to the electrolyte–anode interface due to the applied DC potential. At this interface, the oxygen ion transfers its charge to the anode, combines with another oxygen atom to form oxygen (O2), and diffuses out of the anode.The net reaction was thus 2 CO2 ⟶ {\displaystyle \longrightarrow } 2 CO + O2. Inert gases such as nitrogen gas (N2) and argon (Ar) are not separated from the feed, but returned to the atmosphere with the carbon monoxide (CO) and unused CO2.
S-SodF RNA Summary S-SodF_RNA Their expression is inversely regulated by nickel-specific Fur-family regulator called Nur. When Ni is present Nur directly represses sodF transcription, and indirectly induces sodN. == References ==
Blue bottle experiment History and general concept Vanishing_valentine_experiment > Reactions > History and general concept Thus, the overall net reaction is determined by the sum of all the mechanism steps where the rate depends on the concentration and temperature. The blue bottle experiment illustrates this principle of interacting reactions with different rates.The blue bottle experiment requires only three reagents: potassium hydroxide solution, dextrose solution, and dilute methylene blue solution. These reagents are added to a flask, mixed, and the flask is stoppered.
Johann Bernoulli Works Johann_Bernoulli > Works Parigi: sn. Retrieved 18 June 2015.Bernoulli, Johann (1739). Dissertatio de ancoris (in Latin). Leipzig: sn. Retrieved 20 June 2018.
Silicon transistor Summary Transistor Compared with the vacuum tube, transistors are generally smaller and require less power to operate. Certain vacuum tubes have advantages over transistors at very high operating frequencies or high operating voltages. Many types of transistors are made to standardized specifications by multiple manufacturers.
Causal attribution Correspondent inference Attribution_theory > Theories and models > Correspondent inference Correspondent inferences state that people make inferences about a person when their actions are freely chosen, are unexpected, and result in a small number of desirable effects. According to Edward E. Jones and Keith Davis' correspondent inference theory, people make correspondent inferences by reviewing the context of behavior. It describes how people try to find out an individual's personal characteristics from the behavioral evidence.
Exercise intolerance Low ATP reservoir in muscles (inherited or acquired) Exercise_intolerance > Causes > Low ATP reservoir in muscles (inherited or acquired) Exercise tolerance reflects the combined capacity of components in the oxygen cascade to supply adequate oxygen for ATP resynthesis by oxidative phosphorylation. In individuals with diseases such as cancer, certain therapies can affect one or more components of this cascade and therefore reduce the body's ability to utilise or deliver oxygen, leading to temporary exercise intolerance. Abnormal thyroid function can cause hyperthyroid myopathy and hypothyroid myopathy by affecting myocardial oxygen function.
Nonalcoholic fatty liver disease Summary Non-alcoholic_fatty_liver_disease NAFL is less dangerous than MASH and usually does not progress towards it. When NAFL does progress to MASH, it may eventually lead to complications such as cirrhosis, liver cancer, liver failure, or cardiovascular disease.The umbrella term steatotic liver disease (SLD) covers MAFLD, Alcoholic Liver Disease (ALD) and MetALD, a term describing people with MAFLD who consume more than 140 grams of alcohol per week for women and 210 grams per week for men (an in between MAFLD and ALD).Obesity and type 2 diabetes are strong risk factors for MAFLD. Other risks include being overweight, metabolic syndrome (defined as at least three of the five following medical conditions: abdominal obesity, high blood pressure, high blood sugar, high serum triglycerides, and low serum HDL cholesterol), a diet high in fructose, and older age.
Doppler radio direction finding Pseudo-Doppler Doppler_radio_direction_finding > Pseudo-Doppler The direction to the target transmitter can then be determined in the same fashion as the moving-antenna case, by comparing the phase of this signal to a reference signal. In this case, the reference is the clock signal triggering the switch.Because it has no moving parts and can be built using simple electronics, the pseudo-Doppler technique is very popular. Whilst not quite as fast as to take a measurement as the huff-duff system, in modern systems the measurement is so rapid that there is little practical difference between the two concepts.
Glycogen Liver Glycogen > Functions > Liver As a meal containing carbohydrates or protein is eaten and digested, blood glucose levels rise, and the pancreas secretes insulin. Blood glucose from the portal vein enters liver cells (hepatocytes). Insulin acts on the hepatocytes to stimulate the action of several enzymes, including glycogen synthase.
Causal Inference Economics and political science Causal_Inference > Approaches in social sciences > Economics and political science In the economic sciences and political sciences causal inference is often difficult, owing to the real world complexity of economic and political realities and the inability to recreate many large-scale phenomena within controlled experiments. Causal inference in the economic and political sciences continues to see improvement in methodology and rigor, due to the increased level of technology available to social scientists, the increase in the number of social scientists and research, and improvements to causal inference methodologies throughout social sciences.Despite the difficulties inherent in determining causality in economic systems, several widely employed methods exist throughout those fields.
SRD5A3-CDG Existing Research SRD5A3-CDG > Existing Research SRD5A3-CDG is caused by a single-gene mutation, which makes it an attractive candidate for gene therapy. However, due to the extreme rarity of the disorder, research around it has been limited. Research has predominantly been focused on two types of research models: Cell-based models and model organisms.Common cell-based models include patient cells such as fibroblast cells derived from skin samples (patient-derived fibroblasts ), induced pluripotent stem cells (iPSCs) created by reprogramming fibroblasts, and specialized cells, such as neurons derived from stem cell differentiation. Patient-derived cell models are important preclinical model systems as they contain the same genome and mutation(s) as the patient, allowing researchers to assess potential therapies for individual patients early on in the drug development process.
Bond valuation Accounting treatment Bond_valuation > Accounting treatment In accounting for liabilities, any bond discount or premium must be amortized over the life of the bond. A number of methods may be used for this depending on applicable accounting rules. One possibility is that amortization amount in each period is calculated from the following formula: n ∈ { 0 , 1 , . .
Organisational learning Theoretical models Organisational_learning > Knowledge > Theoretical models The Fang model (2011) shares a major goal with the Huberman model: to gradually decrease the steps towards the final stage. However, this model takes more of a "credit assignment" approach in which credit is assigned to successive states as an organization gains more experience, and then learning occurs by way of credit propagation. This implies that as an organization gains more experience with the task, it is better able to develop increasingly accurate mental models that initially identify the values of states closer to the goal and then those of states farther from the goal. This then leads to a reduced number of steps to reach the organization's final goal and can thus improve overall performance.
Microbial rhodopsin Channelrhodopsins Microbial_rhodopsin > Homologues > Channelrhodopsins It desensitizes to a small conductance in continuous light. Recovery from desensitization is accelerated by extracellular H+ and a negative membrane potential.
Unit impulse Fourier kernels Nascent_delta_function > Representations of the delta function > Fourier kernels In the study of Fourier series, a major question consists of determining whether and in what sense the Fourier series associated with a periodic function converges to the function. The n-th partial sum of the Fourier series of a function f of period 2π is defined by convolution (on the interval ) with the Dirichlet kernel: Thus, where A fundamental result of elementary Fourier series states that the Dirichlet kernel restricted to the interval tends to a multiple of the delta function as N → ∞. This is interpreted in the distribution sense, that for every compactly supported smooth function f. Thus, formally one has on the interval . Despite this, the result does not hold for all compactly supported continuous functions: that is DN does not converge weakly in the sense of measures. The lack of convergence of the Fourier series has led to the introduction of a variety of summability methods to produce convergence. The method of Cesàro summation leads to the Fejér kernel The Fejér kernels tend to the delta function in a stronger sense that for every compactly supported continuous function f. The implication is that the Fourier series of any continuous function is Cesàro summable to the value of the function at every point.
Bernhard Schrader Movies Bernhard_Schrader > Movies published by: IWF Göttingen, 1975 ( see: filmarchives-online.eu Search for = “Bernhard Schrader” ) Vibrations of Free Molecules - 1. Stretching and Bending Vibrations in Ethylene Schwingungen freier Moleküle - 2. Schwingungsformen der Methylgruppe in Propen Schwingungen freier Moleküle - 3. Schwingungsformen aromatischer Ringe in Melamin Oscillations of Molecules in Melamine Crystal Lattices with Hydrogen Bonds
Kalman gain Sensitivity analysis Kalman_gain > Sensitivity analysis The Kalman filtering equations provide an estimate of the state x ^ k ∣ k {\displaystyle {\hat {\mathbf {x} }}_{k\mid k}} and its error covariance P k ∣ k {\displaystyle \mathbf {P} _{k\mid k}} recursively. The estimate and its quality depend on the system parameters and the noise statistics fed as inputs to the estimator. This section analyzes the effect of uncertainties in the statistical inputs to the filter.
Robinson–Foulds metric Strengths and weaknesses Robinson–Foulds_metric > Strengths and weaknesses One example is that moving a tip and its neighbour to a particular point on a tree generates a lower difference value than if just one of the two tips were moved to the same place. Its range of values can depend on tree shape: trees that contain many uneven partitions will command relatively lower distances, on average, than trees with many even partitions. It performs more poorly than many alternative measures in practical settings, based on simulated trees.Another issue to consider when using RF distances is that differences in one clade may be trivial (perhaps if the clade resolves three species within a genus differently) or may be fundamental (if the clade is deep in the tree and defines two fundamental subgroups, such as mammals and birds).
Weighted random early detection Functional Description Weighted_random_early_detection > Functional Description WRED proceeds in this order when a packet arrives: Calculation of the average queue size. The arriving packet is queued immediately if the average queue size is below the minimum queue threshold. Depending on the packet drop probability the packet is either dropped or queued if the average queue size is between the minimum and maximum queue threshold. The packet is automatically dropped if the average queue size is greater than the maximum threshold.
Mass of electron Formation Electron > Formation Electrons (and positrons) are thought to be created at the event horizon of these stellar remnants. When a pair of virtual particles (such as an electron and positron) is created in the vicinity of the event horizon, random spatial positioning might result in one of them to appear on the exterior; this process is called quantum tunnelling. The gravitational potential of the black hole can then supply the energy that transforms this virtual particle into a real particle, allowing it to radiate away into space.
Seismic intensity scales Summary Seismic_intensity_scales Seismic intensity scales categorize the intensity or severity of ground shaking (quaking) at a given location, such as resulting from an earthquake. They are distinguished from seismic magnitude scales, which measure the magnitude or overall strength of an earthquake, which may, or perhaps may not, cause perceptible shaking. Intensity scales are based on the observed effects of the shaking, such as the degree to which people or animals were alarmed, and the extent and severity of damage to different kinds of structures or natural features. The maximal intensity observed, and the extent of the area where shaking was felt (see isoseismal map, below), can be used to estimate the location and magnitude of the source earthquake; this is especially useful for historical earthquakes where there is no instrumental record.
Active management Summary Active_management Active management (also called active investing) is an approach to investing. In an actively managed portfolio of investments, the investor selects the investments that make up the portfolio. Active management is often compared to passive management or index investing.
Glossary of industrial automation A Glossary_of_industrial_automation > A absolute vectorA vector whose start and end points are specified in absolute coordinates. accelerationRate of change of the velocity at the point under consideration per unit of time.
P-Delta Effect Summary P-Delta_Effect The idea is that iteratively repeated linear structural analyses can solve a non linear structural analysis problem. It takes multiple iterations of a linear analysis to compute the final deformed shape of a structure where the P DELTA effect is significant.
Zero-knowledge proof Ethical behavior Zero-knowledge_proofs > Applications > Ethical behavior One of the uses of zero-knowledge proofs within cryptographic protocols is to enforce honest behavior while maintaining privacy. Roughly, the idea is to force a user to prove, using a zero-knowledge proof, that its behavior is correct according to the protocol. Because of soundness, we know that the user must really act honestly in order to be able to provide a valid proof. Because of zero knowledge, we know that the user does not compromise the privacy of its secrets in the process of providing the proof.
POLDAT Summary POLDAT The "CC" prefix is an acronym for Customer and Channel. The complete version being CCPOLDAT an acronym for Customer, Channel, Process, Organisation, Location, Data, Application and Technology. Catalyst is an extensive program, project and operations management methodology with a range of development paths including an Agile like approach.
Rotational symmetries Rotational symmetry with respect to any angle Rotationally_symmetric > Formal treatment > Rotational symmetry with respect to any angle Rotational symmetry with respect to any angle is, in two dimensions, circular symmetry. The fundamental domain is a half-line. In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using cylindrical coordinates and no dependence on either angle using spherical coordinates.

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