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Spinors in three dimensions General remarks Spinors_in_three_dimensions > Examples in physics > General remarks . , + ( S − 1 ) ⋅ ℏ , + S ⋅ ℏ {\displaystyle \sigma =-S\cdot \hbar ,-(S-1)\cdot \hbar ,...,+(S-1)\cdot \hbar ,+S\cdot \hbar } .The total angular momentum operator, J → {\displaystyle {\vec {\mathbb {J} }}} , of a particle corresponds to the sum of the orbital angular momentum (i.e., there only integers are allowed) and the intrinsic part, the spin. One distinguishes bosons (S = 0, ±1, ±2, ...) and fermions (S = ±1/2, ±3/2, ±5/2, ...).
Sympathetic nervous system Organization Sympathetic_nervous_system > Structure > Organization The first cell (the presynaptic cell) sends a neurotransmitter across the synaptic cleft where it activates the second cell (the postsynaptic cell). The message is then carried to the final destination.
Tracheobronchial injury Signs and symptoms Tracheobronchial_injury > Signs and symptoms Coughing may be present, and stridor, an abnormal, high-pitched breath sound indicating obstruction of the upper airway can also occur.Damage to the airways can cause subcutaneous emphysema (air trapped in the subcutaneous tissue of the skin) in the abdomen, chest, neck, and head. Subcutaneous emphysema, present in up to 85% of people with TBI, is particularly indicative of the injury when it is only in the neck. Air is trapped in the chest cavity outside the lungs (pneumothorax) in about 70% of TBI.
Cohomology Axioms and generalized cohomology theories Cohomology > Axioms and generalized cohomology theories Various different flavors of topological K-theory, based on studying a space by considering all vector bundles over it: K O ∗ ( X ) {\displaystyle KO^{}(X)} (real periodic K-theory), k o ∗ ( X ) {\displaystyle ko^{}(X)} (real connective K-theory), K ∗ ( X ) {\displaystyle K^{}(X)} (complex periodic K-theory), k u ∗ ( X ) {\displaystyle ku^{}(X)} (complex connective K-theory), and so on. Brown–Peterson cohomology, Morava K-theory, Morava E-theory, and other theories built from complex cobordism. Various flavors of elliptic cohomology.Many of these theories carry richer information than ordinary cohomology, but are harder to compute. A cohomology theory E is said to be multiplicative if E ∗ ( X ) {\displaystyle E^{*}(X)} has the structure of a graded ring for each space X. In the language of spectra, there are several more precise notions of a ring spectrum, such as an E∞ ring spectrum, where the product is commutative and associative in a strong sense.
Compiled language Summary Compiled_language A compiled language is a programming language whose implementations are typically compilers (translators that generate machine code from source code), and not interpreters (step-by-step executors of source code, where no pre-runtime translation takes place). The term is somewhat vague. In principle, any language can be implemented with a compiler or with an interpreter. A combination of both solutions is also common: a compiler can translate the source code into some intermediate form (often called p-code or bytecode), which is then passed to an interpreter which executes it.
Finite point method Fluid mechanics Finite_point_method > Applications > Fluid mechanics The early lines of research and applications of the FPM to fluid flow problems are summarized in (Fischer, 1996). There, convective-diffusive problems were studied using LSQ and WLSQ polynomial approximations. The study focused on the effects of the cloud of points and weighting functions on the accuracy of the local approximation, which helped to understand the basic behavior of the FPM. The results showed that the 1D FPM approximation leads to discrete derivative forms similar to those obtained with central difference approximations, which are second-order accurate.
Relativity priority dispute Background Relativity_priority_dispute > Background None of them derived the Lorentz transformations on this basis. None of them fully understood the physical implications of these transformations. It all was Einstein's unique feat.
Vascular surgeon Renovascular hypertension Vascular_surgeon > Renovascular hypertension The renal arteries supply oxygenated blood to the kidneys. The kidneys serve to filter the flood and control blood pressure through the renin-angiotensin system. One cause of resistant hypertension is atherosclerotic disease in the renal arteries and is generally referred to as renovascular hypertension. If renovascular hypertension is diagnosed and maximal medical fails to control high blood pressure, the vascular surgeon may offer surgical treatment, either endovascular or open surgical reconstruction.
Xerography Process Xerography > Process The steps of the process are described below as applied on a cylinder, as in a photocopier. Some variants are described within the text. Every step of the process has design variants.
Program optimization Run time Code_optimization > Levels of optimization > Run time Self-modifying code can alter itself in response to run time conditions in order to optimize code; this was more common in assembly language programs. Some CPU designs can perform some optimizations at run time. Some examples include out-of-order execution, speculative execution, instruction pipelines, and branch predictors. Compilers can help the program take advantage of these CPU features, for example through instruction scheduling.
Magnetic polarity Summary Magnetic_polarity The local strength of magnetism in a material is measured by its magnetization. An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel, which greatly enhances the magnetic field produced by the coil.
Area integral Change of variables Double_integral > Methods of integration > Change of variables The limits of integration are often not easily interchangeable (without normality or with complex formulae to integrate). One makes a change of variables to rewrite the integral in a more "comfortable" region, which can be described in simpler formulae. To do so, the function must be adapted to the new coordinates. Example 1a.
Octave programming language Data structures Octave_programming_language > Notable features > Data structures Octave includes a limited amount of support for organizing data in structures. In this example, we see a structure x with elements a, b, and c, (an integer, an array, and a string, respectively):
Normal distributions Sample variance Normal_Distribution > Statistical inference > Estimation of parameters > Sample variance {\displaystyle s^{2}={\frac {n}{n-1}}{\hat {\sigma }}^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\overline {x}})^{2}.} The difference between s 2 {\displaystyle s^{2}} and σ ^ 2 {\displaystyle \textstyle {\hat {\sigma }}^{2}} becomes negligibly small for large n's. In finite samples however, the motivation behind the use of s 2 {\displaystyle s^{2}} is that it is an unbiased estimator of the underlying parameter σ 2 {\displaystyle \sigma ^{2}} , whereas σ ^ 2 {\displaystyle \textstyle {\hat {\sigma }}^{2}} is biased.
Personal Learning Networks Aspects Personal_Learning_Networks > Aspects Moreover, the learner will collaborate and connect differently with various members. The learner will establish stronger relationships with some members and have a low level of connection with others. Not all nodes will be equal. Some of the member roles include searcher, assemblator, designer of data, innovator of subject matter, and researcher.
Discrete calculus Applications Discrete_calculus > Applications Discrete calculus is used for modeling either directly or indirectly as a discretization of infinitesimal calculus in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other. Physics makes particular use of calculus; all discrete concepts in classical mechanics and electromagnetism are related through discrete calculus. The mass of an object of known density that varies incrementally, the moment of inertia of such objects, as well as the total energy of an object within a discrete conservative field can be found by the use of discrete calculus.
Artificial intelligence art Other generative AI Artificial_intelligence_art > Other generative AI Some prototype robots can create what is considered forms of art – such as dynamic cooking robots that can taste and readjust.There also is AI-assisted writing beyond copy-editing (including support in the generation of fictional stories such as helping with writer's block or inspiration or rewriting segments).AI could be and has been used in video game art beyond imagery only, especially for level design (e.g. for custom maps) and creating new content or interactive stories in video games.
Sewerage Water table Sewer_system > Challenges > Water table Sewer system infrastructure often reduces the water table in areas, especially in densely populated areas where rainwater (from house roofs) is directly piped into the system, as opposed to being allowed to be absorbed by the soil. In certain areas it has resulted in a significant lowering of the water table. In the example of Belgium, a lowering of the water table by 100 meters has been the result. The freshwater that is accumulated by the system is then piped to the sea. In areas where this is a concern, vacuum sewers may be used instead, due to the shallow excavation that is possible for them.
Calcium looping Basic concept Calcium_looping > Basic concept It is cooled to approximately 650 °C and is brought into contact with a flue gas containing a low to medium concentration of CO2. The CaO and CO2 react to form CaCO3, thus reducing the CO2 concentration in the flue gas to a level suitable for emission to the atmosphere. This is the 'backward' reaction in the equation above.Note that carbonation is calcination in reverse.
Van der Waals bonding Definition Van_der_Waals_potential > Definition More broadly, intermolecular forces have several possible contributions: A repulsive component resulting from the Pauli exclusion principle that prevents close contact of atoms, or the collapse of molecules. Attractive or repulsive electrostatic interactions between permanent charges (in the case of molecular ions), dipoles (in the case of molecules without inversion centre), quadrupoles (all molecules with symmetry lower than cubic), and in general between permanent multipoles.
Bandwidth Throttling Overview Bandwidth_Throttling > Overview Defined as the intentional slowing or speeding of an internet service by an Internet service provider (ISP). It is a reactive measure employed in communication networks to regulate network traffic and minimize bandwidth congestion. Bandwidth throttling can occur at different locations on the network.
Adrenalism Underproduction of aldosterone/ Hypoaldosteronism Adrenalism > Etiology > Hypoadrenalism > Underproduction of aldosterone/ Hypoaldosteronism Hypoaldosteronism occurs in primary adrenal insufficiency, but not secondary adrenal insufficiency. This is because secondary adrenal insufficiency is related to the pituitary gland and its ability to produce ACTH, which is not a hormone that regulates the production of Aldosterone from the adrenal gland. However, primary adrenal insufficiency is caused by damage to the adrenal glands, which leads to underproduction of the hormones. Primary adrenal insufficiency causes hypoaldosteronism along with hypocortisolism.
CPU instruction Summary Instruction_overlapping "Each instruction causes the CPU to perform a very specific task, such as a load, a store, a jump, or an arithmetic logic unit (ALU) operation on one or more units of data in the CPU's registers or memory. Early CPUs had specific machine code that might break backwards compatibility with each new CPU released. The notion of an instruction set architecture (ISA) defines and specifies the behavior and encoding in memory of the instruction set of the system, without specifying its exact implementation.
Free fall Examples Free_fall > Examples Examples of objects in free fall include: A spacecraft (in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory (ballistics) going up for some minutes, and then down). An object dropped at the top of a drop tube. An object thrown upward or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight).Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g {\displaystyle g} .
Reaction Progress Kinetic Analysis Saturation kinetics Reaction_Progress_Kinetic_Analysis > Catalytic kinetics and catalyst resting state > Saturation kinetics Saturation conditions can be viewed as a special case of pre-equilibrium conditions. At the concentration of substrate examined, formation of the catalyst-substrate complex is rapid and essentially irreversible. The catalyst resting state consists entirely of the bound complex, and is no longer present in the rate law; changing will have no effect on reaction rate because the catalyst is already completely bound and reacting as rapidly as k2 allows. The simplest case of saturation kinetics is the well-studied Michaelis-Menten model for enzyme kinetics.
UML activity diagram Construction UML_activity_diagram > Construction Activity diagrams are constructed from a limited number of shapes, connected with arrows. The most important shape types: stadia represent actions; diamonds represent decisions; bars represent the start (split) or end (join) of concurrent activities; a black circle represents the start (initial node) of the workflow; an encircled black circle represents the end (final node).Arrows run from the start towards the end and represent the order in which activities happen. Activity diagrams can be regarded as a form of a structured flowchart combined with a traditional data flow diagram. Typical flowchart techniques lack constructs for expressing concurrency.
ShakeAlert Detection methods ShakeAlert > Detection methods Lastly, the Virtual Seismologist, known as the VS method, imitated the analysis of a human scientist in terms of capacity, but did so at a faster rate. A Bayesian framework was used with inputs of acceleration, velocity, and displacement. The last step required of all these algorithms is to come together in a decision module. This decision module broadcast the probability, size, and other characteristics of the earthquake. As of 2018, all three of these algorithms had been deprecated and replaced with two new algorithms – earthquake point-source integrated code (EPIC) and finite-fault detector (FinDer).
Nonverbal language Eye contact Non_verbal_communication > Eye contact Encoding is the act of generating information such as facial expressions, gestures, and postures. Some studies have demonstrated that people use their eyes to indicate interest.
Supervised learning Other factors to consider Supervised_Machine_Learning > Algorithm choice > Other factors to consider An advantage of decision trees is that they easily handle heterogeneous data. Redundancy in the data.
Economic agents Summary Economic_agent In economics, an agent is an actor (more specifically, a decision maker) in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem. For example, buyers (consumers) and sellers (producers) are two common types of agents in partial equilibrium models of a single market. Macroeconomic models, especially dynamic stochastic general equilibrium models that are explicitly based on microfoundations, often distinguish households, firms, and governments or central banks as the main types of agents in the economy.
Vector magnetometer Mineral exploration Flux_gate > Uses > Mineral exploration Magnetometric surveys can be useful in defining magnetic anomalies which represent ore (direct detection), or in some cases gangue minerals associated with ore deposits (indirect or inferential detection). This includes iron ore, magnetite, hematite, and often pyrrhotite. Developed countries such as Australia, Canada and USA invest heavily in systematic airborne magnetic surveys of their respective continents and surrounding oceans, to assist with map geology and in the discovery of mineral deposits.
Townsend's mole Behavior, diet, and breeding Townsend's_mole > Behavior, diet, and breeding Townsend's mole spends most of its time underground, foraging in shallow burrows for earthworms, small invertebrates and plant material. It is active year-round. It is mainly solitary except during mating in late winter. The female has a litter of two to four young in a deep burrow.
AnyChart History AnyChart > History AnyChart was first developed in 2003 as a Flash chart component to visualize XML data.In 2007, Oracle licensed AnyChart to implement Flash charting in Oracle Application Express (APEX) used by 100,000 developers monthly as of March 2007.With the APEX 4.2 release in 2012, AnyChart 6 was introduced with the support of HTML5 charts based on SVG rendering in addition to Flash charts. Version 7.x of AnyChart was already completely based on JavaScript and HTML5.AnyChart 8.x first released in 2017 has a modular system and supports more than 90 chart types, including variations of basic charts, Gantt charts, meteorological and environmental data graphs (such as air temperature and precipitation, depth measures ), and maps, along with custom drawing and diverse options to work with data. In 2019, it also became available as visualization extensions for Qlik Sense.
Actuality and potentiality Potentiality Actuality_and_potentiality > Potentiality (As emphasized by Aristotle, this requires his distinction between accidental causes and natural causes.) According to Aristotle, when we refer to the nature of a thing, we are referring to the form, shape or look of a thing, which was already present as a potential, an innate tendency to change, in that material before it achieved that form. When things are most "fully at work" we can see more fully what kind of thing they really are.
Tree box filter Design Considerations Tree_box_filter > Construction > Design Considerations Before construction of the tree box filter, several factors must be considered to maximize the effectiveness and impact of the system. Such factors include: area available area of coverage types of contaminants level of rainfall aesthetic appeal maintenance budget.In order to accommodate such considerations, the location, design, and type of material of the box filter may be altered.
Phenylbutazone Interactions Phenylbutazone > Interactions Other anti-inflammatory drugs that tend to cause GI ulcers, such as corticosteroids and other NSAIDs, can potentiate the bleeding risk. Combination with anticoagulant drugs, particularly coumarin derivatives, also increases the risk of bleeding. Avoid combining with other hepatotoxic drugs. Phenylbutazone may affect blood levels and duration of action of phenytoin, valproic acid, sulfonamides, sulfonylurea antidiabetic agents, barbiturates, promethazine, rifampicin, chlorpheniramine, diphenhydramine, and penicillin G.
Serotonin toxicity Causes Serotonin_toxicity > Causes This has been disputed by other researchers, as none of the cases reported by the FDA met the Hunter criteria for SS. The condition has however occurred in surprising clinical situations, and because of phenotypic variations among individuals, it has been associated with unexpected drugs, including mirtazapine.The relative risk and severity of serotonergic side effects and serotonin toxicity, with individual drugs and combinations, is complex. SS has been reported in patients of all ages, including the elderly, children, and even newborn infants due to in utero exposure.
Robust linear regression Parametric alternatives Robust_regression > Methods for robust regression > Parametric alternatives Parametric approaches have the advantage that likelihood theory provides an "off-the-shelf" approach to inference (although for mixture models such as the ε {\displaystyle \varepsilon } -contamination model, the usual regularity conditions might not apply), and it is possible to build simulation models from the fit. However, such parametric models still assume that the underlying model is literally true. As such, they do not account for skewed residual distributions or finite observation precisions.
Applied Mechanics Mechanics of fluids Engineering_mechanics > Major topics > Mechanics of fluids Rheology Hydraulics Incompressible flow Compressible flow Rarefied flow Multiphase flow Wall Layers (incl boundary layers) Internal flow (pipe, channel, and couette) Internal flow (inlets, nozzles, diffusers, and cascades) Free shear layers (mixing layers, jets, wakes, cavities, and plumes)\ Flow stability Turbulence Electromagneto fluid and plasma dynamics Navel hydromechanics Aerodynamics Machinery fluid dynamics Lubrication Flow measurements and visualization
Calculus with polynomials Summary Power_rule In calculus, the power rule is used to differentiate functions of the form f ( x ) = x r {\displaystyle f(x)=x^{r}} , whenever r {\displaystyle r} is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives.
Autonomic nervous system Summary Autonomous_nervous_system In many cases, both of these systems have "opposite" actions where one system activates a physiological response and the other inhibits it. An older simplification of the sympathetic and parasympathetic nervous systems as "excitatory" and "inhibitory" was overturned due to the many exceptions found. A more modern characterization is that the sympathetic nervous system is a "quick response mobilizing system" and the parasympathetic is a "more slowly activated dampening system", but even this has exceptions, such as in sexual arousal and orgasm, wherein both play a role.There are inhibitory and excitatory synapses between neurons. A third subsystem of neurons has been named as non-noradrenergic, non-cholinergic transmitters (because they use nitric oxide as a neurotransmitter) and are integral in autonomic function, in particular in the gut and the lungs.Although the ANS is also known as the visceral nervous system and although most of its fibers carry non-somatic information to the CNS, many authors still consider it only connected with the motor side. Most autonomous functions are involuntary but they can often work in conjunction with the somatic nervous system which provides voluntary control.
Helium compounds Summary Helium_compounds Helium has been shown to form a crystalline compound with sodium under pressure. Suitable pressures to force helium into solid combinations could be found inside planets. Clathrates are also possible with helium under pressure in ice, and other small molecules such as nitrogen.
Speed ramping Scientific use Speed_ramping > Scientific use In scientific and technical applications it is often necessary to slow motion by a very large factor, for example to examine the details of a nuclear explosion. Examples are sometimes published showing, for example, a bullet bursting a balloon.
Network theory Web link analysis Network_theory > Network analysis > Link analysis > Web link analysis Several Web search ranking algorithms use link-based centrality metrics, including Google's PageRank, Kleinberg's HITS algorithm, the CheiRank and TrustRank algorithms. Link analysis is also conducted in information science and communication science in order to understand and extract information from the structure of collections of web pages. For example, the analysis might be of the interlinking between politicians' websites or blogs. Another use is for classifying pages according to their mention in other pages.
Free vortex Summary Vortex In fluid dynamics, a vortex (PL: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices.
Primary research Steps in conducting research Research_ethics > Steps in conducting research The research question may be parallel to the hypothesis. The hypothesis is the supposition to be tested. The researcher(s) collects data to test the hypothesis.
Sympatry Reinforcement Sympatry > Sympatric speciation > Species discrimination > Reinforcement Reinforcement is the process by which natural selection reinforces reproductive isolation. In sympatry, reinforcement increases species discrimination and sexual adaptation in order to avoid maladaptive hybridization and encourage speciation. If hybrid offspring are either sterile or less-fit than non-hybrid offspring, mating between members of two different species will be selected against. Natural selection decreases the probability of such hybridization by selecting for the ability to identify mates of one's own species from those of another species.
History of quantum field theory Quantum chromodynamics History_of_quantum_field_theory > Quantum chromodynamics In the case of the strong interactions, progress concerning their short-distance/high-energy behavior was much slower and more frustrating. For strong interactions with the electro-weak fields, there were difficult issues regarding the strength of coupling, the mass generation of the force carriers as well as their non-linear, self interactions. Although there has been theoretical progress toward a grand unified quantum field theory incorporating the electro-magnetic force, the weak force and the strong force, empirical verification is still pending. Superunification, incorporating the gravitational force, is still very speculative, and is under intensive investigation by many of the best minds in contemporary theoretical physics. Gravitation is a tensor field description of a spin-2 gauge-boson, the "graviton", and is further discussed in the articles on general relativity and quantum gravity.
Scientific management Scientific Management Principles Scientific_management > Scientific Management Principles Taylor indicated that Scientific Management consisted of four underlying principles:1) the development of a true science: We must scientifically analyze all parts of a job. This consists of examining the elements and steps that required to carry out the work, as well as measuring the optimum time for each task. We also need to know the working time per day for a qualified worker.
Quartic equation Converting to a depressed quartic Quartic_equation > The general case > Converting to a depressed quartic {\displaystyle \ \left(u^{4}-{B \over A}u^{3}+{6u^{2}B^{2} \over 16A^{2}}-{4uB^{3} \over 64A^{3}}+{B^{4} \over 256A^{4}}\right)+{B \over A}\left(u^{3}-{3u^{2}B \over 4A}+{3uB^{2} \over 16A^{2}}-{B^{3} \over 64A^{3}}\right)+{C \over A}\left(u^{2}-{uB \over 2A}+{B^{2} \over 16A^{2}}\right)+{D \over A}\left(u-{B \over 4A}\right)+{E \over A}=0\ .} Collecting the same powers of u yields u 4 + ( − 3 B 2 8 A 2 + C A ) u 2 + ( B 3 8 A 3 − B C 2 A 2 + D A ) u + ( − 3 B 4 256 A 4 + C B 2 16 A 3 − B D 4 A 2 + E A ) = 0 . {\displaystyle \ u^{4}+\left({-3B^{2} \over 8A^{2}}+{C \over A}\right)u^{2}+\left({B^{3} \over 8A^{3}}-{BC \over 2A^{2}}+{D \over A}\right)u+\left({-3B^{4} \over 256A^{4}}+{CB^{2} \over 16A^{3}}-{BD \over 4A^{2}}+{E \over A}\right)=0\ .}
Catalytic cycle Precatalysts Catalyst_activation > Precatalysts Metal oxides are often classified as catalysts, but in fact are almost always precatalysts. Applications include olefin metathesis and hydrogenation. The metal oxides require some activating reagent, usually a reducing agent, to enter the catalytic cycle. Often catalytic cycles show the conversion of a precatalyst to the catalyst.
Transition metal nitrate complex Synthesis Transition_metal_nitrate > Synthesis For routine use, most metal nitrates can be prepared by the dissolving metal oxides or metal carbonates in nitric acid. The main complication with dissolving metals in nitric acid arises from redox reactions, which can afford either nitric oxide or nitrogen dioxide. Anhydrous nitrates can be prepared by the oxidation of metals with dinitrogen tetroxide (often as a mixture with nitrogen dioxide, with which it interconverts). N2O4 undergoes molecular autoionization to give , with the former nitrosonium ion being a strong oxidant.
Bacterial transcription Summary Bacterial_transcription Bacteria have a σ-factor that detects and binds to promoter sites but eukaryotes do not need a σ-factor. Instead, eukaryotes have transcription factors that allow the recognition and binding of promoter sites.Overall, transcription within bacteria is a highly regulated process that is controlled by the integration of many signals at a given time. Bacteria heavily rely on transcription and translation to generate proteins that help them respond specifically to their environment.
Complex number field Complex analysis Imaginary_part > Complex analysis The study of functions of a complex variable is known as complex analysis and has enormous practical use in applied mathematics as well as in other branches of mathematics. Often, the most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions, which are commonly represented as two-dimensional graphs, complex functions have four-dimensional graphs and may usefully be illustrated by color-coding a three-dimensional graph to suggest four dimensions, or by animating the complex function's dynamic transformation of the complex plane.
Capacitor types Film capacitors Paper_capacitor > Types and styles > Film capacitors This contact keeps all current paths very short. The design behaves like a large number of individual capacitors connected in parallel, thus reducing the internal ohmic losses (equivalent series resistance or ESR) and equivalent series inductance (ESL).
Thermal expansion valve Theory of operation Thermal_expansion_valve > Theory of operation The cycle starts when refrigerant enters the compressor in a low-pressure, moderate-temperature, gaseous form. The refrigerant is compressed by the compressor to a high-pressure and high-temperature gaseous state. The high-pressure and high-temperature gas then enters the condenser.
Disk format Low-level formatting (LLF) of hard disks Low_level_format > Disk formatting process > Low-level formatting (LLF) of hard disks Hard disk drives prior to the 1990s typically had a separate disk controller that defined how data was encoded on the media. With the media, the drive and/or the controller possibly procured from separate vendors, users were often able to perform low-level formatting. Separate procurement also had the potential of incompatibility between the separate components such that the subsystem would not reliably store data.User-instigated low-level formatting (LLF) of hard disk drives was common for minicomputer and personal computer systems until the 1990s. IBM and other mainframe system vendors typically supplied their hard disk drives (or media in the case of removable media HDDs) with a low-level format.
Spectral analyzer Resolution bandwidth Spectrum_analyzer > Typical functionality > Resolution bandwidth As discussed in the operation section, the resolution bandwidth filter or RBW filter is the bandpass filter in the IF path. It's the bandwidth of the RF chain before the detector (power measurement device). It determines the RF noise floor and how close two signals can be and still be resolved by the analyzer into two separate peaks.
Four-dimensional Euclidean space Summary Four-dimensional_Euclidean_space Higher-dimensional spaces (greater than three) have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without using such spaces. Einstein's theory of relativity is formulated in 4D space, although not in a Euclidean 4D space.
Square root of a 2 by 2 matrix Summary Square_root_of_a_2_by_2_matrix A square root of a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there can be zero, two, four, or even an infinitude of square-root matrices. In many cases, such a matrix R can be obtained by an explicit formula. Square roots that are not the all-zeros matrix come in pairs: if R is a square root of M, then −R is also a square root of M, since (−R)(−R) = (−1)(−1)(RR) = R2 = M.A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. A positive-definite matrix has precisely one positive-definite square root.
Solenoidal field Examples Solenoidal_vector_field > Examples The magnetic field B (see Gauss's law for magnetism) The velocity field of an incompressible fluid flow The vorticity field The electric field E in neutral regions ( ρ e = 0 {\displaystyle \rho _{e}=0} ); The current density J where the charge density is unvarying, ∂ ρ e ∂ t = 0 {\textstyle {\frac {\partial \rho _{e}}{\partial t}}=0} . The magnetic vector potential A in Coulomb gauge
Natural experiment Family size Natural_experiment > Recent examples > Family size An aim of a study Angrist and Evans (1998) was to estimate the effect of family size on the labor market outcomes of the mother. For at least two reasons, the correlations between family size and various outcomes (e.g., earnings) do not inform us about how family size causally affects labor market outcomes. First, both labor market outcomes and family size may be affected by unobserved "third" variables (e.g., personal preferences). Second, labor market outcomes themselves may affect family size (called "reverse causality").
Passive survivability Passive Solar Passive_survivability > Passive Design Strategies > Passive Solar The ability to passively heat a building is beneficial during the colder winter months to help keep temperature levels up. Passive solar systems collect and distribute energy from the sun without the use of mechanical equipment such as fans or pumps. Passive solar heating consists of equator-facing glazing (south-facing in the northern hemisphere) to collect solar energy and thermal mass to store the heat. A direct-gain system allows short-wave radiation from the sun to enter a room through the window, where the floor and wall surfaces then act as thermal mass to absorb the heat, and the long-wave radiation is trapped inside due to the greenhouse effect.
Radio signal Radio communication Radio_emission > Radio communication The radio waves from many transmitters pass through the air simultaneously without interfering with each other. They can be separated in the receiver because each transmitter's radio waves oscillate at a different rate, in other words each transmitter has a different frequency, measured in kilohertz (kHz), megahertz (MHz) or gigahertz (GHz). The bandpass filter in the receiver consists of one or more tuned circuits which act like a resonator, similarly to a tuning fork.
Grayscale images Numerical representations Gray_scale > Numerical representations This pixel depth allows 256 different intensities (i.e., shades of gray) to be recorded, and also simplifies computation as each pixel sample can be accessed individually as one full byte. However, if these intensities were spaced equally in proportion to the amount of physical light they represent at that pixel (called a linear encoding or scale), the differences between adjacent dark shades could be quite noticeable as banding artifacts, while many of the lighter shades would be "wasted" by encoding a lot of perceptually-indistinguishable increments. Therefore, the shades are instead typically spread out evenly on a gamma-compressed nonlinear scale, which better approximates uniform perceptual increments for both dark and light shades, usually making these 256 shades enough to avoid noticeable increments.Technical uses (e.g. in medical imaging or remote sensing applications) often require more levels, to make full use of the sensor accuracy (typically 10 or 12 bits per sample) and to reduce rounding errors in computations.
Fermi's constant Later developments Fermi_constant > Later developments This hypothesis was put forward by Gershtein and Zeldovich and is known as the Vector Current Conservation hypothesis.In the original theory, Fermi assumed that the form of interaction is a contact coupling of two vector currents. Subsequently, it was pointed out by Lee and Yang that nothing prevented the appearance of an axial, parity violating current, and this was confirmed by experiments carried out by Chien-Shiung Wu.The inclusion of parity violation in Fermi's interaction was done by George Gamow and Edward Teller in the so-called Gamow–Teller transitions which described Fermi's interaction in terms of parity-violating "allowed" decays and parity-conserving "superallowed" decays in terms of anti-parallel and parallel electron and neutrino spin states respectively. Before the advent of the electroweak theory and the Standard Model, George Sudarshan and Robert Marshak, and also independently Richard Feynman and Murray Gell-Mann, were able to determine the correct tensor structure (vector minus axial vector, V − A) of the four-fermion interaction.
Performance and modelling of AC transmission HVDC transmission Performance_and_modelling_of_AC_transmission > Overview > HVDC transmission High-voltage direct current (HVDC) is used to transmit large amounts of power over long distances or for interconnections between asynchronous grids. When electrical energy is to be transmitted over very long distances, the power lost in AC transmission becomes appreciable and it is less expensive to use direct current instead of alternating current. For a very long transmission line, these lower losses (and reduced construction cost of a DC line) can offset the additional cost of the required converter stations at each end.In DC transmission line, the mercury arc rectifier converts the alternating current into the DC. The DC transmission line transmits the bulk power over long distance. At the consumer ends the thyratron converts the DC into the AC.
Plant cultivation Nonfood products Plant > Importance to humans > Nonfood products Renewable fuels from plants include firewood, peat and other biofuels. The fossil fuels coal, petroleum and natural gas are derived from the remains of aquatic organisms including phytoplankton in geological time. Many of the coal fields date to the Carboniferous period of Earth's history.
Convergent prefilter Convergence of nets of sets Cluster_point_of_a_filter > Examples of applications of prefilters > Convergence of nets of sets ) A subset C ⊆ X {\displaystyle C\subseteq X} is closed in X {\displaystyle X} if and only if for every point x ∈ X {\displaystyle x\in X} and every net c ∙ {\displaystyle c_{\bullet }} of subsets of C {\displaystyle C} that is not eventually empty, if c ∙ → x in X {\displaystyle c_{\bullet }\to x{\text{ in }}X} then x ∈ C . {\displaystyle x\in C.} A map f: X → Y {\displaystyle f:X\to Y} is continuous if and only if whenever S {\displaystyle S} and S ∙ {\displaystyle S_{\bullet }} are sets or points in X {\displaystyle X} such that S ∙ → S in X , {\displaystyle S_{\bullet }\to S{\text{ in }}X,} then f ( S ∙ ) → f ( S ) in Y .
Object-relational mapper Summary Object–relational_mapping Object–relational mapping (ORM, O/RM, and O/R mapping tool) in computer science is a programming technique for converting data between a relational database and the heap of an object-oriented programming language. This creates, in effect, a virtual object database that can be used from within the programming language. In object-oriented programming, data-management tasks act on objects that combine scalar values into objects. For example, consider an address book entry that represents a single person along with zero or more phone numbers and zero or more addresses.
Language of mathematics Features Language_of_mathematics > Features The main features of the mathematical language are the following. Use of common words with a derived meaning, generally more specific and more precise. For example, "or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not. Also, a "line" is straight and has zero width.
Gran plot Basis of the calculations Gran_plot > Basis of the calculations = C i v i − c O H v v i + v {\displaystyle ={\frac {C_{i}v_{i}-c_{OH}v}{v_{i}+v}}} where vi is the initial volume of solution, cOH is the concentration of alkali in the burette and v is the titre volume. Equating the two expressions for and simplifying, the following expression is obtained C i v i − c O H v = ( v i + v ) 10 E − E 0 s o r = ( v i + v ) 10 − p H {\displaystyle C_{i}v_{i}-c_{OH}v=(v_{i}+v)10^{\frac {E-E^{0}}{s}}\ or\ =(v_{i}+v)10^{-pH}} A plot of ( v i + v ) 10 E − E 0 s o r ( v i + v ) 10 − p H {\displaystyle (v_{i}+v)10^{\frac {E-E^{0}}{s}}\ or\ (v_{i}+v)10^{-pH}} against v will be a straight line. If E0 and s are known from electrode calibration, where the line crosses the x-axis indicates the volume at the equivalence point, C i v i = c O H v {\displaystyle C_{i}v_{i}=c_{OH}v} . Alternatively, this plot can be used for electrode calibration by finding the values of E0 and s that give the best straight line.
Reticulate evolution Lateral gene transfer Reticulate_evolution > Underlying mechanisms and processes > Lateral gene transfer Lateral gene transfer, or horizontal gene transfer, is the movement of genetic material between unicellular and/or multicellular organisms without a parent-offspring relationship. The horizontal transfer of genes results in new genes, which could give new functions to the recipient and thus could drive evolution.
Human hair growth Growth cycle Hair_growth > Growth cycle The three stages of hair growth are the anagen, catagen, and telogen phases. Each strand of hair on the human body is at its own stage of development. Once the cycle is complete, it restarts and a new strand of hair begins to form. The growth rate of hair varies from individual to individual depending on their age, genetic predisposition and a number of environmental factors.
Sympatry Evolving definitions and controversy Sympatry > Evolving definitions and controversy In 2003, biologist Karen McCoy suggested that sympatry can act as a mode of speciation only when "the probability of mating between two individuals depend on their genotypes, dispersed throughout the range of the population during the period of reproduction". In essence, sympatric speciation does require very strong forces of natural selection to be acting on heritable traits, as there is no geographic isolation to aid in the splitting process. Yet, recent research has begun to indicate that sympatric speciation is not as uncommon as was once assumed.
Introduction to the Higgs field Search before 4 July 2012 Higgs_particle > History > Experimental search > Search before 4 July 2012 The Tevatron was only able to exclude further ranges for the Higgs mass, and was shut down on 30 September 2011 because it no longer could keep up with the LHC. The final analysis of the data excluded the possibility of a Higgs boson with a mass between 147 GeV/c2 and 180 GeV/c2. In addition, there was a small (but not significant) excess of events possibly indicating a Higgs boson with a mass between 115 GeV/c2 and 140 GeV/c2.The Large Hadron Collider at CERN in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson.
Hybrid material Hybrid materials in nature Hybrid_material > Introduction > Hybrid materials in nature Many natural materials consist of inorganic and organic building blocks distributed on the nanoscale. In most cases the inorganic part provides mechanical strength and an overall structure to the natural objects while the organic part delivers bonding between the inorganic building blocks and/or the rest of the tissue. Typical examples include bone and nacre.
Study of animal locomotion Neuromechanical models Study_of_animal_locomotion > Modeling animal locomotion > Neuromechanical models After the skeletal model is built, the next step is to accurately define the attachment points of muscle to the rigid bodies. This assignment is crucial for the rigid bodies to be articulated in a naturalistic way. There are several type of muscle models that simulate the dynamics of muscle activation, contraction, and relaxation, which include Hill-type and Ekeberg-type muscle models.
Parkinsonian tremor Genetic Parkinson's_disease > Causes > Genetic The autosomal dominant genes include SNCA, PARK3, UCHL1, LRRK2, GIGYF2, HTRA2, EIF4G1, TMEM230, CHCHD2, RIC3, and VPS35. Autosomal recessive genes include PRKN, PINK1, DJ-1, ATP13A2, PLA2G6, FBXO7, DNAJC6, SYNJ1, and VPS13C. Some genes are X-linked or have unknown inheritance pattern; those include USP24, PARK12, and PARK16.
Covariant vector Coordinates Covariance_and_contravariance_of_vectors > Coordinates If yi is a different coordinate system and Y 1 = ∂ ∂ y 1 , … , Y n = ∂ ∂ y n , {\displaystyle Y_{1}={\frac {\partial }{\partial y^{1}}},\dots ,Y_{n}={\frac {\partial }{\partial y^{n}}},} then the frame f' is related to the frame f by the inverse of the Jacobian matrix of the coordinate transition: f ′ = f J − 1 , J = ( ∂ y i ∂ x j ) i , j = 1 n . {\displaystyle \mathbf {f} '=\mathbf {f} J^{-1},\quad J=\left({\frac {\partial y^{i}}{\partial x^{j}}}\right)_{i,j=1}^{n}.} Or, in indices, ∂ ∂ y i = ∑ j = 1 n ∂ x j ∂ y i ∂ ∂ x j .
Lipegfilgrastim Medical uses Lipegfilgrastim > Medical uses Lipegfilgrastim is indicated for the reduction in the duration of neutropenia and the incidence of febrile neutropenia in adults treated with cytotoxic chemotherapy for malignancy (with the exception of chronic myeloid leukaemia and myelodysplastic syndromes).
Pioneer factor Summary Pioneer_factor This property is observed in histone fold-domain containing transcription factors (fork head box (FOX) and NF-Y) and other transcription factors that use zinc finger(s) for DNA binding (Groucho TLE, Gal4, and GATA).The eukaryotic cell condenses its genome into tightly packed chromatin and nucleosomes. This ability saves space in the nucleus for only actively transcribed genes and hides unnecessary or detrimental genes from being transcribed. Access to these condensed regions is done by chromatin remodelling by either balancing histone modifications or directly with pioneer factors that can loosen the chromatin themselves or as a flag recruiting other factors. Pioneer factors are not necessarily required for assembly of the transcription apparatus and may dissociate after being replaced by other factors.
Coulometric titration Summary Coulometry It is named after Charles-Augustin de Coulomb. There are two basic categories of coulometric techniques. Potentiostatic coulometry involves holding the electric potential constant during the reaction using a potentiostat. The other, called coulometric titration or amperostatic coulometry, keeps the current (measured in amperes) constant using an amperostat.
Inner planets Humanity's perspective Inner_planets > Humanity's perspective Using a heliocentric model that improved upon Copernicus by allowing orbits to be elliptical as well as circular, and the precise observational data of Tycho Brahe, Kepler produced the Rudolphine Tables, which enabled accurate computations of the positions of the then-known planets. Pierre Gassendi used them to predict a transit of Mercury in 1631, and Jeremiah Horrocks did the same for a transit of Venus in 1639. This provided a strong vindication of heliocentrism and Kepler's elliptical orbits.In the 17th century, Galileo publicized the use of the telescope in astronomy; he and Simon Marius independently discovered that Jupiter had four satellites in orbit around it.
Function (mathematics) In computer science Function_(mathematics) > In computer science Except for computer-language terminology, "function" has the usual mathematical meaning in computer science. In this area, a property of major interest is the computability of a function. For giving a precise meaning to this concept, and to the related concept of algorithm, several models of computation have been introduced, the old ones being general recursive functions, lambda calculus and Turing machine.
K-D-B-tree Informal description K-D-B-tree > Informal description Much like the k-d tree, a K-D-B-tree organizes points in k-dimensional space, useful for tasks such as range-searching and multi-dimensional database queries. K-D-B-trees subdivide space into two subspaces by comparing elements in a single domain. Using a 2-D-B-tree (2-dimensional K-D-B-tree) as an example, space is subdivided in the same manner as a k-d tree: using a point in just one of the domains, or axes in this case, all other values are either less than or greater than the current value, and fall to the left and right of the splitting plane respectively. Unlike a k-d tree, each half-space is not its own node. Instead, as in a B-tree, nodes in the K-D-B-tree are stored as pages and the tree stores a pointer to the root page.
EnCor Biotechnology History EnCor_Biotechnology > History One of these is the phosphorylated, axonal form of the major neurofilament protein heavy chain protein which has the HGNC name NEFH, though is usually referred to as pNF-H in the scientific literature. Two further studies describe novel EnCor assays for UCHL1 and alpha-synuclein, two major brain proteins implicated in the development of Parkinson's and other neurological diseases. In 2022 EnCor, in collaboration with researchers at the University of Florida described a novel class of antibodies to neurofilament light chain with the HGNC name NEFL, although the protein is usually referred to as NF-L.
Animal domestication Categories Animal_domestication > Categories Domestication can be considered as the final phase of intensification in the relationship between animal or plant sub-populations and human societies, but it is divided into several grades of intensification. For studies in animal domestication, researchers have proposed five distinct categories: wild, captive wild, domestic, cross-breeds and feral. Wild animals Subject to natural selection, although the action of past demographic events and artificial selection induced by game management or habitat destruction cannot be excluded. Captive wild animals Directly affected by a relaxation of natural selection associated with feeding, breeding and protection/confinement by humans, and an intensification of artificial selection through passive selection for animals that are more suited to captivity.
Brouwer fixed-point theorem Convexity Brouwer's_fixed_point_theorem > Importance of the pre-conditions > Convexity Convexity is not strictly necessary for BFPT. Because the properties involved (continuity, being a fixed point) are invariant under homeomorphisms, BFPT is equivalent to forms in which the domain is required to be a closed unit ball D n {\displaystyle D^{n}} . For the same reason it holds for every set that is homeomorphic to a closed ball (and therefore also closed, bounded, connected, without holes, etc.). The following example shows that BFPT does not work for domains with holes.
WAVL tree The rank balanced trees framework WAVL_tree > The rank balanced trees framework 2-3 rule, which corresponds to the binarized 2-3 tree: each node is of type 0,1 or 1,1, and no parent of a 0-child is a 0-child. Red black rule, which corresponds to Red-black tree: all rank differences are 0 or 1, and no parent of a 0-child is a 0-child. Note that the red-black rule generalizes the 2-3 rule by allowing for 0,0 type node.So far all these rules are symmetric for the left node and the right node.
Evolution strategy Methods Evolution_strategies > Methods Evolution strategies use natural problem-dependent representations, so problem space and search space are identical. In common with evolutionary algorithms, the operators are applied in a loop. An iteration of the loop is called a generation. The sequence of generations is continued until a termination criterion is met.
Construction field computing Connectivity and computing power Construction_field_computing > Connectivity and computing power An effective device will be able to process data into actionable information and transmit data and information to other devices or persons. The device may not actually perform computation of final communication, but it must appear as though it does. Extra steps to upload and download information will be perceived as a nuisance or waste of time to the user and cause the device to be underutilized. Some IAs are self-contained in that they have computing capacity and software to perform required tasks independent of a server or other devices. Others rely on connectivity with other devices and/or a server to perform required functions.
Gravity battery Large scale Gravity_battery > Types of gravity batteries > Large scale Relatively little infrastructure is required, the batteries can be sited near major population centers, round trip efficiency is 85+%, and the system can be built at a GWh scale.Lifted Weight Storage (LWS) technology uses surplus energy to mechanically lift solid weights vertically, typically on a pulley system. When extra energy is needed, the mass is lowered, and the pulley turns a generator. EnergyVault is designing a LWS system using a tower built from 32-ton concrete blocks, stacked with 120-meter cranes.
Willard Van Orman Quine Set theory Willard_Van_Orman_Quine > Work > Set theory NF allows many "large" sets the now-canonical ZFC set theory does not allow, even sets for which the axiom of choice does not hold. Since the axiom of choice holds for all finite sets, the failure of this axiom in NF proves that NF includes infinite sets. The consistency of NF relative to other formal systems adequate for mathematics is an open question, albeit that a number of candidate proofs are current in the NF community suggesting that NF is equiconsistent with Zermelo set theory without Choice.
Damped harmonic motion Spring/mass system Harmonic_oscillators > Examples > Spring/mass system When a spring is stretched or compressed by a mass, the spring develops a restoring force. Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length: where F is the force, k is the spring constant, and x is the displacement of the mass with respect to the equilibrium position. The minus sign in the equation indicates that the force exerted by the spring always acts in a direction that is opposite to the displacement (i.e. the force always acts towards the zero position), and so prevents the mass from flying off to infinity.
Spinterface Magnetic Tunneling Junction Spinterface > Physics and applications > Magnetic Tunneling Junction Barraud et al., in a Nature Physics paper, develop a spin transport model that takes into account the effect of the spinterface hybridization. What they observed is that the role of this hybridization in the spin tunneling process is not only relevant, but also capable of inverting the sign of the TMR. This opens the door to a new research front, aimed at tailoring the properties of spintronic devices through the right combination of ferromagnetic metals and molecules.
Physical force Combining forces Elastic_force > Combining forces Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors.
Mathematical discipline Biology and chemistry Mathematical_research > Relationship with sciences > Specific sciences > Biology and chemistry Biology uses probability extensively – for example, in ecology or neurobiology. Most of the discussion of probability in biology, however, centers on the concept of evolutionary fitness.Ecology heavily uses modeling to simulate population dynamics, study ecosystems such as the predator-prey model, measure pollution diffusion, or to assess climate change. The dynamics of a population can be modeled by coupled differential equations, such as the Lotka–Volterra equations. However, there is the problem of model validation.
Digestive enzyme Summary Digestion_enzyme Digestive enzymes are a group of enzymes that break down polymeric macromolecules into their smaller building blocks, in order to facilitate their absorption into the cells of the body. Digestive enzymes are found in the digestive tracts of animals (including humans) and in the tracts of carnivorous plants, where they aid in the digestion of food, as well as inside cells, especially in their lysosomes, where they function to maintain cellular survival. Digestive enzymes of diverse specificities are found in the saliva secreted by the salivary glands, in the secretions of cells lining the stomach, in the pancreatic juice secreted by pancreatic exocrine cells, and in the secretions of cells lining the small and large intestines.Digestive enzymes are classified based on their target substrates: Lipases split fatty acids into fats and oils. Proteases and peptidases split proteins into small peptides and amino acids.
Mechanization Summary Mechanization In modern usage, such as in engineering or economics, mechanization implies machinery more complex than hand tools and would not include simple devices such as an ungeared horse or donkey mill. Devices that cause speed changes or changes to or from reciprocating to rotary motion, using means such as gears, pulleys or sheaves and belts, shafts, cams and cranks, usually are considered machines.

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