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In real analysis and complex analysis, branches of mathematics, the identity theorem for analytic functions states: given functions f and g analytic on a domain D (open and connected subset of
$$
\mathbb{R}
$$
or
$$
\mathbb{C}
$$
), if f = g on some
$$
S \subseteq D
$$
, where
$$
S
$$
has an accumulation point in... | https://en.wikipedia.org/wiki/Identity_theorem |
In digital logic, a don't-care term (abbreviated DC, historically also known as redundancies, irrelevancies, optional entries, invalid combinations, vacuous combinations, forbidden combinations, unused states or logical remainders) for a function is an input-sequence (a series of bits) for which the function output doe... | https://en.wikipedia.org/wiki/Don%27t-care_term |
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of . (Equivalently, it is impossible to have wi... | https://en.wikipedia.org/wiki/Necessity_and_sufficiency |
A dictionary coder, also sometimes known as a substitution coder, is a class of lossless data compression algorithms which operate by searching for matches between the text to be compressed and a set of strings contained in a data structure (called the 'dictionary') maintained by the encoder. When the encoder finds suc... | https://en.wikipedia.org/wiki/Dictionary_coder |
In radiometry, radiosity is the radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area, and spectral radiosity is the radiosity of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiosity is... | https://en.wikipedia.org/wiki/Radiosity_%28radiometry%29 |
In computing, an opcode (abbreviated from operation code) is an enumerated value that specifies the operation to be performed. Opcodes are employed in hardware devices such as arithmetic logic units (ALUs), central processing units (
## CPUs
), and software instruction sets. In ALUs, the opcode is directly applied to c... | https://en.wikipedia.org/wiki/Opcode |
Forth is a stack-oriented programming language and interactive integrated development environment designed by Charles H. "Chuck" Moore and first used by other programmers in 1970. Although not an acronym, the language's name in its early years was often spelled in all capital letters as FORTH. The FORTH-79 and FORTH-83... | https://en.wikipedia.org/wiki/Forth_%28programming_language%29 |
Extremely low frequency (ELF) is the ITU designation for electromagnetic radiation (radio waves) with frequencies from 3 to 30 Hz, and corresponding wavelengths of 100,000 to 10,000 kilometers, respectively. In atmospheric science, an alternative definition is usually given, from 3 Hz to 3 kHz. In the related magnetosp... | https://en.wikipedia.org/wiki/Extremely_low_frequency |
In mathematics, more precisely in measure theory, the Lebesgue decomposition theorem provides a way to decompose a measure into two distinct parts based on their relationship with another measure.
## Definition
The theorem states that if
$$
(\Omega,\Sigma)
$$
is a measurable space and
$$
\mu
$$
and
$$
\nu
$$
are ... | https://en.wikipedia.org/wiki/Lebesgue%27s_decomposition_theorem |
Gas is a state of matter that has neither a fixed volume nor a fixed shape and is a compressible fluid. A pure gas is made up of individual atoms (e.g. a noble gas like neon) or molecules of either a single type of atom (elements such as oxygen) or from different atoms (compounds such as carbon dioxide). A gas mixture,... | https://en.wikipedia.org/wiki/Gas |
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (... | https://en.wikipedia.org/wiki/Dimensionless_quantity |
In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
Given any point on a sphere, its antipodal point is the unique point at ... | https://en.wikipedia.org/wiki/Antipodal_point |
A tsunami ( ; from , ) is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and underwater explosions (including detonations, landslides, glacier calvings, meteorite impacts and other disturbances) above or bel... | https://en.wikipedia.org/wiki/Tsunami |
In physical oceanography, the significant wave height (SWH, HTSGW or Hs)
is defined traditionally as the mean wave height (trough to crest) of the highest third of the waves (H1/3). It is usually defined as four times the standard deviation of the surface elevation – or equivalently as four times the square root of th... | https://en.wikipedia.org/wiki/Significant_wave_height |
In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. The theorem is due to Man-Duen Choi. An infinite-dimensional algebraic generalization of Choi's theorem is known as Belavkin's "Radon–Nikodym" theorem for comp... | https://en.wikipedia.org/wiki/Choi%27s_theorem_on_completely_positive_maps |
Guzmán or de Guzmán ( or ) is a Spanish surname. The Portuguese language equivalent is Gusmão.
## Origins
The surname is of toponymic origin, de Guzmán ("of Guzmán"), deriving from the village of Guzmán (es) in the region of Burgos. The earliest individual documented using this surname was Rodrigo Muñoz de Guzmán, who ... | https://en.wikipedia.org/wiki/Guzm%C3%A1n |
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same trajectories and landing at identical times. The extended form by Albert Einstein... | https://en.wikipedia.org/wiki/Equivalence_principle |
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction ... | https://en.wikipedia.org/wiki/Vickrey_auction |
A top tree is a data structure based on a binary tree for unrooted dynamic trees that is used mainly for various path-related operations. It allows simple divide-and-conquer algorithms. It has since been augmented to maintain dynamically various properties of a tree such as diameter, center and median.
A top tree
$$
\... | https://en.wikipedia.org/wiki/Top_tree |
Bradford's law is a pattern first described by Samuel C. Bradford in 1934 that estimates the exponentially diminishing returns of searching for references in science journals. One formulation is that if journals in a field are sorted by number of articles into three groups, each with about one-third of all articles, th... | https://en.wikipedia.org/wiki/Bradford%27s_law |
A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load, and effort, the lever is divided into three types. It is one of the six simple machines identified by Rena... | https://en.wikipedia.org/wiki/Lever |
In computer science, a y-fast trie is a data structure for storing integers from a bounded domain. It supports exact and predecessor or successor queries in time O(log log M), using O(n) space, where n is the number of stored values and M is the maximum value in the domain. The structure was proposed by Dan Willard in ... | https://en.wikipedia.org/wiki/Y-fast_trie |
The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used. The problem has many applications, such as filling up containers, loading trucks with weight c... | https://en.wikipedia.org/wiki/Bin_packing_problem |
The difference-map algorithm is a search algorithm for general constraint satisfaction problems. It is a meta-algorithm in the sense that it is built from more basic algorithms that perform projections onto constraint sets. From a mathematical perspective, the difference-map algorithm is a dynamical system based on a m... | https://en.wikipedia.org/wiki/Difference-map_algorithm |
In mathematics, the interior extremum theorem, also known as Fermat's theorem, is a theorem which states that at the local extrema of a differentiable function, its derivative is always zero. It belongs to the mathematical field of real analysis and is named after French mathematician Pierre de Fermat.
By using the int... | https://en.wikipedia.org/wiki/Interior_extremum_theorem |
In computer science, the Krauss wildcard-matching algorithm is a pattern matching algorithm. Based on the wildcard syntax in common use, e.g. in the Microsoft Windows command-line interface, the algorithm provides a non-recursive mechanism for matching patterns in software applications, based on syntax simpler than tha... | https://en.wikipedia.org/wiki/Krauss_wildcard-matching_algorithm |
In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with
decreasing failure rate, defined on the interval [0, ∞). This distribution is parameterized by two parameters
$$
p\in(0,1)
$$
and
$$
\beta >0
$$
.
## Introduction
The study of lengths of the... | https://en.wikipedia.org/wiki/Exponential-logarithmic_distribution |
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system.
The PSF in many context... | https://en.wikipedia.org/wiki/Point_spread_function |
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville... | https://en.wikipedia.org/wiki/Miquel%27s_theorem |
In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a mult... | https://en.wikipedia.org/wiki/Chi_distribution |
In computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy t... | https://en.wikipedia.org/wiki/Tail_call |
In mathematical analysis, and especially in real, harmonic analysis and functional analysis, an Orlicz space is a type of function space which generalizes the Lp spaces. Like the Lp spaces, they are Banach spaces. The spaces are named for Władysław Orlicz, who was the first to define them in 1932.
Besides the Lp space... | https://en.wikipedia.org/wiki/Orlicz_space |
The QT interval is a measurement made on an electrocardiogram used to assess some of the electrical properties of the heart. It is calculated as the time from the start of the Q wave to the end of the T wave, and approximates to the time taken from when the cardiac ventricles start to contract to when they finish rela... | https://en.wikipedia.org/wiki/QT_interval |
In statistics, Basu's theorem states that any boundedly complete and sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu.
It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other ... | https://en.wikipedia.org/wiki/Basu%27s_theorem |
An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the... | https://en.wikipedia.org/wiki/X-ray |
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competit... | https://en.wikipedia.org/wiki/Optimal_facility_location |
In computer science, B* (pronounced "B star") is a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals). First published by Hans Berliner in 1979, it is related to the A* search algorithm.
## Summary
The algorithm stores interval... | https://en.wikipedia.org/wiki/B%2A |
The volunteer's dilemma is a game that models a situation in which each player can either make a small sacrifice that benefits everybody, or instead wait in hope of benefiting from someone else's sacrifice.
One example is a scenario in which the electricity supply has failed for an entire neighborhood. All inhabitants ... | https://en.wikipedia.org/wiki/Volunteer%27s_dilemma |
A waveplate or retarder is an optical device that alters the polarization state of a light wave travelling through it. Two common types of waveplates are the half-wave plate, which rotates the polarization direction of linearly polarized light, and the quarter-wave plate, which converts between different elliptical pol... | https://en.wikipedia.org/wiki/Waveplate |
In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as . Typically, mathematicians are interested in q-analogs that arise naturally, rather than in arbitrarily contriving q-analogs of know... | https://en.wikipedia.org/wiki/Q-analog |
In computer science, M-trees are tree data structures that are similar to R-trees and B-trees. It is constructed using a metric and relies on the triangle inequality for efficient range and k-nearest neighbor (k-NN) queries.
While M-trees can perform well in many conditions, the tree can also have large overlap and the... | https://en.wikipedia.org/wiki/M-tree |
Wave pounding is the 'sledge hammer' effect of tonnes of water crashing against cliffs. It shakes and weakens the rocks leaving them open to attack from hydraulic action and abrasion. Eroded material gets carried away by the wave. Wave pounding is particularly fierce in a storm, where the waves are exceptionally large,... | https://en.wikipedia.org/wiki/Wave_pounding |
Econophysics is a non-orthodox (in economics) interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Some of its application to the study of financial ... | https://en.wikipedia.org/wiki/Econophysics |
In idempotent analysis, the tropical semiring is a semiring of extended real numbers with the operations of minimum (or maximum) and addition replacing the usual ("classical") operations of addition and multiplication, respectively.
The tropical semiring has various applications (see tropical analysis), and forms the b... | https://en.wikipedia.org/wiki/Tropical_semiring |
In mathematics, Solèr's theorem is a result concerning certain infinite-dimensional vector spaces. It states that any orthomodular form that has an infinite orthonormal set is a Hilbert space over the real numbers, complex numbers or quaternions. Originally proved by Maria Pia Solèr, the result is significant for quant... | https://en.wikipedia.org/wiki/Sol%C3%A8r%27s_theorem |
In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is ... | https://en.wikipedia.org/wiki/Codimension |
The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an isolated system is nonnegative, and can only be zero when the system has ... | https://en.wikipedia.org/wiki/Positive_energy_theorem |
In group theory, a discipline within modern algebra, an element
$$
x
$$
of a group
$$
G
$$
is called a real element of
$$
G
$$
if it belongs to the same conjugacy class as its inverse
$$
x^{-1}
$$
, that is, if there is a
$$
g
$$
in
$$
G
$$
with
$$
x^g = x^{-1}
$$
, where
$$
x^g
$$
is defined as
$$
g^{-1... | https://en.wikipedia.org/wiki/Real_element |
In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances of one decision problem (whether an instance is in
$$
L_1
$$
) to another decision problem (whether an instance is in
$$
L_2
$$
) using a computable function. The r... | https://en.wikipedia.org/wiki/Many-one_reduction |
In statistics, Ward's method is a criterion applied in hierarchical cluster analysis. Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing th... | https://en.wikipedia.org/wiki/Ward%27s_method |
Planetary science (or more rarely, planetology) is the scientific study of planets (including Earth), celestial bodies (such as moons, asteroids, comets) and planetary systems (in particular those of the Solar System) and the processes of their formation. It studies objects ranging in size from micrometeoroids to gas g... | https://en.wikipedia.org/wiki/Planetary_science |
Adaptive
### Replacement
Cache (ARC) is a page replacement algorithm with
better performance than LRU (least recently used). This is accomplished by keeping track of both frequently used and recently used pages plus a recent eviction history for both. The algorithm was developed at the IBM Almaden Research Center. I... | https://en.wikipedia.org/wiki/Adaptive_replacement_cache |
In mathematics, the Hawaiian earring
$$
\mathbb{H}
$$
is the topological space defined by the union of circles in the Euclidean plane
$$
\R^2
$$
with center
$$
\left(\tfrac{1}{n},0\right)
$$
and radius
$$
\tfrac{1}{n}
$$
for
$$
n = 1, 2, 3, \ldots
$$
endowed with the subspace topology:
$$
\mathbb{H}=\bigcup_{... | https://en.wikipedia.org/wiki/Hawaiian_earring |
In number theory, a
### Shimura variety
is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are not algebraic varieties but are families of algebraic varieties. Sh... | https://en.wikipedia.org/wiki/Shimura_variety |
A composite or composite material (also composition material) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finishe... | https://en.wikipedia.org/wiki/Composite_material |
In physics and materials science, plasticity (also known as plastic deformation) is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanen... | https://en.wikipedia.org/wiki/Plasticity_%28physics%29 |
A telephone exchange, telephone switch, or central office is a central component of a telecommunications system in the public switched telephone network (PSTN) or in large enterprises. It facilitates the establishment of communication circuits, enabling telephone calls between subscribers. The term "central office" can... | https://en.wikipedia.org/wiki/Telephone_exchange |
The Fresnel integrals and are two transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function (). They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations:
$$
S(x) = \in... | https://en.wikipedia.org/wiki/Fresnel_integral |
In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain behavior as time approaches infinity.
Mathematically, if
$$
f(t)
$$
in continuous time has (unilateral) Laplace transform
$$
F(s)
$$
, then a final value theorem e... | https://en.wikipedia.org/wiki/Final_value_theorem |
Carleson's theorem is a fundamental result in mathematical analysis establishing the (Lebesgue) pointwise almost everywhere convergence of Fourier series of functions, proved by . The name is also often used to refer to the extension of the result by to functions for (also known as the Carleson–Hunt theorem) and th... | https://en.wikipedia.org/wiki/Carleson%27s_theorem |
The technology of computer keyboards includes many elements. Many different keyboard technologies have been developed for consumer demands and optimized for industrial applications. The standard full-size (100%) computer alphanumeric keyboard typically uses 101 to 105 keys; keyboards integrated in laptop computers are ... | https://en.wikipedia.org/wiki/Keyboard_technology |
In topology, a branch of mathematics, a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither of the two is an n-sphere.
A similar notion is that of an irreducible n-manifold, which is one in which any embedded (n − 1)-sphere bounds an... | https://en.wikipedia.org/wiki/Prime_manifold |
In geometry a conoid () is a ruled surface, whose rulings (lines) fulfill the additional conditions:
(1) All rulings are parallel to a plane, the directrix plane.
(2) All rulings intersect a fixed line, the axis.
The conoid is a right conoid if its axis is perpendicular to its directrix plane. Hence all rulings are per... | https://en.wikipedia.org/wiki/Conoid |
In number theory, Dixon's factorization method (also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike for other factor base methods, its run-time bound comes with a rigorous proof that does not rely on conjectures... | https://en.wikipedia.org/wiki/Dixon%27s_factorization_method |
A Kripke structure is a variation of the transition system, originally proposed by Saul Kripke, used in model checking to represent the behavior of a system.
It consists of a graph whose nodes represent the reachable states of the system and whose edges represent state transitions, together with a labelling function wh... | https://en.wikipedia.org/wiki/Kripke_structure_%28model_checking%29 |
Wave-making resistance or wave resistance is a form of drag that affects any object moving on a surface of a fluid, such as boats and ships moving on the surface of water, and reflects the energy required to push the water out of the way of that body. For example, the hull of a moving watercraft creates waves (a wake) ... | https://en.wikipedia.org/wiki/Wave-making_resistance |
In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection.
The problem was posed by Fred Richman in the American Mathematical Monthly in 1965 and was proved by Paul Monsky in 1970.
## Proo... | https://en.wikipedia.org/wiki/Monsky%27s_theorem |
In physics, the principle of covariance emphasizes the formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate.
Mathematically, the physical quantities must transform covariantly, that is, under a certain re... | https://en.wikipedia.org/wiki/Principle_of_covariance |
A metric tree is any tree data structure specialized to index data in metric spaces. Metric trees exploit properties of metric spaces such as the triangle inequality to make accesses to the data more efficient. Examples include the M-tree, vp-trees, cover trees, MVP trees, and BK-trees.
## Multidimensional search
Most ... | https://en.wikipedia.org/wiki/Metric_tree |
A collimator is a device which narrows a beam of particles or waves. To narrow can mean either to cause the directions of motion to become more aligned in a specific direction (i.e., make collimated light or parallel rays), or to cause the spatial cross section of the beam to become smaller (beam limiting device).
## H... | https://en.wikipedia.org/wiki/Collimator |
In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It h... | https://en.wikipedia.org/wiki/Morley%27s_trisector_theorem |
A subset
$$
S
$$
of a topological space
$$
X
$$
is called a regular open set if it is equal to the interior of its closure; expressed symbolically, if
$$
\operatorname{Int}(\overline{S}) = S
$$
or, equivalently, if
$$
\partial(\overline{S})=\partial S,
$$
where
$$
\operatorname{Int} S,
$$
$$
\overline{S}
$$
a... | https://en.wikipedia.org/wiki/Regular_open_set |
Tidal power or tidal energy is harnessed by converting energy from tides into useful forms of power, mainly electricity using various methods.
Although not yet widely used, tidal energy has the potential for future electricity generation. Tides are more predictable than the wind and the sun. Among sources of renewable... | https://en.wikipedia.org/wiki/Tidal_power |
In mathematics, and specifically in the field of homotopy theory, the Freudenthal suspension theorem is the fundamental result leading to the concept of stabilization of homotopy groups and ultimately to stable homotopy theory. It explains the behavior of simultaneously taking suspensions and increasing the index of t... | https://en.wikipedia.org/wiki/Freudenthal_suspension_theorem |
In statistical quality control, the p-chart is a type of control chart used to monitor the proportion of nonconforming units in a sample, where the sample proportion nonconforming is defined as the ratio of the number of nonconforming units to the sample size, n.
The p-chart only accommodates "pass"/"fail"-type inspect... | https://en.wikipedia.org/wiki/P-chart |
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation.... | https://en.wikipedia.org/wiki/Euler%27s_rotation_theorem |
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relati... | https://en.wikipedia.org/wiki/Multiplication_theorem |
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measur... | https://en.wikipedia.org/wiki/Physical_constant |
In law and economics, the Coase theorem () describes the economic efficiency of an economic allocation or outcome in the presence of externalities.
## The theorem
is significant because, if true, the conclusion is that it is possible for private individuals to make choices that can solve the problem of market externa... | https://en.wikipedia.org/wiki/Coase_theorem |
In probability theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu in 2011. The G-MVLG is a flexible distribution. Skewness and kurtosis are well controlled by the parameters of the distribution. This enables one to c... | https://en.wikipedia.org/wiki/Generalized_multivariate_log-gamma_distribution |
Delamination is a mode of failure where a material fractures into layers. A variety of materials, including laminate composites and concrete, can fail by delamination. Processing can create layers in materials, such as steel formed by rolling and plastics and metals from 3D printing which can fail from layer separation... | https://en.wikipedia.org/wiki/Delamination |
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium.
## Overview
Common components of a phase ... | https://en.wikipedia.org/wiki/Phase_diagram |
In physics, magnetosonic waves, also known as magnetoacoustic waves, are low-frequency compressive waves driven by mutual interaction between an electrically conducting fluid and a magnetic field. They are associated with compression and rarefaction of both the fluid and the magnetic field, as well as with an effective... | https://en.wikipedia.org/wiki/Magnetosonic_wave |
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third way" besides theoretical and experimental sciences, computational mechanics w... | https://en.wikipedia.org/wiki/Computational_mechanics |
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
Perhaps the chief use of the inverse gamma distri... | https://en.wikipedia.org/wiki/Inverse-gamma_distribution |
In mathematics, the pin group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps 2-to-1 to the special orthogonal group.
In general the map from the Pin group to the orthogonal group is not surjective or a universal covering... | https://en.wikipedia.org/wiki/Pin_group |
In the analysis of data, a correlogram is a chart of correlation statistics.
For example, in time series analysis, a plot of the sample autocorrelations
$$
r_h\,
$$
versus
$$
h\,
$$
(the time lags) is an autocorrelogram.
If cross-correlation is plotted, the result is called a cross-correlogram.
The correlogram i... | https://en.wikipedia.org/wiki/Correlogram |
For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian).
For Liouville's equation in quantum mechanics, see Von Neumann equation.
For Liouville's equation in Euclidean space, see Liouville–Bratu–Gelfand equation.
In differential geometry, Liouville's equation, named after Joseph Liouvill... | https://en.wikipedia.org/wiki/Liouville%27s_equation |
The Planck constant, or Planck's constant, denoted by is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle mome... | https://en.wikipedia.org/wiki/Planck_constant |
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence rela... | https://en.wikipedia.org/wiki/Partition_of_a_set |
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase veloci... | https://en.wikipedia.org/wiki/Dispersion_relation |
Ferrofluids can be used to transfer heat, since heat and mass transport in such magnetic fluids can be controlled using an external magnetic field.
B. A. Finlayson first explained in 1970 (in his paper "Convective instability of ferromagnetic fluids", Journal of Fluid Mechanics, 40:753-767) how an external magnetic fie... | https://en.wikipedia.org/wiki/Thermomagnetic_convection |
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resist... | https://en.wikipedia.org/wiki/Norton%27s_theorem |
A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that... | https://en.wikipedia.org/wiki/Dragon_curve |
Biomedical engineering (BME) or medical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare applications (e.g., diagnostic or therapeutic purposes). BME is also traditionally logical sciences to advance health care treatment, including diagnosis, monitorin... | https://en.wikipedia.org/wiki/Biomedical_engineering |
In computer programming, tracing garbage collection is a form of automatic memory management that consists of determining which objects should be deallocated ("garbage collected") by tracing which objects are reachable by a chain of references from certain "root" objects, and considering the rest as "garbage" and colle... | https://en.wikipedia.org/wiki/Tracing_garbage_collection |
Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. The two types of calculus in quantum calculus are q-calculus and h-calculus. The goal of both types is to find "analogs" of mathematical objects, where, after taking a certain li... | https://en.wikipedia.org/wiki/Quantum_calculus |
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers defined from the sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physici... | https://en.wikipedia.org/wiki/Levi-Civita_symbol |
Quantization (in British English quantisation) is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing quantum mechanics from classical mechanics. A generalization involving infinite degrees o... | https://en.wikipedia.org/wiki/Quantization_%28physics%29 |
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, ... | https://en.wikipedia.org/wiki/Wave_vector |
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