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https://en.wikipedia.org/wiki/Symmetric%20difference | In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets and is .
The symmetric difference of the sets A and B is commonly denoted by ... |
https://en.wikipedia.org/wiki/Harmonic%20progression | Harmonic progression may refer to:
Chord progression in music
Harmonic progression (mathematics)
Sequence (music) |
https://en.wikipedia.org/wiki/Rayleigh%20distribution | In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom.
The distribution is named after Lord Rayleigh ().
A Rayleigh distribution is often obser... |
https://en.wikipedia.org/wiki/ECM | ECM may refer to:
Economics and commerce
Engineering change management
Equity capital markets
Error correction model, an econometric model
European Common Market
Mathematics
Elliptic curve method
European Congress of Mathematics
Science and medicine
Ectomycorrhiza
Electron cloud model
Engineered Cellular... |
https://en.wikipedia.org/wiki/Concave%20function | In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.
Definition
A real-valued function on an interval (or, more generally, a convex set in vector space) is said to be concav... |
https://en.wikipedia.org/wiki/Curve%20sketching | In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features.
Basic techniques
The foll... |
https://en.wikipedia.org/wiki/SciPy | SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing.
SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engi... |
https://en.wikipedia.org/wiki/Deviation | Deviation may refer to:
Mathematics and engineering
Allowance (engineering), an engineering and machining allowance is a planned deviation between an actual dimension and a nominal or theoretical dimension, or between an intermediate-stage dimension and an intended final dimension.
Deviation (statistics), the differ... |
https://en.wikipedia.org/wiki/Differential%20operator | In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer scien... |
https://en.wikipedia.org/wiki/Edward%20Tufte | Edward Rolf Tufte (; born March 14, 1942), sometimes known as "ET", is an American statistician and professor emeritus of political science, statistics, and computer science at Yale University. He is noted for his writings on information design and as a pioneer in the field of data visualization.
Biography
Edward Rol... |
https://en.wikipedia.org/wiki/Archimedean%20property | In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.
The property, typically construed, states that given two positive numbers and , there is an int... |
https://en.wikipedia.org/wiki/Archimedean%20group | In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation bet... |
https://en.wikipedia.org/wiki/Zero%20of%20a%20function | In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function , is a member of the domain of such that vanishes at ; that is, the function attains the value of 0 at , or equivalently, is the solution to the equation . A "zero" of a function is thus an input value t... |
https://en.wikipedia.org/wiki/Size%20%28disambiguation%29 | Size is the concept of how big or small something is. It may also refer to:
In statistics (hypothesis testing), the size of the test refers to the rate of false positives, denoted by α
File size, in computing
Magnitude (mathematics), magnitude or size of a mathematical object
Magnitude of brightness or intensity o... |
https://en.wikipedia.org/wiki/Hilbert%20matrix | In linear algebra, a Hilbert matrix, introduced by , is a square matrix with entries being the unit fractions
For example, this is the 5 × 5 Hilbert matrix:
The entries can also be defined by the integral
that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrar... |
https://en.wikipedia.org/wiki/Cosh | Cosh may refer to:
People
Chris Cosh (born 1959), American football coach
John Cosh (1915–2005), British rheumatologist
Science, technology, and mathematics
cosh (mathematical function), hyperbolic cosine, a mathematical function with notation cosh(x)
-COSH, a representation of the thiocarboxylic acid functional ... |
https://en.wikipedia.org/wiki/E%20%28theorem%20prover%29 | E is a high-performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely equational paradigm. It has been integrated into other theorem provers and it has been among the best-placed systems in several theorem proving competitions. E is devel... |
https://en.wikipedia.org/wiki/Finite%20geometry | A finite geometry is any geometric system that has only a finite number of points.
The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite... |
https://en.wikipedia.org/wiki/Jordan%20curve%20theorem | In topology, the Jordan curve theorem asserts that every Jordan curve (a plane simple closed curve) divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of th... |
https://en.wikipedia.org/wiki/Thales%27s%20theorem | In geometry, Thales's theorem states that if , , and are distinct points on a circle where the line is a diameter, the angle is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. It is ge... |
https://en.wikipedia.org/wiki/Synthetic%20geometry | Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms.
The term "synthetic geometry" was coined o... |
https://en.wikipedia.org/wiki/Nonprobability%20sampling | Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular ... |
https://en.wikipedia.org/wiki/Systematic%20sampling | In survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method.
In this approach, progression through the list is treated circularly, with a return to the top once the list ... |
https://en.wikipedia.org/wiki/Clifford%20A.%20Pickover | Clifford Alan Pickover (born August 15, 1957) is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research Center in Yorktown, New York, where he was editor-in-chief of the IBM Journa... |
https://en.wikipedia.org/wiki/Position | Position often refers to:
Position (geometry), the spatial location (rather than orientation) of an entity
Position, a job or occupation
Position may also refer to:
Games and recreation
Position (poker), location relative to the dealer
Position (team sports), a player role within a team
Human body
Human positio... |
https://en.wikipedia.org/wiki/Ineffable%20cardinal | In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by . In the following definitions, will always be a regular uncountable cardinal number.
A cardinal number is called almost ineffable if for every (where is the powerset of ) with the property t... |
https://en.wikipedia.org/wiki/Gumbel%20distribution | In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.
This distribution might be used to represent the distribution of the maximum... |
https://en.wikipedia.org/wiki/Computational%20neuroscience | Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abili... |
https://en.wikipedia.org/wiki/Near%20field | Near field may refer to:
Near-field (mathematics), an algebraic structure
Near-field region, part of an electromagnetic field
Near field (electromagnetism)
Magnetoquasistatic field, the magnetic component of the electromagnetic near field
Near-field communication (NFC) using the magnetic component of the electrom... |
https://en.wikipedia.org/wiki/Weakly%20compact%20cardinal | In mathematics, a weakly compact cardinal is a certain kind of cardinal number introduced by ; weakly compact cardinals are large cardinals, meaning that their existence cannot be proven from the standard axioms of set theory. (Tarski originally called them "not strongly incompact" cardinals.)
Formally, a cardinal κ ... |
https://en.wikipedia.org/wiki/Survey%20methodology | Survey methodology is "the study of survey methods".
As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving t... |
https://en.wikipedia.org/wiki/Catenoid | In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler.
Soap film attached to twin ... |
https://en.wikipedia.org/wiki/Ultraproduct | The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of ... |
https://en.wikipedia.org/wiki/Survey | Survey may refer to:
Statistics and human research
Statistical survey, a method for collecting quantitative information about items in a population
Survey (human research), including opinion polls
Spatial measurement
Surveying, the technique and science of measuring positions and distances on Earth
Types and meth... |
https://en.wikipedia.org/wiki/Martingale%20%28probability%20theory%29 | In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.
History
Originally, martingale referred to a class of betting ... |
https://en.wikipedia.org/wiki/Building%20%28mathematics%29 | In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially introduced by Jacques Tits as a means to understan... |
https://en.wikipedia.org/wiki/Realm%20%28disambiguation%29 | A realm is the dominion of a king or queen; a kingdom. Realm may also more broadly refer to everything which falls within a certain set of parameters.
Realm may also refer to:
Maths and science
biogeographic realm, the largest scale bio-geographic division of the Earth's surface
A hyperplane in geometry
Domain (... |
https://en.wikipedia.org/wiki/Ethical%20calculus | An ethical calculus is the application of mathematics to calculate issues in ethics.
Scope
Generally, ethical calculus refers to any method of determining a course of action in a circumstance that is not explicitly evaluated in one's ethical code.
A formal philosophy of ethical calculus is a development in the study ... |
https://en.wikipedia.org/wiki/Precedence | Precedence may refer to:
Message precedence of military communications traffic
Order of precedence, the ceremonial hierarchy within a nation or state
Precedence (mathematics) for defining the order of operations in a computation
Precedence Entertainment, a defunct American game publisher
Precedence (solitaire),... |
https://en.wikipedia.org/wiki/Deconvolution | In mathematics, deconvolution is the operation inverse to convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement... |
https://en.wikipedia.org/wiki/Range%20of%20a%20function | In mathematics, the range of a function may refer to either of two closely related concepts:
The codomain of the function
The image of the function
Given two sets and , a binary relation between and is a (total) function (from to ) if for every in there is exactly one in such that relates to . The sets ... |
https://en.wikipedia.org/wiki/Time-scale%20calculus | In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid systems. It has applications in any field that requires simultane... |
https://en.wikipedia.org/wiki/Module%20%28mathematics%29 | In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector space, a module is an additive ab... |
https://en.wikipedia.org/wiki/Vector%20bundle | In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space (for example could be a topological space, a manifold, or an algebraic variety): to every point of the space we associate (or "attach") a vector space in such a way ... |
https://en.wikipedia.org/wiki/Fiber%20bundle | In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space and a product space is defined using a continuous surjective map, that in small regi... |
https://en.wikipedia.org/wiki/Exponential%20map%20%28Riemannian%20geometry%29 | In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical affine connection, and the exponential map of the (pseudo) Riemannian manifold is given by the exponenti... |
https://en.wikipedia.org/wiki/Ricci%20curvature | In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs loca... |
https://en.wikipedia.org/wiki/Minimal%20surface | In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models ... |
https://en.wikipedia.org/wiki/Extreme%20value%20theorem | In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed interval , then must attain a maximum and a minimum, each at least once. That is, there exist numbers and in such that:
The extreme value theorem is more specific than the related boundedness theorem, which s... |
https://en.wikipedia.org/wiki/Uniqueness%20quantification | In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" or "∃=1". For example, the formal sta... |
https://en.wikipedia.org/wiki/Root%20system | In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representation theory of semisimple Lie algebras. Since Lie groups (and some analogues su... |
https://en.wikipedia.org/wiki/Weight%20%28representation%20theory%29 | In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its a... |
https://en.wikipedia.org/wiki/Computer%20mathematics | Computer mathematics may refer to:
Automated theorem proving, the proving of mathematical theorems by a computer program
Symbolic computation, the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects
Computational science, constructing numerical s... |
https://en.wikipedia.org/wiki/Mathematics%20and%20architecture | Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms con... |
https://en.wikipedia.org/wiki/TZero | TZero may refer to:
AC Propulsion tzero, automobile
T Zero, a collection of stories by Italo Calvino
t0, a symbol used in mathematics referring to the starting point or the beginning of time within a system |
https://en.wikipedia.org/wiki/Truncated%20tetrahedron | In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncating all 4 vertices of a regular tetrahedron at one third of the original edge length.
A deeper truncation, removing a ... |
https://en.wikipedia.org/wiki/Truncated%20octahedron | In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices. Since each of its faces has point symmetry the tru... |
https://en.wikipedia.org/wiki/Fredholm%20operator | In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm. By definition, a Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional kernel and finite-dimensional (al... |
https://en.wikipedia.org/wiki/Truncated%20cube | In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices.
If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and 2 + .
Area and volume
The area A and the volume V of ... |
https://en.wikipedia.org/wiki/Confidence%20interval | In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or con... |
https://en.wikipedia.org/wiki/Texas%20Academy%20of%20Mathematics%20and%20Science | The Texas Academy of Mathematics and Science (TAMS) is a two-year residential early entrance college program serving approximately 375 high school juniors and seniors at the University of North Texas. Students are admitted from every region of the state through a selective admissions process. TAMS is a member of the Na... |
https://en.wikipedia.org/wiki/Prism%20%28geometry%29 | In geometry, a prism is a polyhedron comprising an polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases... |
https://en.wikipedia.org/wiki/Algebraic%20data%20type | In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types.
Two common classes of algebraic types are product types (i.e., tuples and records) and sum types (i.e., tagged or disjoint unions, coproduc... |
https://en.wikipedia.org/wiki/Dummy%20variable%20%28statistics%29 | In regression analysis, a dummy variable (also known as indicator variable or just dummy) is one that takes a binary value (0 or 1) to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. For example, if we were studying the relationship between biological sex and incom... |
https://en.wikipedia.org/wiki/Unit%20square | In mathematics, a unit square is a square whose sides have length . Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and .
Cartesian coordinates
In a Cartesian coordinate system with coordinates , a unit square is defined as a square consisting of ... |
https://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff%20formula | In mathematics, the Baker–Campbell–Hausdorff formula is the solution for to the equation
for possibly noncommutative and in the Lie algebra of a Lie group. There are various ways of writing the formula, but all ultimately yield an expression for in Lie algebraic terms, that is, as a formal series (not necessarily ... |
https://en.wikipedia.org/wiki/Rhombicosidodecahedron | In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
Names
Johannes Kepler in Harmon... |
https://en.wikipedia.org/wiki/Parallel%20transport | In geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection allows one to transport vectors of the manifold... |
https://en.wikipedia.org/wiki/Sectional%20curvature | In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two-dimensional linear subspace σp of the tangent space at a point p of the manifold. It can be defined geometrically as the Gaussian curvature of the surface ... |
https://en.wikipedia.org/wiki/Scalar%20curvature | In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit f... |
https://en.wikipedia.org/wiki/Gaussian%20curvature | In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and , at the given point:
The Gaussian radius of curvature is the reciprocal of .
For example, a sphere of radius has Gaussian curvature everywhe... |
https://en.wikipedia.org/wiki/Spoke%E2%80%93hub%20distribution%20paradigm | The spoke–hub distribution paradigm is a form of transport topology optimization in which traffic planners organize routes as a series of "spokes" that connect outlying points to a central "hub". Simple forms of this distribution/connection model contrast with point-to-point transit systems, in which each point has a... |
https://en.wikipedia.org/wiki/Limit%20of%20a%20function | Although the function is not defined at zero, as becomes closer and closer to zero, becomes arbitrarily close to 1. In other words, the limit of as approaches zero, equals 1.
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a p... |
https://en.wikipedia.org/wiki/Limit%20of%20a%20sequence | As the positive integer becomes larger and larger, the value becomes arbitrarily close to . We say that "the limit of the sequence equals ."
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ). If such a limit exists, the seque... |
https://en.wikipedia.org/wiki/Truncated%20cuboctahedron | In geometry, the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges. Since each of its faces has point symmetry (equivalently, 180° rotat... |
https://en.wikipedia.org/wiki/Fractal%20dimension | In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured.
It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scale... |
https://en.wikipedia.org/wiki/Social%20statistics | Social statistics is the use of statistical measurement systems to study human behavior in a social environment. This can be accomplished through polling a group of people, evaluating a subset of data obtained about a group of people, or by observation and statistical analysis of a set of data that relates to people a... |
https://en.wikipedia.org/wiki/Modular%20form | In mathematics, a modular form is a (complex) analytic function on the upper half-plane, , that satisfies:
a kind of functional equation with respect to the group action of the modular group,
and a growth condition.
The theory of modular forms therefore belongs to complex analysis. The main importance of the theor... |
https://en.wikipedia.org/wiki/Absorption%20law | In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations.
Two binary operations, ¤ and ⁂, are said to be connected by the absorption law if:
a ¤ (a ⁂ b) = a ⁂ (a ¤ b) = a.
A set equipped with two commutative and associative binary operations ("join") and ("meet") tha... |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Justice | The National Institute of Justice (NIJ) is the research, development and evaluation agency of the United States Department of Justice.
NIJ, along with the Bureau of Justice Statistics (BJS), Bureau of Justice Assistance (BJA), Office of Juvenile Justice and Delinquency Prevention (OJJDP), Office for Victims of Crime ... |
https://en.wikipedia.org/wiki/255%20%28number%29 | 255 (two hundred [and] fifty-five) is the natural number following 254 and preceding 256.
In mathematics
Its factorization makes it a sphenic number. Since 255 = 28 – 1, it is a Mersenne number (though not a pernicious one), and the fourth such number not to be a prime number. It is a perfect totient number, the small... |
https://en.wikipedia.org/wiki/Arne%20Beurling | Arne Carl-August Beurling (3 February 1905 – 20 November 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey. Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The ... |
https://en.wikipedia.org/wiki/Truncated%20icosidodecahedron | In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron or omnitruncated icosahedron is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
It has 62 faces... |
https://en.wikipedia.org/wiki/Snub%20dodecahedron | In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equila... |
https://en.wikipedia.org/wiki/Number%20line | In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
The integers are often shown as specially-marked points evenly spaced on... |
https://en.wikipedia.org/wiki/Inverse%20function%20theorem | In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. The theorem also gives a formula for the derivative of the invers... |
https://en.wikipedia.org/wiki/Transcendental%20extension | In mathematics, a transcendental extension is a field extension such that there exists an element in the field that is transcendental over the field ; that is, an element that is not a root of any univariate polynomial with coefficients in . In other words, a transcendental extension is a field extension that is not ... |
https://en.wikipedia.org/wiki/Pseudo-Riemannian%20manifold | In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed.
Every tangent space of a ... |
https://en.wikipedia.org/wiki/GPR | GPR may refer to:
Science and technology
Gaussian process regression, an interpolation method in statistics
General-purpose register of a microprocessor
G-protein coupled receptor
Ground-penetrating radar
Ground potential rise, in electrical engineering
Other
General practice residency, in dentistry in the Un... |
https://en.wikipedia.org/wiki/Algebraic%20independence | In abstract algebra, a subset of a field is algebraically independent over a subfield if the elements of do not satisfy any non-trivial polynomial equation with coefficients in .
In particular, a one element set is algebraically independent over if and only if is transcendental over . In general, all the elemen... |
https://en.wikipedia.org/wiki/Upper%20half-plane | In mathematics, the upper half-plane, , is the set of points in the Cartesian plane with
. The lower half-plane is defined similarly, by requiring that be negative instead. Each is an example of two-dimensional half-space.
Affine geometry
The affine transformations of the upper half-plane include
shifts , , and
d... |
https://en.wikipedia.org/wiki/Uniformization%20theorem | In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the p... |
https://en.wikipedia.org/wiki/Ricci%20flow | In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due to formal simila... |
https://en.wikipedia.org/wiki/Global%20field | In mathematics, a global field is one of two types of fields (the other one is local field) which are characterized using valuations. There are two kinds of global fields:
Algebraic number field: A finite extension of
Global function field: The function field of an algebraic curve over a finite field, equivalently, a... |
https://en.wikipedia.org/wiki/Risch%20algorithm | In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
The algorithm transforms the problem of integrati... |
https://en.wikipedia.org/wiki/Nilradical%20of%20a%20ring | In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements:
It is thus the radical of the zero ideal. If the nilradical is the zero ideal, the ring is called a reduced ring. The nilradical of a commutative ring is the intersection of all prime ideals.
In the non-commutative ri... |
https://en.wikipedia.org/wiki/Unit%20%28ring%20theory%29 | In algebra, a unit or invertible element of a ring is an invertible element for the multiplication of the ring. That is, an element of a ring is a unit if there exists in such that
where is the multiplicative identity; the element is unique for this property and is called the multiplicative inverse of . The set ... |
https://en.wikipedia.org/wiki/Cram%C3%A9r%27s%20conjecture | In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. It s... |
https://en.wikipedia.org/wiki/Ren%C3%A9%20Maurice%20Fr%C3%A9chet | René Maurice Fréchet (; 2 September 1878 – 4 June 1973) was a French mathematician. He made major contributions to general topology and was the first to define metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire ... |
https://en.wikipedia.org/wiki/EOF | EOF or Eof may refer to:
Science and technology
Electro-osmotic flow, the motion of liquid induced by an applied potential
Empirical orthogonal functions, in statistics and signal processing
Ethyl orthoformate, an organic compound
Computing
End-of-file, a condition where no more data can be read from a data sourc... |
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