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https://en.wikipedia.org/wiki/Entropy%20rate
In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate is the limit of the joint entropy of members of the proc...
https://en.wikipedia.org/wiki/Franz%20Hermann%20Troschel
Franz Hermann Troschel (10 October 1810 – 6 November 1882) was a German zoologist born in Spandau. He studied mathematics and natural history at the University of Berlin, where he was awarded his doctorate in 1834. From 1840 to 1849 he was an assistant to Martin Lichtenstein at the Natural History Museum of Berlin. In...
https://en.wikipedia.org/wiki/C%C3%A9a%27s%20lemma
Céa's lemma is a lemma in mathematics. Introduced by Jean Céa in his Ph.D. dissertation, it is an important tool for proving error estimates for the finite element method applied to elliptic partial differential equations. Lemma statement Let be a real Hilbert space with the norm Let be a bilinear form with the pr...
https://en.wikipedia.org/wiki/Medical%20statistics
Medical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years but the term has not come into general...
https://en.wikipedia.org/wiki/Horocycle
In hyperbolic geometry, a horocycle (), sometimes called an oricycle, oricircle, or limit circle, is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction. It is the two-dimensional case of a horosphere (or orisphere). The centre of a horocycle is the ideal point where all n...
https://en.wikipedia.org/wiki/Qiudong%20Wang
Qiudong Wang is a professor at the Department of Mathematics, the University of Arizona. In 1982 he received a B.S. at Nanjing University and in 1994 a Ph.D. at the University of Cincinnati. Wang is best known for his 1991 paper The global solution of the n-body problem, in which he generalised Karl F. Sundman's resu...
https://en.wikipedia.org/wiki/Q.%20Wang
Q. Wang may refer to: Qiudong Wang, professor of mathematics Q. Wang (artist) (born 1962), Chinese-American primitivist painter
https://en.wikipedia.org/wiki/Langlands%20decomposition
In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product of a reductive subgroup M, an abelian subgroup A, and a nilpotent subgroup N. Applications A key application is in parabolic induction, which leads to the Langlands program: if is a reductive algebraic ...
https://en.wikipedia.org/wiki/Infinitesimal%20character
In mathematics, the infinitesimal character of an irreducible representation ρ of a semisimple Lie group G on a vector space V is, roughly speaking, a mapping to scalars that encodes the process of first differentiating and then diagonalizing the representation. It therefore is a way of extracting something essential f...
https://en.wikipedia.org/wiki/Box%E2%80%93Behnken%20design
In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals: Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as −1, 0, +1. (At least three level...
https://en.wikipedia.org/wiki/Samara%20State%20University
Samara State University () was a classical multi-faculty university and a leading educational institution of higher education in Samara Oblast, Russia. It consists of faculties of Mathematics and Mechanics, Physics, Biology, Chemistry, Philology, History, Sociology, Economy and Management, Psychology, and Law. It is co...
https://en.wikipedia.org/wiki/Proviso%20Mathematics%20and%20Science%20Academy
Proviso Mathematics and Science Academy is a selective enrollment high school in Forest Park, Illinois, United States that opened its doors to 126 freshmen in 2005. It is one of the newest schools in the Proviso Township High Schools District 209. It serves students in many towns in western Cook County including Fore...
https://en.wikipedia.org/wiki/List%20of%20oldest%20and%20youngest%20Academy%20Award%20winners%20and%20nominees
This is a list of oldest and youngest Academy Award winners and nominees in the award categories Acting and Directing. This list is based on "statistics valid through the nomination announcement for the 2015 (88th Academy Awards), announced on January 14, 2016", as documented in The Official Academy Awards Database. ...
https://en.wikipedia.org/wiki/Integro-differential%20equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. General first order linear equations The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form As is typical with differe...
https://en.wikipedia.org/wiki/Equipossibility
Equipossibility is a philosophical concept in possibility theory that is a precursor to the notion of equiprobability in probability theory. It is used to distinguish what can occur in a probability experiment. For example, it is the difference between viewing the possible results of rolling a six sided dice as {1,2,3,...
https://en.wikipedia.org/wiki/Equiprobability
Equiprobability is a property for a collection of events that each have the same probability of occurring. In statistics and probability theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational numbers. If there are events under consideration, the probability of each occu...
https://en.wikipedia.org/wiki/Isomorphism-closed%20subcategory
In category theory, a branch of mathematics, a subcategory of a category is said to be isomorphism closed or replete if every -isomorphism with belongs to This implies that both and belong to as well. A subcategory that is isomorphism closed and full is called strictly full. In the case of full subcategorie...
https://en.wikipedia.org/wiki/Representation%20theory%20of%20SL2%28R%29
{{DISPLAYTITLE:Representation theory of SL2(R)}} In mathematics, the main results concerning irreducible unitary representations of the Lie group SL(2,R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952). Structure of the complexified Lie algebra We choose a basis H, X, Y for the co...
https://en.wikipedia.org/wiki/SL2%28R%29
{{DISPLAYTITLE:SL2(R)}} In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: It is a connected non-compact simple real Lie group of dimension 3 with applications in geometry, topology, representation theory, and physics. SL(2, R) acts on the complex ...
https://en.wikipedia.org/wiki/Eugenio%20Elia%20Levi
Eugenio Elia Levi (18 October 1883 – 28 October 1917) was an Italian mathematician, known for his fundamental contributions in group theory, in the theory of partial differential operators and in the theory of functions of several complex variables. He was a younger brother of Beppo Levi and was killed in action during...
https://en.wikipedia.org/wiki/Parabolic%20induction
In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups. If G is a reductive algebraic group and is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of , ex...
https://en.wikipedia.org/wiki/Complementary%20series%20representation
In mathematics, complementary series representations of a reductive real or p-adic Lie groups are certain irreducible unitary representations that are not tempered and do not appear in the decomposition of the regular representation into irreducible representations. They are rather mysterious: they do not turn up ver...
https://en.wikipedia.org/wiki/Sum-free%20set
In additive combinatorics and number theory, a subset A of an abelian group G is said to be sum-free if the sumset A + A is disjoint from A. In other words, A is sum-free if the equation has no solution with . For example, the set of odd numbers is a sum-free subset of the integers, and the set {N + 1, ..., 2N&hairsp...
https://en.wikipedia.org/wiki/Weyl%E2%80%93Brauer%20matrices
In mathematics, particularly in the theory of spinors, the Weyl–Brauer matrices are an explicit realization of a Clifford algebra as a matrix algebra of matrices. They generalize the Pauli matrices to dimensions, and are a specific construction of higher-dimensional gamma matrices. They are named for Richard Brauer a...
https://en.wikipedia.org/wiki/List%20of%20Canisius%20University%20people
This is a list of notable students, alumni, staff and faculty of Canisius University in Buffalo, New York. Academia Sister Marion Beiter, '44 - mathematician, Chairman of Mathematics for Rosary Hill College H. James Birx - Professor of Anthropology, Canisius University Paul G. Bulger - President of Buffalo State Coll...
https://en.wikipedia.org/wiki/Extouch%20triangle
In Euclidean geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle. Coordinates The vertices of the extouch triangle are given in trilinear coordinates by: or equivalently, where are the lengths of the sides opposite angles respectively, Relate...
https://en.wikipedia.org/wiki/Belt%20problem
The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius r1 and r2 whose centers are separated by a distance P. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congr...
https://en.wikipedia.org/wiki/Chow%27s%20lemma
Chow's lemma, named after Wei-Liang Chow, is one of the foundational results in algebraic geometry. It roughly says that a proper morphism is fairly close to being a projective morphism. More precisely, a version of it states the following: If is a scheme that is proper over a noetherian base , then there exists a pr...
https://en.wikipedia.org/wiki/Ces%C3%A0ro%20equation
In geometry, the Cesàro equation of a plane curve is an equation relating the curvature () at a point of the curve to the arc length () from the start of the curve to the given point. It may also be given as an equation relating the radius of curvature () to arc length. (These are equivalent because .) Two congruent cu...
https://en.wikipedia.org/wiki/Joseph%20O%27Rourke
Joseph O'Rourke may refer to: Joseph Cornelius O'Rourke (1772–1849), Russian nobleman and military leader Joseph O'Rourke (professor), researcher in computational geometry Joseph O'Rourke (activist) (1938–2008), Catholic ex-priest and pro-choice activist
https://en.wikipedia.org/wiki/Kempner%20function
In number theory, the Kempner function is defined for a given positive integer to be the smallest number such that divides the For example, the number does not divide , , but does This function has the property that it has a highly inconsistent growth rate: it grows linearly on the prime numbers but only grow...
https://en.wikipedia.org/wiki/Major%20League%20Soccer%20records%20and%20statistics
Several Major League Soccer teams and players hold various records and statistics. MLS Cup and Supporters' Shield winners MLS Cup finals Teams with most trophies Player records (career) Bold indicates an active player. All statistics are for regular season only. Goals As of the end of the 2023 regular season. G...
https://en.wikipedia.org/wiki/Casus%20irreducibilis
In algebra, () is one of the cases that may arise in solving polynomials of degree 3 or higher with integer coefficients algebraically (as opposed to numerically), i.e., by obtaining roots that are expressed with radicals. It shows that many algebraic numbers are real-valued but cannot be expressed in radicals without...
https://en.wikipedia.org/wiki/William%20Holding%20Echols
William Holding Echols VI (December 2, 1859 – September 25, 1934), generally called "Reddy" Echols, was a professor of mathematics at the University of Virginia. The Echols Scholars Program is named in his honor. William Echols was the son of the fifth of the same name who was a Major in Confederate States of America....
https://en.wikipedia.org/wiki/Proximity%20problems
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously to the ...
https://en.wikipedia.org/wiki/Littelmann%20path%20model
In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie grou...
https://en.wikipedia.org/wiki/Existentially%20closed%20model
In model theory, a branch of mathematical logic, the notion of an existentially closed model (or existentially complete model) of a theory generalizes the notions of algebraically closed fields (for the theory of fields), real closed fields (for the theory of ordered fields), existentially closed groups (for the theory...
https://en.wikipedia.org/wiki/Ian%20Wilson%20%28phonetician%29
Ian Wilson (born in 1966) is a Canadian linguist. Biography Wilson has a Bachelor of Mathematics from the University of Waterloo, he has an M.A. in Teaching English as a Foreign/Second Language from the University of Birmingham and a PhD in Linguistics (phonetics) from the University of British Columbia. He is profes...
https://en.wikipedia.org/wiki/G.%20W.%20Peck
G. W. Peck is a pseudonymous attribution used as the author or co-author of a number of published mathematics academic papers. Peck is sometimes humorously identified with George Wilbur Peck, a former governor of the US state of Wisconsin. Peck first appeared as the official author of a 1979 paper entitled "Maximum an...
https://en.wikipedia.org/wiki/Iktaba
Iktaba () is a Palestinian town located four kilometers Northeast of the city of Tulkarm in the Tulkarm Governorate in the northern West Bank. According to the Palestinian Central Bureau of Statistics (PCBS), the town had a population of 2,665 inhabitants in 2007 and 2,997 by 2017. Refugees make-up 33% of the entire po...
https://en.wikipedia.org/wiki/Protestantism%20in%20Colombia
The National Administrative Department of Statistics (DANE) does not collect religious statistics, and accurate reports are difficult to obtain. However, based on various studies and a survey, about 90% of the population adheres to Christianity, the majority of which (70.9%) are Roman Catholic, while a significant mino...
https://en.wikipedia.org/wiki/Fred%20Galvin
Frederick William Galvin is a mathematician, currently a professor at the University of Kansas. His research interests include set theory and combinatorics. His notable combinatorial work includes the proof of the Dinitz conjecture. In set theory, he proved with András Hajnal that if ℵω1 is a strong limit cardinal, th...
https://en.wikipedia.org/wiki/John%20Brillhart
John David Brillhart (November 13, 1930 – May 21, 2022) was a mathematician who worked in number theory at the University of Arizona. Early life and education Brillhart was born on November 13, 1930, in Berkeley, California. He studied at the University of California, Berkeley, where he received his A.B. in 1953, his...
https://en.wikipedia.org/wiki/W.%20B.%20R.%20Lickorish
William Bernard Raymond Lickorish (born 19 February 1938) is a mathematician. He is emeritus professor of geometric topology in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, and also an emeritus fellow of Pembroke College, Cambridge. His research interests include topology and...
https://en.wikipedia.org/wiki/Mean%20reciprocal%20rank
The mean reciprocal rank is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries, ordered by probability of correctness. The reciprocal rank of a query response is the multiplicative inverse of the rank of the first correct answer: 1 for first place, for seco...
https://en.wikipedia.org/wiki/Self-avoiding%20walk
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously ...
https://en.wikipedia.org/wiki/Lorentz%20curve
Lorentz curve may refer to the Cauchy–Lorentz distribution, a probability distribution the Lorenz curve, a graphical representation of the inequality in a quantity's distribution
https://en.wikipedia.org/wiki/Partial%20linear%20space
A partial linear space (also semilinear or near-linear space) is a basic incidence structure in the field of incidence geometry, that carries slightly less structure than a linear space. The notion is equivalent to that of a linear hypergraph. Definition Let an incidence structure, for which the elements of are call...
https://en.wikipedia.org/wiki/Simplicial%20volume
In the mathematical field of geometric topology, the simplicial volume (also called Gromov norm) is a certain measure of the topological complexity of a manifold. More generally, the simplicial norm measures the complexity of homology classes. Given a closed and oriented manifold, one defines the simplicial norm by mi...
https://en.wikipedia.org/wiki/Trace%20operator
In mathematics, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev space. This is particularly important for the study of partial differential equations with prescribed boundary conditions (boundary value problems), where weak sol...
https://en.wikipedia.org/wiki/Berger%27s%20sphere
In Riemannian geometry, a Berger sphere, named after Marcel Berger, is a standard 3-sphere with Riemannian metric from a one-parameter family, which can be obtained from the standard metric by shrinking along fibers of a Hopf fibration. It is interesting in that it is one of the simplest examples of Gromov collapse. ...
https://en.wikipedia.org/wiki/Automorphic%20factor
In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms. The general case, for general groups, is reviewed in the article 'factor of automorphy'. Definition An automorphic factor of weight k is a function satisfying the f...
https://en.wikipedia.org/wiki/Schouten%E2%80%93Nijenhuis%20bracket
In differential geometry, the Schouten–Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different versions, both rather confusingly called by the same name. The most commo...
https://en.wikipedia.org/wiki/Quasi-birth%E2%80%93death%20process
In queueing models, a discipline within the mathematical theory of probability, the quasi-birth–death process describes a generalisation of the birth–death process. As with the birth-death process it moves up and down between levels one at a time, but the time between these transitions can have a more complicated distr...
https://en.wikipedia.org/wiki/Bracket%20%28mathematics%29
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets ⟨ ⟩, are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operato...
https://en.wikipedia.org/wiki/SPQR%20tree
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex cuts in the graph. An SPQR tree is a tree data structure used in computer science, and more specifically graph algorithms, to represent the triconnected componen...
https://en.wikipedia.org/wiki/Nijenhuis%20bracket
In mathematics there are four different but related brackets named after Albert Nijenhuis, giving Lie superalgebra structures to various spaces of tensors: Frölicher–Nijenhuis bracket (defined on vector valued forms, extending the Lie bracket of vector fields) Nijenhuis–Richardson bracket (defined on vector valued form...
https://en.wikipedia.org/wiki/Spectrum%20bias
In biostatistics, spectrum bias refers to the phenomenon that the performance of a diagnostic test may vary in different clinical settings because each setting has a different mix of patients. Because the performance may be dependent on the mix of patients, performance at one clinic may not be predictive of performanc...
https://en.wikipedia.org/wiki/Albert%20Nijenhuis
Albert Nijenhuis (November 21, 1926 – February 13, 2015) was a Dutch-American mathematician who specialized in differential geometry and the theory of deformations in algebra and geometry, and later worked in combinatorics. His high school studies at the gymnasium in Arnhem were interrupted by the evacuation of Arnhem...
https://en.wikipedia.org/wiki/Dirk%20Kreimer
Dirk Kreimer (born 12 July 1960) is a German physicist who pioneered the Hopf-algebraic approach to perturbative quantum field theory with Alain Connes and other co-authors. He is currently Humboldt professor at the department of mathematics of Humboldt University in Berlin, where he teaches the courses of Quantum Fiel...
https://en.wikipedia.org/wiki/Patrick%20Hughes%20%28cricketer%29
Lewis Patrick Hughes (10 April 1943 – 19 February 2022), also known as Podge Hughes, was an Irish cricketer and maths teacher at Mount Temple Comprehensive School. A right-handed batsman and right-arm fast-medium bowler, he played thirteen times for the Ireland cricket team between 1965 and 1978 including five first-cl...
https://en.wikipedia.org/wiki/Category%20of%20modules
In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all module homomorphisms between left R-modules. For example, when R is the ring of integers Z, it is the same thing as the category of abelian groups. The category of right ...
https://en.wikipedia.org/wiki/Germany%20Billie%20Jean%20King%20Cup%20team
The Germany women's national tennis team represents Germany in Billie Jean King Cup tennis competition and are governed by Deutscher Tennis Bund. Current team Statistics correct as of 16 October 2023. History Germany competed in its first Fed Cup in 1963. They won the Cup in 1987 and 1992, and finished as runners-up...
https://en.wikipedia.org/wiki/Scree%20plot
In multivariate statistics, a scree plot is a line plot of the eigenvalues of factors or principal components in an analysis. The scree plot is used to determine the number of factors to retain in an exploratory factor analysis (FA) or principal components to keep in a principal component analysis (PCA). The procedure ...
https://en.wikipedia.org/wiki/Lai%20Yee%20Hing
Lai Yee Hing () is a Singaporean organic chemistry professor based in the National University of Singapore. He was the principal of NUS High School of Mathematics and Science and held this position from July 2004 to 30 August 2007. Lai Yee Hing graduated with a B.Sc from the former Nanyang University (now National Uni...
https://en.wikipedia.org/wiki/Brian%20Rotman
Brian Rotman is a British-born professor who works in the United States. Trained as a mathematician and now an established philosopher, Rotman has blended semiotics, mathematics and the history of writing in his work and teaching throughout his career. He is currently a distinguished humanities professor in the depar...
https://en.wikipedia.org/wiki/Statistical%20model%20specification
In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income together with years of schooling and on-the-job experience , we might ...
https://en.wikipedia.org/wiki/Pitteway%20triangulation
In computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one of the vertices of the triangle containing p. Alternatively, it is a Delaunay triangulation in which each internal edge crosses its dual Voronoi diagram edge. Pit...
https://en.wikipedia.org/wiki/PMG%20%22Ekzarh%20Antim%20I%22
PPMG "Exarch Antim I" () is a public high school in Vidin, Bulgaria. The school specializes in maths and science. It is attended by students from the fifth to the twelfth grade. Building The school building was built in 1891 with donations provided by the Exarch Antim I. See also Education in Bulgaria External links...
https://en.wikipedia.org/wiki/List%20of%20women%20in%20mathematics
This is a list of women who have made noteworthy contributions to or achievements in mathematics. These include mathematical research, mathematics education, the history and philosophy of mathematics, public outreach, and mathematics contests. A Karen Aardal (born 1961), Norwegian and Dutch applied mathematician, th...
https://en.wikipedia.org/wiki/Covariance%20and%20contravariance
Covariance and contravariance may refer to: Covariance and contravariance of vectors, in mathematics and theoretical physics Covariance and contravariance of functors, in category theory Covariance and contravariance (computer science), whether a type system preserves the ordering ≤ of types See also Covariance, i...
https://en.wikipedia.org/wiki/Quantum%20graph
In mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a length and where a differential (or pseudo-differential) equation is posed on each edge. An example would be a power network consisting of power lines (edges) ...
https://en.wikipedia.org/wiki/Stemm
Stemm may refer to: STEMM, American metal band STEMM, abbreviation for Science, technology, engineering, mathematics, and medicine Stemm, Indiana, a community in the US See also Stem (disambiguation) Stemme, a German light aircraft manufacturer
https://en.wikipedia.org/wiki/New%20York%20State%20Sportswriters%20Association
The New York State Sportswriters Association (NYSSWA), founded in 1967, is a source of reference information and statistics about scholastic athletics in the state. Begun by sportswriters Larry Serrell of the Schenectady Daily Gazette and Chuck Korbar of the Buffalo Evening News, NYSSWA membership grew from 12 in 1967 ...
https://en.wikipedia.org/wiki/Home%20runs%20per%20nine%20innings
In baseball statistics, home runs allowed per 9 innings pitched (HR/9IP or HR/9) or home runs allowed per nine innings (denoted by HR/9) is the average number of home runs given up by a pitcher per nine innings pitched. It is determined by multiplying the number of home runs allowed by nine and dividing by the number ...
https://en.wikipedia.org/wiki/Norman%20Zada
Norman Zada (born Norman Askar Zadeh) is a former adjunct mathematics professor and an entrepreneur. He is the founder of Perfect 10, an adult magazine focusing on women without cosmetic surgery, and runs the United States Investing Competition. Zada is the son of Lotfi Zadeh, the creator of fuzzy logic. Education and...
https://en.wikipedia.org/wiki/Lie%20algebra%20bundle
In mathematics, a weak Lie algebra bundle is a vector bundle over a base space X together with a morphism which induces a Lie algebra structure on each fibre . A Lie algebra bundle is a vector bundle in which each fibre is a Lie algebra and for every x in X, there is an open set containing x, a Lie algebra L and ...
https://en.wikipedia.org/wiki/Matrix%20determinant%20lemma
In mathematics, in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, uvT, of a column vector u and a row vector vT. Statement Suppose A is an invertible square matrix and u, v are column vectors. Then the matrix determinant le...
https://en.wikipedia.org/wiki/Brian%20Hartley
Brian Hartley (15 May 1939 – 8 October 1994) was a British mathematician specialising in group theory. Education Hartley's PhD thesis was completed in 1964 at the University of Cambridge under Philip Hall's supervision. Career and research Hartley spent a year at the University of Chicago, and another at MIT before b...
https://en.wikipedia.org/wiki/Harish-Chandra%20character
In mathematics, the Harish-Chandra character, named after Harish-Chandra, of a representation of a semisimple Lie group G on a Hilbert space H is a distribution on the group G that is analogous to the character of a finite-dimensional representation of a compact group. Definition Suppose that π is an irreducible unit...
https://en.wikipedia.org/wiki/Harish-Chandra%27s%20regularity%20theorem
In mathematics, Harish-Chandra's regularity theorem, introduced by , states that every invariant eigendistribution on a semisimple Lie group, and in particular every character of an irreducible unitary representation on a Hilbert space, is given by a locally integrable function. proved a similar theorem for semisimple...
https://en.wikipedia.org/wiki/Positively%20separated%20sets
In mathematics, two non-empty subsets A and B of a given metric space (X, d) are said to be positively separated if the infimum (Some authors also specify that A and B should be disjoint sets; however, this adds nothing to the definition, since if A and B have some common point p, then d(p, p) = 0, and so the infimu...
https://en.wikipedia.org/wiki/Metric%20outer%20measure
In mathematics, a metric outer measure is an outer measure μ defined on the subsets of a given metric space (X, d) such that for every pair of positively separated subsets A and B of X. Construction of metric outer measures Let τ : Σ → [0, +∞] be a set function defined on a class Σ of subsets of X containing the emp...
https://en.wikipedia.org/wiki/Jeff%20Paris%20%28mathematician%29
Jeffrey Bruce Paris (; born 15 November 1944) is a British mathematician and Professor of Logic in the School of Mathematics at the University of Manchester. Education Paris gained his doctorate supervised by Robin Gandy at Manchester in 1969 with a dissertation on Large Cardinals and the Generalized Continuum Hypot...
https://en.wikipedia.org/wiki/Problem%20of%20points
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected...
https://en.wikipedia.org/wiki/Quartile%20coefficient%20of%20dispersion
In statistics, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of s...
https://en.wikipedia.org/wiki/Implicit%20curve
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation . In general, every implicit curve is defined by an equation of the form for some function F of two variables. Hence ...
https://en.wikipedia.org/wiki/Mims
Mims or MIMS may refer to: Education Manchester Institute for Mathematical Sciences, School of Mathematics, University of Manchester, England Mandarin Immersion Magnet School, Houston, Texas, United States Mandya Institute of Medical Sciences, Mandya, Karnataka, India MediCiti Institute of Medical Sciences, near Hyd...
https://en.wikipedia.org/wiki/Sure
Sure may refer to: Seemingly unrelated regressions Series of Unsurprising Results in Economics (SURE), an economics academic journal Sure, as probability, see certainty Sure (brand), a brand of antiperspirant deodorant Sure (company), a telecommunications company operating in British Crown Dependencies and Overs...
https://en.wikipedia.org/wiki/Alar%20Toomre
Alar Toomre (born 5 February 1937, in Rakvere) is an American astronomer and mathematician. He is a professor of applied mathematics at the Massachusetts Institute of Technology. Toomre's research is focused on the dynamics of galaxies. He is a 1984 MacArthur Fellow. Career Following the Soviet occupation of Estonia ...
https://en.wikipedia.org/wiki/Monotonically%20normal%20space
In mathematics, specifically in the field of topology, a monotonically normal space is a particular kind of normal space, defined in terms of a monotone normality operator. It satisfies some interesting properties; for example metric spaces and linearly ordered spaces are monotonically normal, and every monotonically ...
https://en.wikipedia.org/wiki/Leslie%20Fox
Leslie Fox (30 September 1918 – 1 August 1992) was a British mathematician noted for his contribution to numerical analysis. Overview Fox studied mathematics as a scholar of Christ Church, Oxford graduating with a first in 1939 and continued to undertake research in the engineering department. While working on his D.P...
https://en.wikipedia.org/wiki/Meusnier%27s%20theorem
In differential geometry, Meusnier's theorem states that all curves on a surface passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776, but not published...
https://en.wikipedia.org/wiki/Chinese%20hypothesis
In number theory, the Chinese hypothesis is a disproven conjecture stating that an integer n is prime if and only if it satisfies the condition that is divisible by n—in other words, that an integer n is prime if and only if . It is true that if n is prime, then (this is a special case of Fermat's little theorem), ho...
https://en.wikipedia.org/wiki/Brocard%27s%20problem
Brocard's problem is a problem in mathematics that seeks integer values of such that is a perfect square, where is the factorial. Only three values of are known — 4, 5, 7 — and it is not known whether there are any more. More formally, it seeks pairs of integers and such thatThe problem was posed by Henri Brocar...
https://en.wikipedia.org/wiki/Discrepancy
Discrepancy may refer to: Mathematics Discrepancy of a sequence Discrepancy theory in structural modelling Discrepancy of hypergraphs, an area of discrepancy theory Discrepancy (algebraic geometry) Statistics Discrepancy function in the context of structural equation models Deviance (statistics) Deviation (sta...
https://en.wikipedia.org/wiki/Vertex%20%28geometry%29
In geometry, a vertex (: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. Definition Of an angle The vertex of an angle is the poin...
https://en.wikipedia.org/wiki/Microphone%20Mathematics
"Microphone Mathematics" is the second single by Quasimoto, the rapping alter ego of Madlib. These tracks later appeared on his debut album The Unseen. On the album, however, "Discipline 99" was split into 2 tracks. Part 0 featured "Mr. Herb," while part 1 featured Wildchild of the Lootpack. Track listing Side A Mic...
https://en.wikipedia.org/wiki/Mathematics%20%28Cherry%20Ghost%20song%29
"Mathematics" is the debut single from Manchester band Cherry Ghost. It was released as a digital download on March 26, 2007 and on CD and 7" vinyl on April 9, 2007. It went to #57 on the UK singles chart. "Mathematics" acquired the title "song of the week" on BBC Radio 2 in early 2007, and Zane Lowe of BBC Radio 1 dec...
https://en.wikipedia.org/wiki/Dimension%20function
In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple "diameter to the dimension" power law used in the construction of s-dimensional Hausdorff measure. M...