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Wikipedia:David Shale#0 | David Winston Howard Shale (22 March 1932, New Zealand – 7 January 2016) was a New Zealand-American mathematician, specializing in the mathematical foundations of quantum physics. He is known as one of the namesakes of the Segal–Shale-Weil representation. After secondary and undergraduate education in New Zealand, Shal... |
Wikipedia:David Spence (mathematician)#0 | David Allan Spence (3 January 1926 – 7 September 2003) was a mathematician who applied his mathematical skills in the aeronautics industry, and to the understanding of geophysical problems. He was born and educated in New Zealand, later moving to England, to take up a Doctorate in Engineering at Clare College, Cambridg... |
Wikipedia:David Steurer#0 | David Steurer is a German theoretical computer scientist, working in approximation algorithms, hardness of approximation, sum of squares, and high-dimensional statistics. He is an associate professor of computer science at ETH Zurich. == Biography == David Steurer studied for bachelor's and master's degrees at the Univ... |
Wikipedia:David W. Lewis (mathematician)#0 | David W. Lewis (21 February 1944 in Douglas, Isle of Man—20 August 2021 in Dublin) was a Manx mathematician known for his contributions to quadratic forms theory. He spent his entire career at University College Dublin (UCD), where he was head of the Department of Mathematics (now the School of Mathematics and Statisti... |
Wikipedia:David William Boyd#0 | David William Boyd (born 17 September 1941) is a Canadian mathematician who does research on harmonic and classical analysis, inequalities related to geometry, number theory, and polynomial factorization, sphere packing, number theory involving Diophantine approximation and Mahler's measure, and computer computations. ... |
Wikipedia:David Wood (mathematician)#0 | David Ronald Wood (born in Christchurch, New Zealand in 1971) is a Professor in the School of Mathematics at Monash University in Melbourne, Australia. His research area is discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph col... |
Wikipedia:Dawson–Gärtner theorem#0 | In mathematics, the Dawson–Gärtner theorem is a result in large deviations theory. Heuristically speaking, the Dawson–Gärtner theorem allows one to transport a large deviation principle on a “smaller” topological space to a “larger” one. == Statement of the theorem == Let (Yj)j∈J be a projective system of Hausdorff top... |
Wikipedia:De Gradibus#0 | De Gradibus was an Arabic book published by the Arab physician Al-Kindi (c. 801–873 CE). De gradibus is the Latinized name of the book. An alternative name for the book was Quia Primos. In De Gradibus, Al-Kindi attempts to apply mathematics to pharmacology by quantifying the strength of drugs. According to Prioreschi, ... |
Wikipedia:Deborah Hughes Hallett#0 | Deborah J. Hughes Hallett is a mathematician who works as a professor of mathematics at the University of Arizona. Her expertise is in the undergraduate teaching of mathematics. She has also taught as Professor of the Practice in the Teaching of Mathematics at Harvard University, and continues to hold an affiliation wi... |
Wikipedia:Deborah Kent#0 | Deborah Anne Kent (born 1978) is an American mathematics educator, textbook author, historian of mathematics, and historian of astronomy, with particular interests in game theory, 19th-century mathematics, and historic observations of eclipses. She works in Scotland as Senior Lecturer in History of Mathematics at the U... |
Wikipedia:Debra Boutin#0 | Debra Lynn Boutin (born 1957 in Holyoke, Massachusetts) is an American mathematician, the Samuel F. Pratt Professor of Mathematics at Hamilton College, where she chairs the mathematics department. Her research involves the symmetries of graphs and distinguishing colorings of graphs. == Education == Boutin is a 1975 gra... |
Wikipedia:Dedekind eta function#0 | In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string theory. == Definition == For any complex number τ with Im(τ) > 0, let q = ... |
Wikipedia:Defective matrix#0 | In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n {\displaystyle n\times n} matrix is defective if and only if it does not have n {\displaystyle n} linearly independent eigenvectors. A complete basis... |
Wikipedia:Definite quadratic form#0 | In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic... |
Wikipedia:Deformation ring#0 | In mathematics, a deformation ring is a ring that controls liftings of a representation of a Galois group from a finite field to a local field. In particular for any such lifting problem there is often a universal deformation ring that classifies all such liftings, and whose spectrum is the universal deformation space.... |
Wikipedia:Degree matrix#0 | In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. It is used together with the adjacency matrix to construct the Laplacian matrix of a graph: ... |
Wikipedia:Deirdre Smeltzer#0 | Deirdre Longacher Smeltzer (born 1964) is an American mathematician, mathematics educator, textbook author, and academic administrator. A former professor, dean, and vice president at Eastern Mennonite University, she is Senior Director for Programs at the Mathematical Association of America. == Education and career ==... |
Wikipedia:Delta operator#0 | In mathematics, a delta operator is a shift-equivariant linear operator Q : K [ x ] ⟶ K [ x ] {\displaystyle Q\colon \mathbb {K} [x]\longrightarrow \mathbb {K} [x]} on the vector space of polynomials in a variable x {\displaystyle x} over a field K {\displaystyle \mathbb {K} } that reduces degrees by one. To say that Q... |
Wikipedia:Demonic composition#0 | In mathematics, demonic composition is an operation on binary relations that is similar to the ordinary composition of relations but is robust to refinement of the relations into (partial) functions or injective relations. Unlike ordinary composition of relations, demonic composition is not associative. == Definition =... |
Wikipedia:Denis Higgs#0 | A Higgs prime, named after Denis Higgs, is a prime number with a totient (one less than the prime) that evenly divides the square of the product of the smaller Higgs primes. (This can be generalized to cubes, fourth powers, etc.) To put it algebraically, given an exponent a, a Higgs prime Hpn satisfies ϕ ( H p n ) | ∏ ... |
Wikipedia:Denis Miéville#0 | Denis Miéville (15 September 1946 – 27 October 2018) was a Swiss expert on the logic of Stanislaw Lesniewski and natural logic. == Biography == Denis Miéville was raised in the towns of Colombier (Canton of Neuchâtel) and Essert-Pittet (Canton of Vaud). After studying mathematics and logic at the University of Neuchâte... |
Wikipedia:Denjoy–Carleman–Ahlfors theorem#0 | Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his textbook on complex analysis. == Background == Ahlfors was born in Helsinki, Finland. His mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a profe... |
Wikipedia:Denjoy–Koksma inequality#0 | In mathematics, the Denjoy–Koksma inequality, introduced by Herman (1979, p.73) as a combination of work of Arnaud Denjoy and the Koksma–Hlawka inequality of Jurjen Ferdinand Koksma, is a bound for Weyl sums ∑ k = 0 m − 1 f ( x + k ω ) {\displaystyle \sum _{k=0}^{m-1}f(x+k\omega )} of functions f of bounded variation. ... |
Wikipedia:Denjoy–Luzin theorem#0 | In mathematics, the Denjoy–Luzin theorem, introduced independently by Denjoy (1912) and Luzin (1912) states that if a trigonometric series converges absolutely on a set of positive measure, then the sum of its coefficients converges absolutely, and in particular the trigonometric series converges absolutely everywhere.... |
Wikipedia:Denjoy–Luzin–Saks theorem#0 | In mathematics, the Denjoy–Luzin–Saks theorem states that a function of generalized bounded variation in the restricted sense has a derivative almost everywhere, and gives further conditions of the set of values of the function where the derivative does not exist. N. N. Luzin and A. Denjoy proved a weaker form of the t... |
Wikipedia:Denjoy–Young–Saks theorem#0 | In mathematics, the Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere. Denjoy (1915) proved the theorem for continuous functions, Young (1917) extended it to measurable functions, and Saks (1924) extended it to arbitrary functions. Saks (1937, Chapter ... |
Wikipedia:Dennis Gaitsgory#0 | Dennis Gaitsgory (born 17 November 1973) is an Israeli-American mathematician. He is a mathematician at Max Planck Institute for Mathematics (MPIM) at Bonn and is known for his research on the geometric Langlands program. == Life and career == Born in Chișinău (now in Moldova) he grew up in Tajikistan, before studying ... |
Wikipedia:Denny Gulick#0 | Denny Gulick (born Sidney Lewis Gulick III, July 29, 1936) is an emeritus professor of mathematics at University of Maryland, College Park. == Life == Gulick graduated from Oberlin College, Ohio, then obtained his PhD from Yale University, with his main interest of operator theory. He is the leader of College Mathemati... |
Wikipedia:Dependence relation#0 | In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence. Let X {\displaystyle X} be a set. A (binary) relation ◃ {\displaystyle \triangleleft } between an element a {\displaystyle a} of X {\displaystyle X} and a subset S {\displaystyle S} of X {\displaystyle X} is ... |
Wikipedia:Derangement#0 | In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement num... |
Wikipedia:Derek Corneil#0 | Derek Gordon Corneil is a Canadian mathematician and computer scientist, a professor emeritus of computer science at the University of Toronto, and an expert in graph algorithms and graph theory. == Life == When he was leaving high school, Corneil was told by his English teacher that doing a degree in mathematics and p... |
Wikipedia:Derek W. Moore#0 | Derek William Moore (19 April 1931 – 15 July 2008) was a British mathematician. He was born in South Shields, where his father was a head of department at the nautical college. He was educated at the local grammar school and Jesus College, Cambridge. In 1956 he began research into theoretical fluid dynamics at the Cave... |
Wikipedia:Derek W. Robinson#0 | Derek William Robinson (25 June 1935 – 31 August 2021) was a British-Australian theoretical mathematician and physicist. He was a researcher at the Australian National University. == Early life == Derek W. Robinson was born in southern England. He attended grammar school followed by the University of Oxford where he ea... |
Wikipedia:Derivative algebra (abstract algebra)#0 | In mathematics, a derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: D ( a b ) = a D ( b ) + D ( a ) b . {\displaystyle D(ab)=aD(b)+D(a)b.... |
Wikipedia:Determinant#0 | In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is... |
Wikipedia:Detrended fluctuation analysis#0 | In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation ... |
Wikipedia:Deutsche Mathematik#0 | Deutsche Mathematik (German Mathematics) was a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen. Vahlen was publisher on behalf of the German Research Foundation (DFG), and Bieberbach was chief editor. Other editors were Fritz Kubach, Erich Schönhardt, Werner Weber (all volumes), Ernst August... |
Wikipedia:Devācārya#0 | The Nimbarka Sampradaya (IAST: Nimbārka Sampradāya, Sanskrit निम्बार्क सम्प्रदाय), also known as the Kumāra Sampradāya, Hamsa Sampradāya, and Sanakādi Sampradāya (सनकादि सम्प्रदाय), is the oldest Vaiṣṇava sect. It was founded by Nimbarka, a Telugu Brahmin yogi and philosopher. It propounds the Vaishnava Bhedabheda theo... |
Wikipedia:Dialgebra#0 | In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra. The notion was originally introduced by Lambek as "subequalizers", and named as dialgebras by Tatsuya Hagino. Many algebraic notions have previously been generalized to dialgebras. Dialgebra also attempts to obtain Lie algebras from a... |
Wikipedia:Diamond-square algorithm#0 | The diamond-square algorithm is a method for generating heightmaps for computer graphics. It is a slightly better algorithm than the three-dimensional implementation of the midpoint displacement algorithm, which produces two-dimensional landscapes. It is also known as the random midpoint displacement fractal, the cloud... |
Wikipedia:Didier Dubois (mathematician)#0 | Didier Dubois (born 1952) is a French mathematician. Since 1999, he is a co-editor-in-chief of the journal Fuzzy Sets and Systems. In 1993–1997 he was vice-president and president of the International Fuzzy Systems Association. His research interests include fuzzy set theory, possibility theory, and knowledge represent... |
Wikipedia:Diego Rodríguez (mathematician)#0 | Diego Rodríguez (Atitalaquia c.1596, in Mexico City – 1668) was a mathematician, astronomer, educator, and technological innovator in New Spain. He was one of the most important figures in the scientific field in the colony in the second half of the seventeenth century. == Background == In 1613 he entered the Order of ... |
Wikipedia:Dietrich Stoyan#0 | Dietrich Stoyan (born November 26, 1940, Berlin) is a German mathematician and statistician who made contributions to queueing theory, stochastic geometry, and spatial statistics. == Education and career == Stoyan studied mathematics at Technical University Dresden; applied research at Deutsches Brennstoffinstitut Frei... |
Wikipedia:Dieudonné determinant#0 | In linear algebra, the Dieudonné determinant is a generalization of the determinant of a matrix to matrices over division rings and local rings. It was introduced by Dieudonné (1943). If K is a division ring, then the Dieudonné determinant is a group homomorphism from the group GLn(K ) of invertible n-by-n matrices ove... |
Wikipedia:Diffeology#0 | In mathematics, a diffeology on a set generalizes the concept of a smooth atlas of a differentiable manifold, by declaring only what constitutes the "smooth parametrizations" into the set. A diffeological space is a set equipped with a diffeology. Many of the standard tools of differential geometry extend to diffeologi... |
Wikipedia:Diffeomorphometry#0 | Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging. The study of images in computational anatomy rely on high-dimensional diffeomorphism groups φ ∈ Diff V {\displaystyle \varphi \in \operatorname {Diff} _{V}} which generate orbits of the f... |
Wikipedia:Difference polynomials#0 | In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selberg's polynomials, and the Stirling interpolation polynomials as special cases. == Definition == The general difference ... |
Wikipedia:Differentiable vector-valued functions from Euclidean space#0 | In the mathematical discipline of functional analysis, a differentiable vector-valued function from Euclidean space is a differentiable function valued in a topological vector space (TVS) whose domains is a subset of some finite-dimensional Euclidean space. It is possible to generalize the notion of derivative to funct... |
Wikipedia:Differential coefficient#0 | In physics and mathematics, the differential coefficient of a function f(x) is what is now called its derivative df(x)/dx, the (not necessarily constant) multiplicative factor or coefficient of the differential dx in the differential df(x). A coefficient is usually a constant quantity, but the differential coefficient ... |
Wikipedia:Differential graded module#0 | In algebra, a differential graded module, or dg-module, is a Z {\displaystyle \mathbb {Z} } -graded module together with a differential; i.e., a square-zero graded endomorphism of the module of degree 1 or −1, depending on the convention. In other words, it is a chain complex having a structure of a module, while a dif... |
Wikipedia:Differentiation in Fréchet spaces#0 | In mathematics, in particular in functional analysis and nonlinear analysis, it is possible to define the derivative of a function between two Fréchet spaces. This notion of differentiation, as it is Gateaux derivative between Fréchet spaces, is significantly weaker than the derivative in a Banach space, even between g... |
Wikipedia:Differentiation of integrals#0 | In mathematics, the problem of differentiation of integrals is that of determining under what circumstances the mean value integral of a suitable function on a small neighbourhood of a point approximates the value of the function at that point. More formally, given a space X with a measure μ and a metric d, one asks fo... |
Wikipedia:Differentiation of trigonometric functions#0 | The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angl... |
Wikipedia:Differentiation rules#0 | This article is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. == Elementary rules of differentiation == Unless otherwise stated, all functions are functions of real numbers ( R {\textstyle \mathbb {R} } ) that return real values, although, more generally, the... |
Wikipedia:Difunctional#0 | In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set called the codomain. Precisely, a binary relation over sets X {\displaystyle X} and Y {\displaystyle Y} is a set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where x {\displaystyle x} is an el... |
Wikipedia:Digital root#0 | The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For examp... |
Wikipedia:Digroup#0 | In the mathematical area of algebra, a digroup is a generalization of a group that has two one-sided product operations, ⊢ {\displaystyle \vdash } and ⊣ {\displaystyle \dashv } , instead of the single operation in a group. Digroups were introduced independently by Liu (2004), Felipe (2006), and Kinyon (2007), inspired ... |
Wikipedia:Dilip Madan#0 | Dilip B. Madan is an American financial economist, mathematician, academic, and author. He is professor emeritus of finance at the University of Maryland. Madan is most known for his work on the variance gamma model, the fast Fourier transform method for option pricing, and the development of Conic Finance. Madan is a ... |
Wikipedia:Dima Grigoriev#0 | Dima Grigoriev (Dmitry Grigoryev) (born 10 May 1954) is a Russian mathematician. His research interests include algebraic geometry, symbolic computation and computational complexity theory in computer algebra, with over 130 published articles. Dima Grigoriev was born in Leningrad, Russia and graduated from the Leningra... |
Wikipedia:Dima Von-Der-Flaass#0 | D. G. Von Der Flaass (September 8, 1962 – June 10, 2010) was a Russian mathematician and educator, Candidate of Physical and Mathematical Sciences, senior researcher at the Sobolev Institute of Mathematics. He was a specialist in combinatorics, a popularizer of mathematics, and an author of International Mathematical O... |
Wikipedia:Dimension#0 | In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a numbe... |
Wikipedia:Dimension (vector space)#0 | In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all ... |
Wikipedia:Dimension function#0 | 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. ==... |
Wikipedia:Dimension of an algebraic variety#0 | In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply ... |
Wikipedia:Dimitri Leemans#0 | Dimitri Leemans is a Belgian mathematician born in Uccle in 1972. == Biography == Leemans obtained his Licence en Sciences Mathématiques at the Université libre de Bruxelles in 1994 and his doctorate degree, under the supervision of Francis Buekenhout and Michel Dehon in 1998. He is currently professor at the mathemati... |
Wikipedia:Dimitrie Pompeiu#0 | Dimitrie D. Pompeiu (Romanian: [diˈmitri.e pomˈpeju]; 4 October [O.S. 22 September] 1873 – 8 October 1954) was a Romanian mathematician, professor at the University of Bucharest, titular member of the Romanian Academy, and President of the Chamber of Deputies. == Biography == He was born in 1873 in Broscăuți, Botoșani ... |
Wikipedia:Dimitrije Nešić#0 | Dimitrije Nešić (20 October 1836 – 9 May 1904) was a Serbian mathematician, professor at the Lyceum of the Principality of Serbia and president of the Serbian Royal Academy. == Biography == Nešić was born to Savka and Stojan Nešić in Belgrade, Principality of Serbia. Nešićs left their hometown Novi Pazar under Ottoman ... |
Wikipedia:Dinesh Singh (academic)#0 | Professor Dinesh Singh, chancellor K.R. Mangalam University is an Indian professor of mathematics. He served as the 21st Vice-Chancellor of the University of Delhi, is a distinguished fellow of Hackspace at Imperial College London, and has been an adjunct professor of Mathematics at the University of Houston. For his s... |
Wikipedia:Dini continuity#0 | In mathematical analysis, Dini continuity is a refinement of continuity. Every Dini continuous function is continuous. Every Lipschitz continuous function is Dini continuous. == Definition == Let X {\displaystyle X} be a compact subset of a metric space (such as R n {\displaystyle \mathbb {R} ^{n}} ), and let f : X → X... |
Wikipedia:Dion O'Neale#0 | Dion O'Neale is a New Zealand applied mathematician who specialises in the area of complex systems and network science. His work involves the analysis of empirical data to inform computer simulations to predict how interacting parts and structures of networks can affect the dynamics and properties of systems. During CO... |
Wikipedia:Dionisio Gallarati#0 | Dionisio Gallarati (May 8, 1923 – May 13, 2019) was an Italian mathematician, who specialised in algebraic geometry. He was a major influence on the development of algebra and geometry at the University of Genova. == Life == Born 8 May 1923 in Savona, Italy, Gallarati joined the University of Pisa in 1941. His studies ... |
Wikipedia:Dionys Burger#0 | Dionys Burger (10 July 1892, Amsterdam - 19 April 1987) was a Dutch secondary school physics teacher and author of the novel Sphereland. == References == |
Wikipedia:Diophantus#0 | Diophantus of Alexandria (Ancient Greek: Διόφαντος, romanized: Diophantos) (; fl. 250 CE) was a Greek mathematician who was the author of the Arithmetica in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic equations. Although Joseph-Louis Lagrange called ... |
Wikipedia:Diophantus II.VIII#0 | The eighth problem of the second book of Arithmetica by Diophantus (c. 200/214 AD – c. 284/298 AD) is to divide a square into a sum of two squares. == The solution given by Diophantus == Diophantus takes the square to be 16 and solves the problem as follows: To divide a given square into a sum of two squares. To divide... |
Wikipedia:Dirac operator#0 | In mathematics and in quantum mechanics, a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as a Laplacian. It was introduced in 1847 by William Hamilton and in 1928 by Paul Dirac. The question which concerned Dirac was to ... |
Wikipedia:Direct limit#0 | In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category. The way they are put together is specified by a system of homomorphism... |
Wikipedia:Direct product#0 | In mathematics, a direct product of objects already known can often be defined by giving a new one. That induces a structure on the Cartesian product of the underlying sets from that of the contributing objects. More abstractly, the product in category theory is mentioned, which formalizes those notions. Examples are t... |
Wikipedia:Direct sum of modules#0 | In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which ... |
Wikipedia:Dirichlet eigenvalue#0 | In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of the drum can one deduce. Here a "drum" is thought of as an elastic membrane... |
Wikipedia:Dirichlet kernel#0 | In mathematical analysis, the Dirichlet kernel, named after the German mathematician Peter Gustav Lejeune Dirichlet, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n cos ( k x ) ) = sin ( ( n + 1 / 2 ) x ) sin ( x / 2 ) , {\displaystyle D_{n}(x)=\sum _{k=-n}^{... |
Wikipedia:Dirichlet series#0 | In mathematics, a Dirichlet series is any series of the form ∑ n = 1 ∞ a n n s , {\displaystyle \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}},} where s is complex, and a n {\displaystyle a_{n}} is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in a... |
Wikipedia:Dirichlet–Jordan test#0 | In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a complex-valued, periodic function f {\displaystyle f} to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of th... |
Wikipedia:Dirk Kroese#0 | Dirk Pieter Kroese (born 1963) is a Dutch-Australian mathematician and statistician, and Professor at the University of Queensland. He is known for several contributions to applied probability, kernel density estimation, Monte Carlo methods and rare-event simulation. He is, with Reuven Rubinstein, a pioneer of the Cros... |
Wikipedia:Dirk van Dalen#0 | Dirk van Dalen (born 20 December 1932, Amsterdam) is a Dutch mathematician and historian of science. == Life == Van Dalen studied mathematics and physics and astronomy at the University of Amsterdam. Inspired by the work of Brouwer and Heyting, he received his Ph.D. in 1963 from the University of Amsterdam for the thes... |
Wikipedia:Discontinuous group#0 | In mathematics, a group action of a group G {\displaystyle G} on a set S {\displaystyle S} is a group homomorphism from G {\displaystyle G} to some group (under function composition) of functions from S {\displaystyle S} to itself. It is said that G {\displaystyle G} acts on S {\displaystyle S} . Many sets of transform... |
Wikipedia:Discontinuous linear map#0 | In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation). If the spaces involved are also topological spaces (that is, topological vector spaces), then it ma... |
Wikipedia:Discrete Analysis#0 | Discrete Analysis is a mathematics journal covering the applications of analysis to discrete structures. Discrete Analysis is an arXiv overlay journal, meaning the journal's content is hosted on the arXiv. == History == Discrete Analysis was created by Timothy Gowers to demonstrate that a high-quality mathematics journ... |
Wikipedia:Discrete Laplace operator#0 | In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matr... |
Wikipedia:Discrete Poisson equation#0 | In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place of the Laplace operator. The discrete Poisson equation is frequently used in numerical analysis as a stand-in for the continuous Poisson equation, although it is al... |
Wikipedia:Discrete calculus#0 | Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were u... |
Wikipedia:Disjunction property of Wallman#0 | In mathematics, especially in order theory, a partially ordered set with a unique minimal element 0 has the disjunction property of Wallman when for every pair (a, b) of elements of the poset, either b ≤ a or there exists an element c ≤ b such that c ≠ 0 and c has no nontrivial common predecessor with a. That is, in th... |
Wikipedia:Distance-regular graph#0 | In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs f... |
Wikipedia:Distance-transitive graph#0 | In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1... |
Wikipedia:Distinguished limit#0 | In mathematics, a distinguished limit is an appropriately chosen scale factor used in the method of matched asymptotic expansions. == External links == Singular perturbation theory, Scholarpedia |
Wikipedia:Distribution (number theory)#0 | In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function. The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfying... |
Wikipedia:Distribution algebra#0 | In algebra, the distribution algebra D ( G , K ) {\displaystyle D(G,K)} of a p-adic Lie group G is the K-algebra of K-valued distributions on G. (See the reference for a more precise definition.) == References == Schneider, P.; Teitelbaum, J. (May 18, 2001). " U ( g ) {\displaystyle U({\mathfrak {g}})} -finite locally ... |
Wikipedia:Distributive homomorphism#0 | A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in Schmidt's 1968 work and was subsequent... |
Wikipedia:Distributive property#0 | In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z ) = x ⋅ y + x ⋅ z {\displaystyle x\cdot (y+z)=x\cdot y+x\cdot z} is always true in elementary algebra. For example, in elementary arithmetic, one has 2 ⋅ ( 1 + 3 ) = ( ... |
Wikipedia:Ditkin set#0 | In mathematics, a Ditkin set, introduced by (Ditkin 1939), is a closed subset of the circle such that a function f vanishing on the set can be approximated by functions φnf with φ vanishing in a neighborhood of the set. == References == Ditkin, V. (1939), "On the structure of ideals in certain normed rings", Uchenye Za... |
Wikipedia:Divided differences#0 | In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation. Divided differences is a recursive division process. Given a se... |
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