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https://en.wikipedia.org/wiki/Cofinal%20%28mathematics%29 | In mathematics, a subset of a preordered set is said to be cofinal or frequent in if for every it is possible to find an element in that is "larger than " (explicitly, "larger than " means ).
Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate ge... |
https://en.wikipedia.org/wiki/Hensel%27s%20lemma | In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a univariate polynomial has a simple root modulo a prime number , then this root can be lifted to a unique root modulo any higher power of . More generally, if a polynomial f... |
https://en.wikipedia.org/wiki/Richard%20P.%20Stanley | Richard Peter Stanley (born June 23, 1944) is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gia... |
https://en.wikipedia.org/wiki/Grothendieck%20group | In mathematics, the Grothendieck group, or group of differences, of a commutative monoid is a certain abelian group. This abelian group is constructed from in the most universal way, in the sense that any abelian group containing a homomorphic image of will also contain a homomorphic image of the Grothendieck group ... |
https://en.wikipedia.org/wiki/Semiset | In set theory, a semiset is a proper class that is a subclass of a set. In the typical foundations of Zermelo–Fraenkel set theory, semisets are impossible due to the axiom schema of specification.
The theory of semisets was proposed and developed by Czech mathematicians Petr Vopěnka and Petr Hájek (1972). It is based ... |
https://en.wikipedia.org/wiki/Radical%20of%20an%20integer | In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product:
The radical plays a central role in the statement of the abc conjecture.
Examples
Radical numbers for the first few positi... |
https://en.wikipedia.org/wiki/List%20of%20alternative%20set%20theories | In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.
Alternative set theories
Alternative set theories include:
... |
https://en.wikipedia.org/wiki/Quadratic%20assignment%20problem | The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems first introduced by Koopmans and Beckmann.
The problem models the following real-life problem:
... |
https://en.wikipedia.org/wiki/Bernstein%E2%80%93Sato%20polynomial | In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by and , . It is also known as the b-function, the b-polynomial, and the Bernstein polynomial, though it is not related to the Bernstein polynomials used in approximation theory. It has applicati... |
https://en.wikipedia.org/wiki/Karl%20Mahlburg | Karl Mahlburg is an American mathematician whose research interests lie in the areas of modular forms, partitions, combinatorics and number theory. He is the author of over 40 peer-reviewed journal articles. Mahlburg received his PhD in 2006 from the University of Wisconsin–Madison. Between 2011 and 2021 he was an assi... |
https://en.wikipedia.org/wiki/Flanders%20Mathematics%20Olympiad | The Flanders Mathematics Olympiad (; VWO) is a Flemish mathematics competition for students in grades 9 through 12. Two tiers of this competition exist: one for 9th- and 10th-graders (; JWO), and one for 11th- and 12th-graders. It is a feeder competition for the International Mathematical Olympiad.
History
The Olympi... |
https://en.wikipedia.org/wiki/VWO | VWO may refer to:
Vlaamse Wiskunde Olympiade, a Flemish mathematics competition
Voorbereidend wetenschappelijk onderwijs, a Dutch school system
Voluntary welfare organisation, charitable organisation |
https://en.wikipedia.org/wiki/Geometric%20invariant%20theory | In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper in classical invariant theory.
Geometric invariant theory studies an action of a ... |
https://en.wikipedia.org/wiki/Subquotient | In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject. Subquotients are particularly important in abelian categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory.
In the lit... |
https://en.wikipedia.org/wiki/Mathematical%20Kangaroo | Mathematical Kangaroo (also known as Kangaroo challenge, or jeu-concours Kangourou in French) is an international mathematics competition in over 77 countries. There are six levels of participation, ranging from grade 1 to grade 12. The competition is held annually on the third Thursday of March. The challenge consist... |
https://en.wikipedia.org/wiki/Row | Row or ROW may refer to:
Exercise
Rowing, or a form of aquatic movement using oars
Row (weight-lifting), a form of weight-lifting exercise
Mathematics and informatics
Row vector, a 1 × n matrix in linear algebra
Row(s) in a table (information), a data arrangement with rows and columns
Row (database), a single, ... |
https://en.wikipedia.org/wiki/Quasisimple%20group | In mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S. In other words, there is a short exact sequence
such that , where denotes the center of E and [ , ] denotes the commutator.
Equivalently, a group is quasisimple if it is equal t... |
https://en.wikipedia.org/wiki/Symmetric%20space | In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through ... |
https://en.wikipedia.org/wiki/K%C5%8Dsaku%20Yosida | was a Japanese mathematician who worked in the field of functional analysis. He is known for the Hille-Yosida theorem concerning C0-semigroups. Yosida studied mathematics at the University of Tokyo, and held posts at Osaka and Nagoya Universities. In 1955, Yosida returned to the University of Tokyo.
See also
Einar C... |
https://en.wikipedia.org/wiki/%C3%98ystein%20Ore | Øystein Ore (7 October 1899 – 13 August 1968) was a Norwegian mathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics.
Life
Ore graduated from the University of Oslo in 1922, with a Cand.Real.degree in mathematics. In 1924, the University of Oslo awarded him th... |
https://en.wikipedia.org/wiki/Gabriel%20Andrew%20Dirac | Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian-British mathematician who mainly worked in graph theory. He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin from 1964 to 1966. In 1952, he gave a sufficient condition for a graph to contain a Hamiltonian circuit. The previo... |
https://en.wikipedia.org/wiki/Einar%20Hille | Carl Einar Hille (28 June 1894 – 12 February 1980) was an American mathematics professor and scholar. Hille authored or coauthored twelve mathematical books and a number of mathematical papers.
Early life and education
Hille was born in New York City. His parents were both immigrants from Sweden who separated before ... |
https://en.wikipedia.org/wiki/C0-semigroup | {{DISPLAYTITLE:C0-semigroup }}
In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigrou... |
https://en.wikipedia.org/wiki/Statistical%20Methods%20for%20Research%20Workers | Statistical Methods for Research Workers is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods, together with his The Design of Experiments (1935). It was originally published in 1925, by Oliver &... |
https://en.wikipedia.org/wiki/Trigonal%20pyramidal%20molecular%20geometry | In chemistry, a trigonal pyramid is a molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base, resembling a tetrahedron (not to be confused with the tetrahedral geometry). When all three atoms at the corners are identical, the molecule belongs to point group C3v. Some molecules an... |
https://en.wikipedia.org/wiki/Uniform%204-polytope | In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex prismatic forms, along with 17 cases arisi... |
https://en.wikipedia.org/wiki/Generalized%20Kac%E2%80%93Moody%20algebra | In mathematics, a generalized Kac–Moody algebra is a Lie algebra that is similar to a Kac–Moody algebra, except that it is allowed to have imaginary simple roots.
Generalized Kac–Moody algebras are also sometimes called GKM algebras, Borcherds–Kac–Moody algebras, BKM algebras, or Borcherds algebras. The best known exa... |
https://en.wikipedia.org/wiki/Opposite | Opposite or Opposites may refer to:
Opposite (semantics), a word that means the reverse of a word
Opposite (leaf), an arrangement of leaves on a stem
Opposite (mathematics), the negative of a number; numbers that, when added, yield zero
"The Opposite", a 1994 episode of Seinfeld
Music
The Opposites, Dutch rap gro... |
https://en.wikipedia.org/wiki/Trigonal%20planar%20molecular%20geometry | In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called peripheral atoms, all in one plane. In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°. Such species belong to the poin... |
https://en.wikipedia.org/wiki/Mathematics%2C%20Engineering%2C%20Science%20Achievement | Mathematics, Engineering, Science Achievement (MESA) is an academic preparation program for pre-college, community college and university-level students. Established in 1970 in California, the program provides academic support to students from educationally disadvantaged backgrounds throughout the education pathway so ... |
https://en.wikipedia.org/wiki/No-arbitrage%20bounds | In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in fact the greatest extremes for good–deal bounds.
The most frequent nontrivial example of no-arbitrage bounds is put–ca... |
https://en.wikipedia.org/wiki/Unimodular%20lattice | In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1.
The E8 lattice and the Leech lattice are two famous examples.
D... |
https://en.wikipedia.org/wiki/Random%20matrix | In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice ... |
https://en.wikipedia.org/wiki/List%20of%20Guggenheim%20Fellowships%20awarded%20in%201970 | List of Guggenheim Fellowship winners for 1970.
United States and Canadian fellows
Patrick Ahern, professor of mathematics, University of Wisconsin–Madison.
Michael M. Ames, former director and professor emeritus, Museum of Anthropology, University of British Columbia.
Albert K. Ando, professor of economics and f... |
https://en.wikipedia.org/wiki/Appell%20sequence | In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence satisfying the identity
and in which is a non-zero constant.
Among the most notable Appell sequences besides the trivial example are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every App... |
https://en.wikipedia.org/wiki/Pr%C3%BCfer%20sequence | In combinatorial mathematics, the Prüfer sequence (also Prüfer code or Prüfer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on n vertices has length n − 2, and can be generated by a simple iterative algorithm. Prüfer sequences were first used by Heinz Prüfer to prov... |
https://en.wikipedia.org/wiki/Locally%20compact%20group | In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such groups have a natural measure called the Haar measure. ... |
https://en.wikipedia.org/wiki/Henk%20Barendregt | Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) is a Dutch logician, known for his work in lambda calculus and type theory.
Life and work
Barendregt studied mathematical logic at Utrecht University, obtaining his master's degree in 1968 and his PhD in 1971, both cum laude, under Dirk van Dalen and... |
https://en.wikipedia.org/wiki/Ordinary%20least%20squares | In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differen... |
https://en.wikipedia.org/wiki/Niemeier%20lattice | In mathematics, a Niemeier lattice is one of the 24
positive definite even unimodular lattices of rank 24,
which were classified by . gave a simplified proof of the classification. In the 1970s, has a sentence mentioning that he found more than 10 such lattices in the 1940s, but gives no further details. One example... |
https://en.wikipedia.org/wiki/Toru%20Kumon | was a Japanese mathematics educator, born in Kōchi Prefecture, Japan. He graduated from the College of Science at Osaka University with a degree in mathematics and taught high school mathematics in his home town of Osaka. In 1954, his son, Takeshi, performed poorly in a Year 2 mathematics test. Prompted by his wife, T... |
https://en.wikipedia.org/wiki/Symbolic%20integration | In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a differentiable function F(x) such that
This is also denoted
Discussion
The term symbolic is used to distinguish this problem from that of numerical integration... |
https://en.wikipedia.org/wiki/Inverse-gamma%20distribution | In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
Perhaps the chief use of the inverse gamma distr... |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20Ontario | This is an incomplete list of lakes in Ontario, a province of Canada. There are over 250,000 lakes in Ontario, constituting around 20% of the world's fresh water supply.
Larger lake statistics
This is a list of lakes of Ontario with an area larger than .
#
24 Mile Lake
A
B
C
D
E
F
G
Gananoque Lake
Garson Lake... |
https://en.wikipedia.org/wiki/Method%20of%20undetermined%20coefficients | In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) i... |
https://en.wikipedia.org/wiki/Harald%20Ludvig%20Westergaard | Harald Ludvig Westergaard (April 19, 1853 in Copenhagen – December 13, 1936 in Copenhagen) was a Danish statistician and economist known for his work in demography and the history of statistics.
Harald Westergaard was born in Copenhagen and apart from a period studying in England and Germany in 1877-78 he lived there ... |
https://en.wikipedia.org/wiki/Philip%20Hall | Philip Hall FRS (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups.
Biography
He was educated first at Christ's Hospital, where he won the Thompson Gold Medal for mathematics, and later at King's College, Cambridge. He was ... |
https://en.wikipedia.org/wiki/Heinz%20Pr%C3%BCfer | Ernst Paul Heinz Prüfer (10 November 1896 – 7 April 1934) was a German Jewish mathematician born in Wilhelmshaven. His major contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory.
In 1915 he began his university studies in mathematics, Physics and Chemistry in B... |
https://en.wikipedia.org/wiki/Zerah%20Colburn | Zerah Colburn may refer to:
Zerah Colburn (mental calculator) (1804–1840), American mathematics prodigy
Zerah Colburn (locomotive designer) (1832–1870), American steam locomotive designer and railroad author |
https://en.wikipedia.org/wiki/1023%20%28number%29 | 1023 (one thousand [and] twenty-three) is the natural number following 1022 and preceding 1024.
In mathematics
1023 is the tenth Mersenne number of the form .
In binary, it is also the tenth repdigit 11111111112 as all Mersenne numbers in decimal are repdigits in binary.
It is equal to the sum of five consecutive ... |
https://en.wikipedia.org/wiki/Feit%E2%80%93Thompson%20theorem | In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by .
History
conjectured that every nonabelian finite simple group has even order. suggested using the centralizers of involutions of simple groups as the basis for the classific... |
https://en.wikipedia.org/wiki/Edge-of-the-wedge%20theorem | In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the analytic continuation of Wigh... |
https://en.wikipedia.org/wiki/Integral%20%28disambiguation%29 | Integral is a concept in calculus.
Integral may also refer to:
in mathematics
Integer, a number
Integral symbol
Integral (measure theory), or Lebesgue integration
Integral element
in computer science
Integral data type, a data type that represents some range of mathematical integers
in philosophy and spiritual... |
https://en.wikipedia.org/wiki/RKWard | RKWard is a transparent front-end to the R programming language, a scripting-language with a strong focus on statistics functions. RKWard tries to combine the power of the R language with the ease of use of commercial statistical packages.
RKWard is written in C++ and although it can run in numerous environments, it w... |
https://en.wikipedia.org/wiki/Boris%20Tsirelson | Boris Semyonovich Tsirelson (May 4, 1950 – January 21, 2020) (, ) was a Russian–Israeli mathematician and Professor of Mathematics at Tel Aviv University in Israel, as well as a Wikipedia editor.
Biography
Tsirelson was born in Leningrad to a Russian Jewish family. From his father Simeon's side, he was the great-neph... |
https://en.wikipedia.org/wiki/Mapping%20cylinder | In mathematics, specifically algebraic topology, the mapping cylinder of a continuous function between topological spaces and is the quotient
where the denotes the disjoint union, and ∼ is the equivalence relation generated by
That is, the mapping cylinder is obtained by gluing one end of to via the map . Not... |
https://en.wikipedia.org/wiki/Geometry%20of%20Complex%20Numbers | Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger, and originally published in 1962 as Volume 13 of t... |
https://en.wikipedia.org/wiki/Prime%20model | In mathematics, and in particular model theory, a prime model is a model that is as simple as possible. Specifically, a model is prime if it admits an elementary embedding into any model to which it is elementarily equivalent (that is, into any model satisfying the same complete theory as ).
Cardinality
In contra... |
https://en.wikipedia.org/wiki/Mereotopology | In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts.
History and motivation
Mereotopology begins in philosophy wit... |
https://en.wikipedia.org/wiki/Pullback%20bundle | In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle and a continuous map one can define a "pullback" of by as a bundle over . The fiber of over a point in is just the fiber of over . Thus is the disjoint union of all these f... |
https://en.wikipedia.org/wiki/Euclid%20number | In mathematics, Euclid numbers are integers of the form , where pn # is the nth primorial, i.e. the product of the first n prime numbers. They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers.
Examples
For example, the first three ... |
https://en.wikipedia.org/wiki/Diffusion%20process | In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck pr... |
https://en.wikipedia.org/wiki/Semi-Hilbert%20space | In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm.
The quotient of this space... |
https://en.wikipedia.org/wiki/Fundamental%20polygon | In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only the topology of the surface through its fundamental group but also determines the Riemann surface up to conformal equivalence. By the uniformization theorem, every compact Riemann surface ... |
https://en.wikipedia.org/wiki/Severi%E2%80%93Brauer%20variety | In mathematics, a Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras in such a way that the algebra splits over K if and only if the variety has a rational point over K. ... |
https://en.wikipedia.org/wiki/England%20national%20football%20team%20records%20and%20statistics | The history of the England national football team, also known as the Three Lions, begins with the first representative international match in 1870 and the first officially-recognised match two years later. England primarily competed in the British Home Championship over the following decades. Although the FA had joined... |
https://en.wikipedia.org/wiki/CoCoA | CoCoA (Computations in Commutative Algebra)
is a free computer algebra system developed by the University of Genova, Italy, used to compute with numbers and polynomials. The CoCoA Library (CoCoALib)
is available under GNU General Public License. CoCoA has been ported to many operating systems including Macintosh on PP... |
https://en.wikipedia.org/wiki/Walter%20Feit | Walter Feit (October 26, 1930 – July 29, 2004) was an Austrian-born American mathematician who worked in finite group theory and representation theory. His contributions provided elementary infrastructure used in algebra, geometry, topology, number theory, and logic. His work helped the development and utilization of s... |
https://en.wikipedia.org/wiki/Space%20partitioning | In geometry, space partitioning is the process of dividing an entire space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one ... |
https://en.wikipedia.org/wiki/Hyperfunction | In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato in 1958 in Japanese, (1959, 1960 in English), building upon earlier work ... |
https://en.wikipedia.org/wiki/Fodor%27s%20lemma | In mathematics, particularly in set theory, Fodor's lemma states the following:
If is a regular, uncountable cardinal, is a stationary subset of , and is regressive (that is, for any , ) then there is some and some stationary such that for any . In modern parlance, the nonstationary ideal is normal.
The lemma ... |
https://en.wikipedia.org/wiki/Stationary%20set | In mathematics, specifically set theory and model theory, a stationary set is a set that is not too small in the sense that it intersects all club sets and is analogous to a set of non-zero measure in measure theory. There are at least three closely related notions of stationary set, depending on whether one is looking... |
https://en.wikipedia.org/wiki/Thin%20set | In mathematics, thin set may refer to:
Thin set (analysis) in analysis of several complex variables
Thin set (Serre) in algebraic geometry
In set theory, a set that is not a stationary set
Thin set can also refer to thin set mortar.
See also
Meagre set
Shrinking space
Slender group
Small set
Thin category |
https://en.wikipedia.org/wiki/Diagonal%20intersection | Diagonal intersection is a term used in mathematics, especially in set theory.
If is an ordinal number and
is a sequence of subsets of , then the diagonal intersection, denoted by
is defined to be
That is, an ordinal is in the diagonal intersection if and only if it is contained in the first members of the se... |
https://en.wikipedia.org/wiki/Club%20filter | In mathematics, particularly in set theory, if is a regular uncountable cardinal then the filter of all sets containing a club subset of is a -complete filter closed under diagonal intersection called the club filter.
To see that this is a filter, note that since it is thus both closed and unbounded (see club set)... |
https://en.wikipedia.org/wiki/Triangulated%20category | In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abe... |
https://en.wikipedia.org/wiki/All%20India%20Trade%20Union%20Congress | The All India Trade Union Congress (AITUC) is the oldest trade union federation in India. It is associated with the Communist Party of India. According to provisional statistics from the Ministry of Labour, AITUC had a membership of 14.2 million in 2013. It was founded on 31 October 1920 with Lala Lajpat Rai as its fir... |
https://en.wikipedia.org/wiki/Cycle%20graph%20%28algebra%29 | In group theory, a subfield of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups.
A cycle is the set of powers of a given group element a, where an, the n-th power of an element a is defined as the product of ... |
https://en.wikipedia.org/wiki/Static%20spacetime | In general relativity, a spacetime is said to be static if it does not change over time and is also irrotational. It is a special case of a stationary spacetime, which is the geometry of a stationary spacetime that does not change in time but can rotate. Thus, the Kerr solution provides an example of a stationary spac... |
https://en.wikipedia.org/wiki/Asymptotically%20flat%20spacetime | An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime.
While this notion makes sense for any Lorentzian manifold, it is most of... |
https://en.wikipedia.org/wiki/Monster%20Lie%20algebra | In mathematics, the monster Lie algebra is an infinite-dimensional generalized Kac–Moody algebra acted on by the monster group, which was used to prove the monstrous moonshine conjectures.
Structure
The monster Lie algebra m is a Z2-graded Lie algebra. The piece of degree (m, n) has dimension cmn if (m, n) ≠ (0, 0) a... |
https://en.wikipedia.org/wiki/Forcing%20function | Forcing function can mean:
In differential calculus, a function that appears in the equations and is only a function of time, and not of any of the other variables.
In interaction design, a behavior-shaping constraint, a means of preventing undesirable user input usually made by mistake.
A forcing function is any ta... |
https://en.wikipedia.org/wiki/Nielsen%E2%80%93Thurston%20classification | In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by .
Given a homeomorphism f : S → S, there is a map g isotopic to f such that at least one of the following holds:
g is periodic, i.e. some power of... |
https://en.wikipedia.org/wiki/Olga%20Taussky-Todd | Olga Taussky-Todd (August 30, 1906 – October 7, 1995) was an Austrian and later Czech-American mathematician. She published more than 300 research papers on algebraic number theory, integral matrices, and matrices in algebra and analysis.
Early life
Olga Taussky was born into a Jewish family in what is now Olomouc, Cz... |
https://en.wikipedia.org/wiki/GEANT-3 | GEANT is the name of a series of simulation software designed to describe the passage of elementary particles through matter, using Monte Carlo methods. The name is an acronym formed from "GEometry ANd Tracking". Originally developed at CERN for high energy physics experiments, GEANT-3 has been used in many other fie... |
https://en.wikipedia.org/wiki/Infinity%20plus%20one | In mathematics, infinity plus one is a concept which has a well-defined formal meaning in some number systems, and may refer to:
Transfinite numbers, numbers that are larger than all the finite numbers.
Cardinal numbers, representations of sizes (cardinalities) of abstract sets, which may be infinite.
Ordinal numbe... |
https://en.wikipedia.org/wiki/Hyperrectangle | In geometry, an hyperrectangle (also called a box, hyperbox, or orthotope), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions.
A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. If all of the edg... |
https://en.wikipedia.org/wiki/Probit | In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and specialized regression modeling of binary response variables.
Mathematically... |
https://en.wikipedia.org/wiki/Group%20of%20Lie%20type | In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase group of Lie type does not have a widely accepted precise definition, but th... |
https://en.wikipedia.org/wiki/Oxygen%20difluoride | Oxygen difluoride is a chemical compound with the formula . As predicted by VSEPR theory, the molecule adopts a bent molecular geometry. It is strong oxidizer and has attracted attention in rocketry for this reason. With a boiling point of −144.75 °C, OF2 is the most volatile (isolable) triatomic compound. The compound... |
https://en.wikipedia.org/wiki/Yuri%20Manin | Yuri Ivanovich Manin (; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Life and career
Manin was born on 16 February 1937 in Simferopol, Crimean ASSR, Sovie... |
https://en.wikipedia.org/wiki/Region%201 | Region 1 or Region I can refer to:
Region 1, a DVD region code
Region 1, Northwest Territories, a Statistics Canada census division
Northeastern United States, Region 1 for the US Census Bureau
Region 1, one of the health regions of Canada managed by Horizon Health Network
Former Region 1 (Johannesburg), an admini... |
https://en.wikipedia.org/wiki/Divisor%20%28algebraic%20geometry%29 | In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumford). Both are derived from the notion of divisibility in the integers and ... |
https://en.wikipedia.org/wiki/Triple%20bar | The triple bar or tribar, ≡, is a symbol with multiple, context-dependent meanings indicating equivalence of two different things. Its main uses are in mathematics and logic. It has the appearance of an equals sign with a third line.
Encoding
The triple bar character in Unicode is code point . The closely related co... |
https://en.wikipedia.org/wiki/Currency%20crisis | A currency crisis is a type of financial crisis, and is often associated with a real economic crisis. A currency crisis raises the probability of a banking crisis or a default crisis. During a currency crisis the value of foreign denominated debt will rise drastically relative to the declining value of the home currenc... |
https://en.wikipedia.org/wiki/Planar%20algebra | In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the properties of Khovanov homology with respect ... |
https://en.wikipedia.org/wiki/Hilbert%27s%20ninth%20problem | Hilbert's ninth problem, from the list of 23 Hilbert's problems (1900), asked to find the most general reciprocity law for the norm residues of k-th order in a general algebraic number field, where k is a power of a prime.
Progress made
The problem was partially solved by Emil Artin by establishing the Artin recipro... |
https://en.wikipedia.org/wiki/Hilbert%27s%20fourteenth%20problem | In mathematics, Hilbert's fourteenth problem, that is, number 14 of Hilbert's problems proposed in 1900, asks whether certain algebras are finitely generated.
The setting is as follows: Assume that k is a field and let K be a subfield of the field of rational functions in n variables,
k(x1, ..., xn ) over k.
Conside... |
https://en.wikipedia.org/wiki/Cofibration | In mathematics, in particular homotopy theory, a continuous mapping between topological spaces
,
is a cofibration if it has the homotopy extension property with respect to all topological spaces . That is, is a cofibration if for each topological space , and for any continuous maps and with , for any homotopy fr... |
https://en.wikipedia.org/wiki/Abuse%20of%20notation | In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time). However, since the concept of formal/synta... |
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