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https://en.wikipedia.org/wiki/Wassily%20Hoeffding | Wassily Hoeffding (June 12, 1914 – February 28, 1991) was a Finnish statistician and probabilist. Hoeffding was one of the founders of nonparametric statistics, in which Hoeffding contributed the idea and basic results on U-statistics.
In probability theory, Hoeffding's inequality provides an upper bound on the probab... |
https://en.wikipedia.org/wiki/Dynkin%20system | A Dynkin system, named after Eugene Dynkin, is a collection of subsets of another universal set satisfying a set of axioms weaker than those of -algebra. Dynkin systems are sometimes referred to as -systems (Dynkin himself used this term) or d-system. These set families have applications in measure theory and probabi... |
https://en.wikipedia.org/wiki/Provable%20prime | In number theory, a provable prime is an integer that has been calculated to be prime using a primality-proving algorithm. Boot-strapping techniques using Pocklington primality test are the most common ways to generate provable primes for cryptography.
Contrast with probable prime, which is likely (but not certain) to... |
https://en.wikipedia.org/wiki/Finite%20character | In mathematics, a family of sets is of finite character if for each , belongs to if and only if every finite subset of belongs to . That is,
For each , every finite subset of belongs to .
If every finite subset of a given set belongs to , then belongs to .
Properties
A family of sets of finite character ... |
https://en.wikipedia.org/wiki/End | End, END, Ending, or ENDS may refer to:
End
Mathematics
End (category theory)
End (topology)
End (graph theory)
End (group theory) (a subcase of the previous)
End (endomorphism)
Sports and games
End (gridiron football)
End, a division of play in the sports of curling, target archery and pétanque
End (dominoes), one ... |
https://en.wikipedia.org/wiki/Erwin%20Kreyszig | Erwin Otto Kreyszig (January 6, 1922 in Pirna, Germany – December 12, 2008) was a German Canadian applied mathematician and the Professor of Mathematics at Carleton University in Ottawa, Ontario, Canada. He was a pioneer in the field of applied mathematics: non-wave replicating linear systems. He was also a distinguish... |
https://en.wikipedia.org/wiki/Paul%20Bernays | Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert.
Biography
Bernays was born into a distinguished German-Jewis... |
https://en.wikipedia.org/wiki/Schur%27s%20Inequality | In mathematics, Schur's inequality, named after Issai Schur,
establishes that for all non-negative real numbers
x, y, z, and t>0,
with equality if and only if x = y = z or two of them are equal and the other is zero. When t is an even positive integer, the inequality holds for all real numbers x, y and z.
When , the ... |
https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison%20formula | In mathematics, in particular linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of the sum of an invertible matrix and the outer product, , of vectors and . The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after S... |
https://en.wikipedia.org/wiki/Lagrange%27s%20identity | In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is:
which applies to any two sets {a1, a2, ..., an} and {b1, b2, ..., bn} of real or complex numbers (or more generally, elements of a commutative ring). This identity is a generalisation of the Brahmagupta–Fibonacci identity and a special form of the... |
https://en.wikipedia.org/wiki/Curved%20space | Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in general relativ... |
https://en.wikipedia.org/wiki/Leibniz%20integral%20rule | In calculus, the Leibniz integral rule for differentiation under the integral sign states that for an integral of the form
where and the integrands are functions dependent on the derivative of this integral is expressible as
where the partial derivative indicates that inside the integral, only the variation of wi... |
https://en.wikipedia.org/wiki/Grundz%C3%BCge%20der%20Mengenlehre | (German for "Basics of Set Theory") is a book on set theory written by Felix Hausdorff.
First published in April 1914, was the first comprehensive introduction to set theory. Besides the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were the... |
https://en.wikipedia.org/wiki/Maria%20Simon%20%28actress%29 | Maria Simon (born 6 February 1976) is a German actress.
Family and background
Simon's German father originally hailed from Leipzig and studied mathematics in Leningrad. There he met Simon's Russian-Jewish mother, Olga, who studied electronics and originally hailed from Kazakhstan. The couple married while studying.
... |
https://en.wikipedia.org/wiki/Orthogonal%20trajectory | In mathematics, an orthogonal trajectory is a curve which intersects any curve of a given pencil of (planar) curves orthogonally.
For example, the orthogonal trajectories of a pencil of concentric circles are the lines through their common center (see diagram).
Suitable methods for the determination of orthogonal tra... |
https://en.wikipedia.org/wiki/Mirimanoff%27s%20congruence | In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem. Since the theorem has now been proven, these are now of mainly historical significance, though the Mirimanoff polynomials are i... |
https://en.wikipedia.org/wiki/Volodymyr%20Korolyuk | Volodymyr Semenovych Korolyuk (, 19 August 1925 – 4 April 2020) was a Soviet and Ukrainian mathematician who made significant contributions to probability theory and its applications, academician of the National Academy of Sciences of Ukraine (1976).
Korolyuk was born in Kyiv in August 1925. Between 1949 and 2005 Volo... |
https://en.wikipedia.org/wiki/Narrow%20class%20group | In algebraic number theory, the narrow class group of a number field K is a refinement of the class group of K that takes into account some information about embeddings of K into the field of real numbers.
Formal definition
Suppose that K is a finite extension of Q. Recall that the ordinary class group of K is defin... |
https://en.wikipedia.org/wiki/Polymatroid | In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also described as the multiset analogue of the matroid.
Definition
Let be a finite set and a non-decreasing submodular function, that is, for each we have , and for each we ha... |
https://en.wikipedia.org/wiki/Harmonic%20number%20%28disambiguation%29 | In number theory, the harmonic numbers are the sums of the inverses of integers, forming the harmonic series. Harmonic number may also refer to:
Harmonic, a periodic wave with a frequency that is an integral multiple of the frequency of another wave
Harmonic divisor numbers, also called Ore numbers or Ore's harmoni... |
https://en.wikipedia.org/wiki/Ponta%20Grossa | Ponta Grossa () is a municipality in the state of Paraná, southern Brazil. The estimated population is 355,336 according to official data from the Brazilian Institute of Geography and Statistics and it is the 4th most populous city in Paraná (76th in Brazil). It is also the largest city close to Greater Curitiba region... |
https://en.wikipedia.org/wiki/Picard%20horn | A Picard horn, also called the Picard topology or Picard model, is one of the oldest known hyperbolic 3-manifolds, first described by Émile Picard in 1884. The manifold is the quotient of the upper half-plane model of hyperbolic 3-space by the projective special linear group, . It was proposed as a model for the
shape... |
https://en.wikipedia.org/wiki/Inductive%20set | Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.
In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone oper... |
https://en.wikipedia.org/wiki/Chaos%20game | In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fracti... |
https://en.wikipedia.org/wiki/Integrable%20system | In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its motion is confined to a submanifold
of much smaller di... |
https://en.wikipedia.org/wiki/Fubini%E2%80%93Study%20metric | In mathematics, the Fubini–Study metric (IPA: /fubini-ʃtuːdi/) is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study.
A Hermitian form in (the vector space) Cn+1 d... |
https://en.wikipedia.org/wiki/Fr%C3%B6licher%20spectral%20sequence | In mathematics, the Frölicher spectral sequence (often misspelled as Fröhlicher) is a tool in the theory of complex manifolds, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifolds. It was introduced by . A spectral sequence is set up, the degener... |
https://en.wikipedia.org/wiki/Compactly%20supported%20homology | In mathematics, a homology theory in algebraic topology is compactly supported if, in every degree n, the relative homology group Hn(X, A) of every pair of spaces
(X, A)
is naturally isomorphic to the direct limit of the nth relative homology groups of pairs (Y, B), where Y varies over compact subspaces of X and B va... |
https://en.wikipedia.org/wiki/Duration%20calculus | Duration calculus (DC) is an interval logic for real-time systems. It was originally developed by Zhou Chaochen with the help of Anders P. Ravn and C. A. R. Hoare on the European ESPRIT Basic Research Action (BRA) ProCoS project on Provably Correct Systems.
Duration calculus is mainly useful at the requirements level ... |
https://en.wikipedia.org/wiki/Happy%20ending%20problem | In mathematics, the "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement:
This was one of the original results that led to the development of Ramsey theory.
The happy ending theorem can be proven by a simple case analysis: if fou... |
https://en.wikipedia.org/wiki/Zhou%20Chaochen | Zhou Chaochen (; born 1 November 1937) is a Chinese computer scientist.
Zhou was born in Nanhui, Shanghai, China. He studied as an undergraduate at the Department of Mathematics and Mechanics, Peking University (1954–1958) and as a postgraduate at the Institute of Computing Technology, Chinese Academy of Sciences (CAS... |
https://en.wikipedia.org/wiki/Homogeneity%20and%20heterogeneity%20%28statistics%29 | In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In meta-analysis, which c... |
https://en.wikipedia.org/wiki/Bernoulli%20scheme | In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A systems) exhibit a... |
https://en.wikipedia.org/wiki/MathSciNet | MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal Mathematical Reviews (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original ar... |
https://en.wikipedia.org/wiki/Motor%20variable | In mathematics, a function of a motor variable is a function with arguments and values in the split-complex number plane, much as functions of a complex variable involve ordinary complex numbers. William Kingdon Clifford coined the term motor for a kinematic operator in his "Preliminary Sketch of Biquaternions" (1873).... |
https://en.wikipedia.org/wiki/Two-element%20Boolean%20algebra | In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra "2" has some following in the literatur... |
https://en.wikipedia.org/wiki/Japanese%20theorem%20for%20cyclic%20polygons | In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.
Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic. The Japanese theorem follows from Carnot's theorem; it is a Sangaku problem.
Pr... |
https://en.wikipedia.org/wiki/MLD | MLD may refer to:
Medicine
Manual lymphatic drainage
Metachromatic leukodystrophy, a rare neurometabolic genetic condition
Science and technology
Mean log deviation in statistics and econometrics
Mixed layer depth in hydrography
Multicast Listener Discovery, in computer networking
Million liter per day, in en... |
https://en.wikipedia.org/wiki/Tannaka%E2%80%93Krein%20duality | In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, between compact and discrete commutative topological groups, to groups that are compact but noncommutative. The theory is name... |
https://en.wikipedia.org/wiki/Norman%20Lloyd%20Johnson | Norman Lloyd Johnson (9 January 1917, Ilford, Essex, England – 18 November 2004, Chapel Hill, North Carolina, United States) was a professor of statistics and author or editor of several standard reference works in statistics and probability theory.
Education
Johnson attended Ilford County High School, and went on to ... |
https://en.wikipedia.org/wiki/Bapoo%20Mama | Bapoo Burjorji 'B.B.' Mama (April 8, 1924 in Bombay – March 18, 1995 in Bombay) was a cricket statistician.
Bapoo Mama was a major figure in Indian cricket statistics in the second half of the twentieth century. In the 1970s and eighties, he contributed columns like Follow 'em with BBM, Figures are Fun, Factfile and... |
https://en.wikipedia.org/wiki/Recursive%20Bayesian%20estimation | In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model. The process relies he... |
https://en.wikipedia.org/wiki/Octant | Octant may refer to:
Octant (solid geometry), one of the eight divisions of 3-dimensional space by orthogonal coordinate planes
Octant of a sphere, a spherical triangle with three right angles
Octant (plane geometry), one eighth of a full circle
Octant (instrument) for celestial navigation
Octans, a constellation ... |
https://en.wikipedia.org/wiki/Simple%20linear%20regression | In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a n... |
https://en.wikipedia.org/wiki/Chevalley%20scheme | A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory.
Let X be a separated integral noetherian scheme, R its function field. If we denote by the set of subrings of R, where x runs through X (when , we denote by ), verifies the following three properties
For each , R is the field of fra... |
https://en.wikipedia.org/wiki/Pierpont%20prime | In number theory, a Pierpont prime is a prime number of the form
for some nonnegative integers and . That is, they are the prime numbers for which is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The... |
https://en.wikipedia.org/wiki/Determinacy | Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exis... |
https://en.wikipedia.org/wiki/Bulgarian%20solitaire | In mathematics and game theory, Bulgarian solitaire is a card game that was introduced by Martin Gardner.
In the game, a pack of cards is divided into several piles. Then for each pile, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored).
If is a triangular number... |
https://en.wikipedia.org/wiki/RSSSF | The Rec.Sport.Soccer Statistics Foundation (RSSSF) is an international organization dedicated to collecting statistics about association football. The foundation aims to build an exhaustive archive of football-related information from around the world.
History
This enterprise, according to its founders, was created i... |
https://en.wikipedia.org/wiki/Graham%20Higman | Graham Higman FRS (19 January 1917 – 8 April 2008) was a prominent English mathematician known for his contributions to group theory.
Biography
Higman was born in Louth, Lincolnshire, and attended Sutton High School, Plymouth, winning a scholarship to Balliol College, Oxford. In 1939 he co-founded The Invariant Societ... |
https://en.wikipedia.org/wiki/Noncentral%20chi-squared%20distribution | In probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral distribution) is a noncentral generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptoti... |
https://en.wikipedia.org/wiki/Pierre%20Samuel | Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number ... |
https://en.wikipedia.org/wiki/Reeb%20foliation | In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993).
It is based on dividing the sphere into two solid tori, along a 2-torus: see Clifford torus. Each of the solid tori is then foliated internally, in codimension 1, and the divid... |
https://en.wikipedia.org/wiki/Puiseux%20series | In mathematics, Puiseux series are a generalization of power series that allow for negative and fractional exponents of the indeterminate. For example, the series
is a Puiseux series in the indeterminate . Puiseux series were first introduced by Isaac Newton in 1676 and rediscovered by Victor Puiseux in 1850.
The de... |
https://en.wikipedia.org/wiki/Bitangent | In geometry, a bitangent to a curve is a line that touches in two distinct points and and that has the same direction as at these points. That is, is a tangent line at and at .
Bitangents of algebraic curves
In general, an algebraic curve will have infinitely many secant lines, but only finitely many bitangent... |
https://en.wikipedia.org/wiki/Birational%20invariant | In algebraic geometry, a birational invariant is a property that is preserved under birational equivalence.
Formal definition
A birational invariant is a quantity or object that is well-defined on a birational equivalence class of algebraic varieties. In other words, it depends only on the function field of the variet... |
https://en.wikipedia.org/wiki/Complete%20quadrangle | In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points. Dually, a complete quadrilateral is ... |
https://en.wikipedia.org/wiki/Topological%20divisor%20of%20zero | In mathematics, an element of a Banach algebra is called a topological divisor of zero if there exists a sequence of elements of such that
The sequence converges to the zero element, but
The sequence does not converge to the zero element.
If such a sequence exists, then one may assume that for all .
If is no... |
https://en.wikipedia.org/wiki/Interval%20exchange%20transformation | In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals. They arise naturally in the study of ... |
https://en.wikipedia.org/wiki/Edwin%20Ray%20Guthrie | Edwin Ray Guthrie (; January 9, 1886 – April 23, 1969) was a behavioral psychologist who began his career as a mathematics teacher and philosopher. But, he became a psychologist at the age of 33. He spent most of his career at the University of Washington, where he became full professor and then emeritus professor in p... |
https://en.wikipedia.org/wiki/AUCTeX | AUCTeX is an extensible package for writing and formatting TeX files in Emacs and XEmacs.
AUCTeX provides syntax highlighting, smart indentation and formatting, previews of mathematics and other elements directly in the editing buffer, smart folding of syntactical elements, macro and environment completion. It also su... |
https://en.wikipedia.org/wiki/Positive%20energy%20theorem | The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an isolated system is nonnegative, and can only be zero when the system has ... |
https://en.wikipedia.org/wiki/Artin%20reciprocity%20law | The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from... |
https://en.wikipedia.org/wiki/Rational%20sieve | In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field sieve. While it is less efficient than the general algorithm, it is conceptually simpler. It serves as a helpful first step in understanding how the general number field ... |
https://en.wikipedia.org/wiki/Peetre%27s%20inequality | In mathematics, Peetre's inequality, named after Jaak Peetre, says that for any real number and any vectors and in the following inequality holds:
The inequality was proved by J. Peetre in 1959 and has founds applications in functional analysis and Sobolev spaces.
See also
References
.
.
.
External links
... |
https://en.wikipedia.org/wiki/Rolling%20ball%20argument | In topology, quantum mechanics and geometrodynamics, rolling-ball arguments are used to describe how the perceived geometry and connectedness of a surface can be scale-dependent.
If a researcher probes the shape of an intricately curved surface by rolling a ball across it, then features that are continually curved but... |
https://en.wikipedia.org/wiki/Quadratic%20differential | In mathematics, a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic cotangent bundle. If the section is holomorphic, then the quadratic differential is said to be holomorphic. The vector space of holomorphic quadratic differentials on a Riemann surface has a natural int... |
https://en.wikipedia.org/wiki/Patos%20de%20Minas | Patos de Minas is a municipality in the state of Minas Gerais in Brazil.
Geography
According to the modern (2017) geographic classification by Brazil's National Institute of Geography and Statistics (IBGE), the city is the main municipality in the Intermediate Geographic Region of Patos de Minas.
History
The name is... |
https://en.wikipedia.org/wiki/Gilbert%20Strang | William Gilbert Strang (born November 27, 1934) is an American mathematician known for his contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing mathematics textbooks. Strang was the MathWork... |
https://en.wikipedia.org/wiki/Cylinder%20set | In mathematics, the cylinder sets form a basis of the product topology on a product of sets; they are also a generating family of the cylinder σ-algebra.
General definition
Given a collection of sets, consider the Cartesian product of all sets in the collection. The canonical projection corresponding to some is th... |
https://en.wikipedia.org/wiki/Steven%20Kerckhoff | Steven Paul Kerckhoff (born 1952) is a professor of mathematics at Stanford University, who works on hyperbolic 3-manifolds and Teichmüller spaces.
He received his Ph.D. in mathematics from Princeton University in 1978, under the direction of William Thurston. Among his most famous results is his resolution of the Ni... |
https://en.wikipedia.org/wiki/Commensurability | Two concepts or things are commensurable if they are measurable or comparable by a common standard.
Commensurability most commonly refers to commensurability (mathematics). It may also refer to:
Commensurability (astronomy), whether two orbital periods are mathematically commensurate.
Commensurability (crystal stru... |
https://en.wikipedia.org/wiki/Omega%20network | An Omega network is a network configuration often used in parallel computing architectures. It is an indirect topology that relies on the perfect shuffle interconnection algorithm.
Connection architecture
An 8x8 Omega network is a multistage interconnection network, meaning that processing elements (PEs) are connected... |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Woods%20number | In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property:
there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common factor with one of the endpoints. In other words, is an Erdős–Woods number if t... |
https://en.wikipedia.org/wiki/MSU%20Faculty%20of%20Computational%20Mathematics%20and%20Cybernetics | MSU Faculty of Computational Mathematics and Cybernetics (CMC) (), founded in 1970 by Andrey Tikhonov, is a part of Moscow State University.
Education
CMC is a Russian research and training center in the fields of applied mathematics, computing and software development . Education at CMC combines theoretical studies, ... |
https://en.wikipedia.org/wiki/Faithful%20representation | In mathematics, especially in an area of abstract algebra known as representation theory, a faithful representation ρ of a group on a vector space is a linear representation in which different elements of are represented by distinct linear mappings .
In more abstract language, this means that the group homomorphism... |
https://en.wikipedia.org/wiki/William%20Newton-Smith | William Herbert Newton-Smith (May 25, 1943 – April 8, 2023) was a Canadian philosopher of science.
Biography
Newton-Smith's undergraduate degree from Queen's University was in Mathematics and Philosophy, in 1966. He took an MA from Cornell University in Philosophy, in 1968, and a DPhil in philosophy from Balliol Colle... |
https://en.wikipedia.org/wiki/Gravitational%20instanton | In mathematical physics and differential geometry, a gravitational instanton is a four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations. They are so named because they are analogues in quantum theories of gravity of instantons in Yang–Mills theory. In accordance with this analogy with s... |
https://en.wikipedia.org/wiki/Conformal%20Killing%20vector%20field | In conformal geometry, a conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric (also called a conformal Killing vector, CKV, or conformal colineation), is a vector field whose (locally defined) flow defines conformal transformations, that is, preserve up to scale and preserve ... |
https://en.wikipedia.org/wiki/Coordinate-measuring%20machine | A coordinate measuring machine (CMM) is a device that measures the geometry of physical objects by sensing discrete points on the surface of the object with a probe. Various types of probes are used in CMMs, the most common being mechanical and laser sensors, though optical and white light sensor do exist. Depending on... |
https://en.wikipedia.org/wiki/Flow%20%28mathematics%29 | In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time. More formally, ... |
https://en.wikipedia.org/wiki/Ernst%20Witt | Ernst Witt (26 June 1911 – 3 July 1991) was a German mathematician, one of the leading algebraists of his time.
Biography
Witt was born on the island of Alsen, then a part of the German Empire. Shortly after his birth, his parents moved the family to China to work as missionaries, and he did not return to Europe until... |
https://en.wikipedia.org/wiki/Vector%20flow | In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different contexts, including differential topology, Riemannian geometry and Lie group theory. These related concepts are explored in a spectrum of articles:
exponential ma... |
https://en.wikipedia.org/wiki/Unconditional%20convergence | In mathematics, specifically functional analysis, a series is unconditionally convergent if all reorderings of the series converge to the same value. In contrast, a series is conditionally convergent if it converges but different orderings do not all converge to that same value. Unconditional convergence is equivalent ... |
https://en.wikipedia.org/wiki/Brocard%27s%20conjecture | In number theory, Brocard's conjecture is the conjecture that there are at least four prime numbers between (pn)2 and (pn+1)2, where pn is the nth prime number, for every n ≥ 2. The conjecture is named after Henri Brocard. It is widely believed that this conjecture is true. However, it remains unproven as of 2022.
T... |
https://en.wikipedia.org/wiki/One-to-many | One-to-many may refer to:
Fat link, a one-to-many link in hypertext
Multivalued function, a one-to-many function in mathematics
One-to-many (data model), a type of relationship and cardinality in systems analysis
Point-to-multipoint communication, communication which has a one-to-many relationship
See also
Cardin... |
https://en.wikipedia.org/wiki/Crystal%20Ball%20function | The Crystal Ball function, named after the Crystal Ball Collaboration (hence the capitalized initial letters), is a probability density function commonly used to model various lossy processes in high-energy physics. It consists of a Gaussian core portion and a power-law low-end tail, below a certain threshold. The func... |
https://en.wikipedia.org/wiki/Relative%20risk | The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome.
Statistical use and meaning
Relative ... |
https://en.wikipedia.org/wiki/Champernowne | Champernowne may refer to:
Arthur Champernowne (disambiguation), multiple people
D. G. Champernowne (1912-2000), English economist and mathematician
Champernowne constant, in mathematics
Champernowne distribution, in statistics
Joan Champernowne (died 1553), lady-in-waiting at the court of Henry VIII of England
... |
https://en.wikipedia.org/wiki/Adjustment | Adjustment may refer to:
Adjustment (law), with several meanings
Adjustment (psychology), the process of balancing conflicting needs
Adjustment of observations, in mathematics, a method of solving an overdetermined system of equations
Calibration, in metrology
Spinal adjustment, in chiropractic practice
In statistics,... |
https://en.wikipedia.org/wiki/Autonomous%20category | In mathematics, an autonomous category is a monoidal category where dual objects exist.
Definition
A left (resp. right) autonomous category is a monoidal category where every object has a left (resp. right) dual. An autonomous category is a monoidal category where every object has both a left and a right dual. Rigid ... |
https://en.wikipedia.org/wiki/Georgia%20Academy%20of%20Arts%2C%20Mathematics%2C%20Engineering%20and%20Science | The Georgia Academy of Arts, Mathematics, Engineering and Sciences, (formerly known as GAMES), is a dual-enrollment early college entrance program created in 1997 and facilitated by the University System of Georgia in the United States. Typically, juniors in high school who meet the base requirements of GPA and SAT/ACT... |
https://en.wikipedia.org/wiki/Extensional%20context | In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the ... |
https://en.wikipedia.org/wiki/Pacific%20Journal%20of%20Mathematics | The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisation, and the University of California, Berkeley.
It was founded in 1951 ... |
https://en.wikipedia.org/wiki/Translation%20plane | In mathematics, a translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known non-Desarguesian planes ar... |
https://en.wikipedia.org/wiki/Le%20Cam%27s%20theorem | In probability theory, Le Cam's theorem, named after Lucien Le Cam (1924 – 2000), states the following.
Suppose:
are independent random variables, each with a Bernoulli distribution (i.e., equal to either 0 or 1), not necessarily identically distributed.
(i.e. follows a Poisson binomial distribution)
Then
... |
https://en.wikipedia.org/wiki/Normal%20scheme | In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. ... |
https://en.wikipedia.org/wiki/Rational%20singularity | In mathematics, more particularly in the field of algebraic geometry, a scheme has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map
from a regular scheme such that the higher direct images of applied to are trivial. That is, ... |
https://en.wikipedia.org/wiki/Pentadiagonal%20matrix | In linear algebra, a pentadiagonal matrix is a special case of band matrices.
Its only nonzero entries are on the main diagonal and the first two upper and two lower diagonals.
So, it is of the form.
It follows that a pentadiagonal matrix has at most nonzero entries, where n is the size of the matrix. Hence, pent... |
https://en.wikipedia.org/wiki/Lightface%20analytic%20game | In descriptive set theory, a lightface analytic game is a game whose payoff set A is a subset of Baire space; that is, there is a tree T on which is a computable subset of , such that A is the projection of the set of all branches of T.
The determinacy of all lightface analytic games is equivalent to the existence ... |
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