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https://en.wikipedia.org/wiki/Kernel%20%28linear%20algebra%29 | In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the ... |
https://en.wikipedia.org/wiki/Forward%20algorithm | The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.
The f... |
https://en.wikipedia.org/wiki/Marcel%20Riesz | Marcel Riesz ( ; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras. He spent most of his career in Lund (Sweden).
Marcel is the younger b... |
https://en.wikipedia.org/wiki/Eilenberg%E2%80%93MacLane%20space | In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group.
Let G be a group and n a positive integer. A connected topological space X is called an Eilenberg–MacLane space of type , if it has n-th homotopy group isomorphic to G and all ot... |
https://en.wikipedia.org/wiki/Sigma-additive%20set%20function | In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function... |
https://en.wikipedia.org/wiki/Brown%27s%20representability%20theorem | In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor.
More specifically, we are given
F: Hotcop → Set,
and... |
https://en.wikipedia.org/wiki/Cotton%20tensor | In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric. The vanishing of the Cotton tensor for is necessary and sufficient condition for the manifold to be conformally flat. By contrast, in dimensions ,
the vanishing of the Cotton ... |
https://en.wikipedia.org/wiki/Lebesgue%20space | Lebesgue space may refer to:
Lp space, a special Banach space of functions (or rather, equivalence classes of functions)
Standard probability space, a non-pathological probability space |
https://en.wikipedia.org/wiki/Dedekind-infinite%20set | In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite (i.e., no s... |
https://en.wikipedia.org/wiki/Hyperbolic | Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.
The following phenomena are described as hyperbolic because they manifest hyperbolas, not because something about them is exaggerated.
Hyper... |
https://en.wikipedia.org/wiki/Hans%20Hahn%20%28mathematician%29 | Hans Hahn (; 27 September 1879 – 24 July 1934) was an Austrian mathematician and philosopher who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. In philosophy he was among the main logical positivists of the Vienna Circle.
Biography
Born in ... |
https://en.wikipedia.org/wiki/Vitali%E2%80%93Hahn%E2%80%93Saks%20theorem | In mathematics, the Vitali–Hahn–Saks theorem, introduced by , , and , proves that under some conditions a sequence of measures converging point-wise does so uniformly and the limit is also a measure.
Statement of the theorem
If is a measure space with and a sequence of complex measures. Assuming that each is abs... |
https://en.wikipedia.org/wiki/Hahn%20embedding%20theorem | In mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn.
Overview
The theorem states that every linearly ordered abelian group G can be embedde... |
https://en.wikipedia.org/wiki/AMPL | AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems).
It was developed by Robert Fourer, David Gay, and Brian Kernighan at Bell Laboratories.
AMPL s... |
https://en.wikipedia.org/wiki/List%20of%20homological%20algebra%20topics | This is a list of homological algebra topics, by Wikipedia page.
Basic techniques
Cokernel
Exact sequence
Chain complex
Differential module
Five lemma
Short five lemma
Snake lemma
Nine lemma
Extension (algebra)
Central extension
Splitting lemma
Projective module
Injective module
Projective resolution
Injective resolu... |
https://en.wikipedia.org/wiki/Beit%20Hanoun | Beit Hanoun or Beit Hanun () is a city on the northeast edge of the Gaza Strip. According to the Palestinian Central Bureau of Statistics, the town had a population of 52,237 in 2017. It is administered by the Hamas administration. It is located by the Hanoun stream, just away from the Israeli town of Sderot.
History... |
https://en.wikipedia.org/wiki/Robert%20Lee%20Moore | Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, and for his racist treatment of African-American mathematics students.
Life
... |
https://en.wikipedia.org/wiki/Herbrand%E2%80%93Ribet%20theorem | In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity if and only if p divides the numerator of the n-th Bernoulli number B... |
https://en.wikipedia.org/wiki/Beit%20Lahia | Beit Lahia or Beit Lahiya () is a city in the Gaza Strip north of Jabalia, near Beit Hanoun and the 1949 Armistice Line with Israel. According to the Palestinian Central Bureau of Statistics, the city had a population of 89,838 in 2017. The political party Hamas is still administering the city, together with the entire... |
https://en.wikipedia.org/wiki/Bertrand%27s%20paradox | There are three different paradoxes called Bertrand's paradox or the Bertrand paradox:
Bertrand paradox (probability)
Bertrand paradox (economics)
Bertrand's box paradox
Not to be confused with the famous paradox discovered by Bertrand Russell. |
https://en.wikipedia.org/wiki/Dirac%20operator | In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise formally an operator for Minkowski space, to get a form of quantum theory compati... |
https://en.wikipedia.org/wiki/Adaptive%20Multi-Rate%20Wideband | Adaptive Multi-Rate Wideband (AMR-WB) is a patented wideband speech audio coding standard developed based on Adaptive Multi-Rate encoding, using a similar methodology to algebraic code-excited linear prediction (ACELP). AMR-WB provides improved speech quality due to a wider speech bandwidth of 50–7000 Hz compared to na... |
https://en.wikipedia.org/wiki/Algebraic%20code-excited%20linear%20prediction | Algebraic code-excited linear prediction (ACELP) is a speech coding algorithm in which a limited set of pulses is distributed as excitation to a linear prediction filter. It is a linear predictive coding (LPC) algorithm that is based on the code-excited linear prediction (CELP) method and has an algebraic structure. AC... |
https://en.wikipedia.org/wiki/Chisini%20mean | In mathematics, a function f of n variables x1, ..., xn leads to a Chisini mean M if, for every vector ⟨x1, ..., xn⟩, there exists a unique M such that
f(M,M, ..., M) = f(x1,x2, ..., xn).
The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are their weighted varian... |
https://en.wikipedia.org/wiki/Complex%20polygon | The term complex polygon can mean two different things:
In geometry, a polygon in the unitary plane, which has two complex dimensions.
In computer graphics, a polygon whose boundary is not simple.
Geometry
In geometry, a complex polygon is a polygon in the complex Hilbert plane, which has two complex dimensions.
... |
https://en.wikipedia.org/wiki/Double%20exponential%20distribution | In statistics, the double exponential distribution may refer to
Laplace distribution, or bilateral exponential distribution, consisting of two exponential distributions glued together on each side of a threshold
Gumbel distribution, the cumulative distribution function of which is an iterated exponential function (th... |
https://en.wikipedia.org/wiki/Kronecker%E2%80%93Weber%20theorem | In algebraic number theory, it can be shown that every cyclotomic field is an abelian extension of the rational number field Q, having Galois group of the form . The Kronecker–Weber theorem provides a partial converse: every finite abelian extension of Q is contained within some cyclotomic field. In other words, every ... |
https://en.wikipedia.org/wiki/Topology%20optimization | Topology optimization (TO) is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different from shape optimization and sizing optimization in t... |
https://en.wikipedia.org/wiki/Quadrilateral%20%28disambiguation%29 | A quadrilateral, in geometry, is a polygon with 4 sides.
Quadrilateral may also refer to:
Complete quadrilateral, in projective geometry, a configuration with 4 lines and 6 points
Chicago-Lambeth Quadrilateral, a four-point statement of fundamental doctrine, in the Anglican Communion
Wesleyan Quadrilateral, the fou... |
https://en.wikipedia.org/wiki/Martin%20David%20Kruskal | Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His most celebrated contribution... |
https://en.wikipedia.org/wiki/Von%20Staudt%E2%80%93Clausen%20theorem | In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by
and .
Specifically, if n is a positive integer and we add 1/p to the Bernoulli number B2n for every prime p such that p − 1 divides 2n, we obtain an integer, i.e.,
This fact immed... |
https://en.wikipedia.org/wiki/Agoh%E2%80%93Giuga%20conjecture | In number theory the Agoh–Giuga conjecture on the Bernoulli numbers Bk postulates that p is a prime number if and only if
It is named after Takashi Agoh and Giuseppe Giuga.
Equivalent formulation
The conjecture as stated above is due to Takashi Agoh (1990); an equivalent formulation is due to Giuseppe Giuga, from... |
https://en.wikipedia.org/wiki/Bateman%E2%80%93Horn%20conjecture | In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962. It provides a vast generalization of such conjectures as the Hardy and Littlewood conj... |
https://en.wikipedia.org/wiki/Isogeny | In mathematics, particularly in algebraic geometry, an isogeny is a morphism of algebraic groups (also known as group varieties) that is surjective and has a finite kernel.
If the groups are abelian varieties, then any morphism of the underlying algebraic varieties which is surjective with finite fibres is automatica... |
https://en.wikipedia.org/wiki/Critical%20value | Critical value may refer to:
In differential topology, a critical value of a differentiable function between differentiable manifolds is the image (value of) ƒ(x) in N of a critical point x in M.
In statistical hypothesis testing, the critical values of a statistical test are the boundaries of the acceptance region ... |
https://en.wikipedia.org/wiki/Taut%20submanifold | In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every the distance function
is a perfect Morse function.
If N is not compact, one needs to consider the restriction of the to any of their sublevel sets.
References
Differential geometry
Morse the... |
https://en.wikipedia.org/wiki/Space%20form | In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three most fundamental examples are Euclidean n-space, the n-dimensional sphere, and hyperbolic space, although a space form need not be simply connected.
Reduction to generalized crystallography
The Killing–Hopf ... |
https://en.wikipedia.org/wiki/Bias%20%28disambiguation%29 | Bias is an inclination toward something, or a predisposition, partiality, prejudice, preference, or predilection.
Bias may also refer to:
Scientific method and statistics
The bias introduced into an experiment through a confounder
Algorithmic bias, machine learning algorithms that exhibit politically unacceptable ... |
https://en.wikipedia.org/wiki/Projectionless%20C%2A-algebra | In mathematics, a projectionless C*-algebra is a C*-algebra with no nontrivial projections. For a unital C*-algebra, the projections 0 and 1 are trivial. While for a non-unital C*-algebra, only 0 is considered trivial. The problem of whether simple infinite-dimensional C*-algebras with this property exist was posed in... |
https://en.wikipedia.org/wiki/Frobenius%20normal%20form | In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanne... |
https://en.wikipedia.org/wiki/Frobenius%20endomorphism | In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic , an important class which includes finite fields. The endomorphism maps every element to its -th power. In certain contexts it is an automorphis... |
https://en.wikipedia.org/wiki/Radical%20of%20an%20algebraic%20group | The radical of an algebraic group is the identity component of its maximal normal solvable subgroup.
For example, the radical of the general linear group (for a field K) is the subgroup consisting of scalar matrices, i.e. matrices with and for .
An algebraic group is called semisimple if its radical is trivial, i.... |
https://en.wikipedia.org/wiki/Reductive%20group | In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the m... |
https://en.wikipedia.org/wiki/Mahler%20measure | In mathematics, the Mahler measure of a polynomial with complex coefficients is defined as
where factorizes over the complex numbers as
The Mahler measure can be viewed as a kind of height function. Using Jensen's formula, it can be proved that this measure is also equal to the geometric mean of for on the unit... |
https://en.wikipedia.org/wiki/Identity%20component | In mathematics, specifically group theory, the identity component of a group G refers to several closely related notions of the largest connected subgroup of G containing the identity element.
In point set topology, the identity component of a topological group G is the connected component G0 of G that contains the i... |
https://en.wikipedia.org/wiki/Euler%E2%80%93Tricomi%20equation | In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named after mathematicians Leonhard Euler and Francesco Giacomo Tricomi.
It is elliptic in the half plane x > 0, parabolic at x = 0 and hyperbolic in the half plane x < 0.
Its characterist... |
https://en.wikipedia.org/wiki/Modular%20lattice | In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition,
Modular law implies
where are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phr... |
https://en.wikipedia.org/wiki/Geometry%20pipelines | Geometric manipulation of modelling primitives, such as that performed by a geometry pipeline, is the first stage in computer graphics systems which perform image generation based on geometric models. While geometry pipelines were originally implemented in software, they have become highly amenable to hardware implemen... |
https://en.wikipedia.org/wiki/Biorthogonal%20system | In mathematics, a biorthogonal system is a pair of indexed families of vectors
such that
where and form a pair of topological vector spaces that are in duality, is a bilinear mapping and is the Kronecker delta.
An example is the pair of sets of respectively left and right eigenvectors of a matrix, indexed by eig... |
https://en.wikipedia.org/wiki/DFT%20matrix | In applied mathematics, a DFT matrix is an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied to a signal through matrix multiplication.
Definition
An N-point DFT is expressed as the multiplication , where is the original input signal, is the N-by-N square DFT matrix, a... |
https://en.wikipedia.org/wiki/Non-well-founded%20set%20theory | Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation.
The study of non-well-founded sets was initiated... |
https://en.wikipedia.org/wiki/Igor%20Shafarevich | Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were described as anti-semitic.
Mathematics
From ... |
https://en.wikipedia.org/wiki/Negative%20frequency | In mathematics, signed frequency (negative and positive frequency) expands upon the concept of frequency, from just an absolute value representing how often some repeating event occurs, to also have a positive or negative sign representing one of two opposing orientations for occurrences of those events. The following ... |
https://en.wikipedia.org/wiki/Scorer%27s%20function | In mathematics, the Scorer's functions are special functions studied by and denoted Gi(x) and Hi(x).
Hi(x) and -Gi(x) solve the equation
and are given by
The Scorer's functions can also be defined in terms of Airy functions:
References
Special functions |
https://en.wikipedia.org/wiki/Approximation%20theory | In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application.
A closely related topic is the approximation of functions by gene... |
https://en.wikipedia.org/wiki/Stanley%27s%20reciprocity%20theorem | In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior.
Definitions
A rational cone is the s... |
https://en.wikipedia.org/wiki/Hough%20function | In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such, they are relevant in geophysics and meteorology where they form part of the solutions for atmospheric and ocean waves. These functions are named in honour of Sydney Sa... |
https://en.wikipedia.org/wiki/Parabolic%20fractal%20distribution | In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit ... |
https://en.wikipedia.org/wiki/Morley%27s%20trisector%20theorem | In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It h... |
https://en.wikipedia.org/wiki/Morley%27s%20theorem | Morley's theorem may refer to:
Morley's trisector theorem, a theorem in geometry, discovered by Frank Morley
Morley's categoricity theorem, a theorem in model theory, discovered by Michael D. Morley |
https://en.wikipedia.org/wiki/De%20Morgan%20Medal | The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society.
The medal is awarded every third year (in years divisible by 3) to a mat... |
https://en.wikipedia.org/wiki/Logistic | Logistic may refer to:
Mathematics
Logistic function, a sigmoid function used in many fields
Logistic map, a recurrence relation that sometimes exhibits chaos
Logistic regression, a statistical model using the logistic function
Logit, the inverse of the logistic function
Logistic distribution, the derivative of ... |
https://en.wikipedia.org/wiki/Adams%20Prize | The Adams Prize is one of the most prestigious prizes awarded by the University of Cambridge. It is awarded each year by the Faculty of Mathematics at the University of Cambridge and St John's College to a UK-based mathematician for distinguished research in the Mathematical Sciences.
The prize is named after the math... |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20societies | This article provides a list of mathematical societies.
International
African Mathematical Union
Association for Women in Mathematics
Circolo Matematico di Palermo
European Mathematical Society
European Women in Mathematics
Foundations of Computational Mathematics
International Association for Cryptologic Rese... |
https://en.wikipedia.org/wiki/Hilbert%27s%20Theorem%2090 | In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields with cyclic Galois group G = Gal(L/K) generated by an element and if is a... |
https://en.wikipedia.org/wiki/Salem%20Prize | The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was founded by the widow of Raphael Salem in his memory. The prize is considered ... |
https://en.wikipedia.org/wiki/Eduard%20Vogel | Eduard Vogel (7 March 1829February 1856) was a German explorer in Central Africa.
Early career
Vogel was born in Krefeld. He studied mathematics, botany and astronomy at Leipzig and Berlin, studying with Encke at the latter institution. In 1851, he was engaged as assistant astronomer to director John Russel Hind at G... |
https://en.wikipedia.org/wiki/Isometry%20group | In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function. The elements of the isometry group are sometimes ... |
https://en.wikipedia.org/wiki/Difference%20of%20two%20squares | In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity
in elementary algebra.
Proof
The proof of the factorization identity is straightforward. Starting from the left-hand si... |
https://en.wikipedia.org/wiki/Fractional%20Fourier%20transform | In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate doma... |
https://en.wikipedia.org/wiki/Homotopy%20groups%20of%20spheres | In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geo... |
https://en.wikipedia.org/wiki/Efim%20Zelmanov | Efim Isaakovich Zelmanov (; born 7 September 1955 in Khabarovsk) is a Russian-American mathematician, known for his work on combinatorial problems in nonassociative algebra and group theory, including his solution of the restricted Burnside problem. He was awarded a Fields Medal at the International Congress of Mathema... |
https://en.wikipedia.org/wiki/Hill%20cipher | In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
The following discussion assumes an elementary knowle... |
https://en.wikipedia.org/wiki/Classification%20of%20Clifford%20algebras | In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras for a nondegenerate quadratic form have been completely classified. In each case, the Clifford algebra is algebra isomorphic to a full matrix ring o... |
https://en.wikipedia.org/wiki/Kirby%20calculus | In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J res... |
https://en.wikipedia.org/wiki/Reciprocal%20polynomial | In algebra, given a polynomial
with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by or , is the polynomial
That is, the coefficients of are the coefficients of in reverse order. Reciprocal polynomials arise naturally in linear algebra as the characteristic polyno... |
https://en.wikipedia.org/wiki/Laplace%20distribution | In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced togeth... |
https://en.wikipedia.org/wiki/AWStats | AWStats (Advanced Web Statistics) is an open source Web analytics reporting tool, suitable for analyzing data from Internet services such as web, streaming media, mail, and FTP servers. AWStats parses and analyzes server log files, producing HTML reports. Data is visually presented within reports by tables and bar grap... |
https://en.wikipedia.org/wiki/Smith%20normal%20form | In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right... |
https://en.wikipedia.org/wiki/Annihilator | Annihilator(s) may refer to:
Mathematics
Annihilator (ring theory)
Annihilator (linear algebra), the annihilator of a subset of a vector subspace
Annihilator method, a type of differential operator, used in a particular method for solving differential equations
Annihilator matrix, in regression analysis
Music
An... |
https://en.wikipedia.org/wiki/Linear%20approximation | In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
Definition
Given a twice continuous... |
https://en.wikipedia.org/wiki/Alexander%20polynomial | In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, cou... |
https://en.wikipedia.org/wiki/Felix%20Iversen | Felix Christian Herbert Iversen (22 October 1887 – 31 July 1973) was a Finnish mathematician and a pacifist. He was a student of Ernst Lindelöf, and later an associate professor of mathematics at the University of Helsinki. Although he stopped performing serious research in mathematics around 1922, he continued working... |
https://en.wikipedia.org/wiki/Hasse%20norm%20theorem | In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere, then it is a global norm.
Here to be a global norm means to be an element k of K such that there is an element l of L with ; in other words k is a relative norm ... |
https://en.wikipedia.org/wiki/Tollerton%2C%20Nottinghamshire | Tollerton is an English village and civil parish in the Rushcliffe district of Nottinghamshire, just south-east of Nottingham. Statistics from the 2021 census show the population of the village has increased to 2,486.
Governance
Tollerton has a parish council and is represented on Rushcliffe Borough Council. The Membe... |
https://en.wikipedia.org/wiki/Hasse%E2%80%93Minkowski%20theorem | The Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only if they are equivalent locally at all places, i.e. equivalent over every completion of the field (which may be real, complex, or p-adic). A related result is that a q... |
https://en.wikipedia.org/wiki/Hasse%27s%20theorem | In mathematics, there are several theorems of Helmut Hasse that are sometimes called Hasse's theorem:
Hasse norm theorem
Hasse's theorem on elliptic curves
Hasse–Arf theorem
Hasse–Minkowski theorem
See also
Hasse principle, the principle that an integer equation can be solved by piecing together modular soluti... |
https://en.wikipedia.org/wiki/Calculus%20%28disambiguation%29 | Calculus (from Latin calculus meaning ‘pebble’, plural calculī) in its most general sense is any method or system of calculation.
Calculus may refer to:
Biology
Calculus (spider), a genus of the family Oonopidae
Caseolus calculus, a genus and species of small land snails
Mathematics
Infinitesimal calculus (o... |
https://en.wikipedia.org/wiki/Math%20League | Math League is a math competition for elementary, middle, and high school students in the United States, Canada, and other countries. The Math League was founded in 1977 by two high school mathematics teachers, Steven R. Conrad and Daniel Flegler. Math Leagues, Inc. publishes old contests through a series of books ent... |
https://en.wikipedia.org/wiki/Geometry%20%28Robert%20Rich%20album%29 | Geometry (1991) is an album by the American ambient and electronic musician Robert Rich. Although completed in 1988, this album was not released until three years later.
This album is more active and structured than any of his previous works. The music was inspired in part by the complex patterns of Islamic designs l... |
https://en.wikipedia.org/wiki/Loop-erased%20random%20walk | In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. See also random walk for more general treatment of this topic.
Definition
Assum... |
https://en.wikipedia.org/wiki/Modular%20representation%20theory | Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in othe... |
https://en.wikipedia.org/wiki/Multiplicative%20group | In mathematics and group theory, the term multiplicative group refers to one of the following concepts:
the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is , where 0 refer... |
https://en.wikipedia.org/wiki/Lyons%20group | In the area of modern algebra known as group theory, the Lyons group Ly or Lyons-Sims group LyS is a sporadic simple group of order
283756711313767
= 51765179004000000
≈ 5.
History
Ly is one of the 26 sporadic groups and was discovered by Richard Lyons and Charles Sims in 1972-73. Lyons characterized 517651790... |
https://en.wikipedia.org/wiki/Held%20group | In the area of modern algebra known as group theory, the Held group He is a sporadic simple group of order
21033527317 = 4030387200
≈ 4.
History
He is one of the 26 sporadic groups and was found by during an investigation of simple groups containing an involution whose centralizer is isomorphic to that of an inv... |
https://en.wikipedia.org/wiki/Galois%20cohomology | In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but al... |
https://en.wikipedia.org/wiki/Unordered%20pair | In mathematics, an unordered pair or pair set is a set of the form {a, b}, i.e. a set having two elements a and b with no particular relation between them, where {a, b} = {b, a}. In contrast, an ordered pair (a, b) has a as its first element and b as its second element, which means (a, b) ≠ (b, a).
While the two elem... |
https://en.wikipedia.org/wiki/Monte%20Carlo%20integration | In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand ... |
https://en.wikipedia.org/wiki/Paraconsistent%20mathematics | Paraconsistent mathematics, sometimes called inconsistent mathematics, represents an attempt to develop the classical infrastructure of mathematics (e.g. analysis) based on a foundation of paraconsistent logic instead of classical logic. A number of reformulations of analysis can be developed, for example functions whi... |
https://en.wikipedia.org/wiki/GNU%20Scientific%20Library | The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science. The GSL is written in C; wrappers are available for other programming languages. The GSL is part of the GNU Project and is distributed under the GNU General Public License.
Project history
The GSL ... |
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