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https://en.wikipedia.org/wiki/List%20of%20cities%20in%20Brazil%20by%20population | Brazil has a high level of urbanization with 87.8% of the population residing in urban and metropolitan areas. The criteria used by the IBGE (Brazilian Institute of Geography and Statistics) in determining whether households are urban or rural, however, are based on political divisions, not on the developed environment... |
https://en.wikipedia.org/wiki/L%C3%A9vy%20distribution | In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable. In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile. It is a special case of the inverse-gamma ... |
https://en.wikipedia.org/wiki/Bell%20series | In mathematics, the Bell series is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell.
Given an arithmetic function and a prime , define the formal power series , called the Bell series of modulo as:
Two multiplicative functions ... |
https://en.wikipedia.org/wiki/Normalized%20number | In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point. Thus, a real number, when written out in normalized scientific notation, is as follows:
where n is an integer, are the digits of the number in base 10, and is not zero. T... |
https://en.wikipedia.org/wiki/Essential%20spectrum | In mathematics, the essential spectrum of a bounded operator (or, more generally, of a densely defined closed linear operator) is a certain subset of its spectrum, defined by a condition of the type that says, roughly speaking, "fails badly to be invertible".
The essential spectrum of self-adjoint operators
In formal... |
https://en.wikipedia.org/wiki/Knot%20complement | In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is the 3-sphere minus the space near the knot. To make this precise, suppose that K is a knot in a three-manifold M (most often, M is the 3-sphere). Let N be a tubular ne... |
https://en.wikipedia.org/wiki/Toda%20field%20theory | In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Lie algebra and a specific Lagrangian.
Formulation
Fixing the Lie algebra to have rank , that is, the Cartan subalgebra of the algebra has ... |
https://en.wikipedia.org/wiki/Affine%20Lie%20algebra | In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given an affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, af... |
https://en.wikipedia.org/wiki/Eugene%20Dynkin | Eugene Borisovich Dynkin (; 11 May 1924 – 14 November 2014) was a Soviet and American mathematician. He made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named after him.
Biog... |
https://en.wikipedia.org/wiki/D-ring | A D-ring is a D-shaped metal ring used primarily as a lashing point in a tie-down system. Depending on their function D-rings may vary in composition, geometry, weight, finish, and load capacity. They may be screwed or welded in place, or attached to the end of a cord or a strap.
In permanent applications recessed tie... |
https://en.wikipedia.org/wiki/Tautological | In mathematics, tautological may refer to:
Logic:
Tautological consequence
Geometry, where it is used as an alternative to canonical:
Tautological bundle
Tautological line bundle
Tautological one-form
Tautology (grammar), unnecessary repetition, or more words than necessary, to say the same thing.
See also
Tautol... |
https://en.wikipedia.org/wiki/Modulo%20%28mathematics%29 | In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor. It was initially introduced into... |
https://en.wikipedia.org/wiki/Curve%20%28disambiguation%29 | A curve is a geometrical object in mathematics.
Curve(s) may also refer to:
Arts, entertainment, and media
Music
Curve (band), an English alternative rock music group
Curve (album), a 2012 album by Our Lady Peace
"Curve" (song), a 2017 song by Gucci Mane featuring The Weeknd
Curve, a 2001 album by Doc Walker
"C... |
https://en.wikipedia.org/wiki/Gaussian%20binomial%20coefficient | In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as or , is a polynomial in q with integer coefficients, whose value when q is set to a prime po... |
https://en.wikipedia.org/wiki/Pell%20number | In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numer... |
https://en.wikipedia.org/wiki/Artin%E2%80%93Tits%20group | In the mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by simple presentations. They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin... |
https://en.wikipedia.org/wiki/Reuleaux%20polygon | In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical example, the Reuleaux triangle, which in turn, is named after 19th-century German engineer Franz Reuleaux. The Reuleaux triangle can be constructed from an equilatera... |
https://en.wikipedia.org/wiki/Fibered%20knot | In knot theory, a branch of mathematics, a knot or link
in the 3-dimensional sphere is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family of Seifert surfaces for , where the parameter runs through the points of the unit circle , such that if is no... |
https://en.wikipedia.org/wiki/Nicolae%20Popescu | Nicolae Popescu (; 22 September 1937 – 29 July 2010) was a Romanian mathematician and professor at the University of Bucharest. He also held a research position at the Institute of Mathematics of the Romanian Academy, and was elected corresponding Member of the Romanian Academy in 1997.
He is best known for his contri... |
https://en.wikipedia.org/wiki/Ian%20Grojnowski | Ian Grojnowski is a mathematician working at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.
Awards and honours
Grojnowski was the first recipient of the Fröhlich Prize of the London Mathematical Society in 2004 for his work in representation theory and algebraic geometry... |
https://en.wikipedia.org/wiki/Ansatz | In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.
Use
An ansatz is the establishment of the start... |
https://en.wikipedia.org/wiki/GLS | GLS may refer to:
Science and technology
GBAS landing system, an aircraft landing system
General Lighting Service, a type of light bulb
Generalized least squares, in statistics
Global location sensor
Glutaminase, a gene and enzyme
Gray leaf spot, a fungal plant disease
Guided local search, a search algorithm
O... |
https://en.wikipedia.org/wiki/Pregeometry%20%28model%20theory%29 | Pregeometry, and in full combinatorial pregeometry, are essentially synonyms for "matroid". They were introduced by Gian-Carlo Rota with the intention of providing a less "ineffably cacophonous" alternative term. Also, the term combinatorial geometry, sometimes abbreviated to geometry, was intended to replace "simple ... |
https://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing%20operator | In mathematics, the Gauss–Kuzmin–Wirsing operator is the transfer operator of the Gauss map that takes a positive number to the fractional part of its reciprocal. (This is not the same as the Gauss map in differential geometry.) It is named after Carl Gauss, Rodion Kuzmin, and Eduard Wirsing. It occurs in the study of ... |
https://en.wikipedia.org/wiki/Klein%20transformation | In quantum field theory, the Klein transformation is a redefinition of the fields to amend the spin-statistics theorem.
Bose–Einstein
Suppose φ and χ are fields such that, if x and y are spacelike-separated points and i and j represent the spinor/tensor indices,
Also suppose χ is invariant under the Z2 parity (nothin... |
https://en.wikipedia.org/wiki/Integrally%20closed | In mathematics, more specifically in abstract algebra, the concept of integrally closed has three meanings:
A commutative ring contained in a commutative ring is said to be integrally closed in if is equal to the integral closure of in .
An integral domain is said to be integrally closed if it is equal to its i... |
https://en.wikipedia.org/wiki/Further%20Mathematics | Further Mathematics is the title given to a number of advanced secondary mathematics courses. The term "Higher and Further Mathematics", and the term "Advanced Level Mathematics", may also refer to any of several advanced mathematics courses at many institutions.
In the United Kingdom, Further Mathematics describes a ... |
https://en.wikipedia.org/wiki/Kleinian%20group | In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space . The latter, identifiable with , is the quotient group of the 2 by 2 complex matrices of determinant 1 by their center, which consists of the identity matrix and its product by . has a natur... |
https://en.wikipedia.org/wiki/Kazhdan%27s%20property%20%28T%29 | In mathematics, a locally compact topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology. Informally, this means that if G acts unitarily on a Hilbert space and has "almost invariant vectors", then it has a nonzero invariant vector. Th... |
https://en.wikipedia.org/wiki/4-manifold | In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds which admit no smooth structure,... |
https://en.wikipedia.org/wiki/Quaternion%20%28disambiguation%29 |
In mathematics
The quaternions form a number system that extends the complex numbers.
Quaternion rotation
Quaternion group, a non-abelian group of order 8
Symbols
Imperial quaternions (heraldry of the Holy Roman Empire)
Quaternion Eagle
Military uses
A group of four soldiers in the Roman legion
A fireteam
O... |
https://en.wikipedia.org/wiki/Binary%20data | Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra.
Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in comp... |
https://en.wikipedia.org/wiki/Lambert%20series | In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form
It can be resumed formally by expanding the denominator:
where the coefficients of the new series are given by the Dirichlet convolution of an with the constant function 1(n) = 1:
This series may be inverted by means of ... |
https://en.wikipedia.org/wiki/Band%20sum | In geometric topology, a band sum of two n-dimensional knots K1 and K2 along an (n + 1)-dimensional 1-handle h called a band is an n-dimensional knot K such that:
There is an (n + 1)-dimensional 1-handle h connected to (K1, K2) embedded in Sn+2.
There are points and such that is attached to along .
K is the n-... |
https://en.wikipedia.org/wiki/Noncentral%20F-distribution | In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) F-distribution. It describes the distribution of the quotient (X/n1)/(Y/n2), where the numerator X has a noncentral chi-squared distribution with n1 degrees... |
https://en.wikipedia.org/wiki/Longdean%20School | Longdean School is a secondary school and sixth form with academy status, located in the southeast of Hemel Hempstead, Hertfordshire. The academy specialises in Maths and Computing.
History
Grammar school
Originally called Apsley Grammar School, it began as a state grammar school in Hemel Hempstead. It was founded i... |
https://en.wikipedia.org/wiki/Hellmuth%20Kneser | Hellmuth Kneser (16 April 1898 – 23 August 1973) was a Baltic German mathematician, who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His proof originated the concept of normal surface, a fundamental corner... |
https://en.wikipedia.org/wiki/Oberwolfach%20Research%20Institute%20for%20Mathematics | The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944.
It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research.
The ... |
https://en.wikipedia.org/wiki/Wilhelm%20S%C3%BCss | Wilhelm Süss (7 March 1895 – 21 May 1958) was a German mathematician. He was founder and first director of the Oberwolfach Research Institute for Mathematics.
Biography
He was born in Frankfurt, Germany, and died in Freiburg im Breisgau, Germany.
Süss earned a Ph.D. degree in 1922 from Goethe University Frankfurt, fo... |
https://en.wikipedia.org/wiki/Recurring | Recurring means occurring repeatedly and can refer to several different things:
Mathematics and finance
Recurring expense, an ongoing (continual) expenditure
Repeating decimal, or recurring decimal, a real number in the decimal numeral system in which a sequence of digits repeats infinitely
Curiously recurring templa... |
https://en.wikipedia.org/wiki/Polar%20decomposition | In mathematics, the polar decomposition of a square real or complex matrix is a factorization of the form , where is a unitary matrix and is a positive semi-definite Hermitian matrix ( is an orthogonal matrix and is a positive semi-definite symmetric matrix in the real case), both square and of the same size.
I... |
https://en.wikipedia.org/wiki/Alfred%20Clebsch | Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe. His collaboration with Paul ... |
https://en.wikipedia.org/wiki/Sha%20Tin%20Government%20Secondary%20School | {
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Sha Tin Government Secondary School (STGSS; 沙田官立中學) is located in Sha Tin, Hong Kong. It was founded ... |
https://en.wikipedia.org/wiki/R%C3%B3bert%20Szelepcs%C3%A9nyi | Róbert Szelepcsényi (; born 19 August 1966, Žilina) is a Slovak computer scientist of Hungarian descent and a member of the Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava.
His results on the closure of non-deterministic space under complement, independently obtained in 1987 also b... |
https://en.wikipedia.org/wiki/Cole%20Prize | The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who served the So... |
https://en.wikipedia.org/wiki/Highly%20cototient%20number | In number theory, a branch of mathematics, a highly cototient number is a positive integer which is above 1 and has more solutions to the equation
than any other integer below and above 1. Here, is Euler's totient function. There are infinitely many solutions to the equation for
= 1
so this value is excluded ... |
https://en.wikipedia.org/wiki/Discrete%20symmetry | In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type o... |
https://en.wikipedia.org/wiki/Rooted%20graph | In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots.
Rooted graphs may also be known (depending... |
https://en.wikipedia.org/wiki/Additive%20polynomial | In mathematics, the additive polynomials are an important topic in classical algebraic number theory.
Definition
Let k be a field of prime characteristic p. A polynomial P(x) with coefficients in k is called an additive polynomial, or a Frobenius polynomial, if
as polynomials in a and b. It is equivalent to assume ... |
https://en.wikipedia.org/wiki/Functional%20%28mathematics%29 | In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author).
In linear algebra, it is synonymous with a linear form, which is a linear mapping from a vector space into its field of scalars (that is, it is an element of t... |
https://en.wikipedia.org/wiki/Landscape%20engineering | Landscape engineering is the application of mathematics and science to shape land and waterscapes. It can also be described as green engineering, but the design professionals best known for landscape engineering are landscape architects. Landscape engineering is the interdisciplinary application of engineering and othe... |
https://en.wikipedia.org/wiki/Hans%20Zassenhaus | Hans Julius Zassenhaus (28 May 1912 – 21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.
Biography
He was born in Koblenz in 1912.
His father was a historian and advocate for Reverence for Life as expressed by Albert Schweitzer. Hans ha... |
https://en.wikipedia.org/wiki/Edouard%20Zeckendorf | Edouard Zeckendorf (2 May 1901 – 16 May 1983) was a Belgian doctor, army officer and amateur mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem, though he published over 20 papers, mostly in number theory.
Zeckendorf was born in Liège in... |
https://en.wikipedia.org/wiki/Zeckendorf%27s%20theorem | In mathematics, Zeckendorf's theorem, named after Belgian amateur mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers.
Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in... |
https://en.wikipedia.org/wiki/Covering%20group | In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H h... |
https://en.wikipedia.org/wiki/Orthogonal%20transformation | In linear algebra, an orthogonal transformation is a linear transformation T : V → V on a real inner product space V, that preserves the inner product. That is, for each pair of elements of V, we have
Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transfo... |
https://en.wikipedia.org/wiki/Low-probability-of-intercept%20radar | A low-probability-of-intercept radar (LPIR) is a radar employing measures to avoid detection by passive radar detection equipment (such as a radar warning receiver (RWR), or electronic support receiver) while it is searching for a target or engaged in target tracking. This characteristic is desirable in a radar because... |
https://en.wikipedia.org/wiki/Character%20group | In mathematics, a character group is the group of representations of a group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory. Whenever a group is represented b... |
https://en.wikipedia.org/wiki/Mamadou%20Diallo%20%28footballer%2C%20born%201982%29 | Mamadou Diallo (born 17 April 1982) is a Malian former professional footballer who played as a striker. He spent most of his professional career in France.
Career statistics
Scores and results list Mali's goal tally first, score column indicates score after each Diallo goal.
References
External links
Mamadou ... |
https://en.wikipedia.org/wiki/Long%20tail | In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is o... |
https://en.wikipedia.org/wiki/Max%20Planck%20Institute%20for%20Mathematics | The Max Planck Institute for Mathematics (, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck
and forms part of the Max Planck Society (Max-Planck-Gesellschaft), an association of 84 institutes engaging in fundamental research in the arts and th... |
https://en.wikipedia.org/wiki/Table%20of%20Lie%20groups | This article gives a table of some common Lie groups and their associated Lie algebras.
The following are noted: the topological properties of the group (dimension; connectedness; compactness; the nature of the fundamental group; and whether or not they are simply connected) as well as on their algebraic properties (a... |
https://en.wikipedia.org/wiki/Gaussian%20noise | In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed.... |
https://en.wikipedia.org/wiki/System%20of%20imprimitivity | The concept of system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the basis for his theory of induced unitary representations of locally compact groups.
The simplest case, and the context ... |
https://en.wikipedia.org/wiki/Gilbert%20Walker%20%28physicist%29 | Sir Gilbert Thomas Walker (14 June 1868 – 4 November 1958) was an English physicist and statistician of the 20th century. Walker studied mathematics and applied it to a variety of fields including aerodynamics, electromagnetism and the analysis of time-series data before taking up a teaching position at the University... |
https://en.wikipedia.org/wiki/Transactions%20of%20the%20American%20Mathematical%20Society | The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages.
See also
Bulletin of the American Mathematical Society
Jou... |
https://en.wikipedia.org/wiki/Separated | Separated can refer to:
Marital separation of spouses
Legal separation of spouses
"Separated" (song), song by Avant
Separated sets, a concept in mathematical topology
Separated space, a synonym for Hausdorff space, a concept in mathematical topology
Separated morphism, a concept in algebraic geometry analogous to that... |
https://en.wikipedia.org/wiki/Loop%20group | In mathematics, a loop group is a group of loops in a topological group G with multiplication defined pointwise.
Definition
In its most general form a loop group is a group of continuous mappings from a manifold to a topological group .
More specifically, let , the circle in the complex plane, and let denote the sp... |
https://en.wikipedia.org/wiki/Robert%20Sempill | Robert Sempill (the elder) (c. 1530–1595), in all probability a cadet of illegitimate birth of the noble house of Sempill or Semple, was a Scottish ballad-writer and satirist.
Very little is known of Sempill's life. He was probably a soldier, and must have held some office at the Scottish court, as his name appears in... |
https://en.wikipedia.org/wiki/Reflection%20symmetry | In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure ... |
https://en.wikipedia.org/wiki/Stiefel%20manifold | In mathematics, the Stiefel manifold is the set of all orthonormal k-frames in That is, it is the set of ordered orthonormal k-tuples of vectors in It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold of orthonormal k-frames in and the quaternionic Stiefel mani... |
https://en.wikipedia.org/wiki/Mu%20Alpha%20Theta | Mu Alpha Theta () is the United States mathematics honor society for high school and two-year college students. In June 2015, it served over 108,000 student members in over 2,200 chapters in the United States and in 20 foreign countries. Its main goals are to inspire keen interest in mathematics, develop strong scholar... |
https://en.wikipedia.org/wiki/Shemiran | {
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https://en.wikipedia.org/wiki/PGL2 | PGL2 may refer to
SDHAF2, a gene on chromosome 11 in humans
for the group in mathematics, see projective linear group and modular group |
https://en.wikipedia.org/wiki/Discrete%20Laplace%20operator | In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matr... |
https://en.wikipedia.org/wiki/Dual%20lattice | In the theory of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a lattice is the reciprocal of the geometry of , a perspective which underlies many of its uses.
Dual lattices have many applications inside of lattice theor... |
https://en.wikipedia.org/wiki/Bicubic%20interpolation | In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid. The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtaine... |
https://en.wikipedia.org/wiki/Levi%20graph | In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between... |
https://en.wikipedia.org/wiki/Closed%20monoidal%20category | In mathematics, especially in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in such a way that the structures are compatible.
A classic example is the category of sets, Set, where the monoidal product of sets and is th... |
https://en.wikipedia.org/wiki/Closed%20category | In category theory, a branch of mathematics, a closed category is a special kind of category.
In a locally small category, the external hom (x, y) maps a pair of objects to a set of morphisms. So in the category of sets, this is an object of the category itself. In the same vein, in a closed category, the (object of) ... |
https://en.wikipedia.org/wiki/Overlap | Overlap may refer to:
In set theory, an overlap of elements shared between sets is called an intersection, as in a Venn diagram.
In music theory, overlap is a synonym for reinterpretation of a chord at the boundary of two musical phrases
Overlap (railway signalling), the length of track beyond a stop signal that is... |
https://en.wikipedia.org/wiki/Walk-to-strikeout%20ratio | In baseball statistics, walk-to-strikeout ratio (BB/K) is a measure of a hitter's plate discipline and knowledge of the strike zone. Generally, a hitter with a good walk-to-strikeout ratio must exhibit enough patience at the plate to refrain from swinging at bad pitches and take a base on balls, but he must also have t... |
https://en.wikipedia.org/wiki/Strikeout-to-walk%20ratio | In baseball statistics, strikeout-to-walk ratio (K/BB) is a measure of a pitcher's ability to control pitches, calculated as strikeouts divided by bases on balls.
A hit by pitch is not counted statistically as a walk, and therefore not counted in the strikeout-to-walk ratio.
The inverse of this calculation is the rel... |
https://en.wikipedia.org/wiki/Probability%20function | Probability function may refer to:
Probability distribution
Probability axioms, which define a probability function
Probability measure, a real-valued function on a probability space
See also
Probability distribution function (disambiguation) |
https://en.wikipedia.org/wiki/Generic%20polynomial | In mathematics, a generic polynomial refers usually to a polynomial whose coefficients are indeterminates. For example, if , , and are indeterminates, the generic polynomial of degree two in is
However in Galois theory, a branch of algebra, and in this article, the term generic polynomial has a different, although ... |
https://en.wikipedia.org/wiki/Chen%27s%20theorem | In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes).
It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes.
History
The theorem w... |
https://en.wikipedia.org/wiki/Christoffel%20symbols | In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In differential geometry, an affine co... |
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"properties": { "marker-symbol": "monument", "title": "Ahmedabad" },
... |
https://en.wikipedia.org/wiki/Morley%20rank | In mathematical logic, Morley rank, introduced by , is a means of measuring the size of a subset of a model of a theory, generalizing the notion of dimension in algebraic geometry.
Definition
Fix a theory T with a model M. The Morley rank of a formula φ defining a definable (with parameters) subset S of M
is an ord... |
https://en.wikipedia.org/wiki/%C4%BDudov%C3%ADt%20La%C4%8Dn%C3%BD | Ľudovít Lačný (December 8, 1926 – December 25, 2019) was a Slovak chess problem composer and judge.
Lačný was born in Banská Štiavnica and studied mathematics, working as a teacher, and as a computer programmer.
In 1956 Lačný was appointed an International Judge of Chess Compositions and in 2005 was awarded the Inter... |
https://en.wikipedia.org/wiki/Pandiagonal%20magic%20cube | In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need t... |
https://en.wikipedia.org/wiki/Ultraparallel%20theorem | In hyperbolic geometry, two lines are said to be ultraparallel if they do not intersect and are not limiting parallel.
The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines).
Hilbert's construction
... |
https://en.wikipedia.org/wiki/Midpoint%20method | In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation,
The explicit midpoint method is given by the formula
the implicit midpoint method by
for Here, is the step size — a small positive number, and is the computed approx... |
https://en.wikipedia.org/wiki/Times%20on%20base | In baseball statistics, the term times on base (TOB), is the cumulative total number of times a batter has reached base as a result of a hit, base on balls, or hit by pitch. This statistic does not include times reaching base by way of an error, uncaught third strike, fielder's obstruction or a fielder's choice, making... |
https://en.wikipedia.org/wiki/AA%20postulate | In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent.
The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next ang... |
https://en.wikipedia.org/wiki/Radon%27s%20theorem | In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex hulls is called a Radon point of the set.For example, in the case d = 2, any set of four po... |
https://en.wikipedia.org/wiki/CCR%20and%20CAR%20algebras | In mathematics and physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from the quantum mechanical study of bosons and fermions respectively. They play a prominent role in quantum statistical mechanics and quantum field theory.
CCR and CAR as ... |
https://en.wikipedia.org/wiki/The%20Compendious%20Book%20on%20Calculation%20by%20Completion%20and%20Balancing | The Compendious Book on Calculation by Completion and Balancing (, ; ), also known as al-Jabr (Arabic: ), is an Arabic mathematical treatise on algebra written in Baghdad around 820 CE by the Persian polymath Muḥammad ibn Mūsā al-Khwārizmī. It was a landmark work in the history of mathematics, establishing algebra as a... |
https://en.wikipedia.org/wiki/Don%20Zagier | Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a... |
https://en.wikipedia.org/wiki/Helly%27s%20theorem | Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative proofs by and had already appeared. Helly's theorem gave rise to the notion of a Helly family.
Statement
Let be a finit... |
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