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https://en.wikipedia.org/wiki/Greg%20Lindsay | Gregory John Lindsay AO (b. 1949) was until 2018 the Executive Director of the Australian think tank the Centre for Independent Studies (CIS), which he founded in 1976 when a young mathematics teacher in the western suburbs of Sydney. CIS has become influential in Australia and New Zealand.
Biography
Lindsay initially... |
https://en.wikipedia.org/wiki/Bernard%20Picinbono | Bernard Picinbono is a French scientist born in 1933 in Algiers. His scientific work focuses on statistics and its applications in optics, electronics, signal processing and automation.
Biography
He did his secondary and higher education in Algiers and then in Paris where he obtained the agrégation de sciences physiq... |
https://en.wikipedia.org/wiki/Handle%20decompositions%20of%203-manifolds | In mathematics, a handle decomposition of a 3-manifold allows simplification of the original 3-manifold into pieces which are easier to study.
Heegaard splittings
An important method used to decompose into handlebodies is the Heegaard splitting, which gives us a decomposition in two handlebodies of equal genus.
Exam... |
https://en.wikipedia.org/wiki/Temperley%E2%80%93Lieb%20algebra | In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb. It is also related to integrable models, knot theory and the braid group, quantum groups and subfactors of von Neumann algebras.
Structure
Generators and ... |
https://en.wikipedia.org/wiki/Yves%20Laszlo | Yves Laszlo () is a French mathematician working in the University of Paris-Sud. He specializes in algebraic geometry.
Laszlo obtained his Ph.D. in 1988 from the University of Paris-Sud under the supervision of Arnaud Beauville.
He started the Fondation Mathématique Jacques Hadamard in 2011, and directed it until 201... |
https://en.wikipedia.org/wiki/Algebraic%20holography | Algebraic holography, also sometimes called Rehren duality, is an attempt to understand the holographic principle of quantum gravity within the framework of algebraic quantum field theory, due to Karl-Henning Rehren. It is sometimes described as an alternative formulation of the AdS/CFT correspondence of string theory,... |
https://en.wikipedia.org/wiki/Quaternionic%20projective%20space | In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions Quaternionic projective space of dimension n is usually denoted by
and is a closed manifold of (real) dimension 4n. It is a hom... |
https://en.wikipedia.org/wiki/Variation | Variation or Variations may refer to:
Science and mathematics
Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon
Genetic variation, the difference in DNA among individuals or the differences between populations
Human genetic variation, genetic dif... |
https://en.wikipedia.org/wiki/Pair%20of%20pants%20%28mathematics%29 | In mathematics, a pair of pants is a surface which is homeomorphic to the three-holed sphere. The name comes from considering one of the removed disks as the waist and the two others as the cuffs of a pair of pants.
Pairs of pants are used as building blocks for compact surfaces in various theories. Two important appl... |
https://en.wikipedia.org/wiki/Mid-range | In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the arithmetic mean of the maximum and minimum values of the data set:
The mid-range is closely related to the range, a measure of statistical dispersion defined as the difference between maximum and minimum values.
Th... |
https://en.wikipedia.org/wiki/Elbert%20Frank%20Cox | Elbert Frank Cox (5 December 1895 – 28 November 1969) was an American mathematician. He was the first Black person in history to receive a PhD in mathematics, which he earned at Cornell University in 1925.
Early life
Cox was born in Evansville, Indiana to Johnson D. Cox, a Kentucky-born teacher active in the church,... |
https://en.wikipedia.org/wiki/Gap%20theorem | See also Gap theorem (disambiguation) for other gap theorems in mathematics.
In computational complexity theory, the Gap Theorem, also known as the Borodin–Trakhtenbrot Gap Theorem, is a major theorem about the complexity of computable functions.
It essentially states that there are arbitrarily large computable gaps ... |
https://en.wikipedia.org/wiki/Algebra%20i%20Logika | Algebra i Logika (English: Algebra and Logic) is a peer-reviewed Russian mathematical journal founded in 1962 by Anatoly Ivanovich Malcev, published by the Siberian Fund for Algebra and Logic at Novosibirsk State University. An English translation of the journal is published by Springer-Verlag as Algebra and Logic sinc... |
https://en.wikipedia.org/wiki/G.%20Mike%20Reed | George Michael ("Mike") Reed is an American computer scientist. He has contributed to theoretical computer science in general and CSP in particular.
Mike Reed has a doctorate in pure mathematics from Auburn University, United States, and a doctorate in computation from Oxford University, England. He has an interest in... |
https://en.wikipedia.org/wiki/%CE%98%20%28set%20theory%29 | In set theory, Θ (pronounced like the letter theta) is the least nonzero ordinal α such that there is no surjection from the reals onto α.
If the axiom of choice (AC) holds (or even if the reals can be wellordered), then Θ is simply , the cardinal successor of the cardinality of the continuum. However, Θ is often stu... |
https://en.wikipedia.org/wiki/AD%2B | In set theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy. The axiom, which is to be understood in the context of ZF plus DC (the axiom of dependent choice for real numbers), states two things:
Every set of reals is ∞-Borel.
For any ordinal λ less than Θ, any subset A of ωω, and any ... |
https://en.wikipedia.org/wiki/Classifying%20space%20for%20U%28n%29 | In mathematics, the classifying space for the unitary group U(n) is a space BU(n) together with a universal bundle EU(n) such that any hermitian bundle on a paracompact space X is the pull-back of EU(n) by a map X → BU(n) unique up to homotopy.
This space with its universal fibration may be constructed as either
the ... |
https://en.wikipedia.org/wiki/HNN%20extension | In mathematics, the HNN extension is an important construction of combinatorial group theory.
Introduced in a 1949 paper Embedding Theorems for Groups by Graham Higman, Bernhard Neumann, and Hanna Neumann, it embeds a given group G into another group G' , in such a way that two given isomorphic subgroups of G are conj... |
https://en.wikipedia.org/wiki/Delta%20method | In statistics, the delta method is a result concerning the approximate probability distribution for a function of an asymptotically normal statistical estimator from knowledge of the limiting variance of that estimator.
History
The delta method was derived from propagation of error, and the idea behind was known in t... |
https://en.wikipedia.org/wiki/Link-state%20advertisement | The link-state advertisement (LSA) is a basic communication means of the OSPF routing protocol for the Internet Protocol (IP). It communicates the router's local routing topology to all other local routers in the same OSPF area. OSPF is designed for scalability, so some LSAs are not flooded out on all interfaces, but o... |
https://en.wikipedia.org/wiki/Cayley%E2%80%93Menger%20determinant | In linear algebra, geometry, and trigonometry, the Cayley–Menger determinant is a formula for the content, i.e. the higher-dimensional volume, of a -dimensional simplex in terms of the squares of all of the distances between pairs of its vertices. The determinant is named after Arthur Cayley and Karl Menger.
The pair... |
https://en.wikipedia.org/wiki/Theodosius%20of%20Bithynia | Theodosius of Bithynia (; 2nd–1st century BC) was a Hellenistic astronomer and mathematician from Bithynia who wrote the Spherics, a treatise about spherical geometry, as well as several other books on mathematics and astronomy, of which two survive, On Habitations and On Days and Nights.
Life
Little is known about Th... |
https://en.wikipedia.org/wiki/Traffic%20flow | In mathematics and transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport netw... |
https://en.wikipedia.org/wiki/Isotonic%20regression | In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible.
Applications
Isotonic regression h... |
https://en.wikipedia.org/wiki/Cauchy%27s%20theorem%20%28group%20theory%29 | In mathematics, specifically group theory, Cauchy's theorem states that if is a finite group and is a prime number dividing the order of (the number of elements in ), then contains an element of order . That is, there is in such that is the smallest positive integer with = , where is the identity element of . ... |
https://en.wikipedia.org/wiki/Dusa%20McDuff | Dusa McDuff FRS CorrFRSE (born 18 October 1945) is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at... |
https://en.wikipedia.org/wiki/Calculus%20on%20Manifolds%20%28book%29 | Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates.
Description
Calculus on Manifolds is a brief monograph on the ... |
https://en.wikipedia.org/wiki/Martingale%20central%20limit%20theorem | In probability theory, the central limit theorem says that, under certain conditions, the sum of many independent identically-distributed random variables, when scaled appropriately, converges in distribution to a standard normal distribution. The martingale central limit theorem generalizes this result for random var... |
https://en.wikipedia.org/wiki/Holomorph%20%28mathematics%29 | In mathematics, especially in the area of algebra known as group theory, the holomorph of a group is a group that simultaneously contains (copies of) the group and its automorphism group. The holomorph provides interesting examples of groups, and allows one to treat group elements and group automorphisms in a uniform ... |
https://en.wikipedia.org/wiki/Holomorph | Holomorph may refer to:
Mathematics
Holomorph (mathematics), a group which simultaneously contains (copies of) a group and its automorphism group
Holomorphic functions, the central object of study of complex analysis
Biology
Teleomorph, anamorph and holomorph, applying to portions of the life cycles of fungi in th... |
https://en.wikipedia.org/wiki/Exist | Exist may refer to:
Existence
eXist, an open source database management system built on XML
Existential quantification, in logic and mathematics (symbolized by ∃, read "exists")
Energetic X-ray Survey Telescope, a proposed hard X-ray imaging all-sky deep survey mission
Exist (album), a studio album by Exo
Exist... |
https://en.wikipedia.org/wiki/Spin%20structure | In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essent... |
https://en.wikipedia.org/wiki/Square%20planar%20molecular%20geometry | The square planar molecular geometry in chemistry describes the stereochemistry (spatial arrangement of atoms) that is adopted by certain chemical compounds. As the name suggests, molecules of this geometry have their atoms positioned at the corners.
Examples
Numerous compounds adopt this geometry, examples being espe... |
https://en.wikipedia.org/wiki/Trend%20line | Trend line can refer to:
A linear regression in statistics
The result of trend estimation in statistics
Trend line (technical analysis), a tool in technical analysis |
https://en.wikipedia.org/wiki/Alexander%27s%20trick | Alexander's trick, also known as the Alexander trick, is a basic result in geometric topology, named after J. W. Alexander.
Statement
Two homeomorphisms of the n-dimensional ball which agree on the boundary sphere are isotopic.
More generally, two homeomorphisms of Dn that are isotopic on the boundary are isotopic... |
https://en.wikipedia.org/wiki/Algebraic%20semantics%20%28mathematical%20logic%29 | In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other ... |
https://en.wikipedia.org/wiki/Unifying%20Theories%20of%20Programming | Unifying Theories of Programming (UTP) in computer science deals with program semantics. It shows how denotational semantics, operational semantics and algebraic semantics can be combined in a unified framework for the formal specification, design and implementation of programs and computer systems.
The book of this t... |
https://en.wikipedia.org/wiki/He%20Jifeng | He Jifeng (, born August 1943) is a Chinese computer scientist.
He Jifeng graduated from the mathematics department of Fudan University in 1965. From 1965 to 1985, he was an instructor at East China Normal University. During 1980–81, he was a visiting scholar at Stanford University and the University of San Francisco... |
https://en.wikipedia.org/wiki/List%20of%20uniform%20polyhedra | In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotatio... |
https://en.wikipedia.org/wiki/Riemannian%20submersion | In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projection on tangent spaces.
Formal definition
Let (M, g) and (N, h) be two Riemannian manifolds and a (surjective) submersio... |
https://en.wikipedia.org/wiki/Busemann%20function | In geometric topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds (simply connected complete Riemannian manifolds of nonpositive curvature). They are named after Herbert Busemann, who introduced them; he gave an extensive treatment ... |
https://en.wikipedia.org/wiki/Conjugate%20points | In differential geometry, conjugate points or focal points are, roughly, points that can almost be joined by a 1-parameter family of geodesics. For example, on a sphere, the north-pole and south-pole are connected by any meridian. Another viewpoint is that conjugate points tell when the geodesics fail to be length-mini... |
https://en.wikipedia.org/wiki/Hadamard%20space | In geometry, an Hadamard space, named after Jacques Hadamard, is a non-linear generalization of a Hilbert space. In the literature they are also equivalently defined as complete CAT(0) spaces.
A Hadamard space is defined to be a nonempty complete metric space such that, given any points and there exists a point suc... |
https://en.wikipedia.org/wiki/Five-dimensional%20space | A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. Whether or not the univ... |
https://en.wikipedia.org/wiki/Tetrahemihexahedron | In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges, and 6 vertices. Its vertex figure is a crossed quadrilateral. Its Coxeter–Dynkin diagram is (although this is a double covering of the tetrahemihexahedron).
The ... |
https://en.wikipedia.org/wiki/Whitney%20disk | In mathematics, given two submanifolds A and B of a manifold X intersecting in two points p and q, a Whitney disc is a mapping from the two-dimensional disc D, with two marked points, to X, such that the two marked points go to p and q, one boundary arc of D goes to A and the other to B.
Their existence and embeddedne... |
https://en.wikipedia.org/wiki/Leray%20cover | In mathematics, a Leray cover(ing) is a cover of a topological space which allows for easy calculation of its cohomology. Such covers are named after Jean Leray.
Sheaf cohomology measures the extent to which a locally exact sequence on a fixed topological space, for instance the de Rham sequence, fails to be globall... |
https://en.wikipedia.org/wiki/Ambient%20space%20%28mathematics%29 | In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object along with the object itself. For example, a 1-dimensional line may be studied in isolation —in which case the ambient space of is , or it may be studied as an object embedded in 2-dimensional Euclide... |
https://en.wikipedia.org/wiki/Multi-armed%20bandit | In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are o... |
https://en.wikipedia.org/wiki/Caleb%20Gattegno | Caleb Gattegno (1911–1988) was an Egyptian educator, psychologist, and mathematician. He is considered one of the most influential and prolific mathematics educators of the twentieth century. He is best known for introducing new approaches to teaching and learning mathematics (Visible & Tangible Math), foreign language... |
https://en.wikipedia.org/wiki/IMSL%20Numerical%20Libraries | IMSL (International Mathematics and Statistics Library) is a commercial collection of software libraries of numerical analysis functionality that are implemented in the computer programming languages C, Java, C#.NET, and Fortran. A Python interface is also available.
The IMSL Libraries were developed by Visual Numeric... |
https://en.wikipedia.org/wiki/Noncentral%20chi%20distribution | In probability theory and statistics, the noncentral chi distribution is a noncentral generalization of the chi distribution. It is also known as the generalized Rayleigh distribution.
Definition
If are k independent, normally distributed random variables with means and variances , then the statistic
is distributed... |
https://en.wikipedia.org/wiki/Affine%20involution | In Euclidean geometry, of special interest are involutions which are linear or affine transformations over the Euclidean space Rn. Such involutions are easy to characterize and they can be described geometrically.
Linear involutions
To give a linear involution is the same as giving an involutory matrix, a square matri... |
https://en.wikipedia.org/wiki/Triangular%20prism | In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and sq... |
https://en.wikipedia.org/wiki/Pentagonal%20prism | In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices.
As a semiregular (or uniform) polyhedron
If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third ... |
https://en.wikipedia.org/wiki/Hexagonal%20prism | In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices.
Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of the... |
https://en.wikipedia.org/wiki/Square%20antiprism | In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube.
If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron.
A nonuniform D4-symmetric variant i... |
https://en.wikipedia.org/wiki/Pentagonal%20antiprism | In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of two pentagons joined to each other by a ring of ten triangles for a total of twelve faces. Hence, it is a non-regular dodecahedron.
Geomet... |
https://en.wikipedia.org/wiki/Hexagonal%20antiprism | In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals.
In... |
https://en.wikipedia.org/wiki/Great%20dodecahedron | In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of . It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting each other making a pentagrammic path, with five pentagons meetin... |
https://en.wikipedia.org/wiki/Pentagrammic%20prism | In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.
It is a special case of a right prism with a pentagram as base, which in general has rectangular non-base faces. Topologically it is the same as a con... |
https://en.wikipedia.org/wiki/Variational%20methods%20in%20general%20relativity | Variational methods in general relativity refers to various mathematical techniques that employ the use of variational calculus in Einstein's theory of general relativity. The most commonly used tools are Lagrangians and Hamiltonians and are used to derive the Einstein field equations.
Lagrangian methods
The equation... |
https://en.wikipedia.org/wiki/Geometry%20%26%20Topology | Geometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical Sciences Publishers, a nonprofit academic publishing organisation.
It was foun... |
https://en.wikipedia.org/wiki/Compensation%20of%20employees | Compensation of employees (CE) is a statistical term used in national accounts, balance of payments statistics and sometimes in corporate accounts as well. It refers basically to the total gross (pre-tax) wages paid by employers to employees for work done in an accounting period, such as a quarter or a year.
However,... |
https://en.wikipedia.org/wiki/Hexagonal%20tiling | In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a truncated triangular tiling).
English mathematician John Conway called it a hextille.
The internal angle of the hexagon is 1... |
https://en.wikipedia.org/wiki/Square%20tiling | In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex. Conway called it a quadrille.
The internal angle of the square is 90 degrees so four squares at a point make a full 360 degrees. It is... |
https://en.wikipedia.org/wiki/Triangular%20tiling | In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degre... |
https://en.wikipedia.org/wiki/Truncated%20hexagonal%20tiling | In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each vertex.
As the name implies this tiling is constructed by a truncation operation applies to a hexagonal tiling, leaving dodecagons in place of the original hexagons, an... |
https://en.wikipedia.org/wiki/Truncated%20trihexagonal%20tiling | In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane. There are one square, one hexagon, and one dodecagon on each vertex. It has Schläfli symbol of tr{3,6}.
Names
Uniform colorings
There is only one uniform coloring of a truncated trihexagonal tiling, with faces... |
https://en.wikipedia.org/wiki/Truncated%20square%20tiling | In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex. This is the only edge-to-edge tiling by regular convex polygons which contains an octagon. It has Schläfli symbol of t{4,4}.
Conway calls it a truncated quadrille... |
https://en.wikipedia.org/wiki/Oblique%20reflection | In Euclidean geometry, oblique reflections generalize ordinary reflections by not requiring that reflection be done using perpendiculars. If two points are oblique reflections of each other, they will still stay so under affine transformations.
Consider a plane P in the three-dimensional Euclidean space. The usual re... |
https://en.wikipedia.org/wiki/Rhombitrihexagonal%20tiling | In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of rr{3,6}.
John Conway calls it a rhombihexadeltille. It can be considered a cantellated by Norman Johnson's terminology or an expanded... |
https://en.wikipedia.org/wiki/Trihexagonal%20tiling | In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and... |
https://en.wikipedia.org/wiki/Majorization | In mathematics, majorization is a preorder on vectors of real numbers. Let denote the -th largest element of the vector . Given , we say that weakly majorizes (or dominates) from below (or equivalently, we say that is weakly majorized (or dominated) by from below) denoted as if for all . If in addition , we say ... |
https://en.wikipedia.org/wiki/Snub%20trihexagonal%20tiling | In geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon on each vertex. It has Schläfli symbol sr{3,6}. The snub tetrahexagonal tiling is a related hyperbolic tiling with Schläfli symbol sr{4,6}.
Conway calls it a snu... |
https://en.wikipedia.org/wiki/Elongated%20triangular%20tiling | In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated by rows of squares, and given Schläfli symbol {3,6}:e.
Conway calls it a isosnub quadrille.
There are 3 regular and 8 semi... |
https://en.wikipedia.org/wiki/Snub%20square%20tiling | In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. Its Schläfli symbol is s{4,4}.
Conway calls it a snub quadrille, constructed by a snub operation applied to a square tiling (quadrille).
There are 3 regular and 8 semiregular ... |
https://en.wikipedia.org/wiki/Linearized%20gravity | In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized g... |
https://en.wikipedia.org/wiki/Fusion%20rules | In mathematics and theoretical physics, fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations. The term is often used in the context of two-dimensional conformal field theory where the relevant group is gene... |
https://en.wikipedia.org/wiki/Conformal%20family | In theoretical physics, a conformal family is an irreducible representation of the Virasoro algebra. In most cases, it is uniquely determined by its primary field or the highest weight vector. The family contains all of its descendant fields.
References
See also
Conformal field theory
Conformal field theory |
https://en.wikipedia.org/wiki/Lorentz%20Eichstadt | Lorentz Eichstadt (10 August 1596 – 8 June 1660) was a German mathematician and astronomer. He was a doctor of medicine in Szczecin in Pomerania and taught medicine and mathematics in Danzig.
The lunar crater Eichstadt is named after him.
References
External links
Lunar Republic: Craters. Retrieved October 8, 2005.... |
https://en.wikipedia.org/wiki/Equipotential | In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential ... |
https://en.wikipedia.org/wiki/Rhombille%20tiling | In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angl... |
https://en.wikipedia.org/wiki/Morse%20homology | In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be topologically invariant, and is in fact isomorphic to singular homology. Mo... |
https://en.wikipedia.org/wiki/Cocycle | In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential equation on a closed manifold). They are likewise used in group cohomology. In autonomous dynamical systems, cocycles are used to describe particular kinds of map,... |
https://en.wikipedia.org/wiki/Pohlmeyer%20charge | In theoretical physics Pohlmeyer charge, named for Klaus Pohlmeyer, is a conserved charge invariant under the Virasoro algebra or its generalization. It can be obtained by expanding the holonomies (generating functions)
with respect to the constant matrices T. The gauge field is defined as a combination of and its c... |
https://en.wikipedia.org/wiki/Lottery%20mathematics | Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics, particularly the twelvefold way and combinations without replacement.
Choosing 6 from 49
In a typical 6/49 game, each player chooses six distinct numbers from a range of 1-49. If the six... |
https://en.wikipedia.org/wiki/Interleave%20sequence | In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle.
Let be a set, and let and , be two sequences in The interleave sequence is defined to be the sequence . Formally, it is the sequence given by
Properties
The interleave sequence is convergent if and only if the se... |
https://en.wikipedia.org/wiki/Stolz%E2%80%93Ces%C3%A0ro%20theorem | In mathematics, the Stolz–Cesàro theorem is a criterion for proving the convergence of a sequence. The theorem is named after mathematicians Otto Stolz and Ernesto Cesàro, who stated and proved it for the first time.
The Stolz–Cesàro theorem can be viewed as a generalization of the Cesàro mean, but also as a l'Hôpita... |
https://en.wikipedia.org/wiki/Square%20lattice | In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as . It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group in IUC notation as , Coxeter notation as... |
https://en.wikipedia.org/wiki/Icosahedral%20symmetry | In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron.
Every polyhedron with icosahedral ... |
https://en.wikipedia.org/wiki/Developable%20surface | In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. it can be bent without stretching or compression). Conversely, it is a surface which can be made by transforming a plane (i.e... |
https://en.wikipedia.org/wiki/Judy%20A.%20Holdener | Judy Holdener (née Newhauser) is an American mathematician and educator. She is a professor of mathematics at Kenyon College. She was born in 1965. Holdener's primary interest is in number theory. She discovered a simpler proof of the theorem of Touchard, which states that every perfect number is of the form 2k, 12k+1,... |
https://en.wikipedia.org/wiki/List%20of%20probability%20distributions | Many probability distributions that are important in theory or applications have been given specific names.
Discrete distributions
With finite support
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p.
The Rademacher distribution, which takes value 1 with probab... |
https://en.wikipedia.org/wiki/Parametric%20model | In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters.
Definition
A statistical model is a collection of probability distributio... |
https://en.wikipedia.org/wiki/Quadratrix | In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and E. W. Tschirnhaus, which are both related to the circle.
Quadratrix of Dinostratus
The quadratrix of Dinostratus (also called... |
https://en.wikipedia.org/wiki/Walter%20Trump | Walter Trump (born 1952 or 1953 ) is a German mathematician and retired high school teacher. He is known for his work in recreational mathematics.
He has made contributions working on both the square packing problem and the magic tile problem. In 1979 he discovered the optimal known packing of 11 equal squares in a la... |
https://en.wikipedia.org/wiki/159%20%28number%29 | 159 (one hundred [and] fifty-nine) is a natural number following 158 and preceding 160.
In mathematics
159 is:
the sum of 3 consecutive prime numbers: 47 + 53 + 59.
a Woodall number.
equal to the sum of the squares of the digits of its own square in base 15.
Only 5 numbers (greater than 1) have this property in base ... |
https://en.wikipedia.org/wiki/195%20%28number%29 | 195 (one hundred [and] ninety-five) is the natural number following 194 and preceding 196.
In mathematics
195 is:
the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37
the smallest number expressed as a sum of distinct squares in 16 different ways
a centered tetrahedral number
in... |
https://en.wikipedia.org/wiki/Robust%20statistics | Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation... |
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