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https://en.wikipedia.org/wiki/Combinatorial%20number%20system | In mathematics, and in particular in combinatorics, the combinatorial number system of degree k (for some positive integer k), also referred to as combinadics, or the Macaulay representation of an integer, is a correspondence between natural numbers (taken to include 0) N and k-combinations. The combinations are repres... |
https://en.wikipedia.org/wiki/Wolstenholme%27s%20theorem | In mathematics, Wolstenholme's theorem states that for a prime number , the congruence
holds, where the parentheses denote a binomial coefficient. For example, with p = 7, this says that 1716 is one more than a multiple of 343. The theorem was first proved by Joseph Wolstenholme in 1862. In 1819, Charles Babbage sho... |
https://en.wikipedia.org/wiki/Hurwitz%27s%20automorphisms%20theorem | In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz... |
https://en.wikipedia.org/wiki/Order%20%28ring%20theory%29 | In mathematics, an order in the sense of ring theory is a subring of a ring , such that
is a finite-dimensional algebra over the field of rational numbers
spans over , and
is a -lattice in .
The last two conditions can be stated in less formal terms: Additively, is a free abelian group generated by a basis fo... |
https://en.wikipedia.org/wiki/Lw%C3%B3w-Warsaw%20School | Lwow–Warsaw School may refer to:
Lwów–Warsaw school of logic
Lwów School of Mathematics
Warsaw School of Mathematics
Lwów–Warsaw School of History |
https://en.wikipedia.org/wiki/Exotic%20sphere | In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar... |
https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler%20divergence | In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution is different from a second, reference probability distribution . A simple interpretation of the KL divergence of from... |
https://en.wikipedia.org/wiki/G%20Ring | G Ring may refer to:
, a planetary ring system around Saturn.
G-ring or Grothendieck ring, a type of commutative ring in algebra |
https://en.wikipedia.org/wiki/Leibniz%27s%20rule | Leibniz's rule (named after Gottfried Wilhelm Leibniz) may refer to one of the following:
Product rule in differential calculus
General Leibniz rule, a generalization of the product rule
Leibniz integral rule
The alternating series test, also called Leibniz's rule
See also
Leibniz (disambiguation)
Leibniz' law (d... |
https://en.wikipedia.org/wiki/General%20Leibniz%20rule | In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if and are -times differentiable functions, then the product is also -times differentiable and its th derivative is given by
where is the binomial co... |
https://en.wikipedia.org/wiki/Discrepancy%20theory | In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed wi... |
https://en.wikipedia.org/wiki/Lyapunov%20time | In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent.
Use
The Lyapunov time mirrors the limits of the predictability of the system. ... |
https://en.wikipedia.org/wiki/Type-2%20Gumbel%20distribution | In probability theory, the Type-2 Gumbel probability density function is
for
.
For the mean is infinite. For the variance is infinite.
The cumulative distribution function is
The moments exist for
The distribution is named after Emil Julius Gumbel (1891 – 1966).
Generating random variates
Given a random va... |
https://en.wikipedia.org/wiki/Dirichlet%20distribution | In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted , is a family of continuous multivariate probability distributions parameterized by a vector of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of mul... |
https://en.wikipedia.org/wiki/Landau%20distribution | In probability theory, the Landau distribution is a probability distribution named after Lev Landau.
Because of the distribution's "fat" tail, the moments of the distribution, like mean or variance, are undefined. The distribution is a particular case of stable distribution.
Definition
The probability density function... |
https://en.wikipedia.org/wiki/Stable%20distribution | In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also somet... |
https://en.wikipedia.org/wiki/VSEPR%20theory | Valence shell electron pair repulsion (VSEPR) theory ( , ), is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.
The... |
https://en.wikipedia.org/wiki/Journal%20of%20Recreational%20Mathematics | The Journal of Recreational Mathematics was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue (volume 38, number 2) published in 2014. The initial publisher (of volumes... |
https://en.wikipedia.org/wiki/Terence%20Tao | Terence Chi-Shen Tao (; born 17 July 1975) is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, ... |
https://en.wikipedia.org/wiki/Inner%20model | In set theory, a branch of mathematical logic, an inner model for a theory T is a substructure of a model M of a set theory that is both a model for T and contains all the ordinals of M.
Definition
Let be the language of set theory. Let S be a particular set theory, for example the ZFC axioms and let (possibly the ... |
https://en.wikipedia.org/wiki/Linearization | In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium poin... |
https://en.wikipedia.org/wiki/Arbitrarily%20large | In mathematics, the phrases arbitrarily large, arbitrarily small and arbitrarily long are used in statements to make clear of the fact that an object is large, small and long with little limitation or restraint, respectively. The use of "arbitrarily" often occurs in the context of real numbers (and its subsets thereof)... |
https://en.wikipedia.org/wiki/Logarithmic%20distribution | In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion
From this we obtain the identity
This leads directly to the probability mass function of ... |
https://en.wikipedia.org/wiki/Yule%E2%80%93Simon%20distribution | In probability and statistics, the Yule–Simon distribution is a discrete probability distribution named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution.
The probability mass function (pmf) of the Yule–Simon (ρ) distribution is
for integer and real , where is the beta function... |
https://en.wikipedia.org/wiki/JTS | JTS may refer to:
Alfa Romeo JTS engine, an automobile engine
Java Topology Suite (JTS Topology Suite), a software library
Janesville Transit System, Wisconsin, US
Jakarta Taipei School, Indonesia
Java transaction service, a software library
Jewish Theological Seminary of America, New York City
Jimmy Two-Shoes, ... |
https://en.wikipedia.org/wiki/Schur%20multiplier | In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by in his work on projective representations.
Examples and properties
The Schur multiplier of a finite group G is a finite abelian group whose exponent divides the order of G. If a... |
https://en.wikipedia.org/wiki/Axiom%20of%20real%20determinacy | In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following:
The axiom of real determinacy is a stronger version of the axiom of determinacy (AD), which makes the same statement about games where both players choose integers; ADR is inconsistent with the axiom ... |
https://en.wikipedia.org/wiki/Dedekind%20sum | In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have subsequently been much studied in number theory, and have occurred in some pro... |
https://en.wikipedia.org/wiki/Fifth%20government%20of%20Jordi%20Pujol | The colors indicate the political party affiliation of each member:
So the statistics of the Government composition are:
Cabinets of Catalonia |
https://en.wikipedia.org/wiki/Gyroelongated%20square%20pyramid | In geometry, the gyroelongated square pyramid is one of the Johnson solids (). As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case involves joining a square antiprism to its base.
Applications
The Gyroelongated square pyramid represents the capped square a... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20pyramid | In geometry, the elongated pentagonal pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal pyramid () by attaching a pentagonal prism to its base.
Formulae
The following formulae for the height (), surface area () and volume () can be used if all faces are r... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20pyramid | In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base.
It can also be seen as a diminished icosahedron, an icosahedron with the ... |
https://en.wikipedia.org/wiki/Tridiminished%20icosahedron | In geometry, the tridiminished icosahedron is one of the Johnson solids (). The name refers to one way of constructing it, by removing three pentagonal pyramids () from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal faces.
Related ... |
https://en.wikipedia.org/wiki/Metabidiminished%20icosahedron | In geometry, the metabidiminished icosahedron is one of the Johnson solids (). The name refers to one way of constructing it, by removing two pentagonal pyramids () from a regular icosahedron, replacing two sets of five triangular faces of the icosahedron with two adjacent pentagonal faces. If two pentagonal pyramids a... |
https://en.wikipedia.org/wiki/Kripke%E2%80%93Platek%20set%20theory | The Kripke–Platek set theory (KP), pronounced , is an axiomatic set theory developed by Saul Kripke and Richard Platek.
The theory can be thought of as roughly the predicative part of ZFC and is considerably weaker than it.
Axioms
In its formulation, a Δ0 formula is one all of whose quantifiers are bounded. This mean... |
https://en.wikipedia.org/wiki/Pericyclic%20reaction | In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap in a continuous cycle at the transition state. Pericyclic reactions stand... |
https://en.wikipedia.org/wiki/Statistics%20South%20Africa | Statistics South Africa (frequently shortened to Stats SA) is the national statistical service of South Africa with the goal of producing timely, accurate and official statistics, in order to advance economic growth, development and democracy. To this end, Statistics South Africa produces official demographic, economi... |
https://en.wikipedia.org/wiki/Markov%20decision%20process | In mathematics, a Markov decision process (MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via ... |
https://en.wikipedia.org/wiki/Optimization%20problem | In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:
An optimization problem with discrete ... |
https://en.wikipedia.org/wiki/Invariant%20%28mathematics%29 | In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the... |
https://en.wikipedia.org/wiki/Pisano%20period | In number theory, the nth Pisano period, written as (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774.
De... |
https://en.wikipedia.org/wiki/Sylvester%27s%20law%20of%20inertia | Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if is the symmetric matrix that defines the quadratic form, and is any invertible matrix such that is diagonal, then the number ... |
https://en.wikipedia.org/wiki/Square%20pyramid | In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. If the pyramid's apex lies on a line erected perpendicularly from the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges... |
https://en.wikipedia.org/wiki/Pentagonal%20pyramid | In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual.
The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles. It is one of the ... |
https://en.wikipedia.org/wiki/Triangular%20cupola | In geometry, the triangular cupola is one of the Johnson solids (). It can be seen as half a cuboctahedron.
Formulae
The following formulae for the volume (), the surface area () and the height () can be used if all faces are regular, with edge length a:
Dual polyhedron
The dual of the triangular cupola has 6 tria... |
https://en.wikipedia.org/wiki/Square%20cupola | In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids (). It can be obtained as a slice of the rhombicuboctahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; in this case the base polygon is an octagon.
Formulae
The following formulae for... |
https://en.wikipedia.org/wiki/Pentagonal%20rotunda | In geometry, the pentagonal rotunda is one of the Johnson solids (). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces.
Formulae
The following formulae for volume, surface area, circumradius, and height are valid if all faces are regular, with edge le... |
https://en.wikipedia.org/wiki/Elongated%20square%20cupola | In geometry, the elongated square cupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a square cupola () by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" (another square cupola) removed.
Formulae
The following formu... |
https://en.wikipedia.org/wiki/Elongated%20square%20gyrobicupola | In geometry, the elongated square gyrobicupola or pseudo-rhombicuboctahedron is one of the Johnson solids (). It is not usually considered to be an Archimedean solid, even though its faces consist of regular polygons that meet in the same pattern at each of its vertices, because unlike the 13 Archimedean solids, it lac... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20rotunda | In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J42) with one pentagonal rotunda removed.
Form... |
https://en.wikipedia.org/wiki/Gyroelongated%20square%20cupola | In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J45) with one square bicupola removed.
Area and Vo... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20rotunda | In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J25). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J6) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal birotunda (J48) with one pentagonal rotunda remo... |
https://en.wikipedia.org/wiki/Square%20orthobicupola | In geometry, the square orthobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by joining two square cupolae () along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola ().
The square orthobicupola is the se... |
https://en.wikipedia.org/wiki/Square%20gyrobicupola | In geometry, the square gyrobicupola is one of the Johnson solids (). Like the square orthobicupola (), it can be obtained by joining two square cupolae () along their bases. The difference is that in this solid, the two halves are rotated 45 degrees with respect to one another.
The square gyrobicupola is the second i... |
https://en.wikipedia.org/wiki/Pentagonal%20orthobirotunda | In geometry, the pentagonal orthobirotunda is one of the Johnson solids (). It can be constructed by joining two pentagonal rotundae () along their decagonal faces, matching like faces.
Related polyhedra
The pentagonal orthobirotunda is also related to an Archimedean solid, the icosidodecahedron, which can also be c... |
https://en.wikipedia.org/wiki/Augmented%20tridiminished%20icosahedron | In geometry, the augmented tridiminished icosahedron is one of the
Johnson solids (). It can be obtained by joining a tetrahedron to another Johnson solid, the tridiminished icosahedron ().
External links
Johnson solids |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20gyrobirotunda | In geometry, the elongated pentagonal gyrobirotunda is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal r... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20orthobirotunda | In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda () by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae ()... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20birotunda | In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda (either or the icosidodecahedron) by inserting a decagonal antiprism between its two halves.
The gyroelongated pentagonal birotunda is one of five J... |
https://en.wikipedia.org/wiki/Gyroelongated%20square%20bicupola | In geometry, the gyroelongated square bicupola is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating a square bicupola ( or ) by inserting an octagonal antiprism between its congruent halves.
The gyroelongated square bicupola is one of five Johnson solids which are chiral, mean... |
https://en.wikipedia.org/wiki/Twelfth%20root%20of%20two | The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone () in twelve-tone equal temperament. This number was proposed for the first time in r... |
https://en.wikipedia.org/wiki/Toe%20%28automotive%29 | In automotive engineering, toe, also known as tracking, is the symmetric angle that each wheel makes with the longitudinal axis of the vehicle, as a function of static geometry, and kinematic and compliant effects. This can be contrasted with steer, which is the antisymmetric angle, i.e. both wheels point to the left o... |
https://en.wikipedia.org/wiki/Pentagonal%20cupola | In geometry, the pentagonal cupola is one of the Johnson solids (). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.
Formulae
The following formulae for volume, surface area and circumradius can be used if all ... |
https://en.wikipedia.org/wiki/Diminished%20rhombicosidodecahedron | In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.
Related Johnson solids are:
: parabidiminished rhombicosidodecahedron with two opposing cupolae removed, and
: metabidiminished rhombicosidodecahed... |
https://en.wikipedia.org/wiki/Gyrate%20rhombicosidodecahedron | In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (). It is also a canonical polyhedron.
Related polyhedron
It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees. They have the same faces around each vertex, but vertex configurations along t... |
https://en.wikipedia.org/wiki/Dedekind%20zeta%20function | In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function (which is obtained in the case where K is the field of rational numbers Q). It can be defined as a Dirichlet series, it has an Euler product expansion, it satisfies a func... |
https://en.wikipedia.org/wiki/Weil%20pairing | In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduc... |
https://en.wikipedia.org/wiki/Parabidiminished%20rhombicosidodecahedron | In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (). It is also a canonical polyhedron.
It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron () where one cupola is removed, ... |
https://en.wikipedia.org/wiki/Metabidiminished%20rhombicosidodecahedron | In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids ().
It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae () removed.
Related Johnson solids are:
The diminished rhombicosidodecahedron () where one cupola is removed,
The parabidiminished rhomb... |
https://en.wikipedia.org/wiki/Tridiminished%20rhombicosidodecahedron | In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed.
Related Johnson solids are:
: diminished rhombicosidodecahedron with one cupola removed,
: parabidiminished rhombicosidodecahedron with two o... |
https://en.wikipedia.org/wiki/Trigyrate%20rhombicosidodecahedron | In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron.
It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are:
The gyrat... |
https://en.wikipedia.org/wiki/Snub%20disphenoid | In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a convex polyhedron with twelve equilateral triangles as its faces. It is not a regular polyhedron because some vertices have four faces and others have five. It is a dodecahedron, one of the ... |
https://en.wikipedia.org/wiki/Education%20in%20Taiwan | The educational system in Taiwan is the responsibility of the Ministry of Education. The system produces pupils with some of the highest test scores in the world, especially in mathematics and science. Former president Ma Ying-jeou announced in January 2011 that the government would begin the phased implementation of a... |
https://en.wikipedia.org/wiki/Snub%20square%20antiprism | In geometry, the snub square antiprism is one of the Johnson solids ().
It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids, although it is a relative of the icosahedron that has fourfold symmetry instead of threefold.
Construction
The... |
https://en.wikipedia.org/wiki/Arnoldi%20iteration | In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it part... |
https://en.wikipedia.org/wiki/Hoeffding%27s%20inequality | In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963.
Hoeffding's inequality is a special case of the A... |
https://en.wikipedia.org/wiki/167%20%28number%29 | 167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168.
In mathematics
167 is an emirp, an isolated prime, a Chen prime, a Gaussian prime, a safe prime, and an Eisenstein prime with no imaginary part and a real part of the form .
167 is the smallest number which requires six terms w... |
https://en.wikipedia.org/wiki/Noam%20Elkies | Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At the age of 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist, chess national master and a chess composer.
Early life
Elkies was born to an engineer father and a piano teacher mother. H... |
https://en.wikipedia.org/wiki/Spherical%20cap | In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the... |
https://en.wikipedia.org/wiki/Generalized%20eigenvector | In linear algebra, a generalized eigenvector of an matrix is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector.
Let be an -dimensional vector space and let be the matrix representation of a linear map from to with respect to some ordered basis.
There may n... |
https://en.wikipedia.org/wiki/Bachelor%20of%20Mathematics | A Bachelor of Mathematics (abbreviated B.Math or BMath) is an undergraduate academic degree awarded for successfully completing a program of study in mathematics or related disciplines, such as applied mathematics, actuarial science, computational science, data analytics, financial mathematics, mathematical physics, ... |
https://en.wikipedia.org/wiki/Poul%20Heegaard | Poul Heegaard (; November 2, 1871, Copenhagen - February 7, 1948, Oslo) was a Danish mathematician active in the field of topology. His 1898 thesis introduced a concept now called the Heegaard splitting of a 3-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincaré. Poincaré had over... |
https://en.wikipedia.org/wiki/Complex%20multiplication%20of%20abelian%20varieties | In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for elliptic curves in the nineteenth century. One of the major achievements i... |
https://en.wikipedia.org/wiki/512%20%28number%29 | 512 (five hundred [and] twelve) is the natural number following 511 and preceding 513.
In mathematics
512 is a power of two: 29 (2 to the 9th power) and the cube of 8: 83.
It is the eleventh Leyland number.
It is also the third Dudeney number.
It is a self number in base 12.
It is a harshad number in decimal.
It... |
https://en.wikipedia.org/wiki/Abelian%20integral | In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form
where is an arbitrary rational function of the two variables and , which are related by the equation
where is an irreducible polynomial in ,
whose coefficients , are ... |
https://en.wikipedia.org/wiki/Differential%20of%20the%20first%20kind | In mathematics, differential of the first kind is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential 1-forms. Given a complex manifold M, a differential of the first kind ω is the... |
https://en.wikipedia.org/wiki/Point%20group | In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d). P... |
https://en.wikipedia.org/wiki/Pyotr%20Novikov | Pyotr Sergeyevich Novikov (; 28 August 1901, Moscow – 9 January 1975, Moscow) was a Soviet mathematician.
Novikov is known for his work on combinatorial problems in group theory: the word problem for groups, and the Burnside problem. For proving the undecidability of the word problem in groups he was awarded the Lenin... |
https://en.wikipedia.org/wiki/Bruhat%20decomposition | In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an up... |
https://en.wikipedia.org/wiki/Cartan%20decomposition | In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Él... |
https://en.wikipedia.org/wiki/Iwasawa%20decomposition | In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iw... |
https://en.wikipedia.org/wiki/Hyperbolic%20angle | In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane. The hyperbolic angle parametrises the unit hyperbola, which has hyperbolic functions as coordinates. In mathematics, hyperbolic angle is an invariant measure as it... |
https://en.wikipedia.org/wiki/Squeeze%20mapping | In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping.
For a fixed positive real number , the mapping
is the squeeze mapping with parameter . Since
is a hyperbola, if ... |
https://en.wikipedia.org/wiki/Member | Member may refer to:
Military jury, referred to as "Members" in military jargon
Element (mathematics), an object that belongs to a mathematical set
In object-oriented programming, a member of a class
Field (computer science), entries in a database
Member variable, a variable that is associated with a specific obj... |
https://en.wikipedia.org/wiki/Racks%20and%20quandles | In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams.
While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiom... |
https://en.wikipedia.org/wiki/Siegel%20upper%20half-space | In mathematics, the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over the complex numbers whose imaginary part is positive definite. It was introduced by . It is the symmetric space associated to the symplectic group .
The Siegel uppe... |
https://en.wikipedia.org/wiki/Hebesphenomegacorona | In geometry, the hebesphenomegacorona is one of the Johnson solids (). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. It has 21 faces, 18 triangles and 3 squares, 33 edges, and 14 vertices.
Johnson uses the prefix hebespheno- to ... |
https://en.wikipedia.org/wiki/Sphenomegacorona | In geometry, the sphenomegacorona is one of the Johnson solids (). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.
Johnson uses the prefix spheno- to refer to a wedge-like complex formed by two adjacent lunes, a lune being a square... |
https://en.wikipedia.org/wiki/Sphenocorona | In geometry, the sphenocorona is one of the Johnson solids (). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.
Johnson uses the prefix spheno- to refer to a wedge-like complex formed by two adjacent lunes, a lune being a square wit... |
https://en.wikipedia.org/wiki/Overdetermined | Overdetermined may refer to:
Overdetermined systems in various branches of mathematics
Overdetermination in various fields of psychology or analytical thought |
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