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https://en.wikipedia.org/wiki/Prime%20ring | In abstract algebra, a nonzero ring R is a prime ring if for any two elements a and b of R, arb = 0 for all r in R implies that either a = 0 or b = 0. This definition can be regarded as a simultaneous generalization of both integral domains and simple rings.
Although this article discusses the above definition, prime ... |
https://en.wikipedia.org/wiki/Matrix%20ring | In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and ). Some sets of infinite matrices form infinite matrix rings.... |
https://en.wikipedia.org/wiki/Domain%20%28ring%20theory%29 | In algebra, a domain is a nonzero ring in which implies or . (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain. Mathematical... |
https://en.wikipedia.org/wiki/Directional%20derivative | A directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point.
The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneou... |
https://en.wikipedia.org/wiki/Axiom%20%28computer%20algebra%20system%29 | Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy.
History
Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Griesmer at the request of R... |
https://en.wikipedia.org/wiki/Joseph%20Bertrand | Joseph Louis François Bertrand (; 11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.
Biography
Joseph Bertrand was the son of physician Alexandre Jacques François Bertrand and the brother of archa... |
https://en.wikipedia.org/wiki/Jacobson%20density%20theorem | In mathematics, more specifically non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring .
The theorem can be applied to show that any primitive ring can be viewed as a "dense" subring of the ring of linear transformations of a ve... |
https://en.wikipedia.org/wiki/Fisher%20information%20metric | In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space. It can be used to calculate the informational difference between measuremen... |
https://en.wikipedia.org/wiki/Eckmann%E2%80%93Hilton%20argument | In mathematics, the Eckmann–Hilton argument (or Eckmann–Hilton principle or Eckmann–Hilton theorem) is an argument about two unital magma structures on a set where one is a homomorphism for the other. Given this, the structures are the same, and the resulting magma is a commutative monoid. This can then be used to prov... |
https://en.wikipedia.org/wiki/Artinian%20ring | In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain con... |
https://en.wikipedia.org/wiki/Schl%C3%A4fli%20symbol | In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more than three dimensions and discovered all their convex regular polytopes, incl... |
https://en.wikipedia.org/wiki/Curvature%20form | In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry can be considered as a special case.
Definition
Let G be a Lie group with Lie algebra , and P → B be a principal G-bundle. Let ω be an Ehresmann connection on P ... |
https://en.wikipedia.org/wiki/Focal%20point | Focal point may refer to:
Focus (optics)
Focus (geometry)
Conjugate points, also called focal points
Focal point (game theory)
Unicom Focal Point, a portfolio management software tool
Focal point review, a human resources process for employee evaluation
Focal Point (album), a 1976 studio album by McCoy Tyner
"... |
https://en.wikipedia.org/wiki/Hasse%20principle | In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the com... |
https://en.wikipedia.org/wiki/Jacobian%20variety | In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C, hence an abelian variety.
Introduction
The Jacobian variety is named after Carl Gustav Jacobi, who proved the c... |
https://en.wikipedia.org/wiki/Connected%20sum | In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classification of closed surfaces.
More generally, one can also join manifolds tog... |
https://en.wikipedia.org/wiki/Homological%20conjectures%20in%20commutative%20algebra | In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull ... |
https://en.wikipedia.org/wiki/Basel%20problem | The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withst... |
https://en.wikipedia.org/wiki/121%20%28number%29 | 121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.
In mathematics
One hundred [and] twenty-one is
a square (11 times 11)
the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form , where p is prime (3, in this case).
the... |
https://en.wikipedia.org/wiki/Cancellation%20property | In mathematics, the notion of cancellativity (or cancellability) is a generalization of the notion of invertibility.
An element a in a magma has the left cancellation property (or is left-cancellative) if for all b and c in M, always implies that .
An element a in a magma has the right cancellation property (or is... |
https://en.wikipedia.org/wiki/Glossary%20of%20Riemannian%20and%20metric%20geometry | This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
The following articles may also be useful; they either contain specialised vocabulary or provide more detailed expositions of the definitions given below.
Connection
Curvatur... |
https://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville%20theory | In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form:
for given functions , and , together with some boundary conditions at extreme values of . The goals of a given Sturm–Liouville problem are:
To find the for which there exists a non-t... |
https://en.wikipedia.org/wiki/Weyl%20algebra | In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form
More precisely, let F be the underlying field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F[X].
∂X i... |
https://en.wikipedia.org/wiki/Variational%20principle | In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain... |
https://en.wikipedia.org/wiki/Envelope%20%28disambiguation%29 | An envelope is the paper container used to hold a letter being sent by post.
Envelope may also refer to:
Mathematics
Envelope (mathematics), a curve, surface, or higher-dimensional object defined as being tangent to a given family of lines or curves (or surfaces, or higher-dimensional objects, respectively)
Envelo... |
https://en.wikipedia.org/wiki/Pierre%20Fran%C3%A7ois%20Verhulst | Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model.
Logistic equation
Verhulst developed the logistic function in a series of three papers betwe... |
https://en.wikipedia.org/wiki/Thue%E2%80%93Morse%20sequence | In mathematics, the Thue–Morse sequence or Prouhet–Thue–Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 ... |
https://en.wikipedia.org/wiki/New%20Zealand%20census | The New Zealand Census of Population and Dwellings () is a national population and housing census conducted by government department Statistics New Zealand every five years. There have been 34 censuses since 1851. In addition to providing detailed information about national demographics, the results of the census play ... |
https://en.wikipedia.org/wiki/Inclusion%20map | In mathematics, if is a subset of then the inclusion map (also inclusion function, insertion, or canonical injection) is the function that sends each element of to treated as an element of
A "hooked arrow" () is sometimes used in place of the function arrow above to denote an inclusion map; thus:
(However, som... |
https://en.wikipedia.org/wiki/Bimodule | In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules ... |
https://en.wikipedia.org/wiki/Flat%20module | In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces... |
https://en.wikipedia.org/wiki/Differentiable%20curve | Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus.
Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are repres... |
https://en.wikipedia.org/wiki/Order%20%28group%20theory%29 | In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication,... |
https://en.wikipedia.org/wiki/Deltahedron | In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek upper case delta (Δ), which has the shape of an equilateral triangle. There are infinitely many deltahedra, all having an even number of faces by the handshaking lemma. Of these onl... |
https://en.wikipedia.org/wiki/Alternating%20series | In mathematics, an alternating series is an infinite series of the form
or
with for all . The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges.
Examples
The geometric series 1/2 − 1/4... |
https://en.wikipedia.org/wiki/Kagawa%20District%2C%20Kagawa | is a district located in Kagawa Prefecture, Japan.
As of the January 10, 2006 Takamatsu merger (but with 2003 population statistics), the district consists of the single town of Naoshima and has an estimated population of 3,583 and a density of 251.97 persons per km2. The total area is 14.22 km2.
Towns and villages
N... |
https://en.wikipedia.org/wiki/Free%20algebra | In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded as a free commutative algebra.
Definition
... |
https://en.wikipedia.org/wiki/Petrus%20Apianus | Petrus Apianus (April 16, 1495 – April 21, 1552), also known as Peter Apian, Peter Bennewitz, and Peter Bienewitz, was a German humanist, known for his works in mathematics, astronomy and cartography. His work on "cosmography", the field that dealt with the earth and its position in the universe, was presented in his m... |
https://en.wikipedia.org/wiki/Pullback%20%28differential%20geometry%29 | Let be a smooth map between smooth manifolds and . Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on . This linear map is known as the pullback (by ), and is frequently denoted by . More generally, any covariant tenso... |
https://en.wikipedia.org/wiki/Operator%20topologies | In the mathematical field of functional analysis there are several standard topologies which are given to the algebra of bounded linear operators on a Banach space .
Introduction
Let be a sequence of linear operators on the Banach space . Consider the statement that converges to some operator on .
This could ha... |
https://en.wikipedia.org/wiki/Law%20of%20the%20iterated%20logarithm | In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A. N. Kolmogorov in 1929.
Statement
Let {Yn} be independent, identically di... |
https://en.wikipedia.org/wiki/Cohen%E2%80%93Macaulay%20ring | In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings p... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Hurwitz%20formula | In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many o... |
https://en.wikipedia.org/wiki/Antecedent%20variable | In statistics and social sciences, an antecedent variable is a variable that can help to explain the apparent relationship (or part of the relationship) between other variables that are nominally in a cause and effect relationship. In a regression analysis, an antecedent variable would be one that influences both the i... |
https://en.wikipedia.org/wiki/Centered%20hexagonal%20number | In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal num... |
https://en.wikipedia.org/wiki/Gams%20%28disambiguation%29 | Gams may be:
Acronyms
General Algebraic Modeling System (GAMS), a mathematical optimization computer program
Guide to Available Mathematical Software (GAMS), a project of the National Institute of Standards and Technology
Graduate of Ayurvedic Medicine and Surgery (GAMS), a degree in Ayurvedic Medicine and Surgery ... |
https://en.wikipedia.org/wiki/Dixon%27s%20Q%20test | In statistics, Dixon's Q test, or simply the Q test, is used for identification and rejection of outliers. This assumes normal distribution and per Robert Dean and Wilfrid Dixon, and others, this test should be used sparingly and never more than once in a data set. To apply a Q test for bad data, arrange the data in ... |
https://en.wikipedia.org/wiki/Closed%20graph%20theorem | In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs.
Each gives conditions when functions with closed graphs are necessarily continuous.
Graphs and maps with closed graphs
If is a map between topological spaces then the gra... |
https://en.wikipedia.org/wiki/Steiner%20tree%20problem | In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of settings, they all require an optimal interconnect for a given set o... |
https://en.wikipedia.org/wiki/Initial%20value%20problem | In multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem. In th... |
https://en.wikipedia.org/wiki/115%20%28number%29 | 115 (one hundred [and] fifteen) is the natural number following 114 and preceding 116.
In mathematics
115 has a square sum of divisors:
There are 115 different rooted trees with exactly eight nodes, 115 inequivalent ways of placing six rooks on a 6 × 6 chess board in such a way that no two of the rooks attack each ot... |
https://en.wikipedia.org/wiki/116%20%28number%29 | 116 (one hundred [and] sixteen) is the natural number following 115 and preceding 117.
In mathematics
116 is a noncototient, meaning that there is no solution to the equation , where stands for Euler's totient function.
116! + 1 is a factorial prime.
There are 116 ternary Lyndon words of length six, and 116 irreduc... |
https://en.wikipedia.org/wiki/117%20%28number%29 | 117 (one hundred [and] seventeen) is the natural number following 116 and preceding 118.
In mathematics
117 is the smallest possible length of the longest edge of an integer Heronian tetrahedron (a tetrahedron whose edge lengths, face areas and volume are all integers). Its other edge lengths are 51, 52, 53, 80 and 84... |
https://en.wikipedia.org/wiki/118%20%28number%29 | 118 (one hundred [and] eighteen) is the natural number following 117 and preceding 119.
In mathematics
There is no answer to the equation φ(x) = 118, making 118 a nontotient.
Four expressions for 118 as the sum of three positive integers have the same product:
14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72... |
https://en.wikipedia.org/wiki/Growth%20rate%20%28group%20theory%29 | In the mathematical subject of geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of leng... |
https://en.wikipedia.org/wiki/Growth%20rate | Growth rate may refer to:
By rate
Asymptotic analysis, a branch of mathematics concerned with the analysis of growth rates
Linear growth
Exponential growth, a growth rate classification
Any of a variety of growth rates classified by such things as the Landau notation
By type of growing medium
Economic growth, the inc... |
https://en.wikipedia.org/wiki/%C3%89tienne%20Laspeyres | Ernst Louis Étienne Laspeyres (; 28 November 1834 – 4 August 1913) was a German economist. He was Professor ordinarius of economics and statistics or State Sciences and cameralistics (public finance and administration) in Basel, Riga, Dorpat (now Tartu), Karlsruhe, and finally for 26 years in Gießen. Laspeyres was the ... |
https://en.wikipedia.org/wiki/RSA%20Factoring%20Challenge | The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime fa... |
https://en.wikipedia.org/wiki/Formal%20sum | In mathematics, a formal sum, formal series, or formal linear combination may be:
In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients.
In linear algebra, an element of a vector space, a sum of finitely many elements from a given ... |
https://en.wikipedia.org/wiki/Tensor%20calculus | In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime).
Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of r... |
https://en.wikipedia.org/wiki/Reduce%20%28computer%20algebra%20system%29 | Reduce is a general-purpose computer algebra system geared towards applications in physics.
The development of the Reduce computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development under his direction.
Reduce is written... |
https://en.wikipedia.org/wiki/Tullio%20Levi-Civita | Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro,... |
https://en.wikipedia.org/wiki/Gregorio%20Ricci-Curbastro | Gregorio Ricci-Curbastro (; 12January 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus.
With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. This appears to be the ... |
https://en.wikipedia.org/wiki/Gabriel%20Cramer | Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. He was the son of physician Jean Cramer and Anne Mallet Cramer.
Biography
Cramer showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics at the University of Geneva.
In 1728... |
https://en.wikipedia.org/wiki/Hyperelliptic%20curve | In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form
where f(x) is a polynomial of degree n = 2g + 1 > 4 or n = 2g + 2 > 4 with n distinct roots, and h(x) is a polynomial of degree < g + 2 (if the characteristic of the ground field is not 2, one can take h... |
https://en.wikipedia.org/wiki/Compositional%20data | In statistics, compositional data are quantitative descriptions of the parts of some whole, conveying relative information. Mathematically, compositional data is represented by points on a simplex. Measurements involving probabilities, proportions, percentages, and ppm can all be thought of as compositional data.
Tern... |
https://en.wikipedia.org/wiki/Swallowtail | Swallowtail may refer to:
Swallowtail catastrophe or swallowtail surface, a singularity occurring in the part of mathematics called catastrophe theory
Swallow-tail coat, a formal tailcoat worn traditionally as part of the white tie dress code
Swallowtail butterfly, large colorful butterflies from the family Papilion... |
https://en.wikipedia.org/wiki/600-cell | In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}.
It is also known as the C600, hexacosichoron and hexacosihedroid.
It is also called a tetraplex (abbreviated from "tetrahedral complex") and a polytetrahedron, being bounded by tetrah... |
https://en.wikipedia.org/wiki/Population%20dynamics | Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems.
History
Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope ... |
https://en.wikipedia.org/wiki/Hodge%20theory | In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes und... |
https://en.wikipedia.org/wiki/Ramification%20group | In number theory, more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the ramification phenomena of the extension.
Ramification theory of valuations
In mathematics, the ramification theory of valuati... |
https://en.wikipedia.org/wiki/Rejection%20sampling | In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method. The method works for any distribution in with ... |
https://en.wikipedia.org/wiki/Poisson%20summation%20formula | In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original functi... |
https://en.wikipedia.org/wiki/Diophantine%20geometry | In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of ari... |
https://en.wikipedia.org/wiki/Medial%20magma | In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) which satisfies the identity
, or more simply
for all x, y, u and v, using the convention that juxtaposition denotes the same operation but has higher precedence. This identity has been variously ca... |
https://en.wikipedia.org/wiki/Instituto%20Nacional%20de%20Estat%C3%ADstica%20%28Portugal%29 | The Instituto Nacional de Estatística or INE (Portuguese for "National Institute for Statistics") is the government office for national statistics of Portugal. In the English language it is also branded as Statistics Portugal.
The INE is one of the components of the Portuguese National Statistical System (SEN), which ... |
https://en.wikipedia.org/wiki/Charles%20Fefferman | Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contributions to mathematical analysis.
Early life and education
Fefferman was bor... |
https://en.wikipedia.org/wiki/Remainder | In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividin... |
https://en.wikipedia.org/wiki/Radon%20transform | In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 b... |
https://en.wikipedia.org/wiki/Minkowski%20addition | In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B:
The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) is the corresponding inverse, where produces a set that could be... |
https://en.wikipedia.org/wiki/Hausdorff%20measure | In mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions. It is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in or, more generally, in any metric ... |
https://en.wikipedia.org/wiki/Concyclic%20points | In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle.
Three points in ... |
https://en.wikipedia.org/wiki/Conditional%20probability%20distribution | In probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecifie... |
https://en.wikipedia.org/wiki/Point%20in%20polygon | In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics, computer vis... |
https://en.wikipedia.org/wiki/Point%20location | The point location problem is a fundamental topic of computational geometry. It finds applications in areas that deal with processing geometrical data: computer graphics, geographic information systems (GIS), motion planning, and computer aided design (CAD).
In its most general form, the problem is, given a partition ... |
https://en.wikipedia.org/wiki/Algebraic%20torus | In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by , , or , is a type of commutative affine algebraic group commonly found in projective algebraic geometry and toric geometry. Higher dimensional algebraic tori can be modelled as a product of algebraic groups . These groups were na... |
https://en.wikipedia.org/wiki/Perfect%20field | In algebra, a field k is perfect if any one of the following equivalent conditions holds:
Every irreducible polynomial over k has distinct roots.
Every irreducible polynomial over k is separable.
Every finite extension of k is separable.
Every algebraic extension of k is separable.
Either k has characteristic 0, o... |
https://en.wikipedia.org/wiki/Regular%20sequence | In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This is the algebraic analogue of the geometric notion of a complete intersection.
Definitions
For a commutative ring R and an R-module M, an element r in R is called a ... |
https://en.wikipedia.org/wiki/Iterated%20function%20system | In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981.
IFS fractals, as they are normally called, can be of any number of dimensions, but are ... |
https://en.wikipedia.org/wiki/Computational%20semiotics | Computational semiotics is an interdisciplinary field that applies, conducts, and draws on research in logic, mathematics, the theory and practice of computation, formal and natural language studies, the cognitive sciences generally, and semiotics proper. The term encompasses both the application of semiotics to comput... |
https://en.wikipedia.org/wiki/Sign%20function | In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that returns the sign of a real number. In mathematical notation the sign function is often represented as .
Definition
The signum function of a real number is a piecewise function which is defined as follows:
Properti... |
https://en.wikipedia.org/wiki/Centrum%20Wiskunde%20%26%20Informatica | The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Council (NWO) and is located at the Amsterdam Science Park. This institute is ... |
https://en.wikipedia.org/wiki/Marginal%20distribution | In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. Th... |
https://en.wikipedia.org/wiki/Equivalent%20dose | Equivalent dose is a dose quantity H representing the stochastic health effects of low levels of ionizing radiation on the human body which represents the probability of radiation-induced cancer and genetic damage. It is derived from the physical quantity absorbed dose, but also takes into account the biological effe... |
https://en.wikipedia.org/wiki/Spectral%20theory | In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equat... |
https://en.wikipedia.org/wiki/Regular%20local%20ring | In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension. In symbols, let A be a Noetherian local ring with maximal ideal m, and suppose a1, ..., an is a minimal set of generators of m. Then by... |
https://en.wikipedia.org/wiki/Depth | Depth(s) may refer to:
Science and mathematics
Depth (ring theory), an important invariant of rings and modules in commutative and homological algebra
Depth in a well, the measurement between two points in an oil well
Color depth (or "number of bits" or "bit depth"), in computer graphics
Market depth, in financia... |
https://en.wikipedia.org/wiki/Multifactorial | Multifactorial (having many factors) can refer to:
The multifactorial in mathematics.
Multifactorial inheritance, a pattern of predisposition for a disease process. |
https://en.wikipedia.org/wiki/Double%20factorial | In mathematics, the double factorial of a number , denoted by , is the product of all the positive integers up to that have the same parity (odd or even) as . That is,
Restated, this says that for even , the double factorial is
while for odd it is
For example, . The zero double factorial as an empty product.
The... |
https://en.wikipedia.org/wiki/Hyperfactorial | In mathematics, and more specifically number theory, the hyperfactorial of a positive integer is the product of the numbers of the form from to
Definition
The hyperfactorial of a positive integer is the product of the numbers . That is,
Following the usual convention for the empty product, the hyperfactorial of... |
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