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https://en.wikipedia.org/wiki/CO-OPN | The CO-OPN (Concurrent Object-Oriented Petri Nets) specification language is based on both algebraic specifications and algebraic Petri nets formalisms. The former formalism represent the data structures aspects, while the latter stands for the behavioral and concurrent aspects of systems. In order to deal with large s... |
https://en.wikipedia.org/wiki/Lemniscate%20constant | In mathematics, the lemniscate constant is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of for the circle. Equivalently, the perimeter of the lemniscate is . The lemniscate constant is closely related to the lemniscat... |
https://en.wikipedia.org/wiki/Chord%20%28concurrency%29 | A chord is a concurrency construct available in Polyphonic C♯ and Cω inspired by the join pattern of the join-calculus. A chord is a function body that is associated with multiple function headers and cannot execute until all function headers are called.
Synchronicity
Cω defines two types of functions: synchronous a... |
https://en.wikipedia.org/wiki/Statistica | Statistica is an advanced analytics software package originally developed by StatSoft and currently maintained by TIBCO Software Inc.
Statistica provides data analysis, data management, statistics, data mining, machine learning, text analytics and data visualization procedures.
Overview
Statistica is a suite of analy... |
https://en.wikipedia.org/wiki/World%20Drug%20Report | The World Drug Report is a United Nations Office on Drugs and Crime annual publication that analyzes market trends, compiling detailed statistics on drug markets. Using data, it helps draw conclusions about drugs as an issue needing intervention by government agencies around the world. UNAIDs stated on its website "The... |
https://en.wikipedia.org/wiki/Jason%20John%20Nassau | Jason John Nassau (1893–1965) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruc... |
https://en.wikipedia.org/wiki/B%C3%A9zout%20matrix | In mathematics, a Bézout matrix (or Bézoutian or Bezoutiant) is a special square matrix associated with two polynomials, introduced by and and named after Étienne Bézout. Bézoutian may also refer to the determinant of this matrix, which is equal to the resultant of the two polynomials. Bézout matrices are sometimes ... |
https://en.wikipedia.org/wiki/Beck%27s%20monadicity%20theorem | In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by in about 1964. It is often stated in dual form for comonads. It is sometimes called the Beck tripleability theorem because of the older term triple for a monad.
Beck's monadicit... |
https://en.wikipedia.org/wiki/Beck%27s%20theorem%20%28geometry%29 | In discrete geometry, Beck's theorem is any of several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of lines determined by a set of points in ... |
https://en.wikipedia.org/wiki/Isogonal%20conjugate | __notoc__
In geometry, the isogonal conjugate of a point with respect to a triangle is constructed by reflecting the lines about the angle bisectors of respectively. These three reflected lines concur at the isogonal conjugate of . (This definition applies only to points not on a sideline of triangle .) This i... |
https://en.wikipedia.org/wiki/Going%20up%20and%20going%20down | In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions.
The phrase going up refers to the case when a chain can be extended by "upward inclusion", while going down refers to the case when a chain can be exten... |
https://en.wikipedia.org/wiki/Going%20Up | Going Up may refer to:
Going up and going down, terms in commutative algebra which refer to certain properties of chains of prime ideals in integral extensions
Going Up (musical), a musical comedy that opened in New York in 1917 and in London in 1918
Going Up (film), a 1923 film starring Douglas MacLean
"Going Up" (TV ... |
https://en.wikipedia.org/wiki/MCMC | MCMC may refer to:
Malaysian Communications and Multimedia Commission, a regulator agency of the Malaysian government
Markov chain Monte Carlo, a class of algorithms and methods in statistics
See also
MC (disambiguation)
MC2 (disambiguation) |
https://en.wikipedia.org/wiki/Direct%20sum | The direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently, but analogously, for different kinds of structures. To see how the direct sum is used in abstract algebra, consider a more elementary kind of structure, the abelian group. The direct sum of two a... |
https://en.wikipedia.org/wiki/Artin%27s%20conjecture%20on%20primitive%20roots | In number theory, Artin's conjecture on primitive roots states that a given integer a that is neither a square number nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes. This conjectural density equals Artin's constant or a rational multiple th... |
https://en.wikipedia.org/wiki/Isobel%20Lang | Isobel Dinah Lang (born 16 July 1970 in Lincoln) is a weather presenter for Sky News.
Early life
Lang grew up in Sussex and Hertfordshire. She graduated with a BSc degree in mathematics in 1991 from the University of Exeter, before joining the Met Office in 1991 where she prepared forecasts for the press, and presente... |
https://en.wikipedia.org/wiki/Men%20of%20Mathematics | Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré is a book on the history of mathematics published in 1937 by Scottish-born American mathematician and science fiction writer E. T. Bell (1883–1960). After a brief chapter on three ancient mathematicians, it covers the lives... |
https://en.wikipedia.org/wiki/Small%20group | Small group can mean:
In psychology, a group of 3 to 9 individuals, see communication in small groups
In mathematics, a group of small order, see list of small groups
In connection with churches, a cell group
In jazz, a small ensemble also known as a combo |
https://en.wikipedia.org/wiki/Fibred%20category | Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs) of objects such as vector bundles can be defined. As an example, for each topologic... |
https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres%20coordinates | In general relativity, Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-b... |
https://en.wikipedia.org/wiki/Kernel%20density%20estimation | In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about t... |
https://en.wikipedia.org/wiki/Ubay%2C%20Bohol | Ubay, officially the Municipality of Ubay (; ), is a fast growing 1st class municipality in the province of Bohol, Philippines. Based on the 2020 Philippine Statistics Authority census, it has a population of 81,799 people which is projected to grow to 100,000 in 2030.
Ubay is in the northeast of the province, and ha... |
https://en.wikipedia.org/wiki/Volterra%20integral%20equation | In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind.
A linear Volterra equation of the first kind is
where f is a given function and x is an unknown function to be solved for. A linear Volterra equatio... |
https://en.wikipedia.org/wiki/Stiff%20equation | In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes ... |
https://en.wikipedia.org/wiki/Dym%20equation | In mathematics, and in particular in the theory of solitons, the Dym equation (HD) is the third-order partial differential equation
It is often written in the equivalent form for some function v of one space variable and time
The Dym equation first appeared in Kruskal and is attributed to an unpublished paper b... |
https://en.wikipedia.org/wiki/Radical%20axis | In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal. For this reason the radical axis is also called the power line or power bisector of the two circles. In detail:
For two circles with centers and radii the powers of a point ... |
https://en.wikipedia.org/wiki/Power%20of%20a%20point | In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826.
Specifically, the power of a point with respect to a circle with center and radius is defined by
If is outside the circle, ... |
https://en.wikipedia.org/wiki/Lie%20algebra%20cohomology | In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was first introduced in 1929 by Élie Cartan to study the topology of Lie groups and homogeneous spaces by relating cohomological methods of Georges de Rham to properties of the Lie algebra. It was later extended by to coefficients in an... |
https://en.wikipedia.org/wiki/Keith%20R.%20Thompson | Keith Thompson (1951 - 2022) was a professor at Dalhousie University with a joint appointment in the Department of Oceanography and the Department of Mathematics and Statistics.
Thompson was trained in the UK and obtained his Ph.D. from the University of Liverpool in 1979. His research interests focused on ocean and s... |
https://en.wikipedia.org/wiki/Totally%20positive%20matrix | In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix is a positive number. A totally positive matrix has all entries positive, so it is also a positive matrix; and it has all principal minors positive (and positive eigenva... |
https://en.wikipedia.org/wiki/T-norm | In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to... |
https://en.wikipedia.org/wiki/Mimic%20function | A mimic function changes a file so it assumes the statistical properties of another file . That is, if is the probability of some substring occurring in , then a mimic function , recodes so that approximates for all strings of length less than some . It is commonly considered to be one of the basic techniques fo... |
https://en.wikipedia.org/wiki/Multi-adjoint%20logic%20programming | Multi-adjoint logic programming defines syntax and semantics of a logic programming program in such a way that the underlying maths justifying the results are a residuated lattice and/or MV-algebra.
The definition of a multi-adjoint logic program is given, as usual in fuzzy logic programming, as a set of weighted rule... |
https://en.wikipedia.org/wiki/How%20to%20Lie%20with%20Statistics | How to Lie with Statistics is a book written by Darrell Huff in 1954, presenting an introduction to statistics for the general reader. Not a statistician, Huff was a journalist who wrote many how-to articles as a freelancer.
The book is a brief, breezy illustrated volume outlining the misuse of statistics and errors i... |
https://en.wikipedia.org/wiki/CPMP | CPMP may refer to:
Committee for Proprietary Medicinal Products
Certified Project Management Professional
Core-Plus Mathematics Project
Cyclic pyranopterin monophosphate or fosdenopterin
Commissioning Process Management Professional (ASHRAE) |
https://en.wikipedia.org/wiki/Peter%20Swinnerton-Dyer | Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet, (2 August 1927 – 26 December 2018) was an English mathematician specialising in number theory at the University of Cambridge. As a mathematician he was best known for his part in the Birch and Swinnerton-Dyer conjecture relating algebraic properties of elliptic cu... |
https://en.wikipedia.org/wiki/Cyclically%20reduced%20word | In mathematics, cyclically reduced word is a concept of combinatorial group theory.
Let F(X) be a free group. Then a word w in F(X) is said to be cyclically reduced if and only if every cyclic permutation of the word is reduced.
Properties
Every cyclic shift and the inverse of a cyclically reduced word are cyclicall... |
https://en.wikipedia.org/wiki/P%C3%A9ter%20Frankl | Péter Frankl (born 26 March 1953 in Kaposvár, Somogy County, Hungary) is a mathematician, street performer, columnist and educator, active in Japan. Frankl studied mathematics at Eötvös Loránd University in Budapest and submitted his PhD thesis while still an undergraduate. He holds a PhD degree from the University Par... |
https://en.wikipedia.org/wiki/Master%20of%20Mathematics | A Master of Mathematics (or MMath) degree is a specific advanced integrated Master's degree for courses in the field of mathematics.
United Kingdom
In the United Kingdom, the MMath is the internationally recognized standard qualification after a four-year course in mathematics at a university.
The MMath programme was ... |
https://en.wikipedia.org/wiki/Phase%20plane | In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc. (any pair of variables). It is a t... |
https://en.wikipedia.org/wiki/New%20York%20State%20Mathematics%20League | The New York State Mathematics League (NYSML) competition was originally held in 1973 and has been held annually in a different location each year since. It was founded by Alfred Kalfus. The American Regions Math League competition is based on the format of the NYSML competition. The current iteration contains four sec... |
https://en.wikipedia.org/wiki/Cellular%20homology | In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules.
Definition
If is a CW-complex with n-skeleton , the cellular-homology modules are defined as the homology... |
https://en.wikipedia.org/wiki/Duoprism | In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an -polytope and an -polytope is an -polytope, where and are dimensions of 2 (polygon) or higher.
The lowest-dimensional du... |
https://en.wikipedia.org/wiki/Max%20Planck%20Institute%20for%20Mathematics%20in%20the%20Sciences | The Max Planck Institute for Mathematics in the Sciences (MPI
MiS) in Leipzig is a research institute of the Max Planck Society. Founded on March 1, 1996, the institute works on projects which apply mathematics in various areas of natural sciences, in particular physics, biology, chemistry and material science.
Resea... |
https://en.wikipedia.org/wiki/Meyer%27s%20theorem | In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers nontrivially represents zero. In other words, if the equation:
Q(x) = 0
has a non-zero real solution, then it has a non-zero rational solution (the converse is o... |
https://en.wikipedia.org/wiki/Karl%20Shell | Karl Shell (born May 10, 1938) is an American theoretical economist, specializing in macroeconomics and monetary economics.
Shell received an A.B. in mathematics from Princeton University in 1960. He earned his Ph.D. in economics in 1965 at Stanford University, where he studied under Nobel Prize in Economics winner K... |
https://en.wikipedia.org/wiki/Topological%20manifold | In topology, a branch of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types ... |
https://en.wikipedia.org/wiki/Differentiable%20manifold | In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts... |
https://en.wikipedia.org/wiki/Weak%20convergence%20%28Hilbert%20space%29 | In mathematics, weak convergence in a Hilbert space is convergence of a sequence of points in the weak topology.
Definition
A sequence of points in a Hilbert space H is said to converge weakly to a point x in H if
for all y in H. Here, is understood to be the inner product on the Hilbert space. The notation
is so... |
https://en.wikipedia.org/wiki/Retraction%20%28topology%29 | In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrink... |
https://en.wikipedia.org/wiki/Space%20mathematics | Space mathematics may refer to:
Orbital mechanics
Newton's laws of motion
Newton's law of universal gravitation
Space (mathematics) |
https://en.wikipedia.org/wiki/Polish%20Mathematical%20Society | The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU).
History
The society was established in Kraków, Poland on 2 April 1919 . It was originally called... |
https://en.wikipedia.org/wiki/Gegenbauer%20polynomials | In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenb... |
https://en.wikipedia.org/wiki/Axiomatic%20foundations%20of%20topological%20spaces | In the mathematical field of topology, a topological space is usually defined by declaring its open sets. However, this is not necessary, as there are many equivalent axiomatic foundations, each leading to exactly the same concept. For instance, a topological space determines a class of closed sets, of closure and inte... |
https://en.wikipedia.org/wiki/Borel%20equivalence%20relation | In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology).
Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F, in symbols E ≤B F, if and only if there i... |
https://en.wikipedia.org/wiki/Abstrakt%20Algebra | Abstrakt Algebra was a Swedish experimental metal band with influences from power metal and doom metal. It was founded by bassist Leif Edling in 1994, shortly after his main project Candlemass split up.
They made one album, but Edling had already started working on a second album with a different line-up. However, due... |
https://en.wikipedia.org/wiki/Moving-knife%20procedure | In the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a knife.
The simplest example is a moving-knife equivalent of the I cut, you choose scheme, first described by A.K.Austin ... |
https://en.wikipedia.org/wiki/Central%20binomial%20coefficient | In mathematics the nth central binomial coefficient is the particular binomial coefficient
They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at n = 0 are:
, , , , , , 924, 3432, 12870, 48620, ...;
C... |
https://en.wikipedia.org/wiki/Pascal%27s%20rule | In mathematics, Pascal's rule (or Pascal's formula) is a combinatorial identity about binomial coefficients. It states that for positive natural numbers n and k,
where is a binomial coefficient; one interpretation of the coefficient of the term in the expansion of . There is no restriction on the relative sizes o... |
https://en.wikipedia.org/wiki/Degree%20distribution | In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network.
Definition
The degree of a node in a network (sometimes referred to incorrectly as the connectiv... |
https://en.wikipedia.org/wiki/Fixed-point%20index | In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points.
The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the co... |
https://en.wikipedia.org/wiki/Fermat%27s%20factorization%20method | Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares:
That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N.
Each odd number has such a representation. Indeed, if is a ... |
https://en.wikipedia.org/wiki/Evolutionary%20graph%20theory | Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. That the underlying topology can substantially affect the results of the evolutio... |
https://en.wikipedia.org/wiki/Emacs%20Speaks%20Statistics | Emacs Speaks Statistics (ESS) is an Emacs package for programming in statistical languages. It adds two types of modes to emacs:
ESS modes for editing statistical languages like R, SAS and Julia; and
inferior ESS (iESS) modes for interacting with statistical processes like R and SAS.
Modes of types (1) and (2) work... |
https://en.wikipedia.org/wiki/Prewellordering | In set theory, a prewellordering on a set is a preorder on (a transitive and reflexive relation on ) that is strongly connected (meaning that any two points are comparable) and well-founded in the sense that the induced relation defined by is a well-founded relation.
Prewellordering on a set
A prewellordering on... |
https://en.wikipedia.org/wiki/Ordinal%20arithmetic | In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by ... |
https://en.wikipedia.org/wiki/Finite%20morphism | In algebraic geometry, a finite morphism between two affine varieties is a dense regular map which induces isomorphic inclusion between their coordinate rings, such that is integral over . This definition can be extended to the quasi-projective varieties, such that a regular map between quasiprojective varieties is... |
https://en.wikipedia.org/wiki/Moore%20space%20%28algebraic%20topology%29 | In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of homotopy theory, in the sense that it has only one nonzero homology (rather than homotopy) group.
Formal definition
Given an abelian g... |
https://en.wikipedia.org/wiki/Ordination%20%28disambiguation%29 | Ordination is the process of consecrating clergy.
Ordination may also refer to:
Ordination (statistics), a multivariate statistical analysis procedure
Ordination (1640), a painting in Nicolas Poussin's first Seven Sacraments series
See also
Ordination of women
Ordination mill |
https://en.wikipedia.org/wiki/Ordination%20%28statistics%29 | Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space... |
https://en.wikipedia.org/wiki/Resampling | Resampling may refer to:
Resampling (audio), several related audio processes
Resampling (statistics), resampling methods in statistics
Resampling (bitmap), scaling of bitmap images
See also
Sample-rate conversion
Downsampling
Upsampling
Oversampling
Sampling (information theory)
Signal (information theory)
... |
https://en.wikipedia.org/wiki/Functional%20data%20analysis | Functional data analysis (FDA) is a branch of statistics that analyses data providing information about curves, surfaces or anything else varying over a continuum. In its most general form, under an FDA framework, each sample element of functional data is considered to be a random function. The physical continuum over... |
https://en.wikipedia.org/wiki/Richard%20Fateman | Richard J Fateman (born November 4, 1946) is a professor emeritus of computer science at the University of California, Berkeley.
He received a BS in Physics and Mathematics from Union College in June, 1966, and a Ph.D. in Applied Mathematics from Harvard University in June, 1971. He was a major contributor to the Mac... |
https://en.wikipedia.org/wiki/Notation%20in%20probability%20and%20statistics | Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols.
Probability theory
Random variables are usually written in upper case roman letters: , , etc.
Particular realizations of a random variable are written in corresponding lower... |
https://en.wikipedia.org/wiki/Procept | In mathematics education, a procept is an amalgam of three components: a "process" which produces a mathematical "object" and a "symbol" which is used to represent either process or object. It derives from the work of Eddie Gray and David O. Tall.
The notion was first published in a paper in the Journal for Research i... |
https://en.wikipedia.org/wiki/Glossary%20of%20probability%20and%20statistics | This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design.
A
B
C
D
E
F
G
H
I... |
https://en.wikipedia.org/wiki/Quasi-finite%20morphism | In algebraic geometry, a branch of mathematics, a morphism f : X → Y of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions:
Every point x of X is isolated in its fiber f−1(f(x)). In other words, every fiber is a discrete (hence finite) set.
For every point x of... |
https://en.wikipedia.org/wiki/Ky%20Fan%20inequality | In mathematics, there are two different results that share the common name of the Ky Fan inequality. One is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers of the unit interval. The result was published on page 5 of the book Inequalities by Edwin F. Beckenbach and Richard E. ... |
https://en.wikipedia.org/wiki/Quadratic%20variation | In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales. Quadratic variation is just one kind of variation of a process.
Definition
Suppose that is a real-valued stochastic process defined on a probability space and with time index ranging ... |
https://en.wikipedia.org/wiki/Generalizations%20of%20the%20derivative | In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, geometry, etc.
Fréchet derivative
The Fréchet derivative defines the derivative for general normed vector spaces . Briefly... |
https://en.wikipedia.org/wiki/Multicategory | In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of several variables. Multicategories are als... |
https://en.wikipedia.org/wiki/Ganglia%20%28software%29 | Ganglia is a scalable, distributed monitoring tool for high-performance computing systems, clusters and networks. The software is used to view either live or recorded statistics covering metrics such as CPU load averages or network utilization for many nodes.
Ganglia software is bundled with enterprise-level Linux di... |
https://en.wikipedia.org/wiki/Steenrod%20algebra | In algebraic topology, a Steenrod algebra was defined by to be the algebra of stable cohomology operations for mod cohomology.
For a given prime number , the Steenrod algebra is the graded Hopf algebra over the field of order , consisting of all stable cohomology operations for mod cohomology. It is generated by ... |
https://en.wikipedia.org/wiki/Change%20of%20variables | In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Change of variables is a... |
https://en.wikipedia.org/wiki/Point%20process | In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space.
Point processes can be used for spatial data analysis, which is of interest in such diverse disciplines as forestry, plant ecolog... |
https://en.wikipedia.org/wiki/Invariants%20of%20tensors | In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial
,
where is the identity operator and represent the polynomial's eigenvalues.
More broadly, any scalar-valued function is an inva... |
https://en.wikipedia.org/wiki/Coxeter%20element | In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group. It is named after H.S.M. Coxeter.
Definitions
Note that this article assumes a finite Coxeter group. For infinite Coxeter groups, there are multiple conjugacy classes of Coxeter elements, and they have infinite orde... |
https://en.wikipedia.org/wiki/Plastic%20number | In mathematics, the plastic number (also known as the plastic constant, the plastic ratio, the minimal Pisot number, the platin number, Siegel's number or, in French, ) is a mathematical constant which is the unique real solution of the cubic equation
It has the exact value
Its decimal expansion begins with .
P... |
https://en.wikipedia.org/wiki/Uniformization%20%28set%20theory%29 | In set theory, a branch of mathematics, the axiom of uniformization is a weak form of the axiom of choice. It states that if is a subset of , where and are Polish spaces, then there is a subset of that is a partial function from to , and whose domain (the set of all such that exists) equals
Such a function is... |
https://en.wikipedia.org/wiki/Sieve%20of%20Atkin | In mathematics, the sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer. Compared with the ancient sieve of Eratosthenes, which marks off multiples of primes, the sieve of Atkin does some preliminary work and then marks off multiples of squares of primes, thus achieving a bett... |
https://en.wikipedia.org/wiki/Irving%20S.%20Reed | Irving Stoy Reed (November 12, 1923 – September 11, 2012) was an American mathematician and engineer. He is best known for co-inventing a class of algebraic error-correcting and error-detecting codes known as Reed–Solomon codes in collaboration with Gustave Solomon. He also co-invented the Reed–Muller code.
Reed made ... |
https://en.wikipedia.org/wiki/Gustave%20Solomon | Gustave Solomon (October 27, 1930 – January 31, 1996) was an American mathematician and electrical engineer who was one of the founders of the algebraic theory of error detection and correction.
Career
Solomon completed his Ph.D. in mathematics at the Massachusetts Institute of Technology in 1956 under direction of Ke... |
https://en.wikipedia.org/wiki/Pascal%27s%20simplex | In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
Generic Pascal's m-simplex
Let m (m > 0) be a number of terms of a polynomial and n (n ≥ 0) be a power the polynomial is raised to.
Let denote a Pascal's m-simplex. Each P... |
https://en.wikipedia.org/wiki/Subfunctor | In category theory, a branch of mathematics, a subfunctor is a special type of functor that is an analogue of a subset.
Definition
Let C be a category, and let F be a contravariant functor from C to the category of sets Set. A contravariant functor G from C to Set is a subfunctor of F if
For all objects c of C, G(c)... |
https://en.wikipedia.org/wiki/Antiisomorphism | In category theory, a branch of mathematics, an antiisomorphism (or anti-isomorphism) between structured sets A and B is an isomorphism from A to the opposite of B (or equivalently from the opposite of A to B). If there exists an antiisomorphism between two structures, they are said to be antiisomorphic.
Intuitively, ... |
https://en.wikipedia.org/wiki/Interior%20product | In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, or inner derivation) is a degree −1 (anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition... |
https://en.wikipedia.org/wiki/Northern%20Italy | Northern Italy (, , ) is a geographical and cultural region in the northern part of Italy. The Italian National Institute of Statistics defines the region as encompassing the four Northwestern regions of Piedmont, Aosta Valley, Liguria and Lombardy in addition to the four Northeastern regions of Trentino-Alto Adige, Ve... |
https://en.wikipedia.org/wiki/Central%20Italy | Central Italy ( or just ) is one of the five official statistical regions of Italy used by the National Institute of Statistics (ISTAT), a first-level NUTS region, and a European Parliament constituency.
Regions
Central Italy encompasses four of the country's 20 regions:
Lazio
Marches (Marche)
Tuscany (Toscana)
Um... |
https://en.wikipedia.org/wiki/Insular%20Italy | Insular Italy ( or just , meaning "islands") is one of the five official statistical regions of Italy used by the National Institute of Statistics (ISTAT), a first level NUTS region and a European Parliament constituency. Insular Italy encompasses two of the country's 20 regions: Sardinia and Sicily.
Geography
Insular... |
https://en.wikipedia.org/wiki/Common%20Algebraic%20Specification%20Language | The Common Algebraic Specification Language (CASL) is a general-purpose specification language based on first-order logic with induction. Partial functions and subsorting are also supported.
Overview
CASL has been designed by CoFI, the Common Framework Initiative (CoFI), with the aim to subsume many existing specifica... |
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