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91 relations: A Course of Pure Mathematics, Adrian Lewis, Analytic continuation, Analytic function, Antiderivative, Arg max, Bijection, Boris Mordukhovich, Branch point, Branched covering, Claude Berge, Codomain, Color confinement, Complex analysis, Complex logarithm, Complex number, Complex plane, Constant of integration, Contraction mapping, Convex analysis, Correspondence (mathematics), Crystallographic defect, Cube root, Differential calculus, Differential inclusion, Domain of a function, Dušan Repovš, Duke Mathematical Journal, Equation, Fat link, Fixed-point theorem, G. H. Hardy, Game theory, Gauge theory, General topology, Hagen Kleinert, Hans Rådström, Hélène Frankowska, Hemicontinuity, Heterogeneous relation, Hyperlink, Implicit function theorem, Injective function, Integer, Integral, Interval finite element, Inverse function, Inverse trigonometric functions, Jonathan Borwein, Journal of Mathematical Analysis and Applications, ..., Kakutani fixed-point theorem, Kuratowski and Ryll-Nardzewski measurable selection theorem, List of continuity-related mathematical topics, Logarithm, Magnetic monopole, Manifold, Mathematical analysis, Mathematical economics, Mathematical optimization, Mathematics, Measure (mathematics), Melting, Michael selection theorem, Monodromy, Nash equilibrium, Neighbourhood (mathematics), Nth root, Optimal control, Paracompact space, Partial function, Paul Dirac, Phase transition, Plasticity (physics), Principal value, R. Tyrrell Rockafellar, Real number, Riemann surface, Roger J-B Wets, Semi-continuity, Special functions, Square root, Subderivative, Subset, Superconductivity, Superfluidity, Surjective function, Taylor series, Technische Universität Ilmenau, Topological degree theory, Variational analysis, Vortex. Expand index (41 more) »
A Course of Pure Mathematics
A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy.
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Adrian Lewis
Adrian Lewis (born 21 January 1985) is an English professional darts player currently playing in the PDC.
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Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Arg max
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points of the domain of some function at which the function values are maximized.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Boris Mordukhovich
Boris Mordukhovich is an American mathematician recognized for his research in the areas of nonlinear analysis, optimization, and control theory.
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Branch point
In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.
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Branched covering
In mathematics, a branched covering is a map that is almost a covering map, except on a small set.
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Claude Berge
Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory.
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Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
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Color confinement
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 trillion kelvin (corresponding to energies of approximately 130–140 MeV per particle).
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex logarithm
In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Constant of integration
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.
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Contraction mapping
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M,d) is a function f from M to itself, with the property that there is some nonnegative real number 0\leq k such that for all x and y in M, The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps.
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Convex analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
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Correspondence (mathematics)
In mathematics and mathematical economics, correspondence is a term with several related but distinct meanings.
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Crystallographic defect
Crystalline solids exhibit a periodic crystal structure.
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Cube root
In mathematics, a cube root of a number x is a number y such that y3.
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Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.
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Differential inclusion
In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form where F is a multivalued map, i.e. F(t, x) is a set rather than a single point in \scriptstyle^d.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Dušan Repovš
Dušan D. Repovš (born November 30, 1954) is a Slovenian mathematician from Ljubljana, Slovenia.
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Duke Mathematical Journal
Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press.
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Equation
In mathematics, an equation is a statement of an equality containing one or more variables.
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Fat link
A fat link (also known as a "one-to-many" link, an "extended link") or a "multi-tailed link" is a hyperlink which leads to multiple endpoints; the link is a multivalued function.
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Fixed-point theorem
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x).
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G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.
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Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
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Gauge theory
In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is Professor of Theoretical Physics at the Free University of Berlin, Germany (since 1968), at the West University of Timişoara, at the in Bishkek.
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Hans Rådström
Hans Vilhem Rådström (1919–1970) was a Swedish mathematician who worked on complex analysis, continuous groups, convex sets, set-valued analysis, and game theory.
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Hélène Frankowska
Hélène Frankowska, or Halina Frankowska is a Polish and French mathematician known for her research in control theory and set-valued analysis.
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Hemicontinuity
In mathematics, the notion of the continuity of functions is not immediately extensible to multivalued mappings or correspondences between two sets A and B. The dual concepts of upper hemicontinuity and lower hemicontinuity facilitate such an extension.
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Heterogeneous relation
In mathematics, a heterogeneous relation is a subset of a Cartesian product A × B, where A and B are distinct sets.
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Hyperlink
In computing, a hyperlink, or simply a link, is a reference to data that the reader can directly follow either by clicking, tapping, or hovering.
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Implicit function theorem
In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Interval finite element
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
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Jonathan Borwein
Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia.
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Journal of Mathematical Analysis and Applications
The Journal of Mathematical Analysis and Applications is an academic journal in mathematics, specializing in mathematical analysis and related topics in applied mathematics.
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Kakutani fixed-point theorem
In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions.
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Kuratowski and Ryll-Nardzewski measurable selection theorem
In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a multifunction to have a measurable selection.
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List of continuity-related mathematical topics
In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.
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Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
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Magnetic monopole
A magnetic monopole is a hypothetical elementary particle in particle physics that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa).
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematical economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Melting
Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid.
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Michael selection theorem
In functional analysis, a branch of mathematics, the most popular version of the Michael selection theorem, named after Ernest Michael, states the following.
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Monodromy
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.
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Nash equilibrium
In game theory, the Nash equilibrium, named after American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Nth root
In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.
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Optimal control
Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.
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Paracompact space
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite.
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Partial function
In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.
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Paul Dirac
Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.
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Phase transition
The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma.
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Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces.
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Principal value
In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.
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R. Tyrrell Rockafellar
Ralph Tyrrell Rockafellar (born February 10, 1935) is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
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Roger J-B Wets
Roger Jean-Baptiste Robert Wets (born February 1937) is a "pioneer" in stochastic programming and a leader in variational analysis who publishes as Roger J-B Wets.
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Semi-continuity
In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Square root
In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.
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Subderivative
In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to functions which are not differentiable.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature.
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Superfluidity
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Technische Universität Ilmenau
The Technische Universität Ilmenau (TU Ilmenau) is a German public research university located in Ilmenau, Thuringia, Germany.
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Topological degree theory
In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane.
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Variational analysis
In mathematics, the term variational analysis usually denotes the combination and extension of methods from convex optimization and the classical calculus of variations to a more general theory.
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Vortex
In fluid dynamics, a vortex (plural vortices/vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved.
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Function multivalued, Left-total, Left-total relation, Many-valued function, Multi-valued, Multi-valued function, Multiple valued function, Multiple-valued, Multiple-valued function, Multivalent function, Multivalued Function, Mutli-valued function, Set-valued analysis, Set-valued function, Single-valued, Single-valued function.
References
[1] https://en.wikipedia.org/wiki/Multivalued_function
