- Function
wiktionarypar function Function may refer to Diatonic function , a term in music theory Function biology , explaining why a feature survived selection Function computer science , or subroutine, a portion of code within a larger program, performs a specific task Function engineering , related to the selected property of a system Function language , in linguistics, a way of achieving an aim using language Function mathematics , an abstract entity that associates an input to a corresponding output according to some rule Function model , a structured representation of the functions, activities or processes Function object , or functor or functionoid, a concept of object oriented programming Function Drinks , a beverage company based in Redondo Beach, California. A formal event such as a party or meeting See also Function hall Functional disambiguation Functionalism disambiguation Functor disambig bs Funkcija vor bg ca Funci desambiguaci cs Funkce da Funktion de Funktion et Funktsioon es Funci n eo Funkcio eu Funtzio argipena fr Fonction ko it Funzione lt Funkcija lmo Funziun nl Functie ja no Funksjon pl Funkcja ujednoznacznienie pt Fun o desambigua o ro Func ie dezambiguizare ru simple Function sk Funkcia sl Funkcija razlo itev sr sh Funkcija razvrstavanje sv Funktion olika betydelser th uk zh ... more details
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- T-function
Image VEST Core4 LowLevel.png thumbnail 320px right VEST 4 T function followed by a transposition layer In cryptography , a T function is a bijection bijective mapping that updates every bit of the state computer science state in a way that can be described as math x i x i f x 0, cdots, x i 1 math , or in simple words an update function in which each bit of the state is updated by a linear combination of the same bit and a function of a subset of its less significant bits. If every single less significant bit is included in the update of every bit in the state, such a T function is called triangular . Thanks to their bijectivity no collisions, therefore no entropy loss regardless of the used Boolean function s and regardless of the selection of inputs as long as they all come from one side of the output bit , T functions are now widely used in cryptography to construct block cipher s, stream cipher s, PRNG s and cryptographic hash function hash functions . T functions were first proposed in 2002 by Alexander Klimov A. Klimov and Adi Shamir A. Shamir in their paper A New Class of Invertible Mappings . Ciphers such as TSC 1 , TSC 3 , TSC 4 , ABC stream cipher ABC , Mir 1 and VEST are built with different types of T functions. Because arithmetic operation s such as addition , subtraction and multiplication are also T functions triangular T functions , software efficient word based T functions can be constructed by combining bitwise logic with arithmetic operations. Another important property of T functions based on arithmetic operations is predictability of their period mathematics period , which is highly attractive to cryptographers. Although triangular T functions are naturally vulnerable to guess and determine attacks, well chosen bitwise transposition mathematics transposition ... bit. Subsequent transposition of the output bits and iteration of the T function also do not affect ... and losing the T function bias of depending only on the less significant bits of the state. References ... more details
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- Quasiconvex function
of unimodal ity for functions with a single real argument. Definition and properties A function math ...Image Quasiconvex function.png right thumb A quasiconvex function that is not convex. Image Nonquasiconvex function.png right thumb A function that is not quasiconvex the set of points in the domain of the function for which the function values are below the dashed red line is the union of the two red ... density function of the normal distribution is quasiconcave but not concave. In mathematics , a quasiconvex function is a real number real valued function mathematics function defined on an interval ... of the function and looking down at the remaining part of the domain, an observer always sees ... points does not give a higher a value of the function than do both of the other points, then f is quasiconvex ... a quasi convex function math f x math is to require that each sub levelset math S alpha f x f x leq ... value of the function than one of the other points does. A quasiconcave function is a function whose negative is quasiconvex, and a strictly quasiconcave function is a function whose negative is strictly quasiconvex. Equivalently a function math f math is quasiconcave if math f lambda x 1 lambda y ... ,f y big math Image Monotonicity example2.png right thumb A quasilinear function is both quasiconvex and quasiconcave. Image Quasi concave function graph.png right thumb The graph of a function that is both concave and quasi convex on the nonnegative real numbers. A strictly quasiconvex function has strictly convex lower contour set s, while a strictly quasiconcave function has strictly convex upper contour set s. A function that is both quasiconvex and quasiconcave is quasilinear . Applications ... than do the convex closures provided by Lagrangian function Lagrangian Lagrange duality dual problems ... , quasiconcave utility function s imply that consumers have convex preferences . Quasiconvex ... rbrace math with math w i math non negative composition with a non decreasing function i.e. math g ... more details
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- Omega function
In mathematics, omega function or &omega function may mean Pearson&ndash Cunningham function Lambert W function Wright Omega function mathdab ... more details
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- G-function
Barnes G function , related to the Gamma function Meijer G function , a generalization of the hypergeometric function Siegel G function , a class of functions in transcendence theory mathdab ... more details
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- Transmission function
Transmission function can refer to transfer function propagation constant disambiguation ... more details
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- Riemann function
Riemann function may refer to one of the several function mathematics functions named after the mathematician Bernhard Riemann , including Riemann zeta function Thomae s function Riemann theta function . dab fr Fonction de Riemann ... more details
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- Zeta function
In mathematics , a zeta function is usually a function mathematics function analogous to the original example the Riemann zeta function math zeta s sum n 1 infty frac 1 n s . math Zeta functions include Airy zeta function , related to the zeros of the Airy function Artin Mazur zeta function Artin Mazur zeta function of a dynamical system Barnes zeta function Beurling zeta function of Beurling generalized primes Dedekind zeta function Dedekind zeta function of a number field Real analytic Eisenstein series Epstein zeta function Epstein zeta function of a quadratic form. Goss zeta function of a function field Hasse Weil zeta function Hasse Weil zeta function of a variety Hurwitz zeta function Hurwitz zeta function A generalization of the Riemann zeta function Ihara zeta function Ihara zeta function of a graph Igusa zeta function Igusa zeta function Jacobi zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. L function , a twisted zeta function. Lefschetz zeta function Lefschetz zeta function of a morphism Lerch zeta function Lerch zeta function A generalization of the Riemann zeta function Local zeta function of a characteristic p variety Matsumoto zeta function Minakshisundaram Pleijel zeta function of a Laplacian Motivic zeta function of a motive Mordell Tornheim zeta function of several variables Multiple zeta function Prime zeta function Like the Riemann zeta function, but only summed over primes. Riemann zeta function The archetypal example. Selberg zeta function Selberg zeta function of a Riemann surface Shintani zeta function Weierstrass zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. Witten zeta function of a Lie group Zeta function operator Zeta function of an operator See also Artin conjecture L functions Artin conjecture Birch and Swinnerton Dyer conjecture Riemann hypothesis and the generalized Riemann hypothesis . Selberg class S External links http www.maths.ex.ac.uk ... more details
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- Sigma function
In mathematics, by sigma function one can mean one of the following The Divisor function sum of divisors function sub a sub n , an arithmetic function . Weierstrass sigma function , related to elliptic functions Rado s sigma function, see busy beaver . mathdab de Teilersumme fr Fonction sigma ... more details
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- Pi function
In mathematics , two different function mathematics functions are known as the pi or Pi function math pi x , math pi function &ndash the prime counting function math Pi x , math Pi function &ndash the Gamma function when offset to coincide with the factorial disambig th ... more details
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- Kernel (function)
The phrase Kernel function may refer to a kernel function , i.e., the kernel of an integral operator for that topic see kernel mathematics , or the kernel of a function . disambig ... more details
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- Influence function
In mathematics , influence function is used to mean either a synonym for a Green s function Influence function statistics , the effect on an estimator of changing one point of the sample. disambig ... more details
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- Dedekind function
In number theory , Dedekind function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta function disambig de Dedekindsche Funktion ... more details
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- Partition function
Partition function may refer to Partition function number theory Partition function mathematics , which generalizes its use in statistical mechanics and quantum field theory Partition function statistical mechanics Partition function quantum field theory disambig su Fungsi partisi ... more details
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- Green function
Green function might refer to Green s function of a differential operator. Deligne Lusztig theory Green function in the representation theory of finite groups of Lie type. Green s function many body theory Green s function in many body theory . disambig ... more details
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- Mass function
Mass function may refer to Initial mass function , a function that describes the mass distribution of a population of stars in terms of their initial mass Probability mass function , a function that gives the probability that a discrete random variable is exactly equal to some value disambig ... more details
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- Tau function
Tau function may refer to Tau function Ramanujan tau function , giving the Fourier coefficients of the Ramanujan modular form. Divisor function , an arithmetic function giving the number of divisors of an integer. tau function representation theory Tau function in the representation theory of affine Lie algebra s and integrable system soliton equations . disambig Long comment to prevent listing on Special Shortpages.......................................................................... more details
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- Unary function
A unary function is a function mathematics function that takes one Parameter computer science argument . In computer science , a unary operator is a subset of unary function. Many of the elementary function s are unary functions, in particular the trigonometric functions and hyperbolic function are unary. See also Arity Binary function Binary operator List of mathematical functions Ternary operation References http www.cs.ucl.ac.uk staff W.Langdon FOGP Foundations of Genetic Programming Category Functions and mappings Category Types of functions maths stub bs Unarna funkcija ... more details
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- Eta function
There are two distinct functions called eta function in number theory The Dirichlet eta function The Dedekind eta function Category Mathematical disambiguation Category Number theory disambig ja ... more details
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- Chord function
The term chord function may refer to Diatonic function in music, the role of a chord in relation to a diatonic key in mathematics, the length of a chord of a circle as a trigonometric function of the length of the corresponding arc see in particular Ptolemy s table of chords . disambig ... more details
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- Spherical function
Spherical function can refer to Spherical harmonics Zonal spherical function mathdab Long comment to avoid being listed on short pages ... more details
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- Potential function
The term potential function may refer to A mathematical function mathematics function whose values are a physical potential . The class of functions known as harmonic function s, which are the topic of study in potential theory . The potential function of a potential game . A function used in the potential method of amortized analysis to describe an investment of resources by past operations that can be used by future operations. mathdab ... more details
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- Psi function
Psi function can refer to the Dedekind psi function math psi n math the Chebyshev function math psi x math the polygamma function math psi m z math or its special cases the digamma function math psi z math the trigamma function math psi 1 z math mathdab de Psi Funktion ... more details
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- Function tree
Unreferenced date August 2009 Image Function tree Bolognese.png thumb A function tree for spaghetti bolognese In the systems theory theory of complex systems , a function tree is a diagram showing the dependencies between the functions of a system . It breaks a problem or its solution down into simpler parts. When used in computer programming , a function tree visualizes which Function computer science function calls another. math stub Category Diagrams de Funktionsbaum ... more details
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- Weber function
In mathematics, Weber function can refer to several different families of functions, mostly named after the physicist H. F. Weber . Weber s modular function named after the mathematician H. M. Weber . Weber function is sometimes used as a name for Bessel function s of the second kind. Weber functions E sub &nu sub are solutions of an inhomogeneous Bessel equation, and are linear combinations of Anger function s if &nu is not an integer, or linear combinations of Struve function s if &nu is an integer. Weber Hermite function is another name for parabolic cylinder functions, which are solutions of Weber s differential equation . mathdab ... more details
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