Roman Jakobson defined six functions of language or communication functions , according to which an effective act of verbal communication can be described. ref Waugh, Linda 1980 http www.jstor.org pss 1772352 The Poetic Function in the Theory of Roman Jakobson , Poetics Today ref Each of the functions has an associated factor. For this work, Jakobson was influenced by Karl B hler s Organon Model . Image Roma jakobson theory.png right thumb The six factors of an effective verbal communication. To each one corresponds a communication function not displayed in this picture . ref name Middleton Middleton, Richard 1990 2002 . Studying Popular Music , p.241. Philadelphia Open University Press. ISBN 0335152759. ref The six functions of language The Referential Function corresponds to the factor of Context and describes a situation, object or mental state. The descriptive statements of the referential function can consist of both definite descriptions and deixis deictic words, e.g. The autumn leaves have all fallen now. The Expressive alternatively called emotive or affective Function relates to the Addresser and is best exemplified by interjections and other sound changes that do not alter the denotation denotative meaning of an utterance but do add information about the Addresser s speaker s internal state, e.g. Wow, what a view The Conative Function engages the Addressee directly and is best illustrated by vocative s and imperative mood imperatives , e.g. Tom Come inside and eat The Poetic Function focuses on the message for its own sake ref name Duranti 1997 Duranti 1997 ref and is the operative function in poetry as well as slogans. The Phatic Function is language for the sake of interaction and is therefore associated with the Contact factor. The Phatic Function can be observed in greetings and casual discussions of the weather, particularly with strangers. The Metalingual ... www.signosemio.com jakobson a fonctions.asp The Functions of Language Category Theories of language ... more details
Proto value functions PVFs are automatically learned basis function s that are useful in approximating task specific value functions, providing a compact representation of the powers of transition matrices. They provide a novel framework for solving the Assignment problem credit assignment problem . The framework ... learning problems, using multiscale spectral and manifold learning methods. Proto value functions ... Laplacian . Proto value functions were first introduced in the context of reinforcement learning by Sridhar Mahadevan in his paper, Proto Value Functions Developmental Reinforcement Learning at ICML ... Functions Developmental Reinforcement Learning . Proceedings of the International Conference on Machine ... basis functions , polynomial state encodings, and Cerebellar Model Articulation Controller CMAC s. However, parameters associated with these basis functions often require significant domain specific ... icml07.pdf Constructing Basis Functions from Directed Graphs for Value Function Approximation , International Conference on Machine Learning ICML , 2007 ref Proto value functions attempts to solve this required .... ref name key1 Overview Proto value functions are task independent global basis functions that collectively span the entire space of possible value functions for a given state space. ref name key1 ... have only been explored in the context of discrete Markov decision process MDP s. Proto value functions ... 35.pdf Proto Value Functions A Laplacian Framework for Learning Representation and Control in Markov ... TR 2006 35, 2006 ref Basis functions from graph Laplacian In this approach, we will construct the basis ... operator on the space of functions on the graph, closely related to the random walk operator ... algebra, because the Laplacian eigenvector s can naturally be viewed as functions that map each vertex ... squares approximation. Least squares approximation using proto value functions Let math Phi G left ... of functions Category Spectral theory Category Articles needing attention ... more details
In mathematics, the prolate spheroidal wave functions are a set of functions derived by timelimiting .... The timelimited functions math psi n n math are the Prolate Spheroidal Wave Functions PSWFs . These functions are also encountered in a different context. When solving the Helmholtz equation ... spheroidal wavefunctions can be expanded as a series of Legendre functions. Let us note that if one ... in his 1935 article. There are different normalization schemes for spheroidal functions. A table ... wave functions were introduced by C. Niven in 1880 when studying the conduction of heat in an ellipsoid ... wave functions whose domain is a portion of the surface of the unit sphere are more generally called Slepian functions ref F. J. Simons, M. A. Wieczorek and F. A. Dahlen. Spatiospectral concentration ... ref F. J. Simons and Dahlen, F. A. Spherical Slepian functions and the polar gap in Geodesy ... spheroidal Wave functions Computing in Science & Engineering p. 84, May June 1999. I ... HWCIT Spheroidal functions Proceedings of the National Academy of Sciences USA 21 , 51 1935 C. Flammer Spheroidal Wave Functions. Stanford, CA Stanford University Press, 1957. Josef Meixner .... Little, and Fernando J. Corbat F. J. Corbat , Spheroidal Wave Functions. New York Wiley, 1956. M. Abramowitz and I. Stegun Handbook of Mathematical Functions http www.math.sfu.ca cbm aands page 751.htm ... 1961 articles bstj40 1 43.pdf Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty ... vol40 1961 articles bstj40 1 65.pdf Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty ... bstj vol41 1962 articles bstj41 4 1295.pdf Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty ... 6 3009.pdf Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty IV Extensions to Many Dimensions Generalized Prolate Spheroidal Functions Bell System Technical Journal 43 1964 Slepian, D. http www.alcatel lucent.com bstj vol57 1978 articles bstj57 5 1371.pdf Prolate Spheroidal Wave Functions ... more details
In mathematics , the Jacobi elliptic functions are a set of basic elliptic function s, and auxiliary ... pendulum mathematics . They also have useful analogies to the functions of trigonometry , as indicated by the matching notation sn for sin . The Jacobi elliptic functions occur more often in practical problems than the Weierstrass elliptic functions . They were introduced by Carl Gustav Jakob Jacobi ... construction There are twelve Jacobian elliptic functions. Each of the twelve corresponds to an arrow ... period s. The twelve Jacobian elliptic functions are then pq, where each of p and q is one of the letters s, c, d, n. The Jacobian elliptic functions are then the unique doubly periodic, meromorphic functions satisfying the following three properties There is a simple zero at the corner ... axis, respectively, then the Jacobi elliptic functions pq u will be real functions when u is real. Notation The elliptic functions can be given in a variety of notations, which can make the subject unnecessarily confusing. Elliptic functions are functions of two variables. The first variable might ... of elliptic integrals The above definition, in terms of the unique meromorphic functions satisfying ... the elliptic functions as inverses of the incomplete elliptic integral of the first kind. Let ... the elliptic functions can be thought of as being given by two variables, the amplitude math phi math and the parameter m . The remaining nine elliptic functions are easily built from the above three ... period K . Definition in terms of theta functions Equivalently, Jacobi elliptic functions ... the Jacobi functions are defined in terms of the elliptic modulus math k tau math , we need to invert ... the appropriate value for q . Minor functions Reversing the order of the two letters of the function name results in the reciprocals of the three functions above math begin align operatorname ns ... u & frac 1 operatorname dn u end align math Similarly, the ratios of the three primary functions correspond ... more details
sociology Manifest and latent functions are social concept social scientific concepts first clarified for sociology by Robert K. Merton . ref http www.diligio.com notes26.htm Diligio, 2000 ref Merton appeared interested in sharpening the conceptual tools to be employed in a Structural functionalism functional analysis . Manifest Functionalism sociology function s and Dysfunction sociology dysfunctions are conscious and deliberate, the latent ones the unconscious and unintended. ref name B63 http www.angelfire.com or sociologyshop manlat.html Berger, 1963 ref While functions are intended manifest ... Functions Manifest Functionalism sociology functions are the consequences that people observe or expect ... M2001 http www.as.ua.edu ant Faculty murphy ecologic.htm M.D. Murphy, 2001 ref Latent functions are those ... manifest and latent functions cquote ...the manifest function of anti gambling legislation may ... the manifest functions of social behavior , Merton sees attention to latent functions as increasing ... be manifest or latent. While functions are intended or recognized manifest , and may have a positive ... they are an element. Manifest Functionalism sociology functions are the obvious and intended ... it is a part. Latent functions are less obvious or unintended consequence s. Both manifest and latent functions contribute to the social system s unchanging ongoingness or stasis. In this very specific ... between manifest and latent functions was devised to preclude ... confusion ... between ... Durkheim s... analysis of the social functions of punishment is... focused on its latent functions consequences for the community rather than confined to manifest functions consequences for the criminal ... MANIFEST AND LATENT FUNCTIONS Extract from Robert K. Merton, Social Theory and Social Structure ... or sociologyshop manlat.html Manifest and Latent Functions Excerpt from Invitation to Sociology ... , Manifest and Latent Functions , Philosophical Quarterly , Vol. 21, No. 82 Jan., 1971 , pp. 51 60 ... more details
see also Logic of Computable Functions Logic for Computable Functions LCF is an interactive automated theorem prover developed at the universities of University of Edinburgh Edinburgh and Stanford University Stanford by Robin Milner and others in 1972. LCF introduced the general purpose programming language ML programming language ML to allow users to write theorem proving tactics. Theorems in the system are propositions of a special theorem abstract datatype . The ML type system ensures that theorems are derived using only the inference rule s given by the operations of the abstract type. Successors include Higher Order Logic HOL theorem prover HOL and Isabelle theorem prover Isabelle . References Reflist Refbegin cite web last Gordon first Michael J. C. authorlink Michael J. C. Gordon year 1996 title From LCF to HOL a short history url http www.cl.cam.ac.uk mjcg papers HolHistory.html accessdate 2007 10 11 cite manual author Milner, Robin title Logic for Computable Functions description of a machine implementation. publisher Stanford University date May 1972 url ftp reports.stanford.edu pub cstr reports cs tr 72 288 CS TR 72 288.pdf ref lcf Refend Mathlogic stub Category Logic in computer science Category Proof assistants es LCF ... more details
use dmy dates date January 2012 TOC Special member functions ref cite book last ISO IEC authorlink International Organization for Standardization title ISO IEC 14882 2011 edition 3 publisher ISO IEC year 2011 pages 12 ref in C are functions which the compiler will automatically generate if they are used, but not declared explicitly by the programmer. The special member functions are Default constructor if no other constructor is explicitly declared Copy constructor if no move constructor or move assignment operator is explicitly declared. If a destructor is declared generation of a copy constructor is deprecated. Move constructor if no copy constructor, move assignment operator or destructor is explicitly declared. Assignment operator in C Copy assignment operator if no move constructor or move assignment operator is explicitly declared. If a destructor is declared generation of a copy assignment operator is deprecated. Move assignment operator if no copy constructor, copy assignment operator or destructor is explicitly declared. Destructor computer science Destructor In these cases the compiler generated versions of these functions perform a memberwise operation. For example the compiler generated destructor will destroy each sub object base class or member of the object. The compiler generated functions will be code public code , non virtual function virtual ref Except for the destructor if a base class already has a virtual destructor. ref and the copy constructor and assignment operators will receive code const& code parameters and not be of the Copy constructor Definition alternative legal forms . Example The following example depicts two classes tt Explicit tt for which all Special member functions C 98 C 98 special member functions are explicitly declared and tt Implicit tt for which none are declared. source lang cpp include iostream class Explicit friend class ... functions ref cite book last ISO IEC authorlink International Organization for Standardization ... more details
In computer science , Programming Computable Functions , ref group note PCF is a programming language for computable functions, based on LCF, Scott s logic of computable functions harv Plotkin 1977 . Programming Computable Functions is used by harv Mitchell 1996 . It is also referred to as Programming with Computable Functions or Programming language for Computable Functions . ref or PCF , is a type system typed Functional programming functional language introduced by Gordon Plotkin in 1977. It is based on the Logic of Computable Functions LCF by Dana Scott . It can be considered as an extended version of the typed lambda calculus or a simplified version of modern typed functional languages such as ML programming language ML . A fully abstract model for PCF was first given by Robin Milner Milner 1977 . However, since Milner s model was essentially based on the syntax of PCF it was considered less than satisfactory Ong, 1995 . The first two fully abstract models not employing syntax were formulated during the 1990s. These models are based on game semantics Hyland and Ong, 2000 Abramsky, Jagadeesan, and Malacaria, 2000 and Kripke logical relations O Hearn and Riecke, 1995 . For a time it was felt that neither of these models was completely satisfactory, since they were not effectively presentable. However, Ralph Loader demonstrated that no effectively presentable fully abstract model could exist, since the question of program equivalence in the finitary fragment of PCF is not decidable. Syntax The types of PCF are inductively defined as nat is a type For types and , there is a type A context is a list of pairs x , where x is a variable name and is a type, such that no variable ... as the domain of Scott continuous functions from math sigma , math to math tau , math A context ... sigma n math Terms in context math Gamma vdash x sigma math are interpreted as continuous functions ... functions Y is interpreted by taking the least fixed point of the argument This model is not fully ... more details
File Rational Elliptic Functions n 1,2,3,4, x 1,1 .svg thumb right 300px Plot of elliptic rational functions ... functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic filter elliptic electronic filter s. These functions are sometimes called Chebyshev rational functions , not to be confused with certain other functions of the Chebyshev rational functions same name . Rational elliptic functions are identified by a positive ... s elliptic functions Jacobi elliptic cosine function . K is a complete elliptic integral of the first ... of the form math n 2 a3 b math where a and b are integers, the elliptic rational functions can be expressed using algebraic functions alone. Elliptic rational functions are closely related to the Chebyshev polynomials Just as the circular trigonometric functions are special cases of the Jacobi elliptic functions, so the Chebyshev polynomials are special cases of the elliptic rational functions. Expression as a ratio of polynomials For even orders, the elliptic rational functions may be expressed ... drops to the value of the discrimination factor L sub n sub File Rational Elliptic Functions xi varied ... form without explicit use of the Jacobi elliptic functions, then all math R n math for n of the form ... factor math L m cdot n xi L m L n xi math Limiting values The elliptic rational functions are related ... that poles and zeroes come in pairs such that math x pi x zi xi , math Odd order functions will have ... 0 , math the defining equation for the elliptic rational functions implies that math n frac K 1 ... be algebraically expressed i.e. without the need for calculating the Jacobi ellipse functions then the zeroes ... rational functions of order math 2 i3 j math may be algebraically expressed harv Lutovac 2001 loc ... few elliptic rational functions as math R 1 xi,x x , math math R 2 xi,x frac t 1 x 2 1 t 1 x ... location New Jersey, USA isbn 0 201 36130 2 ref harv DEFAULTSORT Elliptic Rational Functions Category ... more details
In mathematics , the study of special values of L functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi , namely math 1 , , frac 1 3 , , frac 1 5 , , frac 1 7 , , frac 1 9 , , cdots frac pi 4 , math by the recognition that expression on the left hand side is also L 1 where L s is the Dirichlet L function for the Gaussian rational Gaussian field . This formula is a special case of the analytic class number formula , and in those terms reads that the Gaussian field has class number problem class number 1 , and also contains four roots of unity , so accounting for the factor . There are two families of conjectures, formulated for general classes of L function L function s the very general setting being for L functions L s associated to Chow motive s over number field s , the division into two reflecting the questions of a how to replace &pi in the Leibniz formula by some other transcendental number whether or not it is yet possible for transcendental number theory to provide a proof of the transcendence and b how to generalise the rational factor in the formula class number divided by number of roots of unity by some algebraic construction of a rational number that will represent the ratio of the L function value to the transcendental factor. Subsidiary explanations are given for the integer values of n for which such formulae L n can be expected to hold. The conjectures for a are called Beilinson s conjectures , for Alexander Beilinson . ref http wwwmath.uni muenster.de u pschnei publ beilinson volume Schneider.pdf Peter Schneider, Introduction to the Beilinson Conjectures PDF ref ref http people.math.jussieu.fr nekovar ... Kato conjecture on special values of L functions. A survey of known results url http jtnb.cedram.org ... Functions for small moduli eprint 1008.2547 year 2010 bibcode 2010arXiv1008.2547M L functions footer DEFAULTSORT Special Values Of L Functions Category Zeta and L functions ... more details
About the ring of symmetric functions in algebraic combinatorics general properties of symmetric functions ... functions , is a specific limit of the rings of symmetric polynomial s in n indeterminates, as n ... polynomials nor functions . Among other things, this ring plays an important role in the representation ... of symmetric functions is based on that of symmetric polynomials. In a polynomial ring in some ... functions Most relations between symmetric polynomials do not depend on the number n of indeterminates ... elements, there is no fundamental difference between symmetric polynomials and symmetric functions. Defining individual symmetric functions It should be noted that the name symmetric function for elements of &Lambda sub R sub is a misnomer in neither construction the elements are functions ... infinite sums of monomials. We have therefore reverted to the older terminology of symmetric functions ... . The following are fundamental examples of symmetric functions. The monomial symmetric functions ... X sup &alpha sup . The distinct monomial symmetric functions are parametrized by the integer partition ... function can be written as an R linear combination of monomial symmetric functions, and the distinct monomial symmetric functions form a basis of &Lambda sub R sub as R module mathematics module . The elementary symmetric functions e sub k sub , for any natural number k one has e sub k sub ... sum symmetric functions p sub k sub , for any positive integer k one has p sub k sub ... 1. The complete homogeneous symmetric functions h sub k sub , for any natural number k h sub k sub is the sum of all monomial symmetric functions m sub &alpha sub where &alpha is a partition of ... k sub X sub 1 sub ,&hellip , X sub n sub for any n &ge k . The Schur functions s sub &lambda ... do define a symmetric function. A principle relating symmetric polynomials and symmetric functions ... of the ring of symmetric functions implies the following fundamental principle If P and Q are symmetric ... more details
year 1941 cite book author Rene Schilling, Renming Song and Zoran Vondracek title Bernstein functions ... MathWorld page on completely monotonic functions Category Theorems in real analysis Category ... more details
Infobox journal cover File BBFcover.png editor discipline Behavioral neuroscience abbreviation Behav. Brain Funct. publisher BioMed Central country frequency Articles published upon acceptance history 2005 present openaccess Yes impact 2.305 impact year 2010 website http www.behavioralandbrainfunctions.com OCLC 59722804 LCCN 2005243558 CODEN ISSN 1744 9081 eISSN Portal Neuroscience Behavioral and Brain Functions is a peer review peer reviewed scientific journal published by BioMed Central with Open access publishing Open Access to all content. The journal publishes articles on all aspects of neurobiology where the unifying theme is behavior or psychiatry behavioral dysfunction . ref name About cite web url http www.behavioralandbrainfunctions.com info about title About Behavioral and Brain Functions format work accessdate 2009 02 23 ref It was established in 2005 with Terje Sagvolden as founding editor in chief . Abstracting and indexing The journal is indexed by PubMed , Science Citation Index , Chemical Abstracts Service , and Scopus . ref name About According to the Journal Citation Reports , it has a 2010 impact factor of 2.305. ref name WoS cite web url http isiwebofknowledge.com title Web of Science year 2011 accessdate 2011 07 01 ref Article types The journal publishes articles in the following categories ref name About Empirical Research articles Review s Methodology articles Hypothesis Hypotheses Short reports Commentaries Study protocols Debate articles Book review s References Reflist External links Official website http www.behavioralandbrainfunctions.com DEFAULTSORT Behavioral And Brain Functions Category Neuroscience journals Category Behavioral neuroscience Category BioMed Central academic journals Category Publications established in 2005 Category English language journals ... more details
See also splitting lemma in homological algebra . In mathematics , especially in singularity theory the splitting lemma is a useful result due to Ren Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point mathematics critical point . Formal statement Let math scriptstyle f mathbb R n,0 to mathbb R ,0 math be a smooth function germ, with a critical point at 0 so math scriptstyle partial f partial x i 0 0, i 1, dots, n math . Let V be a subspace of math scriptstyle mathbb R n math such that the restriction f V is critical point mathematics non degenerate , and write B for the Hessian matrix of this restriction. Let W be any complementary subspace to V . Then there is a change of coordinates math Phi x,y math of the form math Phi x,y phi x,y ,y math with math scriptstyle x in V, y in W math , and a smooth function h on W such that math f circ Phi x,y textstyle frac12 x TBx h y . math This result is often referred to as the parametrized Morse lemma , which can be seen by viewing y as the parameter. It is the gradient version of the implicit function theorem . Extensions There are extensions to infinite dimensions, to complex analytic functions, to functions invariant under the action of a compact group, . . . References citation first1 Tim last1 Poston first2 Ian last2 Stewart authorlink2 Ian Stewart mathematician title Catastrophe Theory and Its Applications publisher Pitman year 1979 ISBN 978 0273084297 . citation first Th last Brocker title Differentiable Germs and Catastrophes publisher Cambridge University Press year 1975 ISBN 978 0521206815 . Category Singularity theory Category Functions and mappings ... more details
C Standard Library list date December 2011 C mathematical operations are a group of functions in the C standard library standard library of the C programming language implementing basic mathematical functions ... V The Standard ANSI C Library with C99 Additions ref Most of the functions involve the use of floating point numbers. Different C standards provide different albeit backwards compatible, sets of functions. C mathematical functions are inherited in C . Overview of functions Most of the mathematical functions are placed in code math.h code header code cmath code header in C . The functions that operate ... specified in the code stdlib.h code header code cstdlib code header in C . Any functions that operate on angles use radians as the unit of angle. ref name c99 In C89 C version C89 , all functions ... by introducing new sets of functions with code f code and code l code suffixes that work on code ... inline code returns a not a number NaN Exponential functions code man sh exp SUS inline code returns ... code man sh logb SUS inline code extracts exponent of the number Power functions code man sh sqrt ... man sh pow SUS inline code raises a number to the given power Trigonometric functions code man sh sin ... code computes arc tangent, using signs to determine quadrants Hyperbolic functions code man sh sinh ... atanh SUS inline code computes hyperbolic arc tangent Error and gamma functions code man sh erf SUS ... current rounding mode with exception if the result differs Floating point manipulation functions code ... environment C99 adds several functions and types for fine grained control of floating point computations. ref name c primer c99 The additional functions and types are defined in code fenv.h code header ... tangent complex hyperbolic arc tangent Type generic functions anchor tgmath.h expand section date ..., so that the same function name can be used to call functions accepting different types of the arguments ... in C defines several functions that can be used for statistically random number generation ref cite ... more details
In mathematics , Weierstrass s elliptic functions are elliptic function s that take a particularly simple form they are named for Karl Weierstrass . This class of functions are also referred to as P functions ..., for fixed z the Weierstrass functions become modular function s of &tau . In terms of the two ... functions shows that the condition on Weierstrass s function is determined up to addition of a constant ... as functions G sub 4 sub and G sub 6 sub , respectively, of sub 2 sub sub 1 sub with Im ... in terms of theta functions Jacobi s theta functions . This method is very convenient for numerical calculation the theta functions converge very quickly. In the notation of Abramowitz and Stegun ... int e 3 infty frac dz sqrt 4z 3 g 2 z g 3 . math Addition theorems The Weierstrass elliptic functions ... of that curve. The totality of meromorphic doubly periodic functions with given periods defines ... Bbb C wp, wp , math so that all such functions are rational function s in the Weierstrass function ... surface , and regard the elliptic functions associated to a given pair of periods to be functions ... these in terms of theta functions also. We may also express & 8472 in terms of theta functions because ... of Jacobi s elliptic functions Jacobi s functions . This gives one way to convert between Weierstrass ... of typical function in a theory of random entire functions of J. E. Littlewood . Relation to Jacobi elliptic functions For numerical work, it is often convenient to calculate the Weierstrass elliptic function in terms of the Jacobi s elliptic functions . The basic relations are ref cite book author ... k of the Jacobi functions equals math k equiv sqrt frac e 2 e 3 e 1 e 3 math and their argument w .... Akhiezer , Elements of the Theory of Elliptic Functions , 1970 Moscow, translated into English as AMS ... M. Apostol , Modular Functions and Dirichlet Series in Number Theory, Second Edition 1990 , Springer, New York ISBN 0 387 97127 0 See chapter 1. K. Chandrasekharan, Elliptic functions 1980 , Springer ... more details
Integral Transforms and Special Functions is a scientific journal , specialised in topics of mathematical analysis , the theory of differential equation differential and integral equation s, approximation theory , but publishes also papers in other areas of mathematics . It is published monthly by Taylor & Francis . Print ISSN 1065 2469 Online ISSN 1476 8291 2007 Impact Factor 0.322 2007 Cited half life 6.5 years Thomson Reuters , Journal Citation Reports 2008 External links http www.tandf.co.uk journals titles 10652469.asp Journal homepage http www.informaworld.com smpp title content t713643686 access to the papers Category Mathematics journals sci journal stub ... more details
theorem follows from the preceding remark. If two holomorphic functions agree on a possibly ... of power series id 3298 Category Analytic functions holomorphic functions Category Theorems ... more details
This is a list of hash function s, including cyclic redundancy check s, checksum functions, and cryptographic hash function s. Cyclic redundancy checks main Cyclic redundancy check class wikitable Name Length Type BSD checksum 16 bits cyclic redundancy check CRC checksum 32 bits cyclic redundancy check CRC crc16 16 bits cyclic redundancy check CRC crc32 32 bits cyclic redundancy check CRC crc32 mpeg2 32 bits cyclic redundancy check CRC crc64 64 bits cyclic redundancy check CRC SYSV checksum 16 bits cyclic redundancy check CRC Adler 32 is often classified as a CRC, but it uses a different algorithm. Checksums Main Checksum class wikitable Name Length Type sum8 8 bits sum sum16 16 bits sum sum24 24 bits sum sum32 32 bits sum Fletcher s checksum fletcher 4 4 bits sum Fletcher s checksum fletcher 8 8 bits sum Fletcher s checksum fletcher 16 16 bits sum Fletcher s checksum fletcher 32 32 bits sum Adler 32 32 bits sum longitudinal redundancy check xor8 8 bits sum Luhn algorithm 4 bits sum Verhoeff algorithm 4 bits sum Non cryptographic hash functions class wikitable Name Length Type Pearson hashing 8 bits Fowler Noll Vo hash function br FNV Hash 32, 64, 128, 256, br 512, or 1024 bits xor product or br product xor Zobrist hashing variable xor Jenkins hash function 32 or 64 bits xor addition Java hashCode 32 bits Bernstein hash ref http www.partow.net programming hashfunctions index.html ref 32 bits elf64 64 bits hash MurmurHash 32, 64, or 128 bits product rotation SpookyHash 128 bits see Jenkins hash function CityHash 64, 128, or 256 bits Cryptographic hash functions main cryptographic hash function class wikitable Name Length Type BLAKE hash function BLAKE 256 256 bits hash BLAKE hash function BLAKE 512 512 bits hash Elliptic curve only hash ECOH 224 to 512 bits hash Fast Syndrome ... bits hash Notes references Category Hash functions List Category Checksum algorithms Category Cryptography lists and comparisons Hash functions ... more details
In mathematics, infinite compositions of analytic functions ICAF offer alternative formulations of continued fractions , series mathematics series , product mathematics products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence mathematics convergence divergence of these expansions. Some functions can actually be expanded directly as infinite compositions. It addition, it is possible to use ICAF to evaluate solutions of fixed point mathematics ... for iteration of systems of functions rather than a single function. Notation There are several notations ... extensions of the following Contraction theorem for analytic functions Contraction theorem ref ... compositions of contractive functions Forward or inner or right compositions Theorem A Let math left f n right math be a sequence of functions analytic on a simply connected domain math S math ... math be a sequence of functions analytic on a simply connected domain math S math . Suppose there exists ... subset, like theorem A . Infinite compositions of other functions Entire functions Results ref name Gillb ref involving Entire function entire functions include the following, as examples. Set math f ... to F z math , entire. ref name Kojima S.Kojima, Convergence of infinite compositions of entire functions ..., Convergence of infinite compositions of complex functions, www.johngill.net 2011 ref Theorem E3 Let math left f n right math be a sequence of complex functions defined on math S left left z right M right ... that the functions be entire Linear fractional transformations Results ref name Gillb ref for compositions ... Theorem LFT1 If math lim n to infty f n f math and all functions are hyperbolic or loxodromic ... of fixed points Theorem B can be applied to determine the fixed points of functions defined by infinite ... n to infty mathop lim , G n zeta alpha math . Evolution functions Consider a time interval, normalized ... limits 0 1 tdt math . References reflist Category Complex analysis Category Analytic functions Category ... more details
functions is the mathematical process of finding the rate at which a trigonometric function changes ... functions include sin x , cos x and tan x . For example, in differentiating f x sin x , one is calculating ... functions involve the arbitrary variable x , with all differentiation performed with respect to x ... of the other circular trigonometric functions because they can all be expressed in terms ... to give proofs of the derivatives of the other circular trigonometric functions. Finding the derivatives of the inverse trigonometric functions involves using implicit differentiation and the derivatives of regular trigonometric functions also given in the proofs section. Derivatives of trigonometric functions and their inverses math left sin x right cos x math math left cos x right sin x math math ... and cosine functions Limit of sin &theta &theta as &theta 0 File limit circle FbN.jpeg thumb Consider ... limits from Differentiation of trigonometric functions Limit of sin.28.CE.B8.29.2F.CE.B8 as .CE.B8 .E2.86.92 0 this section and Differentiation of trigonometric functions Limit of .5Bcos.28.CE.B8.29 ... Differentiation of trigonometric functions Limit of sin.28.CE.B8.29.2F.CE.B8 as .CE.B8 .E2.86.92 0 this section and Differentiation of trigonometric functions Limit of .5Bcos.28.CE.B8.29 .E2.80.93 ... trigonometric functions The following derivatives are found by setting a Variable mathematics ... trigonometric functions, we can finally express dy dx in terms of x . Differentiating the inverse ... of Mathematical Functions, Edited by Abramowitz and Stegun, National Bureau of Standards, Applied Mathematics Series, 55 1964 . DEFAULTSORT Differentiation Of Trigonometric Functions Category Differential ... more details
Trigonometry In mathematics , the inverse trigonometric functions occasionally called cyclometric functions ... the functions arcsin, arccos, arctan, are usually called asin, acos, atan. Many programming languages ... trigonometric functions are one to one, they must be restricted in order to have inverse functions. Therefore the Range mathematics range s of the inverse functions are subset s of the domains of the original functions For example, just as the square root function math y sqrt x math is defined ... value, called its principal value . These properties apply to all the inverse trigonometric functions ... y arctan x x trigonometric functions tan y all real numbers 2 y 2 90 y 90 arccotangent ... x x Trigonometric functions Reciprocal functions sec y x 1 or 1 x 0 y 2 or 2 y 0 y ... part. Relationships among the inverse trigonometric functions Image Arcsine Arccosine.svg 168px right thumb The usual principal values of the arcsin x red and arccos x blue functions graphed on the cartesian ... x and arccot x functions graphed on the cartesian plane. Image Arcsecant Arccosecant.svg 294px right thumb Principal values of the arcsec x and arccsc x functions graphed on the cartesian plane ... leq 1 math math arctan x 2 arctan frac x 1 sqrt 1 x 2 math Relationships between trigonometric functions and inverse trigonometric functions math sin arccos x cos arcsin x sqrt 1 x 2 math math sin arctan ... 1 x 2 math math tan arccos x frac sqrt 1 x 2 x math General solutions Each of the trigonometric functions ... pi math Derivatives of inverse trigonometric functions Main Differentiation of trigonometric functions ... well defined. Infinite series Like the sine and cosine functions, the inverse trigonometric functions ... integrals of inverse trigonometric functions For real and complex values of x math begin ... identities Other sums of trigonometric functions links here. Fix it if you rename this section ... at Atan2 Variations Atan2 . Logarithmic forms These functions may also be expressed using complex ... more details
Khmelnik1 cite journal last Khmelnik first S.I. title Coding of functions publisher Cybernetics, USSR ... 4 ref ref name Khmelnik2 cite book last Khmelnik first S.I. title Computer Arithmetic of Functions ... machine for operations with functions was presented and developed by Kartsev in 1967 ref name Malinovsky . Among the operations of this computing machine were the functions addition, subtraction and multiplication, functions comparison, the same operations between a function and a number, finding ... of two functions, derivative of two functions, shift of a function along the along X axis etc. By its ... operation on vectors addition and subtraction of functions as addition and subtraction of vectors, computing a definite integral of two functions derivative as computing the vector product of two ... In the year 1966 Khmelnik had proposed a functions coding method ref name Khmelnik1 , i.e. the functions ... with functions are performed as unique computer operations with such codes on a single arithmetic logic unit arithmetic unit . ref name Khmelnik2 Positional codes of one variable functions ref ... k longrightarrow alpha k 1 math . Addition of positional codes of one variable functions is also associated ... nary triangular codes, for these coefficients and functions math y k math have R nary triangular codes ... of the series is also discarded. Such reduction is acceptable if it is known that the series of functions ... M are also multiplied. Positional code for functions of many variables ref name Khmelnik3 cite journal last Khmelnik first S.I. title Several types of positional functions codes publisher Cybernetics ... of the figure math alpha m1,m2,k math , and math y x , z v math certain functions of arguments math ... certain functions of arguments math x i math . A positional code of a function of several variables ... more details
The production functions listed below, and their properties are shown for the case of two factors of production, capital K , and labor L , mostly for heuristic purposes. These functions and their properties are easily generalizable to include additional factors of production like land, natural resources, entrepreneurship, etc. A production function can also be seen as the dynamics of national output national income . This list is to collect production functions & the dynamics of national output income that have been used in literature & textbooks. Technology There are three common ways to incorporate technology or the efficiency with which factors of production are used into a production function Hicks neutral technical change Hicks neutral technology , or factor augmenting math Y AF K,L math Harrod neutral technology, or labor augmenting math Y F K,AL math Solow neutral technology, or capital augmenting math Y F AK,L math Elasticity of substitution The elasticity of substitution between factors of production is a measure of how easily one factor can be substituted for another. With two factors of production, say, K and L, it is a measure of the curvature of a production isoquant . The mathematical definition is math Epsilon frac partial slope partial L K frac L K slope 1 math where slope denotes the slope of the isoquant, given by math slope frac partial F K,L partial K partial F K,L partial L math Return to Scale Increasing return to scale. Constant return to scale. Decreasing returns to scale. Some Famous forms Constant elasticity of substitution CES function math Y A alpha K gamma 1 alpha L gamma frac 1 gamma math , with math gamma isin infty,1 math which includes the special cases of Linear production or perfect substitutes math Y A alpha K 1 alpha L math when math gamma 1 math Cobb Douglas or imperfect complements math Y AK alpha L 1 alpha math when math gamma to 0 ... bKK ln K ln K bLK ln L ln K math The PAR production technology The PAR production functions have such flexible ... more details
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