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- ...<math>f^{-1}</math> of a [[continuous function|continuous]] and [[inverse functions|invertible function]] {{nowrap|<math>f</math>,}} in terms of <math>f^{-1}</ ..., so is an open map and thus a homeomorphism. Since <math>f</math> and the inverse function <math>f^{-1}:I_2\to I_1</math> are continuous, they have antideriv ...10 KB (1,620 words) - 23:03, 14 November 2024
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- *[[Inverse trigonometric functions|arccos]] [[Category:Special functions]] ...994 bytes (117 words) - 13:28, 9 April 2021
- In mathematics, '''Zhegalkin algebra''' is a set of [[Boolean functions]] defined by the nullary operation taking the value <math>1</math>, use of Thus, the basis of Boolean functions <math>\bigl\langle \wedge, \oplus, 1 \bigr\rangle</math> is [[Functional co ...3 KB (425 words) - 11:42, 29 August 2024
- {{Short description|Inverse of the gamma function}} {{Distinguish|Inverse-gamma distribution|Reciprocal gamma function}} ...5 KB (796 words) - 08:05, 31 May 2024
- {{Short description|Important functions in solving differential equations}} ...tric functions of [[complex numbers]]:<ref name="Higham">{{cite book|title=Functions of matrices: theory and computation|author=Nicholas J. Higham|year=2008|pag ...4 KB (563 words) - 13:50, 5 August 2024
- ...tric functions]] and [[elliptic functions]]. This article describes these functions and the corresponding solutions for the orbits. ...handful of forces result in formulae for <math>u</math> in terms of known functions. The solution for <math>\varphi</math> can be expressed as an integral ove ...2 KB (344 words) - 08:07, 28 January 2021
- {{Short description|Theorem in mathematics about plurisubharmonic functions}} ...ould explain why Levi's problem is occasionally referred to as '''Hartogs' Inverse Problem'''. ...4 KB (445 words) - 06:49, 5 February 2025
- The '''local inverse''' is a kind of [[inverse function]] or [[matrix inverse]] used in image and signal processing, as well as in other general areas of ...ion), subtract this recalculated data from the original, and then take the inverse inside the local region using this newly produced data for the outside regi ...10 KB (1,705 words) - 13:42, 4 January 2024
- ...ween [[angle]]s and side lengths of [[triangles]] and uses [[trigonometric functions]], squigonometry focuses on analogous relationships within the context of a ...100}} This approach allows for the integration of [[function (mathematics)|functions]] that are otherwise computationally difficult to handle. ...9 KB (1,349 words) - 22:36, 21 January 2025
- ...utions. They are particularly useful in the study of [[Bayesian inference|inverse problems]] on [[function space]]s for which a Gaussian [[prior probability| Let <math>H</math> be a [[separable space|separable]] [[Hilbert space]] of functions defined on a domain <math>D \subseteq \mathbb{R}^{d}</math>, and let <math> ...6 KB (850 words) - 10:24, 28 August 2024
- ...rst1=L A |last2=Faddeev |first2=Lyudvig D |title=The Quantum Method of the Inverse Problem and the Heisenberg Xyz Model |journal=Russian Mathematical Surveys It can be viewed as a quantized version of the classical [[inverse scattering method]] pioneered by [[Norman Zabusky]] and [[Martin Kruskal]]< ...6 KB (819 words) - 20:40, 9 November 2024
- {{Short description|Mathematical functions}} ...ematics)|functions]] useful in [[functional analysis]] are called '''Young functions'''. ...3 KB (398 words) - 09:52, 18 November 2024
- ...n 1962 by Wolfgang Fuchs and [[Walter Hayman]].<ref>Hayman's ''Meromorphic functions'', Clarendon Press 1964, chapter 4</ref> The general problem concerns the q ...ongress of Mathematicians|ICM]] in Zurich.<ref>Drasin, David. "Meromorphic functions: progress and problems." In ''Proceedings of the International Congress of ...5 KB (716 words) - 03:05, 27 June 2024
- ...<math>f^{-1}</math> of a [[continuous function|continuous]] and [[inverse functions|invertible function]] {{nowrap|<math>f</math>,}} in terms of <math>f^{-1}</ ..., so is an open map and thus a homeomorphism. Since <math>f</math> and the inverse function <math>f^{-1}:I_2\to I_1</math> are continuous, they have antideriv ...10 KB (1,620 words) - 23:03, 14 November 2024
- ...independent set of ''n'' functions), the basis is unisolvent (as a set of functions). This is because any two bases are related by an invertible matrix (the ch Unisolvent systems of functions are widely used in [[interpolation]] since they guarantee a unique solution ...6 KB (920 words) - 03:29, 11 January 2025
- ...uch theorems quantify the difficulty of approximating general functions by functions of special form, such as [[polynomial]]s. In more recent work, the converg ...the inverse problem of the theory of the best approximation of continuous functions | journal=Sochinenya | volume=II | year=1938 | pages=292–294 }} ...3 KB (400 words) - 03:44, 27 January 2025
- ...ity of <math>\psi^{-1}(\ln x)-1</math>, where <math>\psi^{-1}(x)</math> is inverse [[digamma function]]. ==Elementary functions of Bernoulli umbra== ...6 KB (986 words) - 08:46, 24 July 2023
- ...nswered by [[Dimitrie Pompeiu]] by constructing an explicit example; these functions are therefore named after him. ...]]; and by the theorem of differentiation of the [[inverse function]], its inverse {{math|''f'' :{{=}} ''g''<sup>−1</sup>}} has a finite derivative at every p ...5 KB (778 words) - 17:50, 10 March 2024
- ...glorot11a.pdf |conference=AISTATS |quote=Rectifier and softplus activation functions. The second one is a smooth version of the first. }}</ref> and ''SmoothReLU ==Related functions== ...5 KB (688 words) - 12:43, 7 October 2024
- {{About||additive functions in number theory|Additive function|additive functions on the reals|Cauchy's functional equation}} ...th> is an additive group with identity element <math>0</math> and that the inverse of <math>x \in X</math> is denoted by <math>-x.</math> For any <math>x \in ...6 KB (1,104 words) - 21:13, 1 February 2023
- {{Distinguish|Inverse distribution function}} ...ution]]s for [[scale parameter]]s. In the [[algebra of random variables]], inverse distributions are special cases of the class of [[ratio distribution]]s, in ...12 KB (1,746 words) - 00:11, 21 November 2024