Results 11 to 20 of about 1,793,700 (285)
An Analytical and Numerical Detour for the Riemann Hypothesis
Information, 2021 From the functional equation F(s)=F(1−s) of Riemann’s zeta function, this article gives new insight into Hadamard’s product formula. The function S1(s)=d(lnF(s))/ds and its family of associated Sm functions, expressed as a sum of rational fractions, are ...
Michel Riguidel
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Characterizations of generalized entropy functions by functional equations [PDF]
, 2010 We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a different form used ...
Furuichi, Shigeru
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ON A FUNCTIONAL EQUATION [PDF]
The Quarterly Journal of Mathematics, 1958 We have recently discussed in (1) the general solution of a certain functional equation arising in statistical thermodynamics, and we propose in this note to deal with another functional equation arising from the same source(2).The problem is to obtain the most general function f(x) which, for all positive integral values of m, n, satifies the ...
Chaundy, T. W., McLeod, J. B.
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Analytic embedding of pseudo-Helmholtz geometry [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 For modern geometry, the study of maximal mobility geometries is of great importance. Some of these geometries are well studied (Euclidean, pseudo-Euclidean, symplectic, spherical, Lobachevsky, etc.), and others are poorly understood (Helmholtz, pseudo ...
Kyrov, Vladimir A.
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Schwinger-Dyson approach to Liouville Field Theory [PDF]
, 2015 We discuss Liouville field theory in the framework of Schwinger-Dyson approach and derive a functional equation for the three-point structure constant.
Dutta, Parikshit
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The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡
Universe, 2019 In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic ...
Walter Dittrich
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On the stability of a multiplicative type sum form functional equation
Ratio Mathematica, 2021 In this paper we intend to discuss the stability of a sum form functional equation \begin{align*} \sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}f\left(p_iq_j\right)=\sum\limits\limits^n_{i=1}k\left(p_i\right)\sum\limits\limits^m_{j=1}q^{\beta }_j ...
Surbhi Madan +2 more
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Cauchy's functional equation and extensions: Goldie's equation and inequality, the Go{\l}\k{a}b-Schinzel equation and Beurling's equation [PDF]
, 2014 The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its ...
Bingham, N. H., Ostaszewski, A. J.
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Discrete Integrals Based on Comonotonic Modularity
Axioms, 2013 It is known that several discrete integrals, including the Choquet and Sugeno integrals, as well as some of their generalizations, are comonotonically modular functions.
Jean-Luc Marichal, Miguel Couceiro
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Additivity, subadditivity and linearity: automatic continuity and quantifier weakening [PDF]
, 2017 We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are continuous and so ...
Bingham, N. H., Ostaszewski, A. J.
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