Results 21 to 30 of about 1,098,671 (288)
On Cauchy’s functional equation [PDF]
Proceedings of the American Mathematical Society, 1965 for real-valued functions of a real variable. P. Erdos [2] asked, after learning about a preliminary result of S. Hartman [3], whether one obtains all functions satisfying (C) for almost all pairs (x, y) by simply redefining the functions satisfying (C) for all (x, y) in an arbitrary manner on sets of measure zero.
openaire +2 more sources
Functional representation of the negative AKNS hierarchy [PDF]
, 2012 This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows.
Vekslerchik, V. E.
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Axioms, 2019 The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu +2 more
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Enumerating alternating tree families [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We study two enumeration problems for $\textit{up-down alternating trees}$, i.e., rooted labelled trees $T$, where the labels $ v_1, v_2, v_3, \ldots$ on every path starting at the root of $T$ satisfy $v_1 < v_2 > v_3 < v_4 > \cdots$.
Markus Kuba, Alois Panholzer
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Solving multivariate functional equations [PDF]
, 2013 This paper presents a new method to solve functional equations of multivariate generating functions, such as $$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$ giving a formula for $F(r,s)$ in terms of a sum over finite sequences.
Amy Lee +12 more
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Inequalities for Information Potentials and Entropies
Mathematics, 2020 We consider a probability distribution p0(x),p1(x),… depending on a real parameter x. The associated information potential is S(x):=∑kpk2(x). The Rényi entropy and the Tsallis entropy of order 2 can be expressed as R(x)=−logS(x) and T(x)=1−S(x).
Ana Maria Acu +3 more
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Independence Characterization for Wishart and Kummer Random Matrices
Revstat Statistical Journal, 2020 We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let X and Y be independent, non-degenerate random variables valued in (0,∞), then U = Y /(1 +X) and V = X ...
Bartosz Ko lodziejek +1 more
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On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations [PDF]
, 2017 The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the ...
Kiss, Gergely, Vincze, Csaba
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The equality case in some recent convexity inequalities [PDF]
Opuscula Mathematica, 2011 In this paper, we investigate a functional equation related to some recently introduced and investigated convexity type inequalities.
Gyula Maksa, Zsolt Páles
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Methods for deriving functional equations for Feynman integrals
, 2017 We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail.
Tarasov, O. V.
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