Results 31 to 40 of about 4,706,970 (298)
On the equation F(nᵏ-1) = D [PDF]
Notes on Number Theory and Discrete MathematicsWe prove that if F is a completely multiplicative function and k∈{2,3} such that the equation F(nᵏ-1) = 1 holds for every n∈ℕ, n>1, then F is the identity function.
I. Kátai, B. M. M. Khanh, B. M. Phong
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Analytical and numerical investigation of mixed-type functional differential equations [PDF]
, 2009 NOTICE: this is the author’s version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and ...
Ford, Neville J. +3 more
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A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms
Annales Mathematicae Silesianae, 2022 Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y), x,y ∈ S,
Akkaoui Ahmed +2 more
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A Unifying Principle in the Theory of Modular Relations
Mathematics, 2023 The Voronoĭ summation formula is known to be equivalent to the functional equation for the square of the Riemann zeta function in case the function in question is the Mellin tranform of a suitable function.
Guodong Liu +2 more
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Asymptotic behaviour of neutral differential equations of third-order with negative term
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We derive new comparison theorems and oscillation criteria for neutral differential equations of third order with negative term. We show that one can deduce oscillation criteria for the equation with negative term from those for the equation with ...
Zuzana Dosla, Petr Liška
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On Riemann's Functional Equation
The Annals of Mathematics, 1956 constant factor) if it satisfies Riemann's functional equation. This result was placed in an altogether more general setting by Hecke's work [9] on the correspondence between Dirichlet series with given signature (introduced by him), and modular functions. This paper is also concerned with that problem, but from a different approach.
Bochner, Salomon, Chandrasekharan, K.
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Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis
Information, 2020 This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
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Axiomatic Characterizations of Information Measures
Entropy, 2008 Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (
Imre Csiszár
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On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families
Mathematics, 2021 Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
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ON A COMPOSITE FUNCTIONAL EQUATION
Demonstratio Mathematica, 2003 The composite functional equation \[ f(xG(f(x))) = f(x)G(f(x)), \quad x \in \mathbb R_+,\tag{1} \] is considered. \textit{P. Kahlig}, \textit{A. Matkowska} and \textit{J. Matkowski} [Aequationes Math. 52, 260--283 (1996; Zbl 0861.39013)] dealt with the special case: \(G(u) = u^p\). Here the continuous solutions \(f: \mathbb R_+ \to \mathbb R_+\) of (1)
Matkowski, Janusz, Okrzesik, Jolanta
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