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Continuous Choreographies as Limiting Solutions of $N$-body Type Problems with Weak Interaction [PDF]
, 2016 We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-\sigma$-homogeneous potential ...
Castaneira, Reynaldo +2 more
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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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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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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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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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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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ON A SYSTEM OF FUNCTIONAL EQUATIONS
Demonstratio Mathematica, 1998 The authors study the system of functional equations \[ \varphi_i(x)=\sum^n_{j=1}\sum^m_{k=1}a_{ijk}\biggl(x,\varphi_j\bigl(S_{ijk} (x)\bigr)\biggr)+g_i(x),\quad i=1,\dots,n,\quad x\in I\subset\mathbb{R}, \] where \(I\) is an interval and the given functions \(g_i:I\to I\) and \(a_{ijk}:I\times\mathbb{R}\to\mathbb{R}\) are continuous.
Nguyen Thanh Long +3 more
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QED in external fields, a functional point of view [PDF]
, 2001 A functional partial differential equation is set for the proper graphs generating functional of QED in external electromagnetic fields. This equation leads to the evolution of the proper graphs with the external field amplitude and the external field ...
C. J. Burden +16 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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Eigenvalues and Functional Equations [PDF]
Proceedings of the American Mathematical Society, 1957 Abstract : The purpose of this paper was to illustrate how the techniques of the theory of dynamic programming may be used to convert a number of eigenvalue problems, where one is interested only in maximum or minimum values, into problems involving recurrence relations.
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