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The Class Equation and the Commutativity Degree for Complete Hypergroups
Mathematics, 2020 The aim of this paper is to extend, from group theory to hypergroup theory, the class equation and the concept of commutativity degree. Both of them are studied in depth for complete hypergroups because we want to stress the similarities and the ...
Andromeda Cristina Sonea, Irina Cristea
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About one problem of optimal control synthesis [PDF]
E-Journal of Analysis and Applied Mathematics, 2023 This paper tackles the problem of characterizing the natural class, or Riccati rule space, of solutions to a specific e quation. Despite the significant theoretical and practical implications, there is limited research exploring the application of ...
Muhametberdy Rakhimov
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A class of solutions of the equation d(n²) = d(φ(n)) [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 For any positive integer n let d(n) and φ(n) be the number of divisors of n and the Euler's phi function of n, respectively. In this paper we present some notes on the equation d(n²) = d(φ(n)).
Zahra Amroune +2 more
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New Aspects in the Theory of Complete Hypergroups
Computer Sciences & Mathematics Forum, 2023 The aim of this paper is to review the most important properties and applications of the complete hypergroups. We will focus on the reversibility, regularity and reducibility properties, on the class equation and the commutativity degree of the complete ...
Irina Cristea
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From Heun Class Equations to Painlevé Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its confluent cases. The second part of our paper is devoted to Painlevé I-VI equations. Our philosophy is to treat these families of equations in a unified way.
Dereziński, Jan +2 more
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Drake-like Calculations for the Frequency of Life in the Universe
Philosophies, 2021 This article is intended to provide a review of some modifications to the Drake equation, a 1961 concept presented by Frank Drake to determine the number of extra-terrestrial civilizations able to communicate. A reduced version of the Drake equation will
Karl-Florian Platt
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On a class of exponential equations [PDF]
Proceedings of the American Mathematical Society, 1964 Let \(a\) be either 2 or an odd integer. Let \(q_1,\ldots,q_j,r_1,\ldots,r_k\) be distinct primes not dividing \(a\). It is proved that the equation \[ a^x=q_1^{y_1}\cdots q_j^{y_j}+r_1^{z_1}\cdots r_k^{z_k} \] has only a finite number of solutions in non-negative integers \(x,y_1,\ldots, y_j, z_1,\ldots, z_k\).
Rumsey, Howard jun., Posner, Edward C.
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The Burgers equation driven by a stochastic measure
Modern Stochastics: Theory and Applications, 2023 The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation.
Vadym Radchenko
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Journal of Ocean Engineering and Science, 2022 This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili (KdV-KP) equation. This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.
Lanre Akinyemi +3 more
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On Equational Definability of Function Classes [PDF]
2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011 We propose a notion of functional equation for functions of a fixed arity, which is based on a pair of clones. We present necessary conditions for aclass of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.
Miguel Couceiro +2 more
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