Integral representations for local dilogarithm and trilogarithm functions
OMS-Vol. 5 (2021), Issue 1, pp. 337 – 352 Open Access Full-Text PDF
Masato Kobayashi
Abstract:We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apéry, Catalan constants and Legendre \(\chi\) functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.
Some arguments for the wave equation in Quantum theory
OMS-Vol. 5 (2021), Issue 1, pp. 314 – 336 Open Access Full-Text PDF
Tristram de Piro
Abstract:We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.
Moments of generalized order statistics for Pareto-Rayleigh distribution
OMS-Vol. 5 (2021), Issue 1, pp. 306 – 313 Open Access Full-Text PDF
M. Alam, R. U. Khan, Z. Vidović
Abstract:In this paper, we derive the explicit expressions for single and product moments of generalized order statistics from Pareto-Rayleigh distribution using hypergeometric functions. Also, some interesting remarks are presented.
Local convergence for a family of sixth order methods with parameters
OMS-Vol. 5 (2021), Issue 1, pp. 300 – 305 Open Access Full-Text PDF
Christopher I. Argyros, Michael Argyros, Ioannis K. Argyros, Santhosh George
Abstract:Local convergence of a family of sixth order methods for solving Banach space valued equations is considered in this article. The local convergence analysis is provided using only the first derivative in contrast to earlier works on the real line using the seventh derivative. This way the applicability is expanded for these methods. Numerical examples complete the article.
Some new operators for Fermatean fuzzy matrices
ODAM-Vol. 4 (2021), Issue 3, pp. 10 – 23 Open Access Full-Text PDF
I. Silambarasan
Abstract:In this paper, we define some new operators \([(A \$ B),(A \# B),(A\ast B),(A \rightarrow B) ]\) of Fermatean fuzzy matrices and investigate their algebraic properties. Further, the necessity and possibility operators of Fermatean fuzzy matrices are proved. Finally, we have identified and proved several of these properties, particularly those involving the operator \(A\rightarrow B\) defined as Fermatean fuzzy implication with other operators.
\(S\)-norms on anti \(Q\)-fuzzy subgroups
ODAM-Vol. 4 (2021), Issue 3, pp. 1 – 9 Open Access Full-Text PDF
Rasul Rasuli
Abstract:In this paper, by using \(S\)-norms, we defined anti fuzzy subgroups and anti fuzzy normal subgroups which are new notions and considered their fundamental properties and also made an attempt to study the characterizations of them. Next we investigated image and pre image of them under group homomorphisms. Finally, we introduced the direct sum of them and proved that direct sum of any family of them is also anti fuzzy subgroups and anti fuzzy normal subgroups under \(S\)-norms, respectively.
