Volume 7 (2023)

Abstract:In this paper we prove large-time existence and uniqueness of high regularity weak solutions to some initial/boundary value problems involving a nonlinear fourth order wave equation. These sorts of problems arise naturally in the study of vibrations in beams that are hinged at both ends. The method used to prove large-time existence is the Galerkin approximation method.

Abstract:In this paper, we proved that solutions \((\rho,J)\) exist for the 1-dimensional wave equation on \([-\pi,\pi]\). When \((\rho,J)\) is extended to a smooth solution \((\rho,\overline{J})\) of the continuity equation on a vanishing annulus \(Ann(1,\epsilon)\) containing the unit circle \(S^1\), a corresponding causal solution \((\rho,\overline{J}’ \overline{E}, \overline{B})\) to Maxwell’s equations can be obtained from Jefimenko’s equations. The power radiated in a time cycle from any sphere \(S(r)\) with \(r>0\) is \(O\left(\frac{1}{r}\right)\), which ensure that no power is radiated at infinity over a cycle.

Abstract: This study aims to model the statistical behaviour of extreme maximum temperature values in Rwanda. To achieve such an objective, the daily temperature data from January 2000 to December 2017 recorded at nine weather stations collected from the Rwanda Meteorological Agency were used. The two methods, namely the block maxima (BM) method and the Peaks Over Threshold (POT), were applied to model and analyse extreme temperatures in Rwanda. Model parameters were estimated, while the extreme temperature return periods and confidence intervals were predicted. The model fit suggests that Gumbel and Beta distributions are the most appropriate for the annual maximum daily temperature. Furthermore, the results show that the temperature will continue to increase as estimated return levels show it.

Abstract: Using the Kudryashov and Tanh methods, we have obtained novel exact solutions for the Paraxial Wave Dynamical Equation with Kerr law, including various types of wave solutions. These distinct types of wave solutions have important applications in physics and engineering, and their physical characteristics are well defined. These outcomes are a substantial innovation in the study of water waves in mathematical physics and engineering phenomena. The results we have acquired demonstrate the power and effectiveness of the present techniques.

Abstract: In this work, the effect of suction/injection on transient free convective flow in vertical porous (suction/injection on the channel surfaces) channel filled with porous material in the presence of thermal dispersion was studied. The Boussinesq assumption is applied and the nonlinear governing equations of motion and energy are developed. The time dependent problem is solved using implicit finite difference method while steady state problem is solved by perturbation technique method. The solution obtained is graphically represented and the effects of suction/injection, time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. During the course of computation, an excellent agreement was found between the well-known steady state solutions sand transient solutions at large value of time. Furthermore, the time required to reach steady state velocity and temperature field strongly dependent on suction/injection parameter, Prandtl number and thermal dispersion parameter. The introduction of suction/injection has distorted the symmetric nature of the flow formation.

Abstract: In this paper we establish the existence of monads on cartesian products of projective spaces. We give the necessary and sufficient conditions for the existence of monads on \(\mathbf{P}^1\times\cdots\times \mathbf{P}^1\). We construct vector bundles associated to monads on \(X=\mathbf{P}^n\times\mathbf{P}^n\times\mathbf{P}^m\times\mathbf{P}^m\). We study these vector bundles associated to monads on \(X\) and prove their stability and simplicity.

Abstract: In this paper, we established a new integral identity for twice partially differentiable functions. As a consequence, we established some new Simpson’s type integral inequalities for functions of two independent variables whose mixed partial derivative is bounded and \((\alpha_1, m_1)-(\alpha_2, m_2)\)-preinvex on the coordinates in both the first and second sense.

Abstract: Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of $n^{s}\pm1$ as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.

Abstract: In this article, we focus on developing new results regarding normed quasilinear spaces. We provide a definition for soft homogenized quasilinear spaces and obtain some related results. Furthermore, we explore the floor of soft normed quasilinear spaces. Using some soft linearity and soft quasilinearity methods, we derive new results and examples. Finally, we also obtain some new consequences that we believe will facilitate the development of quasilinear functional analysis in a soft inner product quasilinear space.

Abstract: The aim of this paper is to introduce and study BiHom-associative dialgebras. We give various constructions and study their connections with BiHom-Leibniz algebras and BiHom-Poisson dialgebras. Next, we discuss the central extensions of BiHom-associative dialgebras and we describe the classification of \(n\)-dimensional BiHom-associative dialgebras for \(n\leq 4\).