Open Journal of Mathematical Sciences (OMS)

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.

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.

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.

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.

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.

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 \(n\leq 4\).

In this investigation, we aim to investigate the novel exact solutions of nonlinear partial differential equations (NLPDEs) arising in electrical engineering via the -expansion method. New acquired solutions are kink, particular kink, bright, dark, periodic combined-dark bright and combined-dark singular solitons, and hyperbolic functions solutions. The achieved distinct types of solitons solutions contain critical applications in engineering and physics. Numerous novel structures (3D, contour, and density plots) are also designed by taking the appropriate values of involved parameters. These solutions express the wave show of the governing models, actually.