Tamkang Journal of Mathematics

Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions

Matthew A. Beauregard, Burhan Selcuk — Thu, 01 Feb 2024 00:00:00 +0000

This study concerns with the quenching features of solutions of the non-Newtonian filtration equation. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined are certain cases. Numerical experiments are provided to illustrate and provide additional validation of the theoretical predictions to the quenching rates and times.

A different approach for multi-level distance labellings of path structure networks

Laxman Saha — Thu, 01 Feb 2024 00:00:00 +0000

For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|\geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The \emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $\displaystyle\max_{v\in V(G)}f(v)$ and the \emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $\displaystyle\min_{f}\{~span_f(G)\}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $k\in\{n-1, n-2,n-3\}$ in different approach but simple way.

Triharmonic curves along Riemannian submersions

Gizem Koprulu Karakas, Bayram Sahin — Wed, 15 Mar 2023 00:00:00 +0000

The purpose of this paper is to study triharmonic curves along Riemannian submersions from Riemannian manifolds onto Riemannian manifolds. We obtain necessary and sufficient conditions for a triharmonic curve on the total manifold
of Riemannian submersion from a space form ( respectively, a complex space form) to a Riemannian manifold to be triharmonic curve on the base manifold. The above research problem is also studied in the complex setting of the manifold
on which the Riemannian submersion is defined. In addition, we give several results involving curvature conditions for a triharmonic curves along Riemannian submersions.

Existence of positive periodic solutions for a predator-prey model

Chunhua Feng — Thu, 01 Feb 2024 00:00:00 +0000

In this paper, a class of nonlinear predator-prey models with three discrete delays is considered. By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system, two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays. Some numerical simulations are provided to illustrate our theoretical prediction.

An epidemic model for control and possible elimination of Lassa fever

Abayomi Ayoade, Nkuba Nyerere, Mohammed Ibrahim — Thu, 01 Feb 2024 00:00:00 +0000

Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.

Hypergeometric type extended bivariate zeta function

M. A. Pathan, Mohannad Shahwan, Maged Gumman Bin-Saad — Thu, 01 Feb 2024 00:00:00 +0000

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type extended zeta function together with related integral representations, differential relations, finite sums, and series expansions. Also, we present a relationship between the extended zeta function and the Laguerre polynomials. Our hypergeometric type extended zeta function involves several known zeta functions including the Riemann, Hurwitz, Hurwitz-Lerch, and Barnes zeta functions as particular cases.