Malaya Journal of Matematik

Existence results for a self-adjoint coupled system of nonlinear second-order ordinary differential inclusions with nonlocal integral boundary conditions

Bashir Ahmad — 2024-04-01

A coupled system of nonlinear self-adjoint second-order ordinary differential inclusions supplemented with nonlocal non-separated coupled integral boundary conditions on an arbitrary domain is studied. The existence results for convex and non-convex valued maps involved in the given problem are proved by applying nonlinear alternative of Leray-Schauder for multi-valued maps, and Covitz-Nadler's fixed point theorem for contractive multi-valued maps, respectively. Illustrative examples for the obtained results are presented. The paper concludes with some interesting observations.

On vertex-edge corona of graphs and its spectral polynomial

Daneshwari Patil — 2024-04-01

Given a graph \(G_1\), the vertex-corona (corona) and the edge-corona focus only on vertices and edges respectively, in forming the corona product with other graphs. In the present work, we define a new corona by considering both vertices and edges simultaneously in forming the corona aproduct with other graphs, called vertex-edge corona. Further, we study the spectral polynomial for the vertex-edge corona of three arbitrary graphs, followed by some corollaries related to regular graphs for their spectrum, energy and equienergetic graphs.

Modeling and optimal control of the dynamics of narcoterrorism in the Sahel

Mathieu POODA — 2024-04-01

This work explores some aspects of modeling and controlling narcoterrorism in the Sahel. We examine the multidimensional factors underlying this dynamic, identifying interactions and recruitment within the narcoterrorist class. We then develop a preventive model and decision-support tools to optimize resource allocation and formulate more effective counter-narcotics and brigandage policies. This research will certainly contribute to the fight against narcoterrorism in the Sahel by proposing solutions based on rigorous scientific approaches and assessing the benefits and limitations of optimal modeling and control.

Exploring new proofs for three important trigonometric inequalities

Rupali Shinde — 2024-04-01

In this article, we present alternative proofs for three significant inequalities pertaining to various trigonometric functions. The cornerstone of these proofs lies in the utilization of Bernoulli's series expansions.

Polynomial stability of nonlinear Timoshenko system with distributed delay-time

Lamine Bouzettouta — 2024-04-01

In this work, we consider a nonlinear Timoshenko system with distributed delay-time. We prove the polynomial stability of the system for the case of nonequal speeds of wave propagation. This is after verifying the exponential stability in the case of equal speeds.

On derivations and Lie structure of semirings

Madhu Bala Dadhwal — 2024-04-01

In [8], Herstein introduced the notion of the Lie structure of associative rings and established the Lie type theory for rings. This paper extends these ring theoretical results and also extends some well known results of [3, 6, 7] in the framework of semirings, which are very important to investigate the Lie type theory of semirings and their higher commutators. Moreover, we characterize the Lie structure of semirings and thereby explore the action of derivations on Lie ideals of semirings.

Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

Rasheed Olawale Ayinla — 2024-04-01

Abstract. In this exploration, we introduce a certain family of regular (or analytic) functions in association with the righthalf of the Lemniscate of Bernoulli and the well-known Opoola differential operator. For the regular function \(f\) studied in this work, some estimates for the early coefficients, Fekete-Szegö functionals and second and third Hankel determinants are established. Another established result is the sharp upper estimate of the third Hankel determinant for the inverse function \(f^{-1}\) of \(f\).

The outer-independent edge-vertex domination in trees

Kijung Kim — 2024-04-01

Let \(G=(V,E)\) be a finite simple graph with vertex set \(V=V(G)\) and edge set \(E=E(G)\). A vertex \(v \in V\) is edge-vertex dominated by an edge \(e \in E\) if \(e\) is incident with \(v\) or \(e\) is incident with a vertex adjacent to \(v\). An edge-vertex dominating set of \(G\) is a subset \(D \subseteq E\) such that every vertex of \(G\) is edge-vertex dominated by an edge of \(D\). A subset \(D \subseteq E\) is called an \textit{outer-independent edge-vertex dominating set} of \(G\) if \(D\) is an edge-vertex dominating set of \(G\) and the set \(V(G) \setminus I(D)\) is independent, where \(I(D)\) is the set of vertices incident to an edge of \(D\). The outer-independent edge-vertex domination number of \(G\), denoted by \(\gamma_{ev}^{oi}(G)\), is the smallest cardinality of an outer-connected edge-vertex dominating set of \(G\). In this paper, we initiate the study of outer-independent edge-vertex domination numbers. In particular, we prove that \(\frac{n- l +1}{3} \leq \gamma_{ev}^{oi}(T) \leq \frac{2n -s -2}{3}\) for every tree \(T\) of order \(n \geq 3\) with \(l\) leaves and \(s\) support vertices. We also characterize the trees attaining each of the bounds.