International Journal of Mathematical Sciences and Optimization: Theory and Applications

On Rank of Semigroup of Order-Preserving Order-Decreasing Partial Contraction Mappings on a Finite Chain

B. Ali — 2024-09-30

Let [n] = {1, 2, . . . , n} be a finite chain, and ODCPn be the semigroup of order-preserving and order-decreasing partial contraction mappings on [n]. In this paper, we study the rank properties of the two-sided ideals of ODCPn. We show that the rank of Kp = {α ∈ ODCPn : |im α| ≤ p}, for 2 ≤ p ≤ n, is and hence, the rank of ODCPn is 2n

Full Fuzzy parameterized Soft Expert Set with Application to Decision Making

E. E. Edeghagba — 2024-09-30

In this work, the authors consider a generalization of fuzzy parameterized soft expert set introducing the concept of full fuzzy parameterized soft expert set and study their properties. We define its basic operations and develop an algorithm to demonstrate its application in decision making. We also define the optimal choice object, developing and proving propositions relating to it. Finally, we use a concrete example to illustrate our algorithm.

Department of Mathematics, University of Jos, Nigeria.

L. A. Ademola — 2024-10-10

We investigate nonassociative Moufang loops of odd order p1p2 2q4, where p1, p2, q are distinct odd primes satisfying p1 < p2 < q. We show that there exists a normal Hall subloop of order q4 in L, and further prove that subject to some extra conditions the Moufang loop of this order is associative. Notably, the Loops Package gap4r5 does not contain Moufang loops of order p1p2 2q4, indicating a gap in the current knowledge of higher-order Moufang loops. Our results provide new insights into the structure and properties of nonassociative Moufang loops, building upon existing research.

Volatility Modeling and Forecasting Using Range-Based GARCH Models

B. A. Ogunwole — 2024-10-30

This paper investigates the forecast performance of symmetric and asymmetric GARCH models in comparison with symmetric and asymmetric range-based GARCH models. Specifically, we explore whether including the range and assuming asymmetry in the conditional variance equation significantly impacts the forecast performance of range-based GARCH models. The models examined in this study include GARCH(1,1), TARCH(1,1), RGARCH(1,1,1), and RTARCH(1,1,1). Our evaluation of these models utilizes different loss functions.Using daily, weekly and monthly opening, closing, highest and lowest all-share historical prices of the Nigeria Stock Exchange from 2014 to 2024, the results of data analysis reveal that incorporating the range and accounting for asymmetry in the conditional variance equation enhances the forecast performance of range-based GARCH models. Importantly, this finding holds for daily, weekly, and monthly forecast horizons.

On Polian Algebras

E. Ilojide — 2024-11-10

In this paper, polian algebras are introduced. Their properties are investigated. Left absorbing, right absorbing as well as absorbing polian algebras are studied. Manifolds and equipotence are introduced and studied in polian algebras. Moreover, hyperbolic polian algebras are introduced and their properties are investigated.

Note On Hyers-Ulam Stability Criteria for Third Order Nonlinear Differential Equations with Forcing Term

I. Fakunle — 2024-11-30

The stability of the ordinary differential equations has been investigated and the investigation is ongoing. In this paper we are concerned with note on Hyers-Ulam stability(HUs) criteria for third order nonlinear differential equations with forcing term. The third order nonlinear differential equations invesgated were transformed to integral equation, then, applied Bihari inequality and Gronwall-Bellman-Bihari(GBB) type inequality to arrive at our results. New criteria were established to prove HUs of nonlinear third order differential equations. Finally, examples are given to illustrate correctness our results.

On Vector Lyapunov Functions and Uniform Eventual Stability of Nonlinear Impulsive Differential Equations

J. E. Ante — 2024-12-15

In this paper, the uniform eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions which is generalized by a class of piecewise continuous functions. Together with comparison results, sufficient conditions for the uniform eventual stability are presented. Results obtained extends the more restrictive scalar case in the literature to a more comprehensive framework for uniform eventual stability analysis.

Variable exponent Picone identity and p(x) sub-Laplacian first eigenvalue for general vector fields

A. Abolarinwa — 2024-12-15

Picone identity is a powerful tool for proving qualitative properties of differential operators with ubiquitous applications in the analysis of partial differential equations, so generalizing it for different types of differential equations has become a desired venture. p(x)-Laplacian is a non-homogeneous quasilinear partial differential operator arising from various mathematical model with non-standard growth. However, in this paper, we establish a new generalized nonlinear variable exponent Picone identities for p(x)-sub-Laplacian. As applications we prove uniqueness, simplicity, monotonicity and isolatedness of the first nontrivial Dirichlet eigenvalue of p(x)-sub-Laplacian with respect to the general vector fields. Further applications yield Hardy type inequalities and Caccioppoli estimates with variable exponents.

On the Existence of Solutions of Multi-Term Fractional Order Volterra Integro-Differential Equations

D. Umar — 2024-12-15

In this paper, the problem of multi-term fractional order Volterra integro-differential equations is considered. The multi-term fractional order derivative part of the multi-term fractional order Volterra integro-differential equations is converted to its equivalent integral equation and Schauder’s fixed point theorem is applied to establish the existence of solutions for the multi-term fractional order Volterra integro-differential equations under some mild conditions. Furthermore, examples were given to test the applicability of the proposed theorem.

On Induced Matching Numbers of Stacked-Book Graphs

T. C. Adefokun — 2024-12-24

For a simple undirected graph G, an induced matching in G is a set of edges M no two of which have common vertex or are joined by an edge of G in the edge set E(G) of G. Denoted by im(G), the maximum cardinal number of M is known as the induced matching number of G. In this work, we probe im(G) where G = Gm,n, which is the stacked-book graph obtained by the Cartesian product of the star graph Sm and path Pn.