International Journal of Mathematics And its Applications

Some Algorithms for Solving Higher Order Mixed Variational-like Inequalities

2025-07-03T07:51:52+00:00

In this paper, we introduce a new class of variational-like inequalities, which is called higher order mixed variational-like inequality. We proved that the minimum of higher order strongly preinvex function can be characterized by this class of variational-like inequalities. Also, some iterative methods for solving higher order mixed variational-like inequalities are suggested.

On Tri-Edge $\mathbb{Z}_t-$graphs

2025-07-11T07:10:39+00:00

In this paper, we define a new graph, Tri-Edge $\mathbb{Z}_t-$Graph using triangular numbers and the cyclic group $\mathbb{Z}_n$. We introduce the concept of the Tri-Edge Index, $\Omega(G)$, and determine $\Omega(G)$ of some classes of graphs $G$. Moreover, we establish a bound for $\Omega(G)$. We listed all non-isomorphic Tri-Edge $\mathbb{Z}_{\Omega_q}-$Graphs, $G=(p,q)$ for $1\le q\le 7$. Furthermore, we introduce the concept of Weak Tri-Edge $\mathbb{Z}_t$-Graph.

Maximal Degree Domination in Graphs

2025-06-16T14:41:47+00:00

A set $S$ of vertices in a graph $G$ is called a dominating set if every vertex in $V-S$ is adjacent to at least one vertex in $S$. A maximal degree dominating function $(MDDF)$ is a type of function $f:V(G)\arrowvert\left\lbrace 0,1,2,3, ...,(\bigtriangleup(G)+1)\right\rbrace $ having the property that every $v$ in $S$ is assigned the value $deg(v)+1$, and all remaining vertices with zero. The weight of a maximal degree dominating function $f$ is defined by $w(f)=\ds \sum_{v\in S}deg(v)+1$. The maximal degree domination number $\gamma_{mdeg}(G)$ is the minimum weight among all possible $MDDFs$. In this paper, we determine its exact value.

An Approach to Find the Solution of Assignment Problem

2025-05-30T12:21:04+00:00

In this paper we introduce an approach to give a solution for travelling salesman problem(Assignment problem). We consider a salesman problem if he wants to visit a certain number of cities allotted to work. He knows the distance (or cost or time) of journey between every pair of cities, usually denoted by $c_{ij}$, i.e., from city $i$ to city $j$. His problem is to select such a route that starts from his home city, passes through each city once and only once, and returns to his home city in the shortest possible distance and its goal would be to minimize the total distance traveled so that the cost or time will be optimal.

Matrix Representations of Group Algebras of 16 Order Abelian Groups

2025-08-03T17:25:35+00:00

Group algebras of abelian groups of order 16 are represented in terms of block circulant matrices.

A Study on Gourava Bipartite Domination Topological Indices of Some Graphs

2025-07-18T18:17:44+00:00

In this paper, we study the first and second Gourava bipartite domination indices and their corresponding polynomials of a graph. Further, we complete these indices and their corresponding polynomials for some standard graphs, French windmill graphs, friendship graphs, book graphs.

Applications of Fuzzy Baire Spaces

2025-07-17T03:09:22+00:00

The fuzzy sets, in which the elements of the universe have their membership and non-membership degrees in [0,1] is of Zadeh's fuzzy set. In this paper fuzzy sets are used as tools for assessment and decision making. This is useful in cases where one is not sure about the suitability of the linguistic characterizations assigned to each element of the universal set. Applications illustrating our results are also presented.

A Hybrid Fixed Point Algorithm for Solving Convex Optimization Problems

2025-04-09T06:15:11+00:00

This paper introduces a novel hybrid fixed point iterative algorithm aimed at solving convex optimization problems in real Hilbert spaces. The algorithm is designed to find a solution that lies in the intersection of a closed convex set and the fixed point set of a nonexpansive mapping, a common formulation in various applied mathematical and engineering contexts. By integrating projection operators with averaged nonexpansive mappings and gradient-based updates, the proposed scheme ensures strong convergence to an optimal solution under standard and practically verifiable assumptions on the step size parameters. Unlike traditional projection methods or purely fixed point iterations, our hybrid approach leverages the geometric structure of Hilbert spaces to guarantee convergence even in the absence of strong monotonicity or Lipschitz continuity. The theoretical development is supported by rigorous convergence analysis, which confirms that the generated sequence converges strongly to a point that minimizes a given convex objective function over the fixed point set of a nonexpansive mapping. A detailed numerical example in $\mathbb{R}^2$ is provided to illustrate the algorithm’s practical behavior and convergence characteristics, demonstrating its stability and efficiency. The results not only validate the theoretical claims but also highlight the flexibility of the algorithm for potential applications in areas such as signal processing, machine learning, and variational inequalities. Furthermore, our framework unifies and generalizes several well-known iterative schemes in the literature, thereby contributing a fresh perspective and an effective computational tool for solving constrained convex optimization problems through fixed point techniques.

Automorphism Group and Distinguishing Number of Some Shadow Graphs and Some Split Graphs

2025-06-30T12:38:19+00:00

The proposed study asserts the automorphism group and distinguishing number of some shadow graphs along with some split graphs. Automorphism group of path graph $P_{n}$, cycle graph $C_{n}$ and star graph $K_{1,n}$ are well-known groups and also their distinguishing number are well-known. It is full of zest to know what would be the automorphism group of shadow graphs and split graphs of that graphs whose automorphism group are known. Also, it would be interesting to determine the distinguishing number of shadow graphs and split graphs of that graphs whose distinguishing numbers are known. In this paper, shadow graph as well as split graph of path graph $P_{n}$, cycle graph $C_{n}$ and star graph $K_{1,n}$ have been taken into the account to investigate their the automorphism groups and distinguishing numbers. The results are illustrated with the help of examples and the applicability of the proposed theory, related to some shadow graphs and some split graphs, is elaborated successfully.

Algebraic Description of Monadic Second Order Logic

2025-09-14T18:55:38+00:00

A direct algebraic description of monadic second order logic in terms of Boolean algebras of unary and binary relations are given by extending the method of [1].

Relation between Luhn Algorithm and Level sets

2025-08-06T14:30:05+00:00

The Luhn algorithm, a widely used checksum formula, ensures the validity of identification numbers such as credit cards and IMEI numbers by detecting accidental errors. Operating through a simple yet effective process of digit manipulation and summation, it enhances data integrity in financial and technological systems. Though it does not prevent fraud, its efficiency in identifying common mistakes makes it a crucial tool in electronic payment processing. Additionally, the algorithm's mathematical foundation relates to level sets in differential geometry, offering a deeper perspective on credit card number validation. Its continued relevance and public accessibility underscore its enduring impact across industries that require accurate and reliable numeric verification.

Some Remarks on Weakly Tripotent Rings

2025-09-14T16:56:35+00:00

In the mathematical literature there are three approaches to study a weakly tripotent ring. We provide a comparative study of these approaches and exhibit that a weakly tripotent ring defined as per one of these approaches is in harmony with a tripotent ring in various aspects as it is a commutative ring, a reduced ring and satisfies the identity $a^{5}=a$ for each $a \in R$ like tripotent rings however a weakly tripotent ring defined as per rest of two approaches fail to be in harmony with a tripotent ring with respect to these aspects.

On Degree of Approximation of Equi - Convergent Series Associated With Fourier Series

2025-07-18T14:33:43+00:00

This article studies the rate of convergence of equi - convergence series for functions belonging to $Lip(\omega, p )$, $p > 1$ class. Previously Salem and Zygmond have studied the equi - convergence of the series associated with certain integrals for functions of bounded variation class of monotonic type and which is belonging to Lipschitz class.

Image Classification: Pneumonia Detection

2025-09-14T17:02:39+00:00

This article examines the principles underlying supervised machine learning, convolutional neural networks, and transformation layers. These ideas were applied to a dataset of chest X-ray images, categorizing them into healthy and pneumonia classes. The accuracy of the model obtained is 85.3\%. This article illustrates the power of machine learning as a diagnostic tool in medicine.

Breaking Down the Save: A Data-Driven Approach to Penalty Shootouts

2025-08-12T20:45:05+00:00

Penalty shootouts represent one of the most decisive and psychologically demanding moments in competitive soccer, often determining outcomes of tournaments at the highest level. This study presents a data-driven approach to optimizing a goalkeeper’s decision-making process during penalty shootouts by analyzing 161 penalties from the UEFA Champions League spanning the last 20 years. Using statistical tools such as entropy, logistic regression, Chi-Square tests, and Pearson’s correlation coefficient, the paper investigates patterns in ball placement, shooter’s dominant foot, and dive strategies. The results highlight significant correlations between shooting foot and ball placement, revealing exploitable tendencies that enhance prediction accuracy. Further, an optimized strategy based on probabilistic modeling shows that goalkeepers can more than double their expected number of saves compared to random guessing. These findings underscore the practical value of mathematical modeling in sports, providing goalkeepers with actionable insights to improve performance in high-pressure scenarios, while also contributing to the broader dialogue on the application of statistics in real-world decision-making.

A Note on Non-cut Points, VH-sets, Almost VH-sets and COTS

2025-09-14T16:05:39+00:00

Two concepts of VH-sets and almost VH-sets are introduced to study connected ordered topological spaces (COTS). We show that every $R(i)$ subset of a connected space is an almost VH-set. Two characterizations of COTS with endpoints using the concept of almost VH-set have been obtained. It is also proved that if $X$ is a connected non-cut point inclined space and the removal of any two-point disconnected set of it leaves the space disconnected, then each one of $H \cup \{a, b\}$ and $K \cup \{a, b\}$ has exactly two non-cut points, and is homeomorphic to a finite connected subspace of the Khalimsky line where $H$ and $K$ are separating sets of $X \setminus \{a, b\}$, $a, b \in X$.

Multifactor Balanced Asymmetrical Factorial Designs of Type II

2025-09-18T17:16:52+00:00

This manuscript gives methods of constructing multifactor BAFDs of type II. Multi-factor BAFDS of type II are constructed from two factor BAFDs. Two methods of construction are given. The first method is the product of balanced arrays which is similar to the product of orthogonal arrays defined by [4]. The second methods was given by [28] which generates a BAFD from two given BAFD's. These methods can provide efficient BAFD's if efficient two factor BAFD's are used. The designs constructed are balanced with orthogonal factorial structure.

Exact soliton solutions of some Nonlinear Dispersive Equations

2025-09-20T15:24:21+00:00

The functional variable method provides an efficient means of deriving exact soliton solutions for nonlinear partial differential equations. In this study we applied the functional variable method to find soliton solutions of nonlinear dispersive equations. The obtained results are novel and have significant applications in contemporary research areas of mathematical physics.

Notion of Non-archimedean Pseudo-differential Operators Associated with Fractional Fourier Transform

2025-08-21T09:04:49+00:00

In this manuscript, we define the first type of non-archimedean pseudo-differential operator associated with the fractional Fourier transform and Bessel potentials, denoted by $\mathcal{J}^{\omega},~\omega>1$ and second type of non-archimedean pseudo-differential operator $\mathcal{A}^{\omega}$ on $\mathcal{D}(\mathbb{Q}_{p}).$ We show that these operators holds the positive maximum principle and a strongly continuous, positive, contraction semigroup on $ \mathbb{C}_{0}(\mathbb{Q}_{p}).$ Also, we solve Cauchy problem ( the inhomogeneous initial value problem ) related to fractional Fourier transform and these operators.