# Journal of Mathematical Extension Volume:18 Issue: 1, Jan 2024

• تاریخ انتشار: 1403/03/05
• تعداد عناوین: 6
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• Haniye Hajinezhad *, Ali Reza Soheili Page 1

The objective of this paper is to present a finite difference scheme that estimates the solution of space fractional diffusion equation with the Caputo fractional derivative. The proposed scheme’s stability, and convergence are proved. To assess the efficiency of this program, a set of tests is carried out. The results of these tests demonstrate the reliability and accuracy of the proposed scheme.

Keywords: Space Fractional Diffusion Equation, Convergence, Stability, Finite Difference Method
• Maedeh Ghasempour, Hamid Rasouli *, Ali Iranmanesh, Hasan Barzegar, Abolfazl Tehranian Page 2

In the theory of S-acts, there exists a plethora of compelling findings that establish connections between regularity in a monoid S and injectivity (as well as other notions derived from injectivity) of Sacts. In this paper, we introduce the notion of strongly regular elements in a hypermonoid as a generalization of regular elements in a monoid and extend several classic results to hypermonoids and GHS-acts over hypermonoids. Particularly, we show that a hypermonoid S is strongly regular and injective GHS-act if and only if all right hyperideals of S are C-injective.

Keywords: Hypermonoid, Generalized Hyper S-Act, Winjectivity, PW-Injectivity, C-Injectivity, Strong Regularity
• Reza Safakish * Page 3

Let Γ be a k-regular graph with the second maximum eigenvalue λ. Then Γ is a Ramanujan graph if λ ≤ 2 √ k − 1. Let G be a finite group and Γ = Cay(G, S) be a Cayley graph related to G. The aim of this paper is to investigate the Ramanujan Cayley graphs of sporadic groups.

Keywords: Sporadic Group, Character Table, Cayleygraph, Eigenvalue
• Bashir Ali *, Ajio Terlumun Jude Page 4

In this paper, we introduce a new inertial type algorithm with self - adaptive step - size technique for approximating a common element of the set of solutions of pseudomonotone variational inequality problem and the set of common fixed point of a finite family of generic generalized nonspreading mappings in uniformly smooth and 2 - uniformly convex real Banach space. Furthermore, we prove a strong convergence theorem of our algorithm without prior knowledge of the Lipschitz constant of the operator under some mild assumptions. We also give numerical examples to illustrate the performance of our algorithm. Our result generalize and improve many existing results in the literature

Keywords: Variational Inequality Problem, Inertial Subgradient Extragradient Method, Strong Convergence, Monotone Mapping, Fixed Point, Banach Spaces
• Farhad Dorostkar *, Masoud Yahyapour-Dakhel Page 5

In this paper, we introduce the weak integral closure of a filtration relative to a module and the asymptotic prime divisors of a filtration relative to a module. Based on these concepts, we prove some new results. One of the most important points of this paper is to find the effect of contraction, and extension on the integral closure of a filtration relative to a module. Finally, the theorems we prove enable us to characterize the asymptotic prime divisors of contraction of a filtration f relative to a module M according to the asymptotic prime divisors of the filtration f relative to a module M.

Keywords: Integral Closure Of A Filtration Relative To Amodule, The Weak Integral Closure Of A Filtration Relative To A Module, The Asymptotic Prime Divisors Of A Filtration Relative To A Module
• Shaoli Nandi, Sukumar Mondal, Sambhu Charan Barman * Page 6

Centrality measurement plays an important role to identify important/influential vertices and edges in a network or graph from different points of view. It also provide invaluable insights into the structure and functioning of interconnected systems, enabling researchers to identify critical nodes for targeted interventions, predict network behaviors, and optimize network performance. Though there are different centrality measurements in graphs theory, yet closeness centrality is widely used to analyze biological networks, social networks, fuzzy social network, transportation networks, etc. The closeness centrality of a node x in a network/graph is the unit fraction whose denominator is the sum of the distances from x to other nodes. This paper presents theoretical development to compute the closeness centrality of each node/vertex of different corona product graphs between well known graph (path graph, complete graph, cycle graph, wheel graph, star graph and complete bipartite graph) and general graph. Corona graph has lots of applications in signed networks, biotechnology, chemistry, small-world network, etc. We also present a suitable real application of our proposed results by which we can identify the influential nodes in small-world network.

Keywords: Centrality Measurement, Closeness Centrality, Corona Product