University of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601On enumeration of EL-hypergroups of order 3 obtained from ordered semigroups123465210.22098/jhs.2026.18555.1143ENSeyed HosseinGhazaviDepartment of Mathematics, Shahid Ashrafi Isfahani, Isfahan,Iran,SaeedMirvakiliDepartment of Mathematical Sciences, Yazd University, Yazd, Iran,Journal Article20251011The EL-hyperstructures are formed from (quasi) partially ordered (semi)groups through the application of the "Ends Lemma". In this paper, we enumerate EL-hypergroups of order 3, which are derived from ordered semigroups of order 3, using procedures implemented in MATLAB. Our approach is straightforward and accessible, leading to the identification of 27 EL-hypergroups of order 3.https://jhs.uma.ac.ir/article_4652_2f91070d8978e75d9e26511048f168e8.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Intersection graph of amalgamated algebras along an ideal2433464710.22098/jhs.2026.18163.1127ENMaryamSalimiDepartment of Mathematics, ET.C., Islamic Azad University, Tehran, IranElaheNafarieh TalkhoonchehDepartment of Mathematics, SR.C., Islamic Azad
University, Tehran, IranHamidRasouliDepartment of Mathematics, SR.C., Islamic Azad University, Tehran, IranElhamTavasoliDepartment of Mathematics, ET.C., Islamic Azad University, Tehran, IranAbolfazlTehranianDepartment of Mathematics, SR.C., Islamic Azad University, Tehran, IranJournal Article20250822Let f:R→S be a ring homomorphism of commutative rings with identity, and let J be a non-zero proper ideal of S. The amalgamation of R with S along J with respect to f denoted by R∝<sup>f</sup>J, was introduced by D'Anna et al. in 2010. In this paper, we investigate some properties of the intersection graph of ideals of R∝<sup>f</sup>J. We show that Γ(R∝<sup>f</sup>J) is always connected and diam(Γ(R∝<sup>f</sup>J))≤2. We obtain some conditions which implies that for an integer n >0, K_{n} is a subgraph of Γ(R∝<sup>f</sup>J). We show that if R is a local ring, and J⊆Jac(S), where Jac(S) is the Jacobson radical of S, then Γ(R∝<sup>f</sup>J) is planar if and only if Γ(R∝<sup>f</sup>J) is star graph or K<sub>3</sub> or K<sub>4</sub>, provided under certain conditions. Finally, we study the dominating number of Γ(R∝<sup>f</sup>J).https://jhs.uma.ac.ir/article_4647_147d411942c15a0c1cc2a3946fa03de5.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Dual of the duplication of a module along an ideal3442459910.22098/jhs.2025.17652.1101ENFaranakFarshadifarFarhangian UniversityJournal Article20250610Let R be a commutative ring with identity, I be an ideal of R, and M be an R-module. The amalgamated duplication of R along T, denoted by R \bowtie I, is the special subring of R × R defined by R \bowtie I := {(a, a + i) | a ∈ R, i ∈ I}. In this paper, we introduce and investigat a special kind of R \bowtie I-modules, called the dual of the duplication of M along I defined by M\bowtied I= {(m1, m2) ∈ M × M | m1 - m2 × (0 :M AnnR(I))}. In fact the R \bowtie I-module M\bowtied I is a dual of the R \bowtie I-module M \bowtie I := {(m,m') ∈ M × M | m - m' ∈ IM} which is introduced and studied by E. M. Bouba, N. Mahdou and M. Tamekkante.https://jhs.uma.ac.ir/article_4599_94ccbeaa038c7bc172fe301bf9d28da9.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Enumerating group actions of finite cyclic groups on finite sets4348464410.22098/jhs.2026.17929.1117ENArezooHosseiniDepartment of Mathematics Education
Farhangian University0000-0002-4763-0232Journal Article20250727This paper provides a systematic enumeration of actions of a finite cyclic group Z/nZ on a finite set of size k. We prove that the total number of such actions equals the number of permutations in the symmetric group S<sub>k</sub> whose order divides n, and we give an explicit combinatorial sum over cycle type vectors. Furthermore, we show that the number of isomorphism classes of such actions equals the number p<sub>D(n)</sub>(k) of integer partitions of k into parts drawn from the divisor set D(n) of n. The results connect elementary number theory, partition theory, and permutation group combinatorics. We also briefly discuss extensions to free groups and elementary abelian p-groups, identifying obstacles.https://jhs.uma.ac.ir/article_4644_fcc63746886b4b7ad70bd575b081013f.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Normalized distance Laplacian energy change due to edge deletion in complete graph and complete multipartite graph4964464510.22098/jhs.2025.18132.1124ENIndulalGopalMathematics, St Aloysious College, EdathuaJinuMarySB College ChganganacheryJournal Article20250819Let G be a connected graph with a distance matrix D. The eigenvalues of D forms the distance spectrum or D−spectrum<br />of G. The transmission of a vertex v in G is the sum of the distances from v to all other vertices of G and T (G) is the diagonal matrix with transmission of the vertices as diagonal entries. The distance Laplacian matrix is defined as D<sup>L</sup>(G)=T(G)−D(G) and the normalized distance Laplacian matrix as D<sup>L</sup>(G)=T (G)<sup>−1/2</sup>D<sup>L</sup>(G)T (G)<sup>−1/2</sup>. The normalized-distance Laplacian energy is defined as D<sup>L</sup>E(G)=∑<sub>i=1<sup>n</sup></sub> |ρ<sub>i</sub><sup>L</sup>−1|. Let D<sup>L</sup>E(G − e) be the normalized Laplacian energy of distance when an edge e is removed. In this paper we are studying the Normalized Distance Laplacian<br />energy change due to an edge deletion.https://jhs.uma.ac.ir/article_4645_979a3ae8df36b5533bcd677d757ef73e.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Multivariate extended adjacency degree based graphical index: mathematical and chemical significances6582464610.22098/jhs.2026.18161.1126ENBChaluvarajuDeparatment of Mathematics, Jnanabharathi Campus, Bangalore university, Bengaluru-560056HamsapriyaR. S.Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru- 560056Journal Article20250822The Multivariate extended adjacency graphical index, which helps to analyze the molecular structures and predict properties of compounds, is that specific cases for randomly chosen values of the non zero real numbers a, b and c, which are coincide with the vast majority of pre-defined graphical indices being considered. In this paper, we obtained the index value for some specific families of graphs, bounds and characterization in terms of order, size, minimum and maximum degree. Also, we present the chemical applicability for some linear molecular graph of above said graphical indices.https://jhs.uma.ac.ir/article_4646_2cae502f5a5532419348a43859b92f1c.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-8436151202606012-Restricted optimal pebbling number of some dendrimers8390460010.22098/jhs.2026.18742.1152ENJuma GulDehqanDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, IranSaeidAlikhaniDepartment of Mathematics, Yazd University, Yazd , IranAliDelavarkhalafiDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, IranJournal Article20251102This paper studies the 2-restricted optimal pebbling number of certain dendrimer graphs. In graph pebbling, a configuration is a distribution of pebbles on the vertices of a simple connected graph G. A pebbling move removes two pebbles from a vertex and places one on an adjacent vertex. A t-restricted pebbling configuration (tRPC) is an initial placement where no vertex holds more than t pebbles. A configuration is solvable if, for any target vertex v, a sequence of pebbling moves can place at least one pebble on v. The t-restricted optimal pebbling number, denoted π<sub>t</sub><sup>*</sup>(G), is the minimum number of pebbles required for a solvable tRPC on G. We focus on the case t=2 and determine π<sub>2</sub><sup>*</sup>(G) for several classes of dendrimers.https://jhs.uma.ac.ir/article_4600_91748ef94d6fba8716c3ed391a6baf03.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601On α-δ^*-open sets in topological space9198464010.22098/jhs.2026.16214.1060ENKPerarasanAssistant professor
Department of mathematics
Annai Vailankanni Arts and Science College
ThanjavurB. MOHAMEDHARIFDepartment of Mathematics, Government Arts College (Affiliated to Bharathidasan University),
Tiruchirappalli -02, Tamilnadu, India.A. DINESHKUMARDepartment of Mathematics, Khadir Mohideen College (Affiliated to Bharathidasan University),
Adirampattinam, Tamil Nadu, IndiaJournal Article20241118In the study of topological spaces, the concept of α-δ^*-open sets introduces a generalized framework for defining openness beyond traditional topological notions. An α-δ^*open open set is characterized by its adherence to specific conditions denoted by parameters α and δ^*, influencing its properties within the topology of a space. This investigates fundamental operations on α-δ^*-open sets, aiming to establish their behavior under set-theoretic operations and topological constructions. Key operations include union, intersection, complementation, and their implications for maintaining α-δ^*-open openness. Moreover, the abstract explores the interplay between α-δ^*-open sets and classical topological concepts such as interior, closure, and boundary, elucidating how these operations interacts within the broader framework of abstract topology. By examining these operations, this contributes to a deeper understanding of α-δ^*open sets and their role in extending traditional topological principles, thereby enriching the theoretical foundations of topology.https://jhs.uma.ac.ir/article_4640_883169c533851ab6c059f60a8b09eb87.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601An optimal method for finding common solutions to variational inequality problems via simulation function99111433810.22098/jhs.2025.16397.1066ENParvanehLo'lo'Department of Mathematics, Behbahan Khatam Alanbia University of Technology, IranMarziehShamsizadehDepartment of Mathematics
Behbahan Khatam Alanbia University of TechnologyMohamad RezaHeidari TavaniDepartment of Mathematics,
Ramhormoz Branch, Islamic Azad University, Ramhormoz, IranJournal Article20241223In this paper, we study the existence and uniqueness of common best proximity points for new types of generalized Z-contraction pairs, generalized proximal contraction pairs, and generalized Z- proximal contraction pairs of non-self mappings defined on a complete metric spaces. Our results improve and generalize some recent defending in the literature. We provide several examples to illustrate the generality of our main results. As an application, we establish sufficient conditions for the existence of unique common solutions to variational inequality problems in Hilbert spaces.https://jhs.uma.ac.ir/article_4338_4f4bbc3e407534b9b7152b094ab3bf7e.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Fractional order nonlinear random differential equation in separable Banach algebra112122464310.22098/jhs.2026.17768.1107ENKalpana DJagtapDepartment of Mathematics, Dayanad Science College, LaturBhalchandra DKarandeDepartment of Mathematics, Maharashtra Udaygiri Mahavidyalaya, Udgir (413517).Journal Article20250704This paper investigates fractional-order differential equations with random operators in a separable Banach algebra. The main goal is to prove the existence of random solutions for these equations. We focus on an initial value problem involving fractional order differential equations with random operators. By transforming this initial value problem into an<br />equivalent integral form and applying the fixed point theorem along with the Caratheodory condition, we formulate some hypothesis for the existence of random solutions. Additionally, we demonstrate that these random solutions possess local attractivity. This study provides a framework for understanding and solving existence of random solutions for fractional order differential equations with random operators. An illustrative example is also provided to verify and demonstrate the applicability of the main result.https://jhs.uma.ac.ir/article_4643_54dbfb773314fa11d9b448af2e709bbf.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Cayley-Dickson algebra-valued metric spaces and convergent fixed point theory for hypercomplex contractions123137464810.22098/jhs.2025.18293.1134ENMeghlalMallikDepartment of Mathematics, Raiganj Surendranath MahavidyalayaAbhijitMandal2Department of Mathematics, Raiganj Surendranath Mahavidyalaya, West Bengal, IndiaJournal Article20250908This paper introduces a novel theoretical framework for metric spaces valued in Cayley-Dickson algebras, extending beyond the limitations of bicomplex-valued b metric spaces to encompass the entire hierarchy of hypercomplex number systems in cluding quaternions, octonions, and sedenions. We establish a comprehensive theory of Cayley-Dickson algebra-valued metric spaces (CD-metric spaces) with generalized triangle inequalities parameterized by coefficients that account for the non-associative and non-commutative properties inherent in higher-dimensional Cayley-Dickson con<br />structions. Our principal contributions include: (1) the formulation of a consistent partial ordering relation across all finite-dimensional Cayley-Dickson algebras, (2) the development of convergence theory and completeness criteria for CD-metric spaces, (3) the establishment of fixed point theorems for contractive mappings under rational type conditions involving hypercomplex control functions, and (4) novel applications to systems of hypercomplex integral equations. The results significantly generalize existing bicomplex metric space theory and provide new tools for analyzing fixed point<br />problems in non-associative algebraic structures.https://jhs.uma.ac.ir/article_4648_a69eeee832e39a6cc6e92f14aa362ff5.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Fixed point of multi-valued Zamfirescu operator and convergence results in modular metric spaces endowed with graph138155427210.22098/jhs.2025.17087.1083ENKiranDewangan1Department of Mathematics, Government Dudhadhari Bajrang Girls Postgraduate Autonomous College, Raipur, India.0000-0001-6971-4552Jay KumarDewangan2Department of Management, Anjaneya University, Raipur, India.Journal Article20250330This paper contains some convergence results and fixed point of multivalued Zamfirescu operator along with numerical example in the framework of a complete modular metric space endowed with graph. An application of fixed point theory in solution of system of equations for multivalued Zamfirescu operator is described here.https://jhs.uma.ac.ir/article_4272_a93200d8da49b5fce87db0c0a374307b.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601CR-slant warped product submanifolds in nearly Kenmotsu manifold156171464110.22098/jhs.2026.16825.1076ENLakshmiM SDepartment of Mathematics, Jnana Bharathi campus, Bangalore University, Bangalore, IndiaH. G.NagarajaDepartment of Mathematics, Jnana Bharathi Campus, Bangalore University, Bangalore, IndiaJournal Article20250218This paper investigates CR-slant warped product submanifolds of the form B×<sub>f</sub>N<sub>θ</sub> within a nearly Kenmotsu manifold. Here, B is a CR-product submanifold, N<sub>θ</sub> is a slant submanifold and f denotes the warping function. We derive an inequality that relates the squared norm of the second fundamental form to the warping function, considering the behavior of the structure vector field. Additionally, the cases of equality are also explored. Finally, we establish several geometrical consequences of our main theorem.https://jhs.uma.ac.ir/article_4641_86fd78d7bcf86f5c632ac70e65330b6f.pdfUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-843615120260601Mathematical concepts of linear algebra in AI tools: a calculation-based study172180354810.22098/jhs.2024.15660.1038ENRam MilanSinghInstitute for Excellence in Higher Education, Bhopal, India0000-0001-6269-5248Journal Article20240815The rapid advancement of Artificial Intelligence (AI) relies heavily on mathematical foundations, with linear algebra serving as a cornerstone. This paper examines the essential mathematical concepts of vector spaces, matrices, and linear transformations that underpin key AI algorithms, such as machine learning and neural networks. Special attention is given to eigenvalues, eigenvectors, and matrix factorizations, including Singular Value Decomposition (SVD) and Principal Component Analysis (PCA), which are crucial for dimensionality reduction and feature extraction. Additionally, the paper explores the role of quadratic programming and convex optimization in training Support Vector Machines (SVMs) and deep learning models, presenting detailed mathematical formulations of these processes. Computational challenges in handling large-scale matrix operations, such as multiplication, inversion, and sparse matrices, are addressed with a focus on numerical methods that enhance scalability and performance. Supported by worked examples and simulations, this research bridges theoretical rigor and practical applications, offering valuable insights for advancing AI systems.https://jhs.uma.ac.ir/article_3548_afe66aebfdacb4b1276a628a0c2c955a.pdf