https://jhs.uma.ac.ir/ Journal of Hyperstructures en daily 1 Mon, 01 Jun 2026 00:00:00 +0330 Mon, 01 Jun 2026 00:00:00 +0330 https://jhs.uma.ac.ir/article_4652.html The 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_4647.html Let 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∝fJ, was introduced by D'Anna et al. in 2010. In this paper, we investigate some properties of the intersection graph of ideals of R∝fJ. We show that Γ(R∝fJ) is always connected and diam(Γ(R∝fJ))≤2. We obtain some conditions which implies that for an integer n >0, K_{n} is a subgraph of Γ(R∝fJ). 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∝fJ) is planar if and only if Γ(R∝fJ) is star graph or K3 or K4, provided under certain conditions. Finally, we study the dominating number of Γ(R∝fJ). https://jhs.uma.ac.ir/article_4599.html Let 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_4644.html This 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 Sk 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 pD(n)(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_4645.html Let G be a connected graph with a distance matrix D. The eigenvalues of D forms the distance spectrum or D−spectrumof 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 DL(G)=T(G)−D(G) and the normalized distance Laplacian matrix as DL(G)=T (G)−1/2DL(G)T (G)−1/2. The normalized-distance Laplacian energy is defined as DLE(G)=∑i=1n |ρiL−1|. Let DLE(G − e) be the normalized Laplacian energy of distance when an edge e is removed. In this paper we are studying the Normalized Distance Laplacianenergy change due to an edge deletion. https://jhs.uma.ac.ir/article_4646.html The 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_4600.html This 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 πt*(G), is the minimum number of pebbles required for a solvable tRPC on G. We focus on the case t=2 and determine π2*(G) for several classes of dendrimers. https://jhs.uma.ac.ir/article_4640.html In 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_4338.html In 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_4643.html This 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 anequivalent 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_4648.html This 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 constructions. 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 pointproblems in non-associative algebraic structures. https://jhs.uma.ac.ir/article_4272.html This 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_4641.html This paper investigates CR-slant warped product submanifolds of the form B×fNθ within a nearly Kenmotsu manifold. Here, B is a CR-product submanifold, Nθ 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_3548.html The 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_4639.html This paper explores advanced methods in static analysis, focusing on a theoretical and computational study of beam deflection under various loading conditions. We present detailed mathematical calculations, computational simulations, and statistical analysis to validate our results. The study aims to provide insights into the effectiveness of modern computational tools and statistical methods in static analysis. https://jhs.uma.ac.ir/article_4642.html In this paper, we establish a one-to-one correspondence between some hypersurfaces and the images of them under their Gauss mappings. Then, we introduce a class of hypersurfaces, whose images under their Gauss mappings are the same. Moreover, we prove the evenness of the cardinal number of the cross section of a compact hypersurface S ⊆ Rm with a curve α:R→Rm which is nowhere tangent to S, and tends to infinity in directions ±∞. Finally, we clarify how the results, relate to existing literature on Gauss mappings of minimal or finite-type surfaces. Some illustrative examples and an application are also provided. https://jhs.uma.ac.ir/article_4674.html This paper introduces the notions of (meet, extended, symmetrical) EQ-algebras and valued indicator subsets within this framework. We present a new class of EQ-algebras and prove that every finite chain and countable set can be structured as an extended EQ-algebra. A primary contribution is establishing a connection between the class of digraphs and the class of EQ-algebras. To this end, we define the concepts of inverter digraphs and valued indicator digraphs based on EQ-algebras, which are founded on the corresponding notions of inverter subsets and valued indicator subsets. We investigate the relationship between these two types of digraphs, providing conditions under which they are isomorphic and showing that valued indicator digraphs are spanning subgraphs of inverter digraphs under certain constraints. Finally, leveraging this correspondence, we demonstrate a method to extract EQ-algebras from (weakly) strong digraphs. https://jhs.uma.ac.ir/article_4681.html This paper introduces two subclasses of analytic functions associated with the q-Bernardi integral operator. These subclasses are defined by using the q-derivative together with special functions whose coefficients are Bernoulli numbers and generalized telephone numbers. We establish inclusion-type results for the proposed classes and investigate the corresponding quasi-subordination and majorization problems. In particular, sufficient radius conditions are obtained under which the q-derivatives of majorized functions satisfy the required comparison inequalities.  https://jhs.uma.ac.ir/article_4682.html Abstract. For any connected Fuzzy graph G: (V, σ, μ), the strong sum distance between x and y is defined as 𝑑𝑠𝑠𝑑(x, y) = min {L(𝑃𝑠)} where 𝑃𝑠 is the strong x-y path. For any two vertices x and y of a graph G, 𝑑𝑑- distance is defined by considering the degrees of x and y along with the length of the path. In this paper we introduced strong sum 𝑑𝑑 distance in fuzzy graphs by considering distance as strong sum distance and degree of vertex as the sum of membership values of all edges which are incident at that vertex. We study some properties with this new distance. First we prove that the new distance is a metric on the set of vertices of G. Some properties of strong neighbors and eccentric nodes are obtained. https://jhs.uma.ac.ir/article_4683.html This review examines Iterative Learning Control (ILC) from the perspective of fractional calculus, focusing on its theoretical foundation and practical relevance in dynamical systems. The paper introduces ILC and its role in enhancing repetitive control performance, followed by a brief overview of dynamical systems and fractional calculus, including key definitions and types of fractional derivatives. Core ILC schemes—D-type, P-type, PD-type, and PDα-type—are analyzed under fractional-order dynamics. Applications in robotics, time-delay systems, process industries, and biomedical engineering highlight the robustness and accuracy of fractional-order ILC. The review concludes by emphasizing the benefits of incorporating fractional derivatives into ILC design for improved control in dynamic environments. https://jhs.uma.ac.ir/article_4684.html In this paper, we investigate about the transitive closure of a binary relation. We present the algorithms for computing the transitive closure in matrix form and set-theoretic form, as well as their complexity. First, we recall a simple algorithm (Algorithm \ref{transitivematrixalgorithm}) and the Warshall's algorithm(Algorithm \ref{warshallmatrixalgorithm}), along with their complexity, to obtain the matrix of transitive closure. Then, we introduce the Algorithm \ref{transitiverelationalgorithm} and Warshall's algorithm (Algorithm \ref{warshallsetalgorithm}) in set-theoretic form, instead of matrix form, as well their complexity. Finally, the Maple codes of the newly introduced algorithms are provided along with an example of how to use them in Maple. https://jhs.uma.ac.ir/article_4685.html The largest class of hyperstructures is the class of Hv-structures. In this class, equality is replaced by non-empty intersection. This class is extremely large and can, therefore, be used to define various objects that can not be defined within classical hypergroup theory. In the present paper, we deal with strong-inverse elements, which are defined in both hypergroups and Hv-groups, particularly, in cases where there is more than one unit element. We introduce several constructions obtained by the properties of strong-inverse elements in Hv-groups. https://jhs.uma.ac.ir/article_4686.html The main aim of this article is that the distance-based parameters, in particularly the Steiner concept and the hop domination combine to form interesting results in graph theory. A subset W of vertices in a graph G is called the Steiner hop dominating set of G if W is both a Steiner set and a hop dominating set of G. The minimum cardinality of a Steiner hop dominating set of G is its Steiner hop domination number γhs (G). The Steiner hop domination number of some special graphs, such as the middle graph and degree splitting graph of standard graphs are determined. Also, it is determined for lollipop graph, Barbell graph and pop barbell graph https://jhs.uma.ac.ir/article_4721.html The aim of this paper is to modify the Thakur iteration process into hyperbolic metric space where the symmetry condition is satisfied and establish the weak w2-stability and data dependency results for contraction mappings. Next, we establish Δ-convergence and strong convergence theorems for generalized (α, β)-nonexpansive type 1 mappings. We give an example of generalized (α, β)-nonexpansive type 1 mapping which is not nonexpansive mapping. https://jhs.uma.ac.ir/article_4722.html This paper investigates the relationship between coherent configurations of graphs and those of their automorphism groups, with a special focus on tree structures. For Schurian coherent configurations—those derived from permutation group orbitals—we establish an isomorphism between the coherent configuration of a graph and that of its automorphism group. We systematically classify the coherent configurations for three fundamental classes of trees: paths, star graphs, and spoke graphs, along with their generalized spoke variants. Through direct product and direct sum operations, we decompose these configurations into combinations of trivial and discrete coherent configurations. A detailed non-trivial example illustrates the coherent configuration of a spoke graph. This work advances the combinatorial analysis of tree symmetries and provides tools for broader graph family classifications, contributing to frameworks for studying graph isomorphism problems and quantum automorphism groups. https://jhs.uma.ac.ir/article_4723.html This paper presents a comprehensive study of curvature properties on statistical manifolds endowed with mixed 3-Sasakian and mixed 3-cosymplectic structures. We derive necessary and sufficient conditions for mixed 3-Sasakian statistical manifolds to be Einstein, establishing fundamental identities for the Ricci tensor and scalar curvature. Furthermore, we introduce and analyze mixed 3-cosymplectic statistical manifolds, proving that they are necessarily Ricci-flat. The interplay between statistical duality and these geometric structures yields rich curvature constraints that are thoroughly analyzed. We provide explicit examples of both mixed 3-Sasakian Einstein and mixed 3-cosymplectic Ricci-flat statistical manifolds, discussing their physical implications in the context of general relativity and field theories. The results generalize previous work on Sasakian and cosymplectic geometry to the statistical setting, opening new paths for research in information geometry and theoretical physics. https://jhs.uma.ac.ir/article_4724.html Let A be a unital ∗-algebra with the unit I. In this paper, under some mild conditions on A, it is shown that a map Φ : A → A is the mixed Lie triple ∗-derivations on ∗-algebras if and only if Φ is an additive ∗-derivations is an additive ∗-derivations. https://jhs.uma.ac.ir/article_4748.html In this paper, we study ·-ideals in product MV-algebras. We define a ·-closed system. By the notion of ·-closed systems, we show that there exists a congruence relation on product MV-algebras. We prove that if P is an ·-prime ideal of A such that S = A \ P, then A[S] is a local product MV-algebra (fraction relative to a ·-closed systems.) https://jhs.uma.ac.ir/article_4782.html The present paper is to deliberate the class of Sasakian manifolds admitting *-conformal eta-Ricci soliton. In our next section we have given a brief discussion on the above class of manifolds. In continuation to this we have given few preliminary idea on Sasakian manifolds. Among others we have proved several conditions under which Sasakian manifold is an eta-Einstein manifold. Lastly we have cited an example of the above said manifold for verifying our findings. https://jhs.uma.ac.ir/article_4792.html ‎‎‎Let G be a group with identity element e, and let R = ⊕g∈G Rg be a commutative graded ring. Let M be a graded R-module, and let S⊆h(R) be a multiplicatively closed subset of R. The aim of this paper is to introduce and study the concepts of graded S-co-r-submodules and graded S-co-n-submodules. We investigate some of their properties and establish the relationship between graded S-co-r-submodules and graded S-co-n-‎submodules.‎‎‎ https://jhs.uma.ac.ir/article_4902.html ‎All rings R have identities and all modules are unitary‎ ‎right R-modules‎, ‎unless otherwise stated‎. ‎In this paper‎, ‎we discuss about the direct sum of a CS-module with essential socle and a module with zero socle‎. ‎Next‎, ‎we discuss about the direct sum of two CS-modules and also two CLS-modules in some cases‎. https://jhs.uma.ac.ir/article_4915.html We consider a groupoid (X, *) equipped with a poset structure (X, ≤) and study fuzzy partially ordered groupoids where induced by a fuzzy subset μ. We define a set P_μ(*;≤) and explore its properties. Specifically, we demonstrate that if (X, *, 0) is a left zero semigroup or an idempotent groupoid, then (X, *) is fuzzy fully dominated by a poset (X, ≤) induced by a fuzzy subset μ. https://jhs.uma.ac.ir/article_4917.html In this paper, we define 2-conformal vector fields (CVFs) within a Riemannian manifold (RM) and investigate their geometry in both standard static space-time (SSST) and warped product manifolds (WPM). We derive the conditions under which the 2-CVFs are parallel and establish curvature-related results for WPM in terms of 2-CVFs. We characterize 2-CVFs on static and Robertson-Walker space-times. Finally, the relation between such a vector field (VF) and hyperbolic Ricci solitons (HRS) is considered.