https://jhs.uma.ac.ir/ Journal of Hyperstructures en daily 1 Mon, 01 Dec 2025 00:00:00 +0330 Mon, 01 Dec 2025 00:00:00 +0330 https://jhs.uma.ac.ir/article_3539.html The solvability of Sylvester matrix equations is relevant to many issues in control theory and systems theory. Fuzzy numbers should be used to represent at least some of the system’s parameters in many applications instead of crisp ones. The solutions to the fuzzy Sylvester matrix problem are only given with triangular fuzzy numbers in the majority of the earlier literature. Two analytical approaches to the solution of the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation are presented in this study. The Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation is transformed utilising the current arithmetic fuzzy multiplication operations into an analogous system of crisp Sylvester Matrix  Equations. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. Furthermore, the equivalency between the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation and the solution to the Sylvester Matrix Equation system is examined. One example problem is solved to demonstrate the suggested methods. https://jhs.uma.ac.ir/article_4075.html Let R be an associative ring with identity. A ring R is called ZG-regular( resp. strongly ZG-regular) if, for every a in R, there exist positive integer n and g in G, such that ang ∈a^ngRa^ng (resp. a^ng ∈a^(n+1)gR. In this paper, we shall show that the join of all ZG-regular ideals in an arbitrary ring R is a ZG-regular ideal, and so there exists a unique maximal ZG-regular ideal M = M(R) in R, whose structure we investigate. Furthermore, we establish the necessary and sufficient condition for a ring to be a direct sum of its ideals. https://jhs.uma.ac.ir/article_4191.html ‎Let R be a commutative Noetherian ring and I an ideal of R‎. ‎Suppose that S is a Serre subcategory of the category of R-modules which satisfies the condition CI‎. ‎Let $M$ be a ZD-module and N an R-module‎. ‎As a generalization of the notion of S-depth(I‎, ‎M)‎, ‎we define the S-depth of I ‎on the pair (N‎, ‎M) by S-depth(I‎, ‎N‎, ‎M):=S-depth(AnnR(N/IN)‎, ‎M)‎. ‎We investigate the connections between S-depth(I‎, ‎N‎, ‎M)‎, ‎local cohomology modules and Ext functors‎. ‎In particular‎, ‎when N is finitely generated‎, ‎it is shown that‎ ‎S-depth(I‎, ‎N‎, ‎M)=inf {i‎: ‎H{i}I(N‎, ‎M) ∉ S}=inf{i‎: ExtiR(N/{IN}‎, ‎M)∉ S}‎. ‎Moreover‎, ‎various formulas are provided that relate this generalized S-depth to other notions of depth in the literature‎. https://jhs.uma.ac.ir/article_3899.html Let M be a subset of V (G) and let G : (V, σ, μ) be a fuzzy graph. The monophonic domination integrity (MDI) of G is defined by (MDI) ̃(G)^= min{|M|+m(G−M): M is a monophonic dominating set of G}, where |M|=∑_(u∈M)σ(u)and m(G − M) is the order of the greatest component of G−M. The notion of vulnerability parameter MDI in fuzzy graphs is presented in this work. Further, the MDI for complete fuzzy graph, complete bipartite fuzzy graph, join and Cartesian product of two fuzzy graphs and bounds are also discussed. Also, we present a decision-making problem involving the optimization of bus routes and the strategic placement of bus stations using MDI principles. https://jhs.uma.ac.ir/article_4192.html Let G = (V, E) be a simple graph. A set D⊆V (G) is a total outer−connected dominating set of G if D is total dominating, and the induced sub-graph G[V (G) − D] is a connected graph. Let K2,n be the complete bipartite graph and D ̃tc (K2,n,i) denote the family of all total outer-connected dominating sets of K2,n with cardinality i. Let d ̃tc (K2,n,i)=|D ̃tc (K2,n,i)|. In this paper, we obtain recursive formula for d ̃tc (K2,n,i). Using this recursive formula, we construct the polynomial, D~tc (K2,n,x)=∑i=22+nd ̃tc (K2,n,i)xi  which we call total outer−connected domination polynomial of K2,n and obtain some  properties of this polynomial. https://jhs.uma.ac.ir/article_3936.html In the domain of mathematical chemistry and graph theory, topological indices have emerged as vital tools for quantifying the structural properties of molecular graphs. Recently, the Mobius function graph of a finite group has  earned significant attention due to its connections with algebraic and topological structures. However, determination of  the topological indices of these graphs remain largely unexplored. In this paper we compute and investigate the  relationships between several distance-based topological indices, including the Mostar index, weighted Mostar index,  Szeged index, weighted Szeged index, PI index and weighted PI index, for the Mobius function graphs of finite groups.  https://jhs.uma.ac.ir/article_3940.html The Seidel energy of a graph is the sum of the absolute values of the eigenvalues of its Seidel matrix. In this paper, we introduce the concepts of edge Seidel energy E(Ls(G)) and edge covering Seidel energy E(Lsec(G)) for the K1,n and K2,n Graphs, and we have obtained some results. https://jhs.uma.ac.ir/article_4275.html This paper focuses on the computation of NM-polynomial and several topological indices for cycle related graphs such as Wheel graph, Helm graph and Gear graph. The NM-polynomial is a graph invariant that encodes information about the sub graph structure, which is crucial for understanding the connectivity and combinatorial properties of a graph. We  develop formulas and methods for computing the NM-polynomial for specific cycle-related graphs, demonstrating its  utility in capturing key graph characteristics. https://jhs.uma.ac.ir/article_4273.html In this paper, we study a family of graphs related to Johnson graphs, known as bipartite Kneser graphs. Let n and k be integers such that n>k 1≥. We denote by H(n, k) the bipartite Kneser graph, whose vertex set consists of all k-subsets and (n - k)-subsets of the set [n] = {1, 2, ..., n}, where two vertices are adjacent if and only if one is a subset of the other. Mirafzal (S. M. Mirafzal, The automorphism group of the bipartite Kneser graph, Proc. Indian Acad. Sci. (Math. Sci.), (2019) 129 (34), proved that the automorphism group of the bipartite Kneser graph H(n, k) is isomorphic to Sym ([n])×Z2. In this paper, we investigate the distance-transitivity and the diameter of the bipartite Kneser graphs. It is known that H(n, k) is distance-transitive precisely when k=1 or n=2k+1. In this work, we provide new structural proofs of these cases directly within the bipartite Kneser framework, and we determine the diameter of H(n, k) for various ranges of n and k. https://jhs.uma.ac.ir/article_4274.html Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of G, if for every vertex in V\S is adjacent to at least one vertex in S. A subset S of V is called a twain secure perfect dominating set of G (TSPD-set) if for every vertex v ∈ V \S is adjacent to exactly one vertex u ∈ S and (S\{u})∪{v} is a dominating set of G. The minimum cardinality of a twain secure perfect dominating set of G is called the twain secure perfect domination number of G and is denoted by γtsp(G).Let Dtsp(Cn, i) denote the family of all twain secure perfect dominating sets of Cn with cardinality i, for γtsp(Cn)≤ i≤ n. Let dtsp(Cn, i) = |Dtsp(Cn, i)|. In this article, we derive a recursive formula for dtsp(Cn, i) and construct Dtsp(Cn, i). Weconsider the polynomial Dtsp(Cn, x) = Σn i=γtsp(Cn) dtsp(Cn, i)xi, which we refer to as the twain secure perfect domination polynomial of cycles using this recursive formula. In this research, we use a recursive technique to generate all twain secure perfect dominating sets of cycles and twain secure perfect domination polynomials of cycles. https://jhs.uma.ac.ir/article_4056.html This study presents an innovative reconfiguration of the Mittag-Leffler function (MLF) by synergistically combining the Mellin transform and the Sumudu transform. Although the MLF plays a significant role in fractional calculus, its complexity has limited its applicability. By utilizing both the Mellin and Sumudu transforms, new integral representations of the MLF are derived, effectively broadening its scope in addressing fractional differential equations. This integrated approach provides a deeper understanding of the MLF’s properties and enables its extension to a wider range of problems in physics, engineering, and mathematics. The effectiveness of the proposed extension is demonstrated through its application to fractional calculus problems, thereby contributing to the advancement of the field and enhancing its ability to model complex real-world phenomena with greater accuracy. https://jhs.uma.ac.ir/article_4055.html This paper introduces Pentagonal Controlled Intuitionistic Fuzzy Metric Spaces (PCIFMS), a novel extension of intuitionistic fuzzy metric spaces that incorporates a pentagonal control function to better handle uncertainty and imprecision. We establish foundational theorems, provide detailed proofs, and explore practical applications in decision-making, image processing, and complex systems analysis. The proposed model offers significant advantages over existing frameworks, particularly in its ability to adapt to multi-dimensional and context-dependent scenarios. This study contributes to the development of fuzzy theory and its applications, providing a robust tool for modeling complex systems under uncertainty. https://jhs.uma.ac.ir/article_3937.html ‎Every Riemannian metric is R-quadratic, while many Finsler metrics have not this property‎. ‎A Finsler metric is called R-quadratic if its Riemannian curvature is quadratic in all direction at any points of the underlying manifold‎. ‎A Finsler metric on a manifold is called a generalized Berwald metric if there exists a covariant derivative such that the parallel translations induced by it preserve the Finsler function‎. ‎In this paper‎, ‎we study the class of generalized Berwald (α, β)-manifolds with R-quadratic properties and prove a rigidity result‎. ‎We show that such manifolds satisfy S=0 if and only if B=0‎. https://jhs.uma.ac.ir/article_4054.html This manuscript explores the Homotopic embedding of infinite-dimensional Hilbert manifolds into Poincaré complexes, emphasizing the preservation of necessary geometric properties such as curvature and Ricci-flatness. The exploration of infinite-dimensional Hilbert manifolds and their embeddings into Poincaré complexes has opened up new pathways in the fields of functional analysis, algebraic topology, and differential geometry. Recent studies emphasize the preservation of geometric features such as curvature and Ricci-flatness, which have greatly enriched the understanding of symplectic geometry and topological properties of manifolds. https://jhs.uma.ac.ir/article_4105.html Farbod ‎(2024) ‎introduced a‎ ‎‎‎‎‎‎‎ 2-parameter regularly varying discrete distribution generated by Waring-type probability (2-RDWP)‎‎‎. ‎‎ ‎‎In this paper‎, ‎asymptotic properties of maximum likelihood estimators of the unknown parameters are established for the 2-RDWP model‎. ‎Some new plots including cumulative distribution function‎, ‎survival function and hazard rate function are illustrated for the 2-RDWP model‎. ‎Two‎ real data sets of COVID-19 ‎are ‎applied to show the ‎model's‎ ‎applicability ‎‎ compared to ‎other‎ rival distributions‎. ‎‎‎‎‎‎Based on some statistical criteria we see that the 2-RDWP‎, ‎for these real data sets‎, ‎has satisfactory results with respect to rival models‎. ‎Using ‎an‎ optimization ‎algorithm, ‎m‎aximum ‎likelihood ‎estimations of the unknown parameters are proposed. https://jhs.uma.ac.ir/article_3866.html This paper addresses the control of a category of continuous-time linear systems that switch between different modes, where the switching signals are driven by random time-iteration. The system under consideration is subject to uncertainties in the system dynamics and observation noise in the output measurements. We propose a robust control strategy that Accounting for the random nature of the switching signals and the system uncertainties. The learning performance is examined using the Lebesgue-p norm, leading to the derivation of a sufficient condition for convergence. The findings demonstrate that the proposed control law effectively addresses the tracking problem in switched systems, Especially when the switching rules are expanded to the time-iteration domain using a stochastic framework, we introduce a groundbreaking control approach that guarantees the system's performance despite uncertainties and noise. Through rigorous theoretical analysis, we prove the effectiveness of our suggested approach in achieving robust control and estimation performance.The results of this research contribute to the advancement of control theories and have potential applications in various fields, including power systems, robotics, and process control. https://jhs.uma.ac.ir/article_3892.html In this paper, we offered a FTS-based tutorial on rice farming in India. The relevant literature is reviewed, which serves as a basis for the main concepts and models based on different forms of FTS forecasts. In an effort to inspire readers to contribute to this field of study, we also highlight the challenges and recent work that aims to fill in some of these knowledge gaps. Finally, time series forecasting is a useful tool for organizing and making decisions. An increasing number of methods, ranging from traditional statistical models to soft computing and artificial intelligence approaches, have been developed to generate increasingly accurate forecasts. PyFTS is an open-source, free Python library created by the Laboratory of Machine Intelligence and Data Science that implements a number of FTS models that have been published in the literature. In order to determine the interval in the fuzzy time series, Chen's method of FTS, comparing numerous values of n (Number of Interval) is used in this paper. We are interested to minimizing the MSE in the forecasting using PyFTS. 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_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_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.