Shahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601A review on cost-based feature selection algorithms in the various applications of machine learning144487110.22103/jmmr.2025.24028.1696ENSabaBeiranvandDepartment of Computer Engineering, National University of Skills (NUS), Tehran, IranMohammad BagherDowlatshahiDepartment of Computer Engineering, Lorestan University, Khorramabad, IranAminHashemiDepartment of Computer Engineering, Lorestan University, Khorramabad, IranJournal Article20240910Knowledge acquisition is the most important challenge in building an expert system in any field, and one of the sources of knowledge will be the data collected in that field. Traditionally, the data collection process is assumed to have a symmetric cost. For example, this assumption will not be acceptable in the medical due to various expenses. Designing a cost-sensitive classification and a cost-sensitive feature selection method are two approaches to considering cost factors. Cost-effective feature selection improves financial return by significantly saving feature data cost as well as limiting credit losses and this can be used in different areas, for example, computer imaging and medical diagnosis which also have a large number of features that may be irrelevant or redundant. Analysis of the research reviewed in this study shows that cost-sensitive feature selection focuses on selecting a feature subset with minimum total cost while achieving a classification accuracy that is as high as possible. The review of selected studies showed a downward trend in using heuristic methods in this field, Wrapper methods are in the first rank regarding usage in evaluation criteria, and 76\% of selected studies are in the single-objective category. Most of the studies were classified in the single-label category based on the number of determined labels.https://jmmrc.uk.ac.ir/article_4871_6c5fc71fee2bf18310e995fffc395f46.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Some characteristics of tensor-variate skew-normal distribution and its application in image analysis4564490410.22103/jmmr.2025.24813.1763ENSeyed Ali AsgarTajadodDepartment of Statistics, University of Birjand, Birjand, IranFatemehYousefzadehDepartment of Statistics, University of Birjand, Birjand, IranR.B.Arellano-ValleDepartment of Estadistica, Pontificia Universidad Catolica de Chile, Santiago, Chile0000-0002-5121-9702SaraJomhooriDepartment of Statistics, University of Birjand, Birjand, IranJournal Article20250211In recent years, due to the increasing growth of technology and new technologies, data is obtained in more complex structures as the main component in analysis. One of these complex structures is tensors. Therefore, in order to answer this need (analysis of data with tensor structure), it is necessary to expand statistical concepts and methods in the field of data with tensor structure. On the other hand, in reality, we may also encounter skew data. Therefore, in this article, we have introduced the skew normal tensor distribution and obtained some of its important statistical properties. Subsequently, we employed the EM algorithm to obtain maximum likelihood estimates of the parameters and assessed their accuracy through simulation studies. Finally, we have shown the effectiveness of the obtained estimators with real data.https://jmmrc.uk.ac.ir/article_4904_3742467d0006aa28118d5c26c4c68d87.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Unsupervised feature selection using orthogonal locality preserving projections and bipartite graph matching for face image classification65104505610.22103/jmmr.2025.24829.1765ENFiroozehBeiranvandDepartment of Electrical Engineering, Lorestan University, Khoramabad, IranJournal Article20250214Feature selection plays a crucial role in facial image classification by reducing dimensionality and improving robustness to variations in expression, pose, and lighting. However, researchers face challenges when selecting features from high-dimensional, unlabeled data due to the nonlinear manifold structure of facial images. To address this, this paper proposes UFSOLPP, a novel unsupervised feature selection method that consists of three main stages. First, the method employs Orthogonal Locality Preserving Projections (OLPP) for feature extraction, aiming to preserve local data structures and enforce orthogonality without dimensionality reduction. Unlike conventional OLPP, which uses heat kernel to measure similarity, this paper replaces it with cosine distance to better capture angular relationships that are for facial image discrimination. Second, it measures the similarity between the original and orthogonal features using the Pearson correlation distance. Third, it models both feature sets as vertices in a weighted bipartite graph. The edge weights are computed using the Pearson correlation similarity, and the method uses the Hungarian algorithm to compute maximum matching. The method selects the original features involved in the maximum matching as the final subset. This strategy removes noisy, correlated, and redundant features effectively, while preserving interpretability and discriminative power. Experiments demonstrate that UFSOLPP outperforms eight state-of-the-art methods. It achieves 96.00% accuracy and 0.9800 NMI on Jaffe, 68.66% accuracy and 0.7532 NMI on ORL, and 82.33% accuracy and 0.8557 NMI on the high-dimensional Pixraw10P dataset. These results highlight the practical value of UFSOLPP and its ability to handle high-dimensional data efficiently in unsupervised facial image analysis.https://jmmrc.uk.ac.ir/article_5056_42be18ffeecde76d18125c9efa9f6ef8.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Some results on complex $(p,q)-$extension $\alpha-$Chebyshev differential equation for $|x| \leq 1$105114507410.22103/jmmr.2025.25313.1803ENS.ShojaeianDepartment of Mathematics Science, Yazd University, Yazd, IranH.MazaheriDepartment of Mathematics Science, Yazd University, Yazd, IranT.S.JesmaniCurriculum studies, Department of Curriculum studies, Allameh Tabatabaei University, Tehran, IranJournal Article20250522In this paper, we define complex $(p,q)-$extension $\alpha-$Chebyshev differential equations on $|x|\leq 1$. Our consideration is focused on determining properties of generalized Chebyshev polynomials of the first, second, third and Fourth kind, sparking interest in constructing a theory similar to the classical one. We solve the complex $(p,q)-$extension $\alpha-$Chebyshev differential equations on $|x| \leq 1$.https://jmmrc.uk.ac.ir/article_5074_1daa3e7a9de87f4221dd2f3310af6048.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Connectivity of 2-distance graphs115124521710.22103/jmmr.2025.24724.1754ENSayyed HeidarJafariFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranSeyed RezaMusawiFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranJournal Article20250123For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if their distance is $2$ in the graph $G$. In this paper, we characterize all graphs with connected $2$-distance graphs. For graphs with diameter 2, we prove that $D_2(G)$ is connected if and only if $G$ has no spanning complete bipartite subgraphs. For graphs whose diameter is greater than $2$, we define a maximal fine set, and by contracting $G$ with respect to these subsets, we obtain a new graph $\widehat{G}$ such that $D_2(G)$ is connected if and only if $D_2(\widehat{G})$ is connected. In particular, $D_2(G)$ is disconnected if and only if $\widehat{G}$ is bipartite.https://jmmrc.uk.ac.ir/article_5217_1777319dbbd2b056b50001e44ecbb54e.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Geometric properties of second Ricci solitons125134523610.22103/jmmr.2025.25804.1856ENMasoumehKhaliliDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranGhodratallahFasihi-RamandiDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranShahroudAzamiDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranJournal Article20250823This paper introduces the idea of second Ricci solitons. A second Ricci soliton is nothing but a steady hyperbolic Ricci soliton. We study the geometry of closed and compact second Ricci soliton manifolds. Immersed submanifolds as second solitons also will be investigated. Finally, we investigate this structure on warped product manifolds.https://jmmrc.uk.ac.ir/article_5236_9c36fd4749940db5cd60b5e5c1966a8d.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Weak noncompactness in fractional differential boundary problems: existence results135153524310.22103/jmmr.2025.25783.1852ENSomayehSaiedinezhadDepartment of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, IranMaralSangiDepartment of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, IranM. B.GhaemiDepartment of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, IranJournal Article20250818This paper addresses the existence of solutions for a class of fractional differential boundary value problems. The main novelty of this paper lies in providing a new analytical framework to prove solution existence for this class of equations. Our approach is grounded in a combination of a Krasnoselskii-type fixed point theorem with the concept of the measure of weak noncompactness (MWNC) in the Banach space $L^{1}(I)$. This technique allows us to prove existence under more general growth conditions than in previous works that relied on complete continuity. By establishing a set of sufficient conditions, we demonstrate that the boundary value problem under consideration admits at least one solution. Several illustrative examples are presented to highlight the applicability and effectiveness of the obtained results.https://jmmrc.uk.ac.ir/article_5243_be71b5c9b986e76fe7282e053df0b0c8.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601On the duality of function valued frames in $L^2(0,\infty)$155177524410.22103/jmmr.2025.25413.1817ENS.M.MoshtaghiounDepartment of Mathematical Sciences, Yazd University, Yazd, Iran0009-0006-6215-2917M.SimiDepartment of Mathematical Sciences, Yazd University, Yazd, IranJournal Article20250610By the notion of $F_a$-factorable operators, we establish a new version of the Riesz Representation Theorem adapted to this class of operators. Also, for $F_a$-factorable operators $T$ and $T^{\prime}$, we derive some equivalent conditions such that the equation $T^{\prime}=TX$ has a unique solution in the class of $F_a$-factorable operators. Moreover, by using the concept of $F_a$-frame in $L^2(0,\infty)$, which is similar yet distinct from the traditional frame concept, we establish optimal $F_a$-frame bounds, and provide a complete characterization of all corresponding $F_a$-dual frames.https://jmmrc.uk.ac.ir/article_5244_ae7b14e3d9e3a38d66b9fdb1bdbce481.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601PFE-SELF-RAG: Balancing self-RAG evaluation metrics via Pareto efficiency179208530510.22103/jmmr.2026.25661.1841ENFatemehHosseiniDepartment of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, IranMahdiEftekhariDepartment of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20250729Self-RAG enhances Retrieval-Augmented Generation (RAG) by enabling Large Language Models (LLMs) to dynamically retrieve external knowledge and self-evaluate outputs. However, the original Self-RAG heavily relies on a manually tuned weighted-sum mechanism for combining critique scores, rendering the system brittle and poorly adaptable to diverse query distributions. To address these limitations, Pareto Front Enhanced Self-RAG (PFE-SELF-RAG) is proposed as a tuning-free Multi-Objective Optimization(MOO) framework. It first applies Maximal Marginal Relevance (MMR) to enrich context diversity, then incorporates two evaluation strategies: Pareto Front-based selection and Geometric Mean (GM) Aggregation. The primary significance of this approach lies in eliminating fragile manual weight tuning. By mathematically modeling the trade-off between factual accuracy and relevance, PFE-SELF-RAG enables adaptive candidate selection, allowing the number and quality of outputs to vary dynamically. This represents the first formal application of Pareto optimization to candidate ranking in self-reflective RAG systems, establishing a principled alternative to heuristic aggregation. Evaluations on PopQA, ARC Challenge, PubHealth, and TriviaQA demonstrate substantial impact. The Full Pareto Set strategy consistently outperforms the Self-RAG baseline, achieving %58.6 on PopQA (%+3.7), %68.0 on ARC Challenge (%+1.6), %73.0 on PubHealth (%+0.6), and %71.3 on TriviaQA (%+4.3). These improvements underscore the practical impact of replacing brittle heuristics with principled optimization, establishing PFE-SELF-RAG as a robust and scalable standard for self-reflective RAG systems.https://jmmrc.uk.ac.ir/article_5305_524e84fc74d351a34765e39fa61cca62.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Riesz Dunford integral and operators on Hilbert space based on univalent functions with fixed residue209217532010.22103/jmmr.2026.25383.1812ENLidaNobakhtDepartment of Mathematics, Payame Noor University, Tehran, IranShahramNajafzadehDepartment of Mathematics, Payame Noor University, Tehran, IranMohammadrezaForoutanDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20250604In the present paper, we introduce and investigate a new class of meromorphic functions analytic in the open unit disk and applying a $q-$derivative and $q-$differential integral operator associated with quantum calculus. Furthermore, by using the familiar Riesz-Dunford integral of a linear operator on Hilbert space H, a new class of univalent functions with a fixed point is introduced. Coefficient estimate, distortion bound and extreme points are obtained.https://jmmrc.uk.ac.ir/article_5320_8ce5a294f81348cf375ca0c518dceb18.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601The degree variance and geometric degree variance of random trees219227532110.22103/jmmr.2026.26096.1885ENRaminKazemiDepartment of Statistics, Imam Khomeini International University, Qazvin, IranJournal Article20251012The degree variance and the geometric mean of the degrees of the vertices for graph $G$ are defined as $\text{Var}(G)=\frac{1}{n}\sum_{i=1}^{n}\Big(d(v_i)-\frac{2m}{n} \Big)^2$ and $\text{GM}(G)=\Big(\prod_{i=1}^{n}d(v_i)\Big)^\frac{1}{n},$ respectively, where $n$, $m$ and $d(v)$ represent the number of vertices, edges and degree of vertex $v$. Also, the geometric degree variance of graph $G$ defined as $\text{GVAR}(G)=\frac{1}{n}\sum_{i=1}^{n}(d(v_i)-\text{GM}(G))^2$. We determine the two first moment of degree variance in (uniform) random trees. We also show a convergence in probability associated with this quantity. Finally, we present bounds for the expected value of geometric mean of the degrees and geometric degree variance.https://jmmrc.uk.ac.ir/article_5321_4b78780bd758dea9f7a3b47072c34edb.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Comparative analysis of parametric Lorenz curves and alternative convex models with isotonic regression for estimating the Lorenz curve229249532610.22103/jmmr.2026.25196.1795ENZahraBehdaniDepartment of Mathematics and Statistics, Faculty of Energy and Data Sciences, Behbahan Khatam Alanbia University of Technology, Behbahan, IranJournal Article20250502This study develops a systematic comparative framework for estimating Lorenz curves and Gini coefficients, addressing key methodological gaps in measuring income inequality. We employ the Generalized Mean Squared Error (GMSE) to compare several parametric models (such as polynomial, beta, and established functional forms) with isotonic regression as a non-parametric alternative. Extensive Monte Carlo simulations using log-normal and Pareto distributions show that isotonic regression consistently achieves higher accuracy than parametric approaches. An application to Iranian household income data (n = 18,809) further confirms these results. Based on data characteristics and research objectives, the findings offer practical guidance for selecting appropriate estimation methods.https://jmmrc.uk.ac.ir/article_5326_485cd0656ecd240e47ff4a29517e134d.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Fuzzy nonparametric regression based on K-nearest neighbors and the R-neighborhood radius251267533910.22103/jmmr.2026.25799.1855ENEbrahimEbrahimiDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran.MohsenArefiDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran.0000-0003-3187-9647Mohammad GhasemAkbariDepartment of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran.Journal Article20250821In this paper, we present four nonparametric methods to fit some fuzzy regression models, when both the explanatory and response variables are fuzzy quantities. In this approach, we first introduced a distance between triangular fuzzy numbers. Then, two fuzzy nonparametric regression models are presented based on the extended version of K-nearest neighbors (KNN) method on fuzzy data (with the same/modified weights). In addition, a new method is investigated to fit two fuzzy nonparametric regression models based on the R-neighborhood radius (RNR) method on fuzzy data (with the same/modified weights). Among these methods, the two methods of KNN and RNR with the modified weights have the better performances than the methods with the same weights. To evaluate the proposed fuzzy nonparametric regression models, two measures of goodness of fit are presented. The application of the proposed methods are studied in modelling some data sets.https://jmmrc.uk.ac.ir/article_5339_647805336f30e18045022ac019103c23.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601ALCMean’s: Unsupervised community detection using local Laplacian, automatic detection of the number of centers269288534910.22103/jmmr.2026.25756.1849ENShahinMomenzadehDepartment of Computer Engineering, University of Kurdistan, Sanandaj, IranRojiarPir MohammadianiDepartment of Computer Engineering, University of Kurdistan, Sanandaj, IranJournal Article20250813Community detection is a fundamental problem in the analysis of complex networks. It has applications across social, biological, and financial domains. Traditional algorithms, such as Louvain, LPA, and modularity optimization, often require manual parameter tuning. They also suffer from inaccurate cluster center selection. To address these challenges, we propose AlCMean’s, a novel algorithm. AlCMean’s combines Laplacian energy–based automatic center identification with DeepWalk embeddings for robust node representation. Unlike existing Laplacian-based and clustering methods, AlCMean’s eliminates the need to predefine the number of communities, enhances cluster center selection using structural importance, and leverages representation learning for more accurate and stable assignments. Experimental results on benchmark datasets demonstrate 10–20% higher NMI and ARI scores compared to Louvain, Newman–Girvan, LPA, Fast-Greedy, and a recent GNN-based competitor (MAGI, KDD’24). Additional evaluations with modularity and F1-scores confirm the superiority of AlCMean’s. Ablation studies highlight the critical contributions of each component. Despite its reliance on DeepWalk parameters and increased runtime relative to lightweight heuristics, AlCMean’s consistently outperforms state-of-the-art methods. This makes it a promising tool for real-world network analysis. The source code and datasets are publicly available at https://github.com/shahinmomenzadeh/ALCMeans.git<br /><br />https://jmmrc.uk.ac.ir/article_5349_f1cded662de9c22f7bccb45c2a0ab40c.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601On Artinianness, annihilators and coassociated primes of formal local cohomology modules289302536810.22103/jmmr.2026.25571.1832ENShahramRezaeiDepartment of Mathematics, Payame Noor University, Tehran, IranRezvanDarbandiDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20250721In this paper, we obtain some results concerning vanishing, finiteness and artinianness of formal local cohomology modules. Also, we determine annihilators, cosupport and the set of coassociated primes of these modules in some special cases.https://jmmrc.uk.ac.ir/article_5368_e4c39d2f387229c6cd1c88cd6f2aa3e3.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Application of Höhle’s square roots on Hoop algebras303331539310.22103/jmmr.2026.26238.1897ENMohammad MahdiMotamedi NezhadDepartment of Mathematics, Semnan University, Semnan, IranAliMadanshekafDepartment of Mathematics, Semnan University, Semnan, IranJournal Article20251104In this article, we use the square root as a tool to study hoop algebras. To do so, we define square root and make the first attempt to explore the significance properties of this concept in this setting. Then, due to the key role of square roots in obtaining new hoop algebras, we apply them to the filters of hoop algebras, and show that the formation of square roots on quotient structures of hoop algebras by their filters is well-behaved. In addition, a new class of hoop algebras having square roots, so-called good hoop algebras, is introduced, and some relationships with other classes of ordered algebras such as Boolean algebras and Gödel algebras are explored. Several examples are provided as well. Ultimately, it is shown that the class of all (good) bounded V-hoop algebras with square roots is a variety.https://jmmrc.uk.ac.ir/article_5393_97c6434a75ae5acb202c3ec93bc5b0af.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Prime power Sylow numbers333338540610.22103/jmmr.2026.26388.1909ENAlirezaKhalili AsboeiDepartment of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran0000-0002-7518-0347Journal Article20251125In this paper, we study finite groups with a prime-power number of Sylow \(p\)-subgroups. Motivated by the work of Yang et al.~(2022), who characterized non-solvable groups with a prime-power number of Sylow $2$-subgroups, we investigate the corresponding problem for odd primes. We prove that if a finite group \(G\) has a non-abelian composition factor whose order is divisible by an odd prime \(p\), and the number of Sylow \(p\)-subgroups is a prime power, then \(p\) must be a Mersenne prime and \(n_p(G)=2^k\) for some integer \(k\ge 2\).https://jmmrc.uk.ac.ir/article_5406_ab097385dc87f3c37ca25c509f79dba5.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Statistical approaches to point estimation of Yongting’s capability index339360542310.22103/jmmr.2026.26003.1876ENAbbasParchamiDepartment of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranHamidehIranmaneshDepartment of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20250927Yongting capability index is a suitable criterion for measuring and evaluating the eficiency of industrial processes to produce items conforming the fuzzy quality. This paper develops and applies several statistical estimation approaches for evaluating Yongting’s capability index based on the fuzzy quality and provides a comprehensive comparative study of their performance. This enhances the methodological toolkit available for researchers and practitioners engaged in evaluating and improving industrial production processes. The proposed and discussed approaches in this paper are: (1) Kernel density estimation, (2) Monte Carlo estimation, (3) method of moments estimation and (4) maximum likelihood estimation. The proposed estimation approaches are compared in a simulation case study to show the performance discussed approaches. https://jmmrc.uk.ac.ir/article_5423_6e2e1a519d69f6599fd3b9a4bf2080e2.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Exactness preservation by functors mapping modules to semimodules of varieties of submodules361376542610.22103/jmmr.2026.26025.1880ENHakimehPirzadeh MoghaddamDepartment of Mathematics, University of Birjand, Birjand, IranHosseinFazaeli MoghimiDepartment of Mathematics, University of Birjand, Birjand, IranFatemehRashediDepartment of Basic Sciences, Technical and Vocational University (TVU), Tehran, IranJournal Article20251002Let $R$ be a commutative ring with identity, and $M$ be an $R$-module. We denote by $\zeta(M)$ the semimodule consisting of all varieties of submodules of $M$ over the semiring $\zeta(R)$ of varieties of ideals of $R$. In this article, we introduce two functors from the category of $R$-modules to the category of $\zeta(R)$-semimodules and investigate conditions under which these functors preserve the short exact sequences of modules. They are the hom-functors $\operatorname{Hom}_{\zeta(R)}(\zeta(P),\zeta(-))$ and $\operatorname{Hom}_{\zeta(R)}(\zeta(-),\zeta(E))$ associated with $R$-modules $P$ and $E$, respectively. It is shown that $\zeta$ is exact and both $\operatorname{Hom}_{\zeta(R)}(\zeta(P),\zeta(-))$ and $\operatorname{Hom}_{\zeta(R)}(\zeta(-),\zeta(E))$ are left exact on any short exact sequence $0\rightarrow M' \xrightarrow{f} M\xrightarrow{g} M'' \rightarrow 0$ with $M''$ a radical module. In particular, we provide conditions under which the hom-functors preserve short exact sequences of modules. https://jmmrc.uk.ac.ir/article_5426_e8577c54419ce14735576250db9d5d0e.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Nonparametric kernel estimation of Tsallis-type cumulative residual entropy under length-biased lifetime data377394543310.22103/jmmr.2026.26632.1924ENMasoudAjamiDepartment of Statistics,Faculty of Mathematical Sciences,Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.RahelehZaminiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University , Tehran, IranJournal Article20260105We develop nonparametric inference methods for Tsallis-based cumulative residual entropy functionals when dealing with length-biased lifetime observations. The paper introduces kernel-type estimators for both the static measure and its time-dependent version, with explicit corrections for the sampling mechanism that systematically oversamples longer-lived units. We derive large-sample approximations for bias and variance under standard smoothness assumptions and appropriate bandwidth choices, establish weak and $L^2$-consistency, and prove central limit theorems. Numerical experiments using exponential and Weibull distributions examine finite-sample behavior through bias, variance, and mean squared error calculations, while normality diagnostics validate the asymptotic approximations. We also apply the methodology to automotive component durability data, where results confirm the stable performance and practical value in realistic length-biased scenarios where standard sampling assumptions break down.https://jmmrc.uk.ac.ir/article_5433_9631939d1231f62e1dc7410d4114c4bc.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601SH-graph automata with applications395432543910.22103/jmmr.2026.26343.1905ENTianYuZhangSchool of Science, XI'an Polytechnic University, Shaanxi, China0009-0009-8137-3338Xiao LongXinBusiness School, Xi'an International University, Shaanxi, ChinaMohammad MehdiZahediDepartment of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, IranJournal Article20251120In this paper, because semihoops are the most basic residuated structure that contain all logical algebras based on Galois connections, therefore we introduce a new type fuzzy graph and its complement based on semihoops, denoted by $SH$-graph $G$ and $G^\prime$, respectively. Then, the $SH$-graph automata related to the $SH$-graph $G$ and a minimum zero forcing set are introduced, denoted by $A(Z(G))$. After that, the concepts of isomorphism between two $SH$-graphs $G_1$ and $G_2$ and isomorphism between two $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are introduced. Then, we prove that if two $SH$-graphs $G_1$ and $G_2$ are isomorphic, then two $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are isomorphic; otherwise it is not true. In addition, the concept of equivalence of $SH$-graph automata is proposed. Moreover, we prove that $SH$-graph automata obtained from the same $SH$-graphs are equivalent under different zero forcing sets in some special $SH$-graphs. And then, we know that $SH$-graph automata $A(Z(G_1))$ and $A(Z(G_2))$ are equivalent can not be characterized by $SH$-graphs $G_1$ and $G_2$ being isomorphic. Finally, we introduce a several of simple practical applications of $SH$-graph and $SH$-graph automata.https://jmmrc.uk.ac.ir/article_5439_ed2de60acbf6939bad9a21514079ba1c.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601A numerical cardinal strategy to solve multi-order fractional differential equations with Caputo derivatives433455544610.22103/jmmr.2026.25014.1780ENSaraMirshojaeiDepartment of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IranElyasShivanianDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, IranBakhtyarGhayebiDepartment of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IranSeyyed JalalHosseini GhonchehDepartment of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IranJournal Article20250322In this article, a numerical method to solve multi-order fractional diff erential equations with Caputo derivatives is suggested. Shifted Chebyshev cardinal functions are employed as basic functions. The corresponding fractional derivative operator matrix for these cardinal functions is computed. By approximating the unknown expression of the problem in terms of the shifted Chebyshev cardinal functions, applying their fractional derivative operator matrix, and utilizing the collocation method, solving the equation under question is converted into solving a system of algebraic equations. By<br />solving this system, the approximate solution of the problem is obtained. Finally, the accuracy and effi ciency of the proposed method are examined by solving several numerical examples. The results show that the method presented in this article is an effi cient and highly accurate method to solve such multi-order fractional diff erential equations.https://jmmrc.uk.ac.ir/article_5446_85a8aa869d1d698a2418570bd648e493.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Fuzzy function approximation for multi-choice goal programming in transportation problems457476545710.22103/jmmr.2026.25444.1820ENZahraAramiDepartment of mathematics, Faculty of Mathematics, University of Sistan and Baluchestan,
Zahedan, IranMaryamArabameriDepartment of mathematics, Faculty of Mathematics, University of Sistan and Baluchestan,
Zahedan, IranHasanMishmast NehiDepartment of mathematics, Faculty of Mathematics, University of Sistan and Baluchestan,
Zahedan, IranJournal Article20250621Transportation problems are widely used decision-making models in logistics, production, and supply-chain management. In real-world applications, the input parameters such as costs, supplies, and demands are often uncertain or imprecise, making classical crisp formulations inadequate. To address this challenge, this study proposes a fuzzy multi-choice goal programming (FMCGP) model enhanced with fuzzy function-approximation techniques. Unlike previous works, where fuzzy transportation problems are treated using direct defuzzification or ranking approaches, our method integrates fuzzy least-squares linear regression and a fuzzy binary polynomial approximation to represent and approximate multi-choice fuzzy goals flexibly. This dual approach allows the decision-maker to simultaneously handle multiple fuzzy objectives and constraints within a unified framework. A key feature of the proposed methodology is that all comparisons between fuzzy and crisp values are evaluated using the necessity measure with a degree of 0.8, ensuring mathematically consistent and practically interpretable inequality relations. To demonstrate the model's applicability, we present a case study of a transportation planning problem under uncertainty. The numerical experiments illustrate how the proposed approach outperforms existing fuzzy transportation methods in terms of solution feasibility, interpretability, and computational efficiency. The results confirm that the FMCGP model with fuzzy function approximation provides a powerful and flexible tool for decision-making under uncertainty, offering improved accuracy and robustness compared with classical fuzzy transportation approaches. In addition, the framework is general enough to be extended to other types of fuzzy optimization problems beyond transportation.https://jmmrc.uk.ac.ir/article_5457_e2888916675883acce6d1131328d6cab.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Application of Tsallis entropy in defining a new generalized strong and weak secrecy477498546110.22103/jmmr.2026.25899.1867ENS.JalayeriDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran0000-0002-8464-5871G. R.Mohtashami BorzadaranDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranM.KhorashadizadehDepartment of Statistics, University of Birjand, Birjand, IranJournal Article20250910In this paper, we explore the diverse applications and distinctive properties of Tsallis entropy by introducing generalized definitions of strong and weak secrecy. Tsallis entropy suggests that generalized weak secrecy and strong secrecy are commonly employed in information-theoretic security challenges. Additionally, we examine the interplay between Tsallis entropy and the criteria for strong and weak secrecy. The primary motivation behind this study is to elucidate the concept of “generalized weak secrecy,” a widely utilized notion. Also, this research delves into the precise relationship between conditional entropy and the minimum adversarial error probability, illustrating how generalized weak security can be translated into practical guarantees. For static and memoryless sources, it is demonstrated that the vanishing of the leakage rate requires the adversarial error probability to reach its upper bound. Moreover, generalized strong security, characterized by the vanishing of the variational distance, results in the complete operational failure of the adversary. These findings underscore the critical role of Tsallis entropy in assessing the security of systems.https://jmmrc.uk.ac.ir/article_5461_b6c03b16c3dc546703b5ec508ef37388.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Right dc-Noetherian $S$-posets499509546810.22103/jmmr.2026.26326.1904ENLeilaShahbazDepartment of Mathematics, University of Maragheh, P.O.Box 55181-83111, Maragheh, IranJournal Article20251118In the present paper, the right dc-Noetherianity for $S$-posets is defined and studied. Some fundamental properties of right dc-Noetherian $S$-posets are presented, and the relation of right dc-Noetherian $S$-posets with sub $S$-posets, factor $S$-posets, products, and coproducts are studied. Finally, the relations between right po-Noetherian $S$-posets, right dc-Noetherian $S$-posets and right Noetherian ordered pomonoids are investigated.https://jmmrc.uk.ac.ir/article_5468_d21e4d60a3de92a0e5767e022fa7e33f.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601Schatten class Toeplitz operators on Bergman spaces with almost standard weights511533546910.22103/jmmr.2026.26719.1929ENKobraEsmaeiliFaculty of Engineering, Ardakan University, P. O. 184, Ardakan, IranJournal Article20260126We study Schatten class Toeplitz operators on weighted Bergman spaces induced by almost standard radial weights on the unit disk. We obtain a complete characterization of such operators generated by positive Borel measures. The characterization is given in terms of the Berezin transform, integrability of localized averages with respect to the M\"obius invariant measure, and discrete summability over pseudohyperbolic lattices. For Toeplitz operators generated by complex Borel measures, we establish sufficient conditions for Schatten class membership in terms of discrete lattice averages of the total variation, together with corresponding norm estimates. As an application, we derive Schatten class bounds for differences of such operators.https://jmmrc.uk.ac.ir/article_5469_b415923e52a3f7f68196e9ab56a12a13.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795215220260601E-Groups and isomorphism theorems535554547010.22103/jmmr.2026.26861.1945ENAkbarRezaeiDepartment of Mathematics,
Payame Noor University,
Tehran, Iran0000-0002-6003-3993Journal Article20260218We present and explore the fundamental structural theory of e-groups, a generalization of groups introduced by Borumand et al. (2018). We introduce the notions of full e-subgroups and normal full e-subgroups, and we construct the quotient of an e-group under these conditions. Moreover, we define and investigate generated e-subgroups, establish their basic properties, and characterize cyclic e-subgroups. A detailed analysis of the kernel of an e-homomorphism reveals that the subset kernel is not suitable for isomorphism theorems; to resolve this, we adopt the universal algebraic perspective and employ the congruence kernel. Using this approach, we establish the First Isomorphism Theorem for e-groups and provide concrete examples illustrating the result. Furthermore, we discuss the formulation of the Second and Third Isomorphism Theorems within the congruence framework, and we examine the relationship between congruences and normal full e-subgroups.https://jmmrc.uk.ac.ir/article_5470_8755feb33566bab8e30e3c6db765a616.pdf