Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Fixed k-watchman routes under the Min-Max criterion in staircase polygons271282553610.22060/ajmc.2024.23104.1228ENRahmatGhasemiDepartment of Computer Engineering, SR.C., Islamic Azad University, Tehran, Iran0000-0001-8116-5234AlirezaBagheriDepartment of Computer Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran0000-0002-3542-7763FatemehKeshavarz-KohjerdiDepartment of Computer Science, Shahed University, Tehran, Iran0000-0002-7006-2675FaezehFarivarDepartment of Computer Engineering, SR.C., Islamic Azad University, Tehran, IranJournal Article20240418In this paper, the problem of multiple watchman routes in staircase polygons is studied. The watchman route problem (WRP) is a variation of the art gallery problem (AGP) in computational geometry, where each point in the given polygon must be visible from at least one point along the route taken by one of the watchmen. A greedy algorithm is presented for the min-max criterion, where we minimize the maximum route length. We assume some starting points of the watchmen may dominate the others. This algorithm finds an optimal solution in $O(n^2 \cdot k^2 \cdot \log{n})$ time, where $n$ represents the number of vertices of the give polygon, and $k$ represents the number of watchmen.https://ajmc.aut.ac.ir/article_5536_1134ac57b5b1d38b7d70c1b6feaa28cf.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Homology groups and decomposition of the game complex283291550610.22060/ajmc.2024.20822.1216ENNedaShojaeeDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranAidinFallahDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20240217In this paper, we introduce a novel simplicial complex named Game Complex for finite non-cooperative games in the strategic form. We prove that the number of Nash equilibrium in non-cooperative games with more than two players is the rank of the first homology group of the game complex. Furthermore, we give a decomposition of the game complex.https://ajmc.aut.ac.ir/article_5506_99b410aa504a6f67da128d333896ecd4.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Product type operators on $(\alpha,p)$-Besov-Zygmund spaces293302569410.22060/ajmc.2025.22758.1191ENSepidehNasresfahaniDepartment of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, IranMostafaHassanlouEngineering Faculty of Khoy, Urmia University of Technology, Urmia, IranDaryoushMolaeiDepartment of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran0009-0006-6203-4670EbrahimAbbasiDepartment of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, IranJournal Article20231017In this paper, we consider the boundedness and compactness of operator $M_uC_\psi$ between $(\alpha,p)$-Besov-Zygmund spaces in terms of Carleson-type measures. Also we obtain some equivalent statements for the boundedness and compactness of a generalized product type operator $T_{u_1,u_2,\psi}$ which is well-known as Stevi'c-Sharma operator between $(\alpha,p)$-Besov-Zygmund spaces.https://ajmc.aut.ac.ir/article_5694_b0d6951563a26ffeb2405a9653b3b422.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Computing the matrix square root: A problem-solving approach using Mathematica and Pólya's strategies303320568610.22060/ajmc.2025.23508.1262ENMandanaMoccariDepartment of Mathematics, Ha. C., Islamic Azad University, Hamedan, IranJournal Article20240905This paper introduces a novel method for solving the matrix equation $X^2 - A = 0$ by computing matrix square roots. Inspired by George Pólya's structured problem-solving strategies and leveraging Wolfram Mathematica, the approach offers a systematic, efficient, and clear solution to the problem. The method extends the computation of matrix square roots to large matrices and those with complex eigenvalues, significantly broadening its applicability in diverse fields, including control theory, quantum physics, and signal processing. The approach is demonstrated through comprehensive examples and original Mathematica code, providing a practical toolkit for solving similar mathematical challenges. The method is designed to be both intuitive and versatile, making it a valuable resource for educators, students, and researchers engaged in advanced mathematical problem-solving.https://ajmc.aut.ac.ir/article_5686_07bb5fdef1ee99d35eaccce14f8b5540.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701The undirected power graph on the conjugacy classes of a finite group321324567910.22060/ajmc.2025.23715.1293ENSajjadMahmood RobatiDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranJournal Article20241128Let $G$ be a finite group. The undirected power graph on the conjugacy classes of $G$ is the simple graph $\mathcal{P_C}(G)$ whose vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent if one is a subset of a power of the other. In this paper, we show that the graph $\mathcal{P_C}(G)$ is $2$-connected whenever either $|\pi(G)|>1$ or ${\rm Z}(G)$ is cyclic. Moreover, we classify finite groups $G$ whose associated graph $\mathcal{P_C}(G)-\{e\}$ are bipartite.https://ajmc.aut.ac.ir/article_5679_166cee72e93a992007a89b39eb29628b.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Group analysis and numerical approximation of proliferating and maturing cellular populations model325335567610.22060/ajmc.2025.23231.1243ENMohammad HadiNoori EskandariFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranS. RezaHejaziFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranHamidErfanian Oraei DehrokhiFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranJournal Article20240527Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset $S$ of the vertices of a graph $G$ is an adjacency resolving set for $G$ if for each pair of distinct vertices $x, y \in V(G)\setminus S$, there exists $s \in S$ which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of $G$. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.https://ajmc.aut.ac.ir/article_5676_3a01fc0853ebeba94fde4d1cc6fb842a.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701On the adjacency dimension of some star related trees337346564010.22060/ajmc.2025.23136.1233ENElhamHardaniDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranAliBehtoeiDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranJournal Article20240424Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset $S$ of the vertices of a graph $G$ is an adjacency resolving set for $G$ if for each pair of distinct vertices $x, y \in V(G)\setminus S$, there exists $s \in S$ which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of $G$. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.https://ajmc.aut.ac.ir/article_5640_d0f5722f11a0cc839fa2ca6ea49d8585.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701On stochastic comparisons of finite $\alpha$-mixture of additive hazard rate models347359566010.22060/ajmc.2025.23236.1244ENAqeelLazam RazzaqDepartment of Statistics, Razi University, Kermanshah, IranIsaacAlmasiDepartment of Statistics, Razi University, Kermanshah, Iran0009-0005-4639-4505GhobadSaadat Kia (Barmalzan)Department of Basic Science, Kermanshah University of Technology, Kermanshah, IranJournal Article20240529This paper discusses stochastic comparisons on the finite $\alpha$-mixture of additive hazard models. Sufficient conditions on the underlying distribution parameters and the mixing probabilities are established for the comparisons of different $\alpha$-mixtures of survival or distribution functions of these models with respect to the usual stochastic order and the hazard rate order, respectively. Several examples are also presented to illustrate the theoretical findings.https://ajmc.aut.ac.ir/article_5660_fa1839c55070bf5cb53fd4a2e523641c.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Construction of an iterative method for solving a class of complex symmetric generalized Lyapunov matrix equation and application to Helmholtz equation361376591610.22060/ajmc.2025.24112.1366ENAkbarShirilordDepartment of Applied Mathematics,
Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran polytechnic), No. 424, Hafez Ave., 15914, Tehran, IranMehdiDehghanDepartment of Applied Mathematics,
Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran polytechnic), No. 424, Hafez Ave., 15914, Tehran, Iran0000-0002-2573-9755Journal Article20250429The Lyapunov matrix equations occur in many branches of control theory, such as stability analysis and optimal control. In this work, we introduce a novel iterative approach to address the generalized Lyapunov matrix equation within the framework of complex matrices. At each iteration, the procedure involves solving two conventional Lyapunov equations with real-valued coefficient matrices. The scheme incorporates two positive parameters, for which we establish sufficient conditions to guarantee the convergence of the method under certain assumptions. Then we solve the Lyapunov equation arising by applying a finite difference procedure to Helmholtz equation by proposed method.https://ajmc.aut.ac.ir/article_5916_c5f441cd5f43eb2f2c024e1f8b5d00cd.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497320260701Bayesian regression for capital asset pricing model377383595510.22060/ajmc.2025.23793.1307ENMohammadZareDepartment of statistics, Faculty of Mathematical Sciences, Al Zahra university, Tehran, Iran0000-0001-8757-4880Journal Article20250101In this paper, we critically evaluate the Capital Asset Pricing Model (CAPM) and its limitations in predicting future returns using Linear Regression (LR) models. We propose an alternative approach, Bayesian Regression, which offers a more informative and accurate prediction framework. Our study compares the performance of LR and Bayesian Regression models in forecasting the returns of popular cryptocurrencies, Doge (for asset) and Bitcoin (for market). Through the use of Mean Squared Error (MSE), we demonstrate that the Bayesian Regression model outperforms the LR model in terms of prediction accuracy. The findings highlight the advantages of Bayesian methods in capturing the complex relationships and uncertainties inherent in financial markets. Our research contributes to the ongoing discourse on investment decision-making, providing valuable insights into the effectiveness of Bayesian Regression in the context of cryptocurrency investments.https://ajmc.aut.ac.ir/article_5955_a67c8c9a961b4182688768dd9ba015fe.pdf