Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120241117A bivariate α-power transformed family: Theory and application118558410.22060/ajmc.2024.23495.1261ENVahidNekoukhouDepartment of Statistics, Khansar Campus, University of Isfahan, Iran0000-0001-9169-827XHamidBidramDepartment of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, IranAshkanKhalifehDepartment of Statistics, Yazd University, Yazd, IranJournal Article20240831In this paper, some general classes of bivariate semi-parametric continuous distributions are introduced. Some important properties of this family of distributions will be illustrated. It is seen that the bivariate distribution corresponds to the known Ali-Mikhail-Haq copula. Hence, some important properties such as the $\hbox{TP}_2$ property are justified. It will be shown that the marginals are kind of heavy tailed weighted distributions whose hazard rate functions can take variety of shapes. The behavior of the hazard rate function is mathematically illustrated. In addition, the $\alpha$-power transformed distributions of a second type, which are introduced for the first time here, can be verified as special cases of the marginals. Some members of the new bivariate classes are studied in details. The estimation of the parameters is illustrated by means of an efficient expectation-maximization algorithm, and some real data sets are also analyzed for illustrative purposes.https://ajmc.aut.ac.ir/article_5584_033daef61ea8721921fbbeebb6f87313.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Supersingular elliptic curves, binary quadratic forms and isogenies1931556410.22060/ajmc.2024.23144.1245ENLeilaGoodarziFaculty of mathematical sciences, University of Kashan, Kashan, IranHassanDaghighFaculty of mathematical sciences, University of Kashan, Kashan, IranJournal Article20240530Many researchers have explored the construction of isogenies between particular elliptic curves, largely due to the extensive range of their practical applications. In this paper, we use the relationship between supersingular elliptic curves over $\mathbb{F}_{p}$ and binary quadratic forms to generate isogenies connecting supersingular elliptic curves over $\mathbb{F}_{p}$.https://ajmc.aut.ac.ir/article_5564_853bb47a93581ead37b1bcd749d34787.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Pseudo-duals and closeness of continuous g-frames in Hilbert spaces3344554810.22060/ajmc.2024.23279.1247ENMortezaMirzaee AzandaryaniDepartment of Mathematics, University of Qom, Qom, Iran0000-0003-2386-3311ZeinabJavadiDepartment of Mathematics, University of Qom, Qom, Iran0009-0001-9654-5552Journal Article20240617The paper deals with pseudo-duals of continuous $g$-frames and their characterizations in Hilbert spaces. Mainly, the pseudo-duals constructed by bounded operators inserted between the synthesis and analysis operators of the Bessel mappings are considered. Duals and approximate duals, which are two important classes of pseudo-duals, are also studied here. Moreover, the concepts of closeness and nearness of continuous $g$-frames are focused and some of their properties are obtained. It is shown that there are close relationships between the closeness and nearness of $g$-frames and their approximate duals. Also, the above-mentioned concepts are related to the notions of partial equivalence, equivalent frames, and continuous Riesz-type $g$-frames.https://ajmc.aut.ac.ir/article_5548_d10ddbe86fe1df4e50c91d66087cbc6a.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Solving the optimum control problem constrained with Volterra integro-differential equations using Chebyshev wavelets and particle swarm optimization4561558210.22060/ajmc.2024.23406.1254ENAsiyehEbrahimzadehDepartment of Mathematics Education, Farhangian University, P. O. Box 14665-889, Tehran, Iran0000-0002-4684-7640Journal Article20240802To handle a type of optimum control problems (OCP) for systems controlled described by Volterra integro-differential equations (VIDE), we introduce in this study a direct Chebyshev wavelet collocation approach, which is utilized in applied science and engineering. The proposed direct approach turns the OCP into a nonlinear programming (NLP) problem, in which the wavelet coefficients are the optimization variables. To solve the resulting NLP, we use the particle swarm optimization (PSO) technique. In addition, we illustrate the suggested method's convergence. Under certain sufficient conditions, it is shown that a sequence of optimal solutions for the finite-dimensional optimization problems corresponding to $\overline{\mathcal{P}}$ approximates the optimal solution of the original problem $\mathcal{P}$ in a desirable manner. To demonstrate the method's applicability and efficiency, we provide several numerical examples that emphasize the PSO algorithm's effectiveness in solving the resulted NLP.https://ajmc.aut.ac.ir/article_5582_c2368d3d45705a56e51ec5940e187f8d.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Quantile regression for capital asset pricing model6368557910.22060/ajmc.2024.23203.1240ENMohammaadZare MohammadkhaniDepartment of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran0000-0001-8757-4880Journal Article20240519In this paper, we examine the Capital Asset Pricing Model (CAPM) and demonstrate that when the log returns of an asset are subject to extreme risks or outliers or nonlinear relationship, the Linear Regression (LR) model may not perform well in predicting future returns. Instead, we propose using Quantile Regression, which is more robust to such data anomalies and provides better predictions.https://ajmc.aut.ac.ir/article_5579_36f4d832825380f102846560a5104c90.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Finiteness of fundamental groups in extended complete Einstein-type manifolds6975592110.22060/ajmc.2025.23648.1278ENAyoubMohammadalipourDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranBehrozBidabadDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0003-3993-4268MohamadYar AhmadiDepartment of Mathematics, Faculty of the Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20241102Here, an extension of the complete non-compact Einstein-type manifolds is studied and shows that it has a finite fundamental group. This paper generalizes Wylie's results to the setting of extended Einstein-type manifolds for certain parameters. Some direct corollaries of this result are also pointed out. For instance, the sphere bundle $SM$ has a finite fundamental group. These findings not only generalize previous results but also offer new insights into the applications of Einstein-type manifolds across mathematics and physics, particularly in the structure of associated bundles and the behavior of geometric flows.https://ajmc.aut.ac.ir/article_5921_b59442085644532ef03417a3e5a76437.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101Some trace functional inequalities for operator (p, h)-convex functions7783575710.22060/ajmc.2025.23749.1299ENOmidPourbahri RahpeymaDepartment of Mathematics, Chalous Branch,
Islamic Azad University, Chalous, IranMehdiBakanDepartment of Pure Mathematics, Faculty of Mathematical Sciences,
Tarbiat Modares University, Tehran, IranAbasaltBodaghiDepartment of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, IranJournal Article20241212In this paper, we present a theorem pertinent to singular value inequalities for positive and compact operators on a Hilbert space. Moreover, we obtain several trace inequalities for operator $(p,h)$-convex functions.https://ajmc.aut.ac.ir/article_5757_a13e00b0854808128933f99f4955f338.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24497120260101A systematic survey and empirical comparison of hybrid methods for imbalanced fraud detection: Combining resampling and machine learning85116591310.22060/ajmc.2025.24642.1446ENBehnamYousefimehrDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0009-0003-0954-635XMehdiGhateeDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-9558-8286Journal Article20250828The accurate identification of fraudulent activities has been a significant focus of computational research, leading to the development of diverse methodologies ranging from traditional statistical tests to advanced machine learning and deep learning models. A persistent and critical challenge undermining these approaches is the inherent class imbalance present in most real-world fraud datasets, where genuine transactions vastly outnumber fraudulent ones, often causing models to exhibit bias toward the majority class. To mitigate this issue, a promising paradigm has emerged: hybrid frameworks that synergistically integrate data resampling techniques with robust machine learning algorithms. These frameworks are particularly valuable for their potential to facilitate accurate, real-time automated detection systems. This survey provides a comprehensive examination of the efficacy and impact of such hybrid techniques on the field of fraud detection. To quantitatively evaluate their performance, we conduct a rigorous numerical study using auto insurance fraud as a case study. Employing the car fraud datasets, we perform a detailed comparative analysis of various detection algorithms, each coupled with different resampling methods. Our empirical results demonstrate that the performance of each fraud detection algorithm is profoundly contingent upon the specific resampling strategy employed, highlighting the necessity for careful methodological selection tailored to the dataset's characteristics. Code for analysis is available at \url{https://github.com/behnamy2010/Car-Claims-Compression}.https://ajmc.aut.ac.ir/article_5913_941c377c73c0efed759c993f1b859526.pdf