AUT JOURNAL OF MATHEMATICS AND COMPUTING
Year:2026 | Volume:7 | Issue:1|Papers Count:8

In 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.

Many 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 $\mathbb{F}_{p}$.

The 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.

To 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.

In 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.

Here, 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.

In 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.

The 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}.