https://ajmc.aut.ac.ir/ AUT Journal of Mathematics and Computing en daily 1 Wed, 01 Apr 2026 00:00:00 +0330 Wed, 01 Apr 2026 00:00:00 +0330 https://ajmc.aut.ac.ir/article_5499.html Abstract: Loop closure detection (LCD) and trajectory generation are critical components of visual simultaneous localization and mapping (vSLAM). In this paper, we aim to solve the LCD and trajectory generation problem in vSLAM using a newly devised vector quantization (VQ) algorithm. The proposed new VQ algorithm is constructed based on a self-supervised deep convolutional autoencoder (AE). The new VQ step is then incorporated into the two famous SLAM algorithms fast appearancebased mapping (FABMAP) and ORB-SLAM, which we now call AE-FABMAP and AE-ORB-SLAM, respectively. Experiments show that using self-supervised autoencoders in the VQ step is far more efficient in terms of speed and memory consumption with respect to other methods such as graph convolutional neural networks. Furthermore, the newly presented algorithms, AE-ORB-SLAM and AE-FABMAP outperform the standard FABMAP2 and ORB SLAM, and in large-scale SLAM, the new approaches improve the accuracy and recall of the LCD. https://ajmc.aut.ac.ir/article_5506.html In 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_5610.html The work employs a numerical method for the solution of Fractional Fokker-Planck Equation (FFPE) using the Homotopy Perturbation and Aboodh Transform Method (HPATM). Fractional derivatives issues are successfully solved using the hybrid approach, which yields rapidly convergent solutions. By resolving two cases and contrasting estimated outcomes with exact solutions for various fractional orders, the correctness of the technique was proven. The accuracy of the technique is demonstrated by the good match between the precise and approximation solutions at $\alpha=1$. The findings indicate that fractional differential equations may be solved with a strong and dependable approach using HPATM, which can also be used to describe anomalous diffusion and other intricate physical phenomena. https://ajmc.aut.ac.ir/article_5619.html A subset $D$ of vertices of a simple graph ‎$‎G‎$ ‎is ‎an exact double dominating set if each vertex $v$ of $G$ is dominated by exactly two vertices of $D$‎, ‎i.e. $|N_G[v]\cap D|=2$‎, ‎in ‎which ‎‎$‎N_G[v]‎$ ‎is ‎the closed neighborhood of $v$ in ‎$‎G‎$‎.‎ The generalized Sierpi\'{n}ski graph $S(G,t)$ is a fractal-like graph that uses $G$ as a building block and can be constructed recursively in ‎$‎t‎$ ‎steps ‎from the base graph $G$. ‎In this paper we study and determine the existence of exact double dominating sets in generalized Sierpi\'nski graphs $S(P_n,t)$‎, ‎$S(C_n,t)$‎, ‎$S(K_{1,n},t)$ and $S(K_n,t)$‎. https://ajmc.aut.ac.ir/article_5605.html In this paper, the ordinary character table of a finite extension of structure $\overline{G}=2^7{:}G_2(2)$ is computed via the Fischer-Clifford matrices technique. The group $\overline{G}$ sits maximally in the affine subgroup $2^7{:}Sp_6(2)$ of the symplectic group $Sp_8(2)$. https://ajmc.aut.ac.ir/article_5632.html We show that every quasi-multiplier $‎\phi‎‎:‎L^1(G)‎\times ‎L^1(G)‎‎\longrightarrow ‎L^1(G)‎$, ‎where‎‎‎ ‎‎$‎G‎$ is a locally compact group, is of the form ‎‎‎‎$$‎‎‎‎‎‎‎‎‎‎‎\phi(f,g)=f‎\star ‎‎\mu‎\star ‎‎g‎,\ \ \ \ \ f,g\in ‎L^1(G),‎$$ for a unique measure ‎‎$‎\mu\in ‎‎‎‎M(G)‎$. ‎‎‎As a consequence‎, ‎we obtain a well-known result due to Wendel.‎ ‎We also prove the analogues ‎result ‎for ‎‎$‎C^*‎$‎-algebras.‎ Moreover, we introduce the notion of quasi Jordan multipliers and prove that each such map on a $‎C^*‎$‎-algebra, as well as group algebra ‎$‎L^1(G)‎$‎, is a quasi-multiplier. https://ajmc.aut.ac.ir/article_5618.html In this paper, we investigate the conditions under which a lifted almost complex structure ‎$‎J‎$‎ on the tangent bundle ‎$‎TM‎$‎ of a manifold ‎$‎M‎$‎ exhibits various Kählerian properties. We establish several characterizations relating the geometry of ‎$‎(TM, J)‎$‎ to the cosymplectic structure on ‎$‎M‎$‎. Specifically, we show that ‎$‎(TM, J)‎$‎ is Kählerian if and only if ‎$‎(M, \eta, \xi, \varphi)‎$‎ is cosymplectic and ‎$‎R = 0‎$‎. Similarly, we prove that ‎$‎(TM, J)‎$‎ is nearly Kählerian under the same conditions on ‎$‎M‎$‎. Furthermore, we present an alternative criterion for ‎$‎(TM, J)‎$‎ to be Kählerian, involving a nearly cosymplectic condition on ‎$‎M‎$‎ alongside a specific curvature relation. Finally, we demonstrate that ‎$‎(TM, J)‎$‎ is semi-Kählerian if and only if ‎$‎(M, \eta, \xi, \varphi)‎$‎ is semi-cosymplectic with ‎$‎R(X, Y) \varphi Z = 0‎$‎. These results reveal intricate connections between cosymplectic structures on ‎$‎M‎$‎ and Kählerian-type structures on ‎$‎TM‎$‎, contributing to the broader understanding of almost complex geometry on tangent bundles. https://ajmc.aut.ac.ir/article_5659.html In this paper, we introduce new general location model for mixed responses including correlated nominal, ordinal and continuous outcomes by using latent variable approach. We discuss regression methods for jointly analysis of continuous and categorical (nominal and ordinal) responses. After presenting the Leon and Carri\`ere \' general location model (2007), new general location model is introduced. A full likelihood-based approach is used to obtain maximum likelihood estimations of the models parameters. The proposed model is applied to BMI, Steatosis and Osteoporosis data. https://ajmc.aut.ac.ir/article_5637.html In this brief note, we present a proof for a general form of the Serre-Swan theorem. https://ajmc.aut.ac.ir/article_5624.html This article presents the interpolative fixed point theorem with reference to complete partial metric spaces, by taking the multi-valued contraction into account. In particular, the idea of multivalued interpolative Reich–Rus–\'{C}iri\'{c} type contractions is introduced and criteria for the existence of fixed points' of such operators are established. A nontrivial example is provided to support the validity of the obtained results. https://ajmc.aut.ac.ir/article_5980.html This review paper focuses on the numerical solution of the time-fractional diffusion equation using various discretization techniques. For the time-fractional derivative, we consider methods such as L-type approximations and Grunwald-Letnikov-based formulas, while for the spatial diffusion term, we utilize the compact finite difference method, finite element method, spectral element method, meshless method, Chebyshev spectral method, and finite block method. In addition, stability and convergence theorems are presented, accompanied by numerical examples that confirm the theoretical results. https://ajmc.aut.ac.ir/article_5536.html In 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 of a route of a watchman. A greedy algorithm is presented for the min-max criterion, where we minimize the maximum route length. We assume that the watchmen's starting points may dominate eachother. This algorithm finds an optimal solution in $O(n^2 \cdot k^2 \cdot \log{n})$ time, where $n$ is the number of vertices and $k$ is the number of watchmen. https://ajmc.aut.ac.ir/article_5563.html In this paper, we present a formula for the Waldschmit constant of edge ideals of some classes of hypergraphs. We will also see that if $G$ is a simple graph with binomial edge ideal $J_G$, then the Waldschmit constant of $J_G$ is always 2. Furthermore, the symbolic defect of umbrella hypergraphs is presented. https://ajmc.aut.ac.ir/article_5574.html Systemic risk in the interbank market is the topic of this article. This market is modeled as a directed graph, where the edges are the bank-to-bank liabilities and bank-to-end users liabilities and the nodes are the banks. Our study extends the modeling paradigm of Amini et al. by adding a second Central node to the system and using the equilibrium equation of the Veraart et al. with some modifications that are better suited to our model. We study the effects of two central nodes on a financial network. It is evident that two central nodes can reduce the end-users shortfall and increase the predicted surplus of the banks when compared to a single central node. We provide a few straightforward examples to demonstrate our findings. https://ajmc.aut.ac.ir/article_5640.html ‎Locating 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_5660.html This 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_5666.html Abstract: Natural Language Understanding (NLU) is important in today’s technology as it enables machines to comprehend and process human languages, leading to improved human-computer interactions and advancements in fields such as virtual assistants, chatbots, and language-based AI systems. This paper highlights the significance of advancing the field of NLU for low-resource languages. With intent detection and slot filling being crucial tasks in NLU, the widely used datasets ATIS and SNIPS have been utilized in the past. However, these datasets only cater to the English language and do not support other languages. In this work, we aim to address this gap by creating a Persian benchmark for joint intent detection and slot filling based on the ATIS dataset. To evaluate the effectiveness of our benchmark, we employ state-of-the-art methods for intent detection and slot filling. https://ajmc.aut.ac.ir/article_5674.html Enhanced index tracking (EIT) problems aim to construct portfolios that track market-index movements while delivering superior performance. Although various optimization models have been proposed for the EIT problem, to the best of our knowledge, there has been no comprehensive comparison of these models to date. This paper addresses this issue by conducting a thorough evaluation of existing EIT optimization models over real-life datasets, taken from the Tehran stock market. The methodology used to compare models offer valuable insights for financial professionals and investors and help them in selecting the most effective strategies to improve their investment performance. https://ajmc.aut.ac.ir/article_5675.html This article presents a unified approach for estimating $P(X>Y)$, also known as the area under the receiver operating characteristic (ROC) curve (AUC) or stress–strength model in the generalized scale-exponential family of distributions. The proposed framework includes the derivation of the maximum likelihood estimator and the construction of both asymptotic and percentile boot confidence intervals. https://ajmc.aut.ac.ir/article_5676.html ‎‎The present paper focuses on the symmetry analysis and numerical simulation of a type of delay PDEs called proliferating and maturing cellular population equations, which includes a delay $\tau > 0$ and a shrinked argument $a x$. The aim of this research is to establish the symmetry group of the considered equation by extending the Lie group analysis of differential equations to delay differential equations. Subsequently, an extended Jacobi-pseudo-spectral (JPS) method is applied to find numerical solutions to the equation. https://ajmc.aut.ac.ir/article_5679.html Let $G$ 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_5686.html This 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_5694.html ‎‎In 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-knows as Stevi'c-Sharma operator between $(\alpha,p)$-Besov Zygmund spaces‎. https://ajmc.aut.ac.ir/article_5695.html We prove some theorems about the Killing vector fields on compact and connected pseudo-Riemannian manifolds. Among other results, we present a relationship between curvature of a compact pseudo-Riemannian manifold $M$ and existence of Killing vector fields on $M$. https://ajmc.aut.ac.ir/article_5698.html Let $D$ be a division ring with uncountable center $C$. Suppose that \( K \) is a sub-division ring of \( D \) containing $C$ and that \( a \in D \setminus C \). The purpose of this paper is to prove that if either \( axa^{-1}x^{-1} \) or \( xy - yx \) is right algebraic over \( K \) for all \( x, y \in D \setminus \{0\} \), then \( D \) is also right algebraic over \( K \). This result provides the affirmative answers to [8, Problems 1 and 5] for division rings with uncountable center. https://ajmc.aut.ac.ir/article_5740.html The special unitary group $SU_{n}(q)$ has a maximal imprimitive subgroup with the structure $(q+1)^{n-1}{:}S_{n}$. The exceptions when the subgroup is not maximal are $SU_{3}(5)$, $SU_{4}(3)$ and $SU_{6}(2)$. In this paper, the ordinary character table of the maximal imprimitive subgroup $\overline{G}=3^{6}{:}S_{7}$ of $SU_{7}(2)=U_{7}(2)$ is computed by the Fischer-Clifford matrices technique. A combinatorial approach is adopted in the computation of the Fischer-Clifford matrices of $\overline{G}$. https://ajmc.aut.ac.ir/article_5758.html Intensity Modulated Radiation Therapy (IMRT) is a well-known technique of radiation therapy for treating cancer patients. Increasing the number of beam angles in IMRT leads to longer treatment plan time and, sub-sequentially, the possibility of patient movement, disturbing the plan. Then, a treatment plan is admirable if it contains a small number of beam angles among candidate beams that can provide the desired dose. This paper proposes a new sparse optimization problem to choose the minimum number of angles to provide a treatment plan with desirable quality. Since the model is not tractable in real-life cases, by converting the optimization problem to a linear fractional problem, we develop a novel iterative approach to find the optimal solution. The performance of the proposed method is evaluated by solving the problem for some cases of real data sets of liver cancer from the TROTS data set. The results show the computational advantage of the iterative proposed method, which significantly saves time compared to exact methods and provides an optimal set of beam angles that attain lower deviation doses. https://ajmc.aut.ac.ir/article_5773.html In this paper, in the context of an important class of locally compact hypergroups i.e. $\mathcal{K}_{\rho}$ which were introduced by Dunkl and Ramirez, we find some sufficient condition on a weight $(w_n)_{n=0}^\infty\subseteq (0,\infty)$ so that the set \begin{equation*}\left\{\big((f_k)_k,(g_k)_k\big)\in L^p(\mathcal{K}_{\rho})\times L^q(\mathcal{K}_{\rho}):\sum_{k=1}^\infty |f_kg_k|w_k^2\,\rho ^{k-1}<\infty\right\}\end{equation*}to be a $\sigma$-$c$-lower porous set. https://ajmc.aut.ac.ir/article_5774.html In this paper, we consider a family of cosine operators indexed by a Furstenberg family $\mathcal{F}$ on an Orlicz space in the context of a locally compact hypergroup, and give some applicable sufficient conditions for this collection to be $p$-topologically multiply $(\mathcal{F},E)$-recurrent. https://ajmc.aut.ac.ir/article_5776.html ‎‎Let $\mathfrak{U}$ be a $\phi$-Johnson amenable Banach algebra where $\phi \in\Delta(\mathfrak{U})$ ($\Delta(\mathfrak{U})$ is the character space of $\mathfrak{U}$)‎. ‎Suppose that $X$ is a Banach $\mathfrak{U}$-bimodule such that $a.x=\phi(a)x$ for all $a\in \mathfrak{U}$‎, ‎$x\in X$ or $x.a=\phi(a)x$ for all $a\in \mathfrak{U}$‎, ‎$x\in X$‎. ‎We show that any Lie derivation (not necessarily continuous) $\delta:\mathfrak{U}\rightarrow X$ with the property that $\mathfrak{S}(\delta)\subseteq \mathcal{Z}_{\mathfrak{U}}(X)$ ($\mathfrak{S}(\delta)$ is the separating space of $\delta$) can be decomposed into the sum of a continuous derivation and a center-valued trace‎. https://ajmc.aut.ac.ir/article_5781.html After classification  of finite simple groups, the  researchers dissucced about  groups characterization by property. Properties, such as element order, the set of elements with the same order, graphs,etc. In other words  if $G$ be a finite group  and  $M$ be a property  then we say the group $G$ is characterized by property $M$ if by isomorphic $G$ be a only group by property $M$.  One of the methods, is group characterization by largest element order. In other wrds, we say the group $G$ is characterized by largest element order $k(G)$  and order of $G$ if there exists the group $H$, so that  if $k(G)=k(H)$ and $|G|=|H|$, then $G\cong H$.  In this paper, we prove that the simple $K_5$-groups $PSL(6,2)$ and $PSU(6,2)$ can be uniquely determined by their order and the largest order of elements. https://ajmc.aut.ac.ir/article_5782.html Bayesian semiparametric modeling for constant stress accelerated life test (CSALT) under type-II progressive censoring scheme (T-II PCS) is provided. In this model, lifetimes follow generalized exponential and Weibull distributions, relationships between lifetime characteristics and accelerated stresses are described by nonparametric functions, and P-spline approach is used to approximate the functions. The calculation of full conditional distributions for the parameters within the Bayesian framework is challenging due to the complex structure of the likelihood functions arising from the nonparametric relationships. Consequently, the application of Markov chain Monte Carlo (MCMC) methods demonstrates inefficiency. This paper resolves the issue by employing Laplace P-splines (LPS) in the analysis of the CSALT data based on the T-II PCS. The integration of the P-spline smoothers with a Laplace approximation within the LPS framework provides a unified approach for quick and flexible inference. This approach offers a highly precise approximation of the posterior distribution of penalized parameters. Conversely, the accuracy of the Laplace approximation for nonpenalized parameters’ posterior distributions can be affected by sparse information derived from likelihood and their priors. Therefore, the parameter space is partitioned into two subsets. Compared to the Laplace method that uniformly manages posterior values, dichotomizing the parameter space improves estimation accuracy by creating a unique treatment of the parameters. This version of LPS operates without the need for sampling, which allows it to execute calculations more rapidly than MCMC methods. The simulation study and analysis of a real data set serve to show the performance of the suggested model. https://ajmc.aut.ac.ir/article_5787.html In the current investigation, we define s-multi-radical mappings, characterize the structure of such mappings and then obtain an equation for describing them. In fact, we find a necessary and sufficient condition for a multiple mapping to be s-multi-radical. We also deal with the Hyers-Ulam stability in the spirit of Gavruta for an s-multi-radical equation by applying the so-called direct (Hyers) method in the setting of 2-Banach spaces. For a typical case, by means of a norm, induced from a 2-norm of $\mathbb R^m$, we investigate the stability of a mapping $f:\mathbb R^{mn} \longrightarrow \mathbb R^{m}$ by a known fixed point method. https://ajmc.aut.ac.ir/article_5867.html ‎In this paper‎, ‎we study induced deformed non linear connections on Finsler sub-manifolds and prove that every non linear‎ ‎connection on a Finslerian sub-manifold is an induced deformed non-linear connection‎. ‎In addition‎, ‎we provide some conditions‎ ‎under which Finslerian sub-manifolds are Landsbergian manifolds‎. https://ajmc.aut.ac.ir/article_5883.html In this paper, a stable block integrator was derived from continuous formulation of midpoint method for numerical solutions of differential equations with focus on predator-prey system and Oregonator model. The newly derived block method was consistent, zero stable and convergent. Further analysis of the method indicated that it is $A$-stable and also satisfies a highly desirable property; it is $L$-stable. Its implementation on predator-prey and highly stiff Oregonator model showed that it competes favourably with in-built Matlab ode23s which had been designed for stiff problems. This study helped to solve problems of instability usually associated with explicit midpoint method especially when used to solve stiff problems; also difficulty associated with the use of inappropriate method to kick-start midpoint method was addressed using block method approach. Compact outlook of the newly developed block method underscores its ease of implementation. https://ajmc.aut.ac.ir/article_5916.html The 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. The procedure involves solving two conventional Lyapunov equations with real-valued coefficient matrices at each iteration. 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 from applying a finite difference procedure to the Helmholtz equation by the proposed method. https://ajmc.aut.ac.ir/article_5929.html Our main goal here is to show that many of essential results in quantized functional analysis rely on the algebraic structure of the unital ring $B(H)$ of bounded operators on a Hilbert space $H$. The wide spectrum of structures on this ring is the main motivation for investigating the role of algebraic structure of $B(H)$ in different major results in this field. Our strategy for dealing with this general problem is finding the right category, containing operator algebras, in which a specific result remains true. The authors and their collaborators, have approached this problem from three directions, a survey of which is presented here. In the first approach, major theorems of quantized functional analysis such as Arveson's extension theorem, Ruan's theorem and Choi-Effros characterization of operator systems were proved in the much larger category of unital $*$-algebras. Moreover we unify all generalizations of the notion of operator systems. The second approach is devoted to investigating existence of projections properties in the category of $*$-algebras and constructing some noncommutative topology results. In particular some characterizations of Rickart $*$-algebras and some other types of $*$-algebras in terms of topological properties, were proved. In the third approach we work in the category of Baer $*$-rings ,that is, $*$-rings which only possess the lattice structure of projections of $B(H)$ but not necessarily the other structures. In this part major decomposition theorems of Wold, Nagy-Foias-Langer and Halmos-Wallen were proved in the purely algebraic setting. https://ajmc.aut.ac.ir/article_5934.html For $C^*$-algebras $\mathfrak{A}, A$ and $B$ where $A$ and $B$ are $\mathfrak{A}$-bimodules with compatible actions, we consider amalgamated $\mathfrak{A}$-module tensor product of $A$ and $B$ and study its relation with the $C^*$-tensor product of $A$ and $B$ for the min and max norms. We introduce and study the notions of module tensorizing maps, module exactness, and module nuclear pairs of $C^*$-algebras in this setting. We illustrate our results for the concrete examples of $C^*$-algebras on inverse semigroups. https://ajmc.aut.ac.ir/article_5945.html In this paper, we propose GERIS, a game-theoretic framework for instance selection in the data augmentation phase of license plate recognition systems. During augmentation, synthetic license plate images are generated and transformed using stochastic noise to simulate real-world conditions. However, certain noise configurations lead to highly distorted, unreadable images that degrade model performance by introducing instance-dependent label noise. GERIS formulates a non-cooperative game in which each noise vector competes for inclusion in the training set based on its similarity to labeled data and its contribution to model reliability. By identifying and pruning low-quality instances, GERIS improves the overall quality of the augmented dataset. Unlike traditional black-box learning methods, GERIS offers a transparent, theoretically grounded mechanism for data filtering. Experimental results demonstrate that GERIS outperforms existing instance selection methods in terms of classification accuracy and robustness. https://ajmc.aut.ac.ir/article_5952.html This paper investigates two interconnected themes in statistical geometry: the lifting of statistical structures from a Lie group to its tangent Lie group and the study of locally product-like statistical manifolds. We first explore the geometric and algebraic properties of lifting statistical structures, focusing on the compatibility conditions and invariance properties that allow such structures to be naturally extended to the tangent Lie group. Key results include the construction of lifted connections, the behavior of statistical curvature tensors, and the preservation of conjugate symmetry under the lifting process. In the second part, we study locally product-like statistical manifolds, which generalize the notion of product manifolds in the context of statistical geometry. We characterize these manifolds by their decomposition into orthogonal statistical submanifolds and analyze their curvature properties, conjugate symmetry, and compatibility with statistical connections. Explicit examples are provided to illustrate both the lifting process and the structure of locally product-like statistical manifolds. These findings deepen the understanding of statistical geometry in the context of Lie groups, tangent bundles, and product-like structures, offering new insights into their geometric and algebraic properties. https://ajmc.aut.ac.ir/article_5953.html Let $\mathrm{R}$ be a commutative Noetherian local ring, $\mathrm{M}$ be a non-zero finitely generated $\mathrm{R}$-module of dimension $d$ and $\Phi$ be a system of ideals of $\mathrm R$. For each $i>d,$ $\large H_{ \Phi}^i (M)$ is zero and $\large H_{ \Phi}^d (M)$ is Artinian. In this paper, we determine the annihilator and the set of attached prime ideals of top general local cohomology module $\large H_{ \Phi}^d (M).$ https://ajmc.aut.ac.ir/article_5954.html Vaidya spacetime describes the dynamical collapse of a null fluid under gravity and this spacetime model is capable to cover key characteristics of a astrophysical events such as gravitational wave emission and black hole generation. In this paper, we study existence of a geometric vector field named Ricci bi-conformal vector field in such spacetimes. We completely classify these geometric vector fields on Vaidya and Schwarzschid spacetimes. We show such vector fields are not gradient. https://ajmc.aut.ac.ir/article_5955.html In 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_5956.html Recently, Wireless Sensor Networks (WSNs) have seen a surge in interest as a promising research domain, largely due to their pivotal role in a multitude of applications. Typically, WSNs are comprised of numerous nodes that function collaboratively to acquire data from their surrounding environment. The effectiveness of a WSN is strongly contingent upon the methodology employed for node placement. This study undertakes a review of various node deployment strategies and their consequential effects on both coverage and connectivity. Coverage, a key performance indicatorin WSNs, quantifies the extent to which the sensor field is monitored. Consequently, robust coverage control is indispensable for WSNs. To mitigate superfluous energy expenditure and optimize network performance, energy efficiency and coverage rates are both primary factors in WSN considerations. Furthermore, ensuring connectivity during the deployment phase is critical for guaranteeing the reliable and efficient operation of the WSN in data transmission. This research also delves into the categorization of diverse coverage strategies, including computational geometry-basedapproaches, force-directed techniques, network-centric methods, and meta-heuristic algorithms while contrasting their respective strengths and weaknesses. A thorough analysis of performance metrics and a comparative study of various WSN simulation tools are also presented. https://ajmc.aut.ac.ir/article_5957.html In this paper, we prove that every Liouville transformation of a locally Minkowskian Randers metric must be a homothety. This gives a natural extension of the Kuhnel-Rademacher's theorem which proved the homothety of Liouville transformation for semi-Riemannian metrics. https://ajmc.aut.ac.ir/article_5958.html The prevalence of hate speech on social media platforms is increasing, prompting considerable attention from the research community to detect such harmful content. Recent studies have focused on refining language models (LMs) to effectively identify hate speech, resulting in notable advancements in performance. Nonetheless, the majority of these studies are confined to identifying hate speech exclusively in English, disregarding the vast amount of hateful content produced in other languages, notably those considered low-resource languages. Constructing a classifier capable of effectively detecting hate speech in a low-resource language with limited data poses a formidable challenge. To address the existing gap, we perform comparative study for five large language models and three Parameter-Efficient Fine-Tuning Methods, to determine which model and method excel in detecting hate speech proficiently on two languages that have limited linguistic resources available. Specifically, we evaluate three approaches: Sequence Classification based fine-tuning (SEQ_CLS), Causal language modeling-based fine-tuning (CLM), and In-context learning approach (ICL). Our findings emphasize the ability of generative models to address the challenges of data scarcity and enhance model performance through these methods and approaches. https://ajmc.aut.ac.ir/article_5959.html This study investigates the transmission dynamics of Schistosomiasis using a fractional-order model and the generalized Mittag-Leffler function method (GMLFM). The human population is classified into susceptible, infected, and recovered groups, while the snail population is divided into susceptible and infected compartments. The stability of equilibrium points is analyzed, and sensitivity analysis with contour plots is conducted to examine the influence of key parameters on the basic reproduction number. The proposed numerical approach demonstrates accuracy and efficiency in handling multidimensional fractional-order differential equations, offering more profound insights into the progression of parasitic diseases and providing a basis for future model extensions. https://ajmc.aut.ac.ir/article_6020.html An accurate and efficient multilevel v-cycle algorithm for radial basis function-based finite difference (RBF-FD) method is presented in this paper. The primary goal of the algorithm is level-by-level calculation from finest level to coarsest level and then level-by-level correction from coarsest level to finest level. The algorithm produces an accurate solution by solving corresponding error equations of the discretized equations from coarsest level to coarser level and then finer level to desired finest level. Convection-dominated problems are taken to demonstrate the validity of the algorithm. The computing time of the proposed algorithm is calculated, and it saves at least 51% of computation time than the general RBF-FD method. The necessary and sufficient convergence conditions of the iteration matrix of the proposed method were verified numerically. The tests show that the developed algorithm is accurate, which accelerates to a significant reduction in computational cost compared with the general RBF-FD method. https://ajmc.aut.ac.ir/article_6031.html ‎In the present paper‎, ‎we obtain some necessary‎, ‎sufficient and equivalent conditions for some special sequences in a Hilbert C*-module to constitute a standard g-Bessel sequence or a K-g-frame‎, ‎where K is an adjointable operator on the underlying Hilbert C*-module‎. ‎Mainly‎, ‎it is shown that standard g-Bessel sequences and K-g-frames are stable under the different kinds of perturbations‎. ‎Then‎, ‎as a special kind of K-duals for a standard g-frame‎, ‎its $\alpha$-duals are considered and characterized ($\alpha$ is an integer)‎. ‎Moreover‎, ‎we get some conditions under which standard g-Bessel sequences‎, K-g-frames and $\alpha$-duals are preserved under the action of adjointable operators‎.