https://ajmc.aut.ac.ir/ AUT Journal of Mathematics and Computing en daily 1 Thu, 01 Oct 2026 00:00:00 +0330 Thu, 01 Oct 2026 00:00:00 +0330 https://ajmc.aut.ac.ir/article_5773.html In this paper, in the context of an important class of locally compact hypergroups, namely $\mathcal{K}_{\rho}$, which were introduced by Dunkl and Ramirez, we find some sufficient conditions on a weight $(w_n)_{n=0}^\infty\subseteq (0,\infty)$ such 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*}is a $\sigma$-$c$-lower porous set. 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_5563.html In this paper, we present a formula for the Waldschmidt constant of edge ideals of some classes of hypergraphs. We also show that if $G$ is a simple graph with binomial edge ideal $J_G$, then the Waldschmidt constant of $J_G$ is always 2. Furthermore, the symbolic defect of umbrella hypergraphs is presented. 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_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. [3] by adding a second Central node to the system and using the equilibrium equation of the Veraart et al. [11] 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_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_5666.html Natural Language Understanding ($\textbf{NLU}$) 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 $\textbf{NLU}$ for low-resource languages. With intent detection and slot filling being crucial tasks in $\textbf{NLU}$, the widely used datasets $\textbf{ATIS}$ and $\textbf{SNIPS}$ 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 $\textbf{ATIS}$ 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_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_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_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_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 \cite[Problems 1 and 5]{Pa_ChFoLe} for division rings with uncountable center. 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_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_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_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_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_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_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. https://ajmc.aut.ac.ir/article_6081.html ‎This paper deals with a multidimensional variant of the direct incomplete orthogonalization method to solve generalized tensor equations based on the tensor format. With the aid of truncation approach, the incomplete orthogonalization method is a desirable variant of Krylov subspace method for solving tensor equations due to its low computational cost, compared to the other iteration solvers. We investigate also locally orthogonality and some properties of the residual tensors of the proposed method. Finally, we give some numerical experiments to demonstrate the effciency and validity of the presented method. https://ajmc.aut.ac.ir/article_6082.html In this paper, we study projective algebra of the new class of $(\alpha, \beta)$-metrics introduced by Piscoran-Mishra in Finsler geometry. The projective algebra of a Finsler space is a finite-dimensional Lie algebra with respect to the usual Lie bracket. We show that if to this class of Finsler metrics, admits a projective vector field, then this is a conformal vector field with respect to Riemannian metric $\alpha$ or $F$ has vanishing $S$-curvature. https://ajmc.aut.ac.ir/article_6083.html ‎Let $n\in\mathbb{N}$ and $\alpha>0$‎. ‎The $n$th weighted space $\mathcal{W}^n_‎\alpha‎$‎, ‎consists of all analytic functions on $\mathbb{D}$ such that‎‎$$\|f\|_{\mathcal{W}^n_‎\alpha‎}=\sum_{i=0}^{n-1}|f^{(i)}(0)|+\sup_{z\in\mathbb{D}}(1-|z|^2)^‎\alpha‎|f^{(n)}(z)|<\infty.$$‎‎In this paper‎, ‎the isometry of the composition operator $C_‎\varphi‎‎: ‎\mathcal{W}^n_‎\alpha‎\to \mathcal{W}^n_‎\alpha‎$ will be investigated‎, ‎and the spectrum of isometric composition operators will be determined‎. ‎Furthermore‎, ‎we establish that for $\alpha>n$‎, ‎the subspace $\mathcal{W}^n_{‎\alpha‎,0}$‎​ ‎(defined as the closure of functions satisfying $\lim_{|z|\rightarrow 1}\mu(z)|f^{(n)}(z)|=0$) supports a hypercyclic composition operator $C_\varphi$ and for $0<\alpha\leq n$‎, ‎no such hypercyclic composition operator exists on $\mathcal{W}^n_{‎\alpha‎,0}$‎.‎ https://ajmc.aut.ac.ir/article_6084.html Automatic recognition of exercise types using data from wearable sensors is a key challenge in the feld of digital health and ftness. This study presents a machine learning–based strategy for classifying physical activities using data collected from ftness trackers. We employ a cost-sensitive and optimized Long Short-Term Memory (LSTM) network to better handle class imbalances and model temporal dependencies in the sensor data. During preprocessing, raw signals are cleaned, normalized, and transformed into meaningful features. The customized LSTM model is then trained to learn hidden patterns with an emphasis on minimizing misclassifcation costs. Evaluation using standard performance metrics shows that the proposed costsensitive LSTM approach signifcantly outperforms traditional methods, achieving an accuracy of 99%. Precision, recall, and F1-score also indicate excellent performance, demonstrating the method’s strong capability in accurate activity recognition. Unlike many previous studies focused on non-sequential or standard LSTM models, this research highlights the advantages of tailored recurrent architectures in enhancing the robustness and accuracy of exercise classifcation systems. https://ajmc.aut.ac.ir/article_6085.html The goal of this article is to initiate the study of fractional $C_{0}$-$\alpha$-semigroups of continuous linear operators on locally convex spaces. In particular, we prove an extension of the Hille-Yosida theorem for an equicontinuous (resp. exponentially equicontinuous) $C_{0}$-$\alpha$-semigroups of continuous linear operators on a sequentially complete locally convex Hausdorff space. https://ajmc.aut.ac.ir/article_6086.html In this paper, we consider the generalized the conformal Kropina transformation with m-th root metric and find that if generalized conformal Kropina change is Einstein metric, then this comes out to be Ricci flat. Besides, if generalized conformal Kropina transformation of m-th root metric is weak Einstein metric, then this comes out to be Ricci flat. https://ajmc.aut.ac.ir/article_6087.html Neoadjuvant therapies are commonly used in the treatment of estrogen receptor-positive breast cancer to reduce tumor burden and metastasis risk. This study employs mathematical modeling, using concepts of dynamic evolution, to determine the optimal neoadjuvant combination of aromatase inhibitors and anti-PD-L1 treatments for reducing both tumor burden and metastasis risk. The problem is formulated as an optimal control problem, and the outcomes of all combination therapies are evaluated, with the optimal therapies identified on the Pareto boundary. The results suggest that the most effective neoadjuvant treatment over a 6-month period involves two months of aromatase inhibitor treatment followed by continuous anti-PD-L1 treatment to minimize tumor volume and metastasis risk. Furthermore, continuous anti-PD-L1 administration is recommended in all treatment strategies on the Pareto boundary. https://ajmc.aut.ac.ir/article_6088.html The highest posterior density credible interval, known as the highest density interval, is the shortest interval for any continuous unimodal posterior distribution. However, this unique property, does not hold in the frequentist setting. In this note, we unveil the necessary and sufficient conditions under which a highest density interval is also the shortest confidence interval within the scale-exponential family of distributions. https://ajmc.aut.ac.ir/article_6089.html ‎In this paper‎, ‎we present a new class of hyperideals ‎called weakly strongly quasi-primary (briefly‎, ‎$wsq$-primary) hyperideal‎. ‎For this purpose we first need to introduce‏‎ ‎the notion of quasi-primary hyperideals. ‏‎Then we define a subclass of the concept called ‎strongly quasi-primary hyperideals‎. ‎After the definition and investigation of them‎, ‎we propose an extension of the ‎strongly quasi-primary hyperideals called weakly strongly quasi-primary hyperideals‎.‎ Several properties and characterizations concerning the concept are presented‎. ‎The stability of this new concept with respect to various hyperring-theoretic constructions is studied‎. https://ajmc.aut.ac.ir/article_6090.html This paper proposed an ensemble learning algorithm to enhance classification accuracy in agricultural dataset based on S-approximation. In the field of agriculture, the use of these algorithms can provide valuable insights into crop growth patterns, disease outbreaks and other important factors. Four ensemble learning methods, including Random Forest, boosting, bagging and majority voting, were employed and were used with a real agricultural dataset. The proposed method identifies the dependency degree of attributes and selects reducts that are most relevant for classification tasks. These reducts are subsequently used to train an ensemble of base classifiers. This hybrid approach combines the strengths of S-approximation with ensemble learning techniques to provide a robust classification framework. To evaluate the proposed algorithm, experiments were conducted on a real-world crop yield dataset, categorizing crop yields into “Low”, “Medium”, and “High” production levels. Production and Fertilizer, were identified as critical predictors. The dataset was pre-processed to address missing values, normalize attributes and to address class imbalance, the Synthetic Minority Oversampling Technique (SMOTE) was employed, ensuring equitable representation of all classes. The result demonstrates that Random Forest achieved the highest accuracy (99.08\%) with balanced precision, recall and F1-score, confirming its robustness and reliability. The Voting Classifier, integrating the strengths of individual models, also delivered high accuracy (99.04\%), showcasing the efficacy of the ensemble approach. This work highlights the potential of integrating S-approximation with ensemble learning to improve classification tasks in agricultural datasets, providing actionable insights for optimizing crop yields and supporting data-driven agricultural decision-making. https://ajmc.aut.ac.ir/article_6102.html In this paper, we give an operational matrix method based on the multivariate Lagrange polynomial basis to find the approximate solution of the multi-dimensional nonlinear Schrodinger (NLS) equation. The NLS equation is discretized through the Leap-Frog method with respect to the time variable. For space discretization, we first compute the differentiation matrix in the multivariate Lagrange polynomial basis. Then the NLS equation is discretized by an operational matrix method. We analyze the unique solvability and stability of the presented method. Finally, in order to observe the validity, effectiveness and accuracy of the proposed method, we give numerical examples for both two and three dimensional NLS equations. https://ajmc.aut.ac.ir/article_6169.html This paper is dedicated to the complete classification of Riemann solitons and Ricci bi-conformal vector fields on Bardeen spacetimes. Additionally, we identify which of these vector fields correspond to Killing vector fields, Ricci collineation vector fields, and gradient vector fields. https://ajmc.aut.ac.ir/article_6182.html Background: The pelvic plays an important role in human movement, and it is the foundation that provides stability during activities such as walking. Abnormal condition of the pelvic area, whether it is an abnormality of alignment or function, requires timely treatment intervention. Traditionally, pelvic examination has been performed through static two-dimensional imaging with very limited insight into real-time pelvic dynamics. Inertial measurement unit (IMU) sensors are already very powerful in acquiring all nuances of movement mechanics; with the addition of ML techniques, they can serve as an effective methodology for diagnosing pelvic movement patterns for different activities. Material and Methods: This study investigates the gait pattern of 50 female patients with spinal sagittal imbalance (SSI) compared to 50 controls. Various machine learning (ML) models were applied using IMU data collected during gait analysis in order to identify and assess abnormalities in movement. Results: Results: While the Support Vector Machine (SVM) achieved the highest classification accuracy (99.07%) in identifying pelvic movement disorders using IMU data, the Linear Discriminant Analysis (LDA) model showed the most balanced performance with the highest F1-score (99.00%) and precision (98.00%). This indicates that LDA may be preferable in settings where minimizing false positives and achieving balanced classification is critical. https://ajmc.aut.ac.ir/article_6183.html As the world becomes increasingly interconnected, social media platforms like Twitter play a pivotal role in shaping public discourse. One significant topic that has emerged in recent years is the Arbaeen walk, a religious and political movement that has attracted global attention. This paper has two main objectives: first, to construct the Arbaeen Tweets Dataset, curated specifically for sentiment analysis; and second, to analyze Persian tweets related to the Arbaeen walk from 2021 to 022. By employing natural language processing (NLP) techniques—namely Latent Dirichlet Allocation (LDA) and BERTopic—we aim to uncover prevalent themes and sentiments, referred to as “topics” in topic modeling. The Arbaeen Tweets Dataset consists of 2,622 colloquial Persian texts from Twitter, labeled for sentiment analysis. Our findings indicate that while LDA demonstrates slightly superior quantitative performance, BERTopic offers greater coherence in topic interpretation. https://ajmc.aut.ac.ir/article_6191.html Throughout history, humans have leveraged technology to enhance healthcare and medical treatment. Traditional approaches relied on limited methods and tools to assess and predict an individual’s health status. However, with recent advancements in pervasive computing, data mining, and deep learning, it has become possible to provide personalized health prediction and assistance with greater accuracy and efficiency. While research on electronic health records (EHRs) has opened new opportunities, it has also introduced significant challenges—particularly in predicting a patient’s condition after hospital discharge or during hospitalization. In this paper, we propose a novel method based on a Supervised Variational Autoencoder (SVAE) for predicting patient health outcomes. The model is designed to address post-discharge and in-hospital prediction tasks while maintaining simplicity in preprocessing and input requirements. Our proposed approach achieves performance comparable to or better than state-of-the-art methods, despite relying on fewer input variables. The results demonstrate the potential of the SVAE framework for real-world healthcare data analysis and its practical applicability in clinical decision-support systems. https://ajmc.aut.ac.ir/article_6184.html This article investigates the time-space fractional advection-dispersion equation $(TSFADE)$. In this work, a efficient and precise numerical method (Novel Shifted Jacobi Operational Matrix technique) is applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of this scheme is its ability to transform linear and nonlinear $(PDEs)$ into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested scheme is effectively utilized for the mentioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the introduced scheme. To showcase the efficacy and accuracy of this technique, the numerical results from the examples are presented in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the performance of the current method is regarded as quite simple and general for many numerical techniques. https://ajmc.aut.ac.ir/article_6185.html The Bonus-Malus system (BMS) is a premium-setting system in which low-risk policyholders are encouraged by determining lower premiums and high-risk are penalized by paying higher premiums. Designing a fair Bonus-Malus system is essential for risk management. Insurance companies can attract low-risk policyholders by setting a lower premium rate and repel high-risk policyholders by placing a higher premium. This article presents a fair optimal Bonus-Malus system for third-party car insurance policyholders, in which insurance premiums are calculated based on the number and severity of the policyholders' accidents and some of their characteristics. To calculate insurance premiums as fairly as possible, this article considers Negative Binomial and Pareto distributions, respectively, for the severity and number of claims in the form of the Bayesian additive model for location, scale, and shape (BAMLSS) structure. Then, it models how to determine the future premiums using this structure as a Bonus-Malus system. https://ajmc.aut.ac.ir/article_6186.html Implementing efficient emergency supply planning is one of the most challenging tasks. This article addresses the issue of emergency supply planning, considering both the emergency positioning before a disaster and the dynamic transportation planning after the disaster, taking into account the traffic reduction of the transportation network. The problem is modeled as a bi-level, two-stage stochastic programming model. In the first level, the objective is to minimize the total expected cost related to mitigation, preparation, and various response decisions. In the second level, the objective is to reduce the network traffic. The model is transformed to a single level using the KarushKuhnTucker (KKT) conditions. After utilizing linearization techniques and convexification, a specific rule based on lagrangean relaxation has been employed to minimize the scale of the model. Then a Benders decomposition algorithm is used to solve the reduced-size lagrangean single-level model. This method is significantly effective for solving this type of problem. Lastly, a case study for hurricane threat in the southeastern United States is conducted to demonstrate the benefits of the model and provide insight into optimal network mitigation, pre positioning planning, and transportation planning. It has been shown that the consideration of bi level models to reduce traffic congestion affects dynamic transportation plans and provides spatial and temporal flexibility to achieve better emergency supply plans. The suggested solution approach has been evaluated against two other well-known methods, and a comprehensive sensitivity analysis has been conducted on the model parameters. https://ajmc.aut.ac.ir/article_6187.html This paper considers exponential $(\alpha,\beta)$-metrics with a conformally flat structure that have weakly isotropic scalar curvature. It proves that such metrics necessarily reduce to Riemannian or locally Minkowski metrics, in which case the scalar curvature vanishes. Similar results are presented for two specific $\beta$-change of exponential $(\alpha,\beta)$-metrics: the Kropina change and the generalized Randers change. Consequently, we provide a classification of these $(\alpha,\beta)$-metrics. https://ajmc.aut.ac.ir/article_6188.html The Jaya algorithm is a population-based metaheuristic algorithm used for solving optimization problems. The algorithm's fundamental principle revolves around generating an initial random population. Through iterative refinement using update rules, the goal is to bring the solution closer to the optimal outcome while concurrently distancing it from suboptimal results. This paper presents the application of the Jaya algorithm in solving the Lane-Emden type equations using rational Chebyshev polynomials and standard polynomials as base functions. The results indicate that the Jaya algorithm is a reliable and capable method for solving the Lane-Emden type equations. https://ajmc.aut.ac.ir/article_6189.html Health disparities during epidemics expose structural inequities in health systems: during COVID-19, marginalized groups experienced mortality more than 2.8 times that of privileged populations due to cumulative disadvantages spanning housing, occupational exposure, access to care, and social capital. While machine learning (ML) shows promise for mitigating such disparities, prevailing approaches rarely codesign fairness into the pipeline or engage stakeholders in ways that are viable for resource-constrained settings. Following PRISMA 2020 and PRISMA-AI, we conducted a systematic review of 76 peer-reviewed studies (2019–2024) to identify which established ML methods most reliably support equitable epidemic management. The review synthesized evidence on diagnostic and operational gains as well as recurring barriers—algorithmic bias, infrastructural defcits, and limited community participation—that impede equitable deployment. Guided by these fndings, we propose a three-layer integration framework—prediction, allocation, and governance—that embeds fairness at design time rather than as a post-hoc fx. To aid interdisciplinary readers, we defne key terms at frst use: equity checkpoints are formal decision points in the ML lifecycle at which group-wise error, beneft, and burden gaps are tested against pre-specifed thresholds; if thresholds are exceeded, the system triggers model reweighting, constraint tuning, or data collection updates before proceeding. The framework draws on statistical learning theory, convex optimization, and algorithmic fairness to preserve accuracy and equity guarantees within a single optimization procedure. We then validate the framework via simulation—not as an isolated modeling exercise, but as a direct test of the design principles distilled from the review. Across diverse scenarios, disparity metrics improve by 40–55Policy implications include mandatory algorithmic impact assessments with equity criteria, independent audits, and targeted digital-equity investments. Collectively, the review-informed framework and its validation demonstrate a practical path for deploying established ML methods that measurably reduce health disparities without sacrifcing system performance. https://ajmc.aut.ac.ir/article_6190.html Chitrakavya, a distinctive form of Indic visual poetry, embeds poetic texts within images having intricate spatial layouts, such as geometric shapes, artistic work and cultural motifs. Tracing the poetic flow in these non-linear designs challenges human readers leave alone machines. This study proposes graphbased traversal algorithms to model the poetic flow in Odia Chitrakavya, addressing contour-prioritized connectivity, self-loops, sequential transitions, and non-sequential jumps. We introduce five Contour-Prioritized Spatial (CPS) algorithms: CPS-DFS No Memoization, CPS-DFS Memoization, CPS-DFS Prune, Contour-Prioritized Spatial Heuristic-Driven Search (CPS-HDS), and a CPS-DFS + CPS-HDS Hybrid. These algorithms, evaluated on Odia Chitrakavya graphs (up to 104 nodes), incorporate dynamic heuristics (weighted contour distance and shape-based similarity) and CUDA accelerated multi-path exploration. Robustness is tested on error injected graphs with 5–10% missing nodes. The CPS algorithms successfully trace poetic flow, achieving 54–63 sequential steps and 1–10 jumps in a 52-node graph and a target string of length 64, outperforming traditional DFS and BFS (7 steps, no jumps, unable to trace the flow) with runtimes of 0.0016–0.0361 seconds. CUDA parallelization reduces runtimes between 15–30% for 52-node graphs (up to 30% for larger graphs), with the hybrid version achieving 0.0014 seconds. The hybrid algorithm yields 94% path optimality. A publicly available JavaScript-based interactive visualization (referenced in the main text), a standardized Odia Chitrakavya dataset, and accompanying Python source code are provided to support reproducible research. These algorithms are script-independent and can be applied to visual poetry traditions in other languages.