AUT Journal of Mathematics and Computing
https://ajmc.aut.ac.ir/
AUT Journal of Mathematics and Computingendaily1Wed, 01 Jan 2025 00:00:00 +0330Wed, 01 Jan 2025 00:00:00 +0330An efficient computational approach for numerical solution of non-smooth dynamical systems
https://ajmc.aut.ac.ir/article_5286.html
In this paper, an efficient computational approach based on the fantastic Simpson integral formula is developed for the numerical solution of non-smooth dynamical equations. In the proposed approach, at first, the integral reformulation of the target problem is intended. Then, the Simpson formula is employed to discretize the obtained integral equation. It is mentioned that, the implementation of the method is simple, so, the method can be simply and quickly used to solve a wide variety of non-smooth dynamical systems arising in the various engineering models. Numerical experiments of two benchmark examples are presented at the end and the efficiency of the method is reported.A distributionally robust approach for the risk-parity portfolio selection problem
https://ajmc.aut.ac.ir/article_5269.html
Risk-parity is one of the most recent and interesting strategies in the portfolio selection area. Considering the mean-standard-deviation risk measure, this paper studies the risk-parity problem under the uncertainty of the covariance matrix. Assuming that the uncertainty is represented by a finite set of scenarios,\linebreak the problem is formulated as a scenario-based stochastic programming model. Then, since the occurrence probabilities of scenarios are not known with certainty, two ambiguity sets of distributions are considered, and corresponding to each one, a distributionally robust optimization model is presented. Computational experiments on real-world instances taken from the literature confirm the importance of the proposed models in terms of stability, volatility and Sharpe-ratio.Efficient deep learning algorithms for lower grade gliomas cancer MRI image segmentation: A case study
https://ajmc.aut.ac.ir/article_5261.html
This study explores the use of efficient deep learning algorithms for segmenting lower grade gliomas (LGG) in medical images. It evaluates various pre-trained atrous-convolutional architectures and U-Nets, proposing a novel transformer-based approach that surpasses traditional methods. DeepLabV3+ with MobileNetV3 backbone achieved the best results among pre-trained models, but the transformer-based approach excelled with superior segmentation accuracy and efficiency. Transfer learning significantly enhanced model performance on the LGG dataset, even with limited training samples, emphasizing the importance of selecting appropriate pre-trained models. The transformer-based method offers advantages such as efficient memory usage, better generalization, and the ability to process images of arbitrary sizes, making it suitable for clinical applications. These findings suggest that advanced deep learning techniques can improve diagnostic tools for LGG and potentially other cancers, highlighting the transformative impact of deep learning and transfer learning in medical image segmentation.$C^*$-algebra-valued $S_{b}$-metric spaces and applications to integral equations
https://ajmc.aut.ac.ir/article_5282.html
We first introduce the concept of $C^{*}$-algebra-valued $S_{b}$-metric space, then we prove Banach contraction principle in this space. Finally, existence and uniqueness results for one type of integral equation is discussed.Driver cellphone usage detection using wavelet scattering and convolutional neural networks
https://ajmc.aut.ac.ir/article_5229.html
This paper provides an automated system based on machine learning and computer vision to detect cellphone usage during driving. We used Wavelet Scattering Networks, which is a simple and efficient type of architecture. The presented model is straightforward and compact and requires little hyper-parameter tuning. The speed of this model is similar to the Convolutional Neural Networks. We monitored the driver from two viewpoints: a frontal view of the driver&rsquo;s face and a side view of the driver&rsquo;s whole body. We created a new dataset for the first viewpoint, and used a publicly available dataset for the second viewpoint. Our model achieved the test accuracy of 91% for our new dataset and 99% for the publicly available one.A novel mobile robot path planning method based on neuro-fuzzy controller
https://ajmc.aut.ac.ir/article_5262.html
In recent years, the navigation of mobile robots has been of great interest. One of the important challenges in the navigation of mobile robots is the obstacle avoidance problem so that the robots do not collide with each other and obstacles, during their movement. Hence, for good navigation, a reliable obstacle avoidance methodology is needed. On the other hand, some of the other most important challenges in robot control are in the field of motion planning. The main goal of motion planning is to compile (interpret) high-level languages into a series of primary low-level movements. In this paper, a novel online sensor-based motion planning algorithm that employs the Adaptive Neuro-Fuzzy Inference System (ANFIS) controller is proposed. Also, this algorithm is able to distance the robots from the obstacles (i.e. it provides a solution to the obstacle avoidance problem). In the proposed motion planning algorithm, three distances (i.e. the distance of the robot from the obstacles in three directions: right, left, and front) have been used to prioritize the goal search behavior and obstacle avoidance behavior and to determine the appropriate angle of rotation. Then, for determining the linear velocity, the nearest distance from obstacles and distance from the goal have been used. The proposed motion planning algorithm has been implemented in the gazebo simulator (by using Turtlebot) and its performance has been evaluated. Finally, to improve the performance of the proposed motion planning algorithm, We have used type-1, interval type-2, and interval type-3 fuzzy sets, then, we have evaluated and compared the efficiency of the proposed algorithm for each of these fuzzy sets under specific criteria.Two-stage stochastic capacitated Lot-Sizing problem by Lot-Size adaptation approach
https://ajmc.aut.ac.ir/article_5281.html
In this paper, a two-stage stochastic capacitated lot-sizing problem with random demand, and service level constraints under static and static-dynamic uncertainty strategies is introduced. A static strategy determines the setup period and lot sizing at the beginning of planning period, whereas a static-dynamic strategy allows the lot size to be adjusted during the planning period. A new model formulation of the demand differential adjustment policy in a multi-stage production system is proposed. Lot-sizing adjustments depend on the difference in demand between actual and expected demand. To quantify the economics of our uncertainty strategy for multi-level lot size the problems, the number of test instances with different parameter settings is evaluated. Computational experiments show that the additional costs of semi-finished products, and the lack of storage capacity in the downstream processes reduce the potential for cost savings via multi-volume reform. Also a robust model is developed and as the robust model under study is NP-hard, it solved by a hybrid heuristic using the proposed stochastic model, a robust model is developed, which is solved by a hybrid heuristic algorithm based on Lagrangian relaxation and Bender's decomposition algorithms. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.Finding the extreme efficient solutions of multi-objective pseudo-convex programming problems
https://ajmc.aut.ac.ir/article_5280.html
In this paper, we present two methods to find the strictly efficient and weakly efficient points of multi-objective programming (MOP) problems in which their objective functions are pseudo-convex and their feasible sets are polyhedrons. The obtained efficient solutions in these methods are the extreme points. Since the pseudo-convex functions are quasi-convex as well, therefore the presented methods can be used to find efficient solutions of the (MOP) problem with the quasi-convex objective functions and the polyhedron feasible set. Two experimental examples are presented.Structure theory of Clifford-Weyl algebras and representations of ortho-symplectic Lie superalgebras
https://ajmc.aut.ac.ir/article_5310.html
In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra structures. The Clifford-Weyl superalgebras can be realized as tensor product of the algebra of alternating and symmetric tensors respectively, on the even and odd parts of their underlying superspace. For Physical applications in elementary particles, we add star structures to these algebras and investigate the basic relations. Ortho-symplectic Lie algebras are naturally present in these algebras and their representations on these algebras can be described easily.On conformal transformation of $\Xi$-curvature
https://ajmc.aut.ac.ir/article_5316.html
In this paper, we study the conformal transformation of recent defined non-Riemannian curvature in Finsler Geometry, namely $\Xi$-curvature. Indeed, we obtain the necessary and sufficient condition under which the conformal transformation preserves the $\Xi$-curvature.A remark on the metric dimension in Riemannian manifolds of constant curvature
https://ajmc.aut.ac.ir/article_5326.html
We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weighted metricdimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G = (V,E)$ embedded in a Riemannin manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V| &minus; 1$.Perfectness of the essential graph for modules over commutative rings
https://ajmc.aut.ac.ir/article_5327.html
&lrm;Let $R$ be a commutative ring and $M$ be an $R$-module&lrm;. &lrm;The essential graph of $M$&lrm;, &lrm;denoted by $EG(M)$ is a simple graph with vertex set $Z(M) \setminus {\rm{Ann}}_R(M)$ and two&lrm; &lrm;distinct vertices $x,y \in Z(M) \setminus {\rm{Ann}}_R(M)$ are adjacent if and only if&lrm; &lrm;${\rm{Ann}}_M(xy)$ is an essential submodule of $M$&lrm;. &lrm;In this paper&lrm;, &lrm;we investigate&lrm; &lrm;the dominating set&lrm;, &lrm;the clique and the chromatic numbers and the metric dimension&lrm; &lrm;of the essential graph for Noetherian modules&lrm;. &lrm;Let&lrm; &lrm;$M$ be a Noetherian $R$-module such that $\mid {\rm MinAss}_R(M)\mid=n\geq 2$&lrm; &lrm;and let $EG(M)$ be a connected graph&lrm;. &lrm;We prove that&lrm; &lrm;$EG(M)$ is weakly prefect, &lrm;that is&lrm;, $\omega(EG(M))=\chi(EG(M))$&lrm;. Furthermore&lrm;, it is shown that ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n)$, whenever $r({\rm{Ann}}(M) )\neq{\rm{Ann}}(M)$ and ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n-2)$&lrm;, whenever $r({\rm{Ann}}(M) )= {\rm{Ann}}(M)$&lrm;.Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries
https://ajmc.aut.ac.ir/article_5329.html
The Kaluza-Klein theory can be reckoned as a classical unified field theory of two of the significant forces of nature gravitation and electromagnetism. This formulation geometrically demonstrates the effects of a gravitational and an electromagnetic field by investigating a five-dimensional space with a metric constructed via the spacetime metric and the four-potential of the electromagnetic field. For the purpose of exploring the influences of dimensionality on the distinct physical variables, inquiring into stationary Kaluza-Klein rotating fluids is of particular significance. In this research, an extensive investigation of the variational symmetries for a specific vacuum solution of the (4+1)-dimensional Einstein field equations with negative cosmological constant is presented. For this purpose, first of all, the variational symmetries of our analyzed model are completely determined and the construction of the Lie algebra of the resulted symmetries is accurately analyzed. It is represented that the Lie algebra of local symmetries interrelated to the system of geodesic equations is non-solvable and not semi-simple and the algebraic organization of the derived quotient Lie algebra is accurately evaluated. Mainly, the adjoint representation group is effectively utilized intended for establishing an optimal system of group invariant solutions; which unequivocally yields a conjugate relation in the set of all one-dimensional symmetry subalgebras. Accordingly, the associated set of invariant solutions can be regarded as the slightest list from that the alternative invariant solutions of one-dimensional subalgebras are thoroughly determined unambiguously by virtue of transformations. Literally, all the corresponding local conservation laws of the resulted variational symmetries are totally calculated. Indeed, the symmetries of the metric of our analyzed space-time lead to the constants of motion for the point particles.Dynamic monopolies in simple graphs
https://ajmc.aut.ac.ir/article_5350.html
This paper studies a repetitive polling game played on an $n$-vertex graph $G$. At first, each vertex is colored, Black or White. At each round, each vertex (simultaneously) recolors itself by the color of the majority of its closed neighborhood. The variants of the model differ in the choice of a particular tie-breaking rule. We assume the tie-breaking rule is Prefer-White and we study the relation between the notion of ``dynamic monopoly" and ``vertex cover" of $G$. In particular, we show that any vertex cover of $G$ is a dynamic monopoly or reaches a $2-$periodic coloring. Moreover, we compute $\rm{dyn}(G)$ for some special classes of graphs including paths, cycles and links of some graphs.A new relaxation technique based on fractional representation to solve bilinear models: Application to the long horizon crude oil scheduling problem
https://ajmc.aut.ac.ir/article_5357.html
This paper proposes a novel relaxation technique based on the fractional representation of bilinear terms. This technique is embedded into an iterative two-step MILP-NLP algorithm based on piecewise relaxation and domain reduction strategies. To evaluate the performance of the algorithm, it is compared to the recently addressed iterative MILP-NLP algorithm based on piecewise McCormick relaxation techniques over a variety of instances. Our method is also applied to the crude oil scheduling problem as an application. The results confirm the efficiency of the proposed algorithm from both solution quality and running time.A secure method of voting and planning based on quadratic voting
https://ajmc.aut.ac.ir/article_5367.html
Recently, an innovative voting method named quadratic voting (QV) has been proposed which allows people to vote as much as they want, according to the intensity of their preferences. Little research has been done on the safe implementation of this method. In this paper, we first present a voting method based on QV. This method combines voting and planning and gives the ability to voters to express their opinions about the candidate&rsquo;s programs in addition to voting. Then, a secure electronic voting protocol is proposed for implementing the given method. This protocol gives the voters to check the verifiability of ballots and the safety of payment so that they would be sure that their votes are counted correctly.Machine learning approach for bipolar disorder analysis and recognition based on handwriting digital images
https://ajmc.aut.ac.ir/article_5383.html
In some cases, handwriting is a manifestation of the human mind, and it can reveal various psychological characteristics and mental disorders. Among these disorders, bipolar disorder is a well-known and widely studied condition in cognitive science and psychotherapy, and it can be detected in handwriting. In this research, we applied image processing techniques to analyze the handwriting characteristics of people with bipolar disorder based on their responses to a survey. We also proposed a machine learning model that can classify whether a person has bipolar disorder or not by using their handwriting as an input.Left $\phi$-biflatness and $\phi$-biprojectivity of certain Banach algebras with applications
https://ajmc.aut.ac.ir/article_5384.html
This paper continues the investigation initially begun for left $\phi$-biflatness and left $\phi$-biprojectivity. We show that left $\phi$-biflatness and left $\phi$-biprojectivity are closely related to the notions of left $\phi$-amenability and $\phi$-inner amenability. We characterize left $\phi$-biprojectivity and left $\phi$-biflatness of certain semigroup algebras and some algebras related to a locally compact group. We discuss non left $\phi$-biflatness of some specified triangular Banach algebras.A new characterization of Chevalley groups $\mathbf{G_2(3^n)}$ by the order of the group and the number of elements with the same order
https://ajmc.aut.ac.ir/article_5385.html
In this paper, we prove that chevalley groups $G_2(q)$, where $q=3^n$ and $q^2+q+1$ is a prime numbers can be uniquely determined by the order of group and the number of elements with the same order.Power study of goodness of fit tests for the Rayleigh distribution based on the empirical distribution function with application to real data
https://ajmc.aut.ac.ir/article_5397.html
The Rayleigh distribution is widely used to model events that occur in different fields such as medicine and natural sciences. In this article, we suggest some test statistics for examining the Rayleigh goodness of fit based on the empirical distribution function. Critical points and power of the tests are obtained by Monte Carlo simulation. We show that the proposed tests have a good performance against different alternatives and therefore these tests can be confidently used in practice. Finally, the proposed tests are illustrated by real data examples.A new central-upwind scheme for solving the shallow water equations
https://ajmc.aut.ac.ir/article_5515.html
We have conducted a study where we applied one-dimensional central-upwind methods to estimate solutions of the Saint-Venant (SV) system. Our approach carefully considers the source terms associated with bottom topography. Within the context of the SV system, there are steady-state solutions that arise when the non-zero gradients of flux are exactly balanced by the corresponding source terms. Maintaining this delicate equilibrium with numerical approaches presents a challenging problem. Finding slight variations in these states proves to be extremely difficult in the field of computing. To address this, we propose an extension of semi-discrete central schemes, commonly employed in hyperbolic conservation law systems, to encompass balance laws (BL). In our approach, we specifically focus on discretizing the source term with great care and attention. To verify the superior accuracy, precise preservation of the C-property, and outstanding resolution of our approach, we perform comprehensive one-dimensional simulations on both continuous and discontinuous solutions.On Zermelo’s navigation problem and weighted Einstein Randers metrics
https://ajmc.aut.ac.ir/article_5403.html
This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, $F$ and $\tilde{F}$ are considered, which are generated by navigation representations $(h, W)$ and $(F, V)$, respectively, where $W$ represents a vector field, and $V$ represents a conformal vector field on the manifold $M$. The main focus is on identifying the necessary and sufficient condition for the Randers metric $F$ to qualify as a quasi-Einstein metric. Additionally; we establish the relationship between the curvatures of the given Finsler metrics $F$ and $\tilde{F}$.An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight
https://ajmc.aut.ac.ir/article_5412.html
This paper discusses the existence of nontrivial weak solutions for a class of $p(x)$-Kirchhoff-type equation plus an indefinite potential under Robin boundary condition. The variable exponent theory of generalized Lebesgue-Sobolev spaces, mountain pass theorem and Ekeland variational principle are used for this purpose.The competition of robust methods in linear and nonlinear regression with heavy-tailed stable errors
https://ajmc.aut.ac.ir/article_5404.html
Robust regression methods including Least Trimmed Squares are one of the most important methodologies to compute exact coeﬃcient estimators when data is polluted with outliers. There is interest to generalize Least Trimmed Squares for regression models with heavy-tailed stable errors. In this manuscript, we compare estimating coeﬃcients methods with the robust Least Trimmed Squares method in stable errors case. Therefore, we propose Stable Least Trimmed Squares and Nonlinear Stable Least Trimmed Squares methods for linear/nonlinear regression models with stable errors, respectively. The joint distribution of ordered errors is used with the ﬁnite variance property of ordered stable errors, whose indexes are deﬁned by cut-oﬀ points. We make many comparisons using simulated and real datasets.The chi-square statistic as an income inequality index
https://ajmc.aut.ac.ir/article_5413.html
This article presents a novel concept known as the chi-square inequality index, developed through the utilization of the chi-square distance function. The study delves into the essential characteristics necessary for an effective inequality index. Additionally, a detailed formulation for the chi-square inequality curve is provided within key inequality models. A comparative analysis between the chi-square curve and the conventional Lorenz curve is conducted. Furthermore, a stochastic order based on the chi-square inequality curve is introduced. The research includes a simulation analysis to explore the statistical properties of the proposed sampling estimator. To conclude, the article highlights the effectiveness of this index through an application to real-world data.DRP-VEM: Drug repositioning using voting ensemble model
https://ajmc.aut.ac.ir/article_5429.html
Conventional approaches to drug discovery are both expensive and time-intensive. To circumvent these challenges, drug repurposing or repositioning (DR) has emerged as a prevalent strategy. A noteworthy advancement in this field involves the widespread application of machine learning techniques. The effectiveness of these methods depends on the quality of features, their representations, and the underlying dataset. Notably, the issue of redundancy in feature sets can detrimentally impact the overall performance of these methods. Furthermore, the careful selection of a suitable training set plays a pivotal role in enhancing the accuracy of machine learning approaches in addressing drug repurposing challenges. Discovering the appropriate training set faces two significant challenges. Firstly, many methods utilize known drug-disease pairs for positives and unknown pairs for negatives. The stark imbalance in the number of known and unknown pairs often results in a bias towards the larger group, introducing errors in machine learning performance. Secondly, the absence of a documented drug-disease association indicates that it hasn't been experimentally approved yet, and this status may change in the future. This paper introduces DRP-VEM, a novel approach designed for predicting drug repositioning, specifically customized to tackle the challenges previously outlined. DRP-VEM evaluates the effectiveness of binary-based and similarity-based representations of drugs and diseases in enhancing the model's performance. Additionally, it proposes a voting ensemble training strategy, adept at managing imbalanced datasets. The assessment of DRP-VEM spans a range of parameters, including its efficacy in representing both diseases and drugs, the proficiency of its classification methods, and the application of voting ensemble training approaches using heterogeneous evaluation criteria. Significantly, DRP-VEM achieves an AUC-ROC of 81.8% and AUC-PR of 76.6%. Comparative analysis with other studies highlights the superior performance of the proposed model, underscoring its effectiveness in drug repositioning prediction.Co-even domination number of a modified graph by operations on a vertex or an edge
https://ajmc.aut.ac.ir/article_5457.html
Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V-D$. The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper, we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph.SCAD regression model selection with information criteria for multivariate response models
https://ajmc.aut.ac.ir/article_5460.html
This paper provides an objective function for smoothly clipped absolute deviation (SCAD) regression models with multivariate responses. The log-likelihood of a multivariate normal distribution is considered instead of L2 norm to create the model&rsquo;s objective function. Additionally, the SCAD penalty has a tuning parameter, and the information criteria, suitable for the proposed model are presented to select the tuning parameter. Based on numerical studies, the consistency of the proposed information criteria is checked via simulation experiments. Moreover, the best criterion is introduced using simulated and real datasets.Geometry of Ricci solitons admitting a new geometric vector field
https://ajmc.aut.ac.ir/article_5486.html
&lrm;In this paper&lrm;, &lrm;we define a new geometric vector field on (semi-)Riemannaian manifolds&lrm;. &lrm;These new vector fields on 3-dimensional Walker manifolds will be derived&lrm;. &lrm;Then&lrm;, &lrm;we study Ricci solitons admitting this new vector field (called semi-Killing vector field) as their potential&lrm;. &lrm;In Riemannain setting&lrm;, &lrm;we prove that Ricci solitons with semi-Killing potential vector field are Einstein&lrm;. &lrm;Also&lrm;, &lrm;It will be shown that such Lorentzian solitons have constant scalar curvature&lrm;. &lrm;Finally&lrm;, &lrm;application of this new structure in physics will be investigated&lrm;. &lrm;In fact&lrm;, &lrm;we propose that semi-Killing vector fields are in relation to the notion of dark energy in general relativity&lrm;.Loop closure detection in visual appearance-based SLAM using deep autoencoders
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.Homology groups and decomposition of the game complex
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.Non-oscillatory central schemes for the Saint-Venant system
https://ajmc.aut.ac.ir/article_5516.html
The research aims to develop a well-balanced numerical method for solving the shallow water equations, which account for the balance laws and the source term related to the seabed slope. The proposed method combines a Runge-Kutta scheme for accurate time integration and the natural continuous extension method for spatial discretization. To achieve high-order spatial accuracy, the method employs central non-staggered (CNS) reconstructions of the conservative variables and the water surface elevation. This is achieved through two key steps. The initial step involves determining the specific values of the flux derivative and the bed slope source term at individual points. The subsequent step entails integrating the source term spatially. Both of these steps are designed to preserve the C-{\it property}, which ensures the exact preservation of the quiescent flow solution. The method is verified using a variety of standard one-dimensional test cases, including smooth and discontinuous solutions, to demonstrate its accuracy and resolution properties.Fixed k-watchman routes under the Min-Max criterion in staircase polygons
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.Weighted composition, Stević-Sharma, Volterra integral and integral type operators between Dirichlet-Zygmund spaces
https://ajmc.aut.ac.ir/article_5546.html
In this paper, we study the boundedness and compactness of weighted composition operators between Dirichlet-Zygmund spaces. We also briefly investigate boundedness and compactness of the Stević-Sharma, Volterra-integral and integraltype operators between Dirichlet-Zygmund spaces.Pseudo-duals and closeness of continuous g-frames in Hilbert spaces
https://ajmc.aut.ac.ir/article_5548.html
&lrm;The paper deals with pseudo-duals of continuous g-frames and their characterizations in Hilbert spaces&lrm;. &lrm;Mainly&lrm;, &lrm;the pseudo-duals constructed by bounded operators inserted between the synthesis and analysis operators of the Bessel mappings are considered&lrm;. &lrm;Duals and approximate duals&lrm;, &lrm;which are two important classes of pseudo-duals&lrm;, &lrm;are also studied here&lrm;. &lrm;Moreover&lrm;, &lrm;the concepts of closeness and nearness of continuous g-frames are focused and some of their properties are obtained&lrm;. &lrm;It is shown that there are close relationships between the closeness and nearness of g-frames and their approximate duals&lrm;. &lrm;Also&lrm;, &lrm;the above-mentioned concepts are related to the notions of partial equivalence&lrm;, &lrm;equivalent frames&lrm;, &lrm;and continuous Riesz-type g-frames.Waldschmidt constant of some classes of hypergraphs
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.Supersingular elliptic curves‎, ‎binary quadratic forms and isogenies
https://ajmc.aut.ac.ir/article_5564.html
Many &lrm;of researchers have explored the construction of isogenies between particular elliptic curves&lrm;, &lrm;largely due to the extensive range of their practical applications&lrm;. In this paper&lrm;, &lrm;we use the relationship between supersingular elliptic curves over $\mathbb{F}_{p}$ and binary quadratic forms to generate isogenies connecting supersingular elliptic curves over $\mathbb{F}_{p}$&lrm;.Systemic Risk in Financial Networks with Two Central Institutions
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.Quantile Regression for Capital Asset Pricing Model
https://ajmc.aut.ac.ir/article_5579.html
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.