AUT Journal of Mathematics and Computing
https://ajmc.aut.ac.ir/
AUT Journal of Mathematics and Computingendaily1Mon, 01 Apr 2024 00:00:00 +0430Mon, 01 Apr 2024 00:00:00 +0430On the tree-number of the power graph associated with some finite groups
https://ajmc.aut.ac.ir/article_5064.html
Given a group $G$, we define the power graph $\mathcal{P}(G)$ as follows: the vertices are the elements of $G$ and two vertices $x$ and $y$ are joined by an edge if $\langle x \rangle \subseteq \langle y \rangle$ or $\langle y \rangle \subseteq \langle x \rangle$. Obviously the power graph of any group is always connected, because the identity element of the group is adjacent to all other vertices. We consider $\kappa(G)$, the number of spanning trees of the power graph associated with a finite group $G$. In this paper, for a finite group $G$, first we represent some properties of $\mathcal{P}(G)$, then we are going to find some divisors of $\kappa(G)$, and finally we prove that the simple group $A_6\cong L_2(9)$ is uniquely determined by tree-number of its power graph among all finite simple groups.Unsupervised feature selection by integration of regularized self-representation and sparse coding
https://ajmc.aut.ac.ir/article_5066.html
Due to the development of social networks and the Internet of things, we recently have faced with large datasets. High-dimensional data is mixed with redundant and irrelevant features, so the performance of machine learning methods is reduced. Feature selection is a common way to tackle this issue with aiming of choosing a small subset of relevant and non-redundant features. Most of the existing feature selection works are for supervised applications, which assume that the information of class labels is available. While in many real-world applications, it is not possible to provide complete knowledge of class labels. To overcome this shortcoming, an unsupervised feature selection method is proposed in this paper. The proposed method uses the matrix factorization-based regularized self-representation model to weight features based on their importance. Here, we initialize the weights of features based on the correlation among features. Several experiments are performed to evaluate the effectiveness of the proposed method. Then the results are compared with several baselines and state-of-the-art methods, which show the superiority of the proposed method in most cases.Approximate left $\varphi$-biprojectivity of $\theta$-Lau product algebras
https://ajmc.aut.ac.ir/article_4896.html
We continue \cite{sp1 glas} and we discuss approximately left $\varphi$-biprojectivity for $\theta$-Lau product algebras. We give some Banach algebras among the category of $\theta$-Lau product algebras which are not approximately left $\varphi$-biprojective. In fact, some class of matrix algebras under the notion of approximate left $\varphi$-biprojectivity is also discussed here.On binary decision hypertree (hyperdiagram)
https://ajmc.aut.ac.ir/article_5045.html
In computer science, a binary decision diagram is a data structure that is used to represent a Boolean function and to consider a compressed representation of relations. This paper considers the notation of T.B.T (total binary truth table), and introduces a novel concept of binary decision (hyper)tree and binary decision (hyper)diagram, directly and in as little time as possible, unlike previous methods. This study proves that every T.B.T corresponds to a binary decision (hyper)tree via minimum Boolean expression and presents some conditions on any given T.B.T for isomorphic binary decision (hyper)trees. Finally, for faster calculations and more complex functions, we offer an algorithm and so Python programming codes such that for any given T.B.T, it introduces a binary decision (hyper)tree.Generalized Ricci solitons on homogeneous Siklos space-times
https://ajmc.aut.ac.ir/article_5106.html
The class of homogeneous Siklos space-times is considered from algebraic point of view and the generalized Ricci solitons are completely classified.A modification of Hardy-Littlewood maximal-function on Lie groups
https://ajmc.aut.ac.ir/article_5157.html
For a real-valued function $f$ on a metric measure space $(X,d,\mu)$ the Hardy-Littlewood centered-ball maximal-function of $f$ is given by the `supremum-norm':$$Mf(x):=\sup_{r&gt;0}\frac{1}{\mu(\mathcal{B}_{x,r})}\int_{\mathcal{B}_{x,r}}|f|d\mu.$$In this note, we replace the supremum-norm on parameters $r$ by $\mathcal{L}_p$-norm with weight $w$ on parameters $r$ and define Hardy-Littlewood integral-function $I_{p,w}f$. It is shown that $I_{p,w}f$ converges pointwise to $Mf$ as $p\to\infty$. Boundedness of the sublinear operator $I_{p,w}$ and continuity of the function $I_{p,w}f$ in case that $X$ is a Lie group, $d$ is a left-invariant metric, and $\mu$ is a left Haar-measure (resp. right Haar-measure) are studied.The novel self-organizing map combined with fuzzy C-means and K-means convolution for a soft and hard natural digital image segmentation
https://ajmc.aut.ac.ir/article_5127.html
Digital image segmentation plays an important role in noise reduction and pixel clustering for pre-processing of deep learning or feature extraction. The classic Self-Organizing Map (SOM) algorithm is a well-known unsupervised clustering neural network model. This classic method works on continuous data instead of discrete data sets with a widely scattered distribution. The novel SOM(SOM2) modelling solved this problem for the classic, simple tabular discrete data set but not for the digital image data. As the essence of digital image pixels data are different from tabular datasets, we have to look at them differently. This paper proposes exploiting the novel SOM method with a hybrid combination of the fuzzy C-Means and K-means convolution filter as image segmentation and noise reduction with soft and hard segmentation as entropy reduction for natural digital images. The main approach of this paper is the segmentation of image contents for the reduction of noises and saturation pixels by entropy criteria. Based on the resulting paper, the combination of SOM2 with FCM for soft segmentation 47%-and the combination of SOM2 with k-means convolution for hard segmentation 33% can reduce the entropy of the original image on average.On a group of the form $2^{11}:M_{24}$
https://ajmc.aut.ac.ir/article_5189.html
The Conway group $Co_{1}$ is one of the $26$ sporadic simple groups. It is the largest of the three Conway groups with order $4157776806543360000=2^{21}.3^9.5^4.7^2.11.13.23$ and has $22$ conjugacy classes of maximal subgroups. In this paper, we discuss a group of the form $\overline{G}=N\colon G$, where $N=2^{11}$ and $G=M_{24}$. This group $\overline{G}=N\colon G=2^{11}\colon M_{24}$ is a split extension of an elementary abelian group $N=2^{11}$ by a Mathieu group $G=M_{24}$. Using the computed Fischer matrices for each class representative $g$ of $G$ and ordinary character tables of the inertia factor groups of $G$, we obtain the full character table of $\overline{G}$. The complete fusion of $\overline{G}$ into its mother group $Co_1$ is also determined using the permutation character of $Co_1$.On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^{*}$-closed ideal
https://ajmc.aut.ac.ir/article_5164.html
In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra $A$ with respect to its $w^*$-closed ideal $I$ , say $I$-Connes biprojectivity. Some matrix algebras and Banach sequence algebras are studied under this new notion. Also with some mild assumptions, the relation between $I$-Connes biprojectivity and left $\varphi$-contractibility is given, where $\varphi$ is a $w^*$-continuous multiplicative linear functional on $A$. As an application, we characterize Connes biprojectivity of some Lipschitz algebras.Existence and convergence of fixed point results for noncyclic $\varphi$-contractions
https://ajmc.aut.ac.ir/article_5171.html
In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp&iacute;nola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.Text steganography by changing the black color
https://ajmc.aut.ac.ir/article_5177.html
Recently, a serious problem in communications is security. Hiding data is one of the most important security techniques. Steganography is the art and science of hiding information in a cover media. Texts are the most usual method of communication and so they are very suitable for cover objects. In this paper, we give a new technique for text steganography. There exist different models, such as RGB, HSL, HSV to determine a color. The main goal of the proposed algorithm is the fact that some different but very similar colors in RGB have the same code in HSL. We use this fact to hide data. For this purpose, first we find a color $B'$ in RGB, which is very similar to black in such a way that they have the same code in HSL. Then, by changing the color of each character of the text to black or $B'$, we conceal the information. We will show that the capacity of this method is better than some other methods of text steganography, and then we show that the invisibility of this algorithm is very high, which is the most prominent feature of the proposed technique.Almost Ricci soliton in $Q^{m^{\ast}}$
https://ajmc.aut.ac.ir/article_5190.html
In this paper, we will focus our attention on the structure of h-almost Ricci solitons on complex hyperbolic quadric. We will prove non-existence a contact real hypersurface in the complex hyperbolic quadric $Q^{m^{\ast}}, m\geq3,$&nbsp;admitting the gradient almost Ricci soliton. Moreover, the gradient almost Ricci soliton function f is trivial.&nbsp;Generalized Lorentz Ricci solitons on $3$-dimensional Lie groups associated to Bott connection
https://ajmc.aut.ac.ir/article_5195.html
In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat = \lambda g$ associated to the Bott connection $\nabla^B$, here ${X}$ is a vector field and $\lambda , a, b, c$ are real constants such that $c\neq 0$. A complete classification of this structure on $3$-dimensional Lorentzian Lie groups will be presented.Variational problem, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation
https://ajmc.aut.ac.ir/article_5197.html
The goal of this article is to compute conservation law, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation using the homotopy operator, the $\mu$-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the $\mu$-conservation law of these three equation.Strong domination number of a modified graph
https://ajmc.aut.ac.ir/article_5207.html
Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertices and edges of $G$.Composition operators from Zygmund spaces into Besov Zygmund-type spacesâ€Ž
https://ajmc.aut.ac.ir/article_5211.html
&lrm;In this paper first&lrm;, &lrm;the boundedness and compactness of a composition operator from Zygmund space to Besov Zygmund-type space are studied&lrm;. &lrm;Then we study this concepts for this operator by using the hyperbolic-type analytic Besov Zygmund-type class&lrm;. &lrm;Finally&lrm;, &lrm;we show the relation between the hyperbolic-type analytic Besov Zygmund-type class and the meromorphic (or spherical) Besov Zygmund-type class&lrm;.Lipschitzness effect of a loss function on generalization performance of deep neural networks trained by Adam and AdamW optimizers
https://ajmc.aut.ac.ir/article_5213.html
The generalization performance of deep neural networks with regard to the optimization algorithm is one of the major concerns in machine learning. This performance can be affected by various factors. In this paper, we theoretically prove that the Lipschitz constant of a loss function is an important factor to diminish the generalization error of the output model obtained by Adam or AdamW. The results can be used as a guideline for choosing the loss function when the optimization algorithm is Adam or AdamW. In addition, to evaluate the theoretical bound in a practical setting, we choose the human age estimation problem in computer vision. For assessing the generalization better, the training and test datasets are drawn from different distributions. Our experimental evaluation shows that the loss function with a lower Lipschitz constant and maximum value improves the generalization of the model trained by Adam or AdamW.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 survey on usage of smartphone accelerometer sensor in intelligent transportation systems
https://ajmc.aut.ac.ir/article_5238.html
The numerous capabilities of smartphones have made them suitable alternative to expensive tools and methods in intelligent transportation systems. This study surveys the literature on the role of the accelerometer of smartphones in intelligent transportation applications. At first, the opportunities and challenges of using the accelerometer are stated. Then, the architecture of using this sensor including preprocessing, feature extraction, mode detection, reorientation and applications are explained. Finally, different applications that have used the accelerometer of mobile phones in the intelligent transportation systems have been investigated.Interpolatory four-parametric adaptive method with memory for solving nonlinear equations
https://ajmc.aut.ac.ir/article_5248.html
The adaptive technique enables us to achieve the highest efficiency index theoretically and practically. The idea of introducing an adaptive self-accelerator (via all the old infor-mation for Steffensen-type methods) is new and efficient to obtain the highest efficiency index.In this work,we have used four self-accelerating parameters and have increased the order of convergence from 8 to 16.I.e.any new function evaluations the convergence order improve up to 100%. The numerical results are compared without and with memorymethods and confirm that the proposed methods have more efficiency index than other methods.Some results concerning asymptotic distribution of functional linear regression with points of impact
https://ajmc.aut.ac.ir/article_5255.html
Lately, issues related to functional linear regression models with points of impact have garnered significant interest. While the literature has addressed the estimation of parameters for this model with scalar response, less attention has been paid to the asymptotic distribution of the impact points coefficients estimators. In recent literature, the asymptotic distribution has been pointed out in a particular case, but the demonstration of its validity has not been adequately addressed. By explicating the necessary requirements, we derive an important part of the asymptotic distribution of the impact points coefficients estimators in a general setting. This is a fundamental result for finding the asymptotic distribution of the impact points coefficients estimators. Moreover, we perform a simulation study to exhibit the efficiency of the obtained results.$K$-contact generalized square Finsler manifolds
https://ajmc.aut.ac.ir/article_5257.html
We study almost contact generalized square Finsler manifolds and introduce the notion of $K$-contact Finsler structures. Then, we characterize generalized square $K$-contact almost contact manifolds. As an application, we show that every $3$-dimensional Lie group admits a left-invariant generalized square Finsler structure.Exploring the use of efficient deep learning algorithms for lower grade gliomas cancer MRI image segmentation: A case study
https://ajmc.aut.ac.ir/article_5261.html
This paper presents a study on the use of efficient deep learning algorithms for lower grade gliomas (LGG) cancer image segmentation. The study compares the performance of various pretrained atrous-convolutional architectures and pre-trained U-Nets, and proposes a transformer-based approach for fast and efficient LGG segmentation. The study evaluated the performance of various models and found that DeepLabV3+ with MobileNetV3 as a backbone achieved the best per-formance among the pretrained models. However, the proposed transformer-based approach surpassed the aforementioned methods and achieved competitive results with higher scores. The study also employed transfer learning techniques to fine-tune the pretrained models on the LGG dataset, which significantly im-proved segmentation performance with a relatively low amount of training samples. The study highlights the importance of selecting the appropriate pre-trained model for the specific segmentation task. The proposed transformer-based approach offers several advantages over traditional convolutional neural networks, including efficient use of memory and better generalization. It can also process images of arbitrary sizes, making it more flexible and scalable for use in clinical settings. Segmenting medical images presents a difficult task because of the complexity of medical images and variations in imaging conditions. The use of efficient deep learning algorithms can help address these challenges by reducing computational cost, training time, and improving segmentation performance. The findings of this study can be useful in the development of accurate and efficient diagnostic tools for LGG cancer detection and treatment planning. The proposed transformer-based approach has the potential to improve medical image segmentation for other types of cancers and diseases. Overall, this study demonstrates the potential impact of deep learning and transfer learning application in medical image segmentation, with significant implications for improving cancer diagnosis and treatment.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.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, 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.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.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.$C^*$-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.An 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.Structure 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.An iterative scheme for a class of generalized Sylvester matrix equations
https://ajmc.aut.ac.ir/article_5358.html
Utilizing the AOR approach, we have devised an iterative scheme to tackle the generalized Sylvester matrix equation, which has proven to be a complicated and challenging problem to solve. Our focus is to conduct a thorough analysis of the convergence properties of this new method. To showcase the effectiveness of the proposed approach, we provide a numerical example that demonstrates its practical application.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.