Journal of Mahani Mathematical Research
Volume:13 Issue: 2, Summer and Autumn 2024

The main purpose of the present paper is about characterizing the properties of the perfect fluid space-time that admits the gradient Ricci-Bourguignon soliton. This gives some results about the stability of the energy-momentum tensor and also under some conditions pursues that a perfect fluid space-time is Ricci symmetric. As a special case, when a perfect fluid space-time is equipped with the Ricci-Bourguignon soliton which has Ricci biconformal vector field, we show that the metric of this space is Einstein.

Recently, Alizadeh and Shafaei (2023) introduced some estimators for varentropy of a continuous random variable. The present article applies these estimators and construct some tests of fit for Inverse Gaussian distribution. Percentage points and type I error of the new tests are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests.

In this paper, we delve into Bayesian inference related to multi-component stress-strength parameters, focusing on non-identical component strengths within a two-parameter Rayleigh distribution under the progressive first failure censoring scheme. We explore various scenarios: the general case, and instances where the common location parameter is either unknown or known. For each scenario, point and interval estimates are derived using methods including the MCMC method, Lindley's approximation, exact Bayes estimates, and HPD credible intervals. The efficacy of these methods is evaluated using a Monte Carlo simulation, and their practical applications are demonstrated with a real data set.

In this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated. Moreover, some results about the Moore-Penrose inverse, the Drazin inverse and the numerical range of some reciprocal matrices are obtained. In particular, the relations between reciprocal matrices, Drazin-Dagger matrices and star order are established. Also, some properties of the generalized inverses of the conjugate EP matrices are studied. To illustrate the results, some numerical examples are also given.

‎Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a graph with non-central conjugacy classes of $G$ as its vertex set. Two vertices $L$ and $K$ in $\Gamma(G)$ are adjacent if there are $a \in L$ and $b \in K$ such that $ab = ba$.    This graph  is called the commuting conjugacy class graph of $G$.  The purpose of this paper is to compute  the commuting conjugacy class graph of the finite $2-$groups $G_n(m)$ and $G[n]$.

The Fruit Fly Optimization algorithm is an intelligent optimization algorithm. To improve accuracy, convergence speed, as well as jumping out of local optimum, a modified Fruit Fly Optimization algorithm (MFFOV) is proposed in this paper. The proposed algorithm uses velocity in particle swarm optimization and improves smell based on dimension and random perturbations. As a result of testing ten benchmark functions, the convergence speed and accuracy are clearly improved in Modified Fruit Fly Optimization (MFFOV) compared to algorithms of Fruit Fly Optimization (FFO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Teaching-Learning-Based Optimization (TLBO), Genetic Algorithms (GA), Gravitational Search Algorithms (GSA), Differential Evaluations (DEs) and Hunter–Prey Optimizations (HPOs). A performance verification algorithm is also proposed and applied to two engineering problems. Test functions and engineering problems were successfully solved by the proposed algorithm.

Recently, infinite and finite dimensional generalized Hilbert tensors have been introduced. In this paper, the authors further introduce infinite and finite dimensional generalized Cesaro tensors as a generalization of Cesaro matrices and discuss the properties of these structured tensors. Next, some  upper bounds of $Z_{1}$-spectral radius of generalized Cesaro tensors  and  generalized Hilbert tensors are given,  which improves the existing ones. Finally, we obtain conditions under which a generalized Cesaro tensor is column sufficient tensor.

‎In this paper, we delve into frame theory to create an innovative iterative method for resolving the operator equation $ Lu=f $. In this case, $ L:H\rightarrow H $, a bounded, invertible, and self-adjoint linear operator, operates within a separable Hilbert space denoted by $H$. Our methodology, which is based on the GMRES projective method, introduces an alternate search space, which brings another dimension to the problem-solving process. Our investigation continues with the assessment of convergence, where we look at the corresponding convergence rate. This rate is intricately influenced by the frame bounds, shedding light on the effectiveness of our approach. Furthermore, we investigate the ideal scenario in which the equation finds an exact solution, providing useful insights into the practical implications of our work.

In this paper, an operational matrix method based on the Bell polynomials  has been presented to find approximate solutions of high-order Volterra integro-differential equations. This method  uses a simple computational manner to obtain a quite acceptable approximate solution. The main characteristic behind this method lies in the fact that on the one hand, the problem will be reduced to a system of algebraic equations and on the other hand, the efficiency and accuracy of the Bell polynomials  for solving these equations are acceptable. The convergence analysis of  this method will be shown by preparing some theorems. Moreover, we will obtain an estimation of the error bound for this algorithm. Finally, some examples are presented to illustrate the applicability, efficiency and accuracy of this  scheme in comparison with some  other well-known methods such as Legendre, Bernoulli, Taylor and Bessel polynomial algorithms

In this article, we define probabilistic normed quasi-linear spaces and provide some introductions and examples to clarify the structure of these spaces. We then investigate the generalized Hyers-Ulam stability of the (additive) Cauchy functional equation in probabilistic normed quasi-linear spaces by using a version of the fixed point theorem.

We apply the basic Lie symmetry method to investigate the time-dependent negative-order Calogero-Bogoyavlenskii-Schiff (vnCBS) equation‎. ‎In this case‎, ‎the symmetry classification problem is answered‎. ‎We obtain symmetry algebra‎ ‎and create the optimal system of Lie subalgebras. We obtain the symmetry reductions and invariant solutions of the considered equation using these vector fields‎. ‎Finally‎, ‎we determine the conservation laws of the vnCBS equation via the Bluman-Anco homotopy formula‎.

In the present paper, we introduce a new subclass of normalized analytic and univalent functions in the open unit disk associated with Sigmoid function. Coefficient estimates, convolution conditions, convexity and some other geometric properties for functions in this class are investigated. Also, subordination and inclusion results are obtained.

In this paper, we are going to obtain some normal supercharacter theories of a group of order $6n$ with the presentation  $ U_{6n} = <a, b: a^{2n} = b^{3 } = 1, a^{-1}ba = b^{-1}>$ in special cases.  We will  also prove  that the automorphic supercharacter theories of this group can be computed  with the other methods.

‎‎‎‎‎In this paper, we define a new concept called ``strongly orthogonality preserving mappings '' for inner product modules, which extends the existing notion of ``orthogonality preserving mappings". Also, we provide a condition that is both necessary and sufficient for a linear map between inner product modules to be strongly orthogonality preserving. Some examples on the definition are given.

‎‎In this note, we present an equivalent condition for linear preservers of group majorization induced by closed subgroup $G$ of $O(\mathbb{R}^n)$. Moreover, a new concept of majorization  is defined on $\mathbb{R}^3$ as acu-majorization and this is extended for $3 \times m$ matrices. Then we characterize all its linear preservers on $\mathbb{R}^3$ and $M_{3,m}$.

Let $V$ be a unitary vector space. Suppose $G$ is a permutation group of degree $m$ and $\Lambda$ is an irreducible unitary representation of $G$. We denote by $V_{\Lambda}(G)$ the generalized symmetry class of tensors associated with $G$ and $\Lambda$. In this paper, we prove the existence of orthogonal bases consisting of generalized decomposable symmetrized tensors for the generalized symmetry classes of tensors associated with unitary irreducible representations of group $U_{6n}$, as well as dihedral and dicyclic groups.

For a finite group $G$, define $ \psi^{\prime \prime}(G)=\psi(G)/|G|^2 $, where $\psi(G)=\sum_{g\in G}o(g)$ and $o(g)$ denotes the order of $g \in G $.  In this paper, we give a criterion for $p$-solvability by the function  $\psi''$, where $ p \in \{7,  11\} $. We prove that if $ G $ is a  finite group and $\psi''(G)>\psi''({\rm PSL}(2, p))$, where $p \in \{7, 11\}$, then $G$ is a $p$-solvable group.

One of the special cases of type-2 fuzzy sets are the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that have imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods.

Let $R$ be a commutative ring with identity. In this paper, we study 2-prime ideals of a Dedekind domain and a Pr\"{u}fer domain. We prove that a nonzero ideal $I$ of a Dedekind domain $R$ is 2-prime if and only if $I=P^{\alpha}$, for some maximal ideal $P$ of $R$ and positive integer $\alpha$. We give some results of ring $R$ in which every ideal $I$ is 2-prime. Finally, we define almost 2-prime, almost 2-primary and weakly 2-primary ideals, and investigate some properties of these ideals.

A semi-analytical solution is proposed for the bioheat equation, which includes the epidermis, dermis, and hypodermis layers in the presence of a surface pulsed heat source. A switching time surface heating/cooling source, which has therapeutic applications in human tissue burning, is used. The interface temperature is calculated by matching the temperature and heat flux between two adjacent layers. A high-performance computing algorithm is designed and implemented by combining semigroups theory, Laplace transform, and convolution operators in each layer. It is proved that proposed solution is consistent, convergent and stable. The reliability, performance and efficiency of semi-analytical solutions are compared using the bioheat transfer module of COMSOL software based on standard finite element methods. Numerical results for three different medical examples are given. Influences of blood pressure on temperature along the layered skin for different switching and final times are discussed.

The Index Generalized Minimal RESidual (IGMRES) algorithm is designed to compute the Drazin-inverse solution of a linear system of equations $Ax=b$, where $A$ is an arbitrary square matrix with index $\gamma$. If $\gamma=0$, then the this method method coincide with Generalized Minimal RESidual (GMRES) method. Also, the {$k^{th}$} ideal index generalized minimal residual polynomial of $A$ is introduced and the roots of these polynomials are studied. Moreover, by numerical results the convergence rate of these methods are compared by two examples.

The Restricted Mean Survival Time (RMST) serves as a valuable and extensively utilized metric in clinical trials. However, its application becomes intricate when dealing with data affected by length-biased sampling, rendering traditional inference strategies inadequate. To overcome this challenge, we advocate for the adoption of nonparametric techniques. One notably promising approach is the Empirical Likelihood (EL) method, which furnishes robust results without the need for stringent parametric assumptions. In practical scenarios, the underlying sampling distributions often remain elusive, necessitating adjustments in the case of parametric methodologies. The EL method has demonstrated its efficacy in addressing such complexities. Consequently, this paper introduces the EL method for computing RMST in situations involving both length-biased and right-censored data. Additionally, we introduce the concept of adjusted empirical likelihood (AEL) to further enhance the coverage probability, particularly when dealing with smaller sample sizes. To gauge the performance of the EL and AEL methods, we conduct simulations and rigorously compare their results. The findings unequivocally demonstrate that AEL-based confidence intervals consistently provide superior coverage probability when juxtaposed with EL-based intervals. Lastly, we substantiate the practical applicability of our proposed method by employing it in the analysis of a real dataset.

Thermal-aware virtual machine (VM) placement has emerged as a critically significant research domain in response to the escalating demand for energy-efficient and dependable cloud data centers. Addressing the imperative need for resource optimization and reduced energy consumption, the virtual machine placement problem seeks to strategically allocate VMs to physical servers while adhering to stringent thermal constraints. This paper intricately surveys the state-of-the-art techniques employed in thermal-aware VM placement, encompassing both static and dynamic approaches. Our comprehensive analysis delves into influential factors, including workload characteristics, server heterogeneity, and advanced thermal management techniques. By elucidating the intricacies of these considerations, our review offers a nuanced understanding of the complex VM placement landscape. Importantly, we spotlight key challenges and identify open research issues, presenting a roadmap for future investigations. This review paper stands as a pivotal resource, providing invaluable insights for researchers and practitioners navigating the evolving landscape of thermal-aware virtual machine placement in cloud data centers.

‎In this paper‎, ‎we define the concept of $J$-hyperideals which is a generalization of $n$-hyperideals‎. ‎A proper hyperideal $I$ of a multiplicative hyperring $R$ is said to be a $J$-hyperideal if $x,y\in R$ such that $x \circ y \subseteq I$‎, ‎then either $x \in J(R)$ or $y \in I$‎. ‎We study and investigate the behavior of the $J$-hyperideals to introduce several results‎. ‎Moreover‎, ‎we extend the notion of $J$-hyperideals to quasi $J$-hyperideals and 2-absorbing $J$-hyperideals‎. ‎Various characterizations of them are provided‎.

In this paper, we consider large-scale low-rank Sylvester differential matrix equations. We present two iterative methods for the approximate solution of such differential matrix equations. In the first method, exploiting the extended block Krylov method, we approximate the exponential matrix in the exact solution. In the second method, we first project the initial value problem onto an extended block Krylov subspace and acquire a low-dimensional low-rank Sylvester differential matrix equation. Then the reduced Sylvester differential matrix equation is solved by the backward differentiation formula method (BDF) and the derived solution is used to construct the low-rank approximate solution of the original initial value problem. The iterative approaches are followed until some certain accuracy is obtained. We give some theoretical results and some numerical examples to show the efficiency of the proposed methods.

The aim of this paper is to introduce the cyclic-Fibonacci hybrid sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid sequence modulo $m$, the method will be given to determine the period lengths of this sequence according to the different $m$ values. In the final part of this paper, we study the cyclic-Fibonacci hybrid sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups $(2,2,2)$, $(2,n,2)$ and $(n,2,2)$ as applications of the results produced.

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an operational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black-Scholes model

This survey proposes a new application of the inverse data envelopment analysis (InvDEA) in the problem of merging decision-making units (DMUs) to improve the performance of DMUs by removing congestion. Congestion is a factor in reducing production; therefore, removing it decreases costs and increases outputs. There are two significant subjects in the merging DMUs. Estimating the inherited inputs and outputs of a new production DMU with no congestion is the first problem while achieving a pre-specified efficiency level from the merged DMU is the second one. Both problems are examined using the ideas of inverse DEA and congestion. Using Pareto solutions to multiple-objective programming problems, sufficient conditions for inherited input/output estimates with no congestion and increasing efficiency are created. Besides, an example is perused for the reliability of the proposed approach in basic research institutes in the Chinese Academy of Science (CAS) in 2010.

In this paper, we determine the fuzzy similarity measures of the U. S. state rankings with respect to domestic violence, female homicide, and sexual violence against teens. We find that the fuzzy similarity measures are low. We then consider the best state rankings and determine the fuzzy similarity measures of this ranking a with the previous three rankings. We also develop some theoretical results concerning fuzzy similarity measures.

The aim of this paper is to introduce a generalized $(3+1)$-Kadomtsev-Petviashvili equation which is used to describe waves in a ferromagnetic medium. The equation's bilinear form is created and the new homoclinic test approach based on the Hirota bilinear form is used to find numerous novel precise solutions. These accurate solutions, which are depicted in the contour, two-dimensional and three-dimensional graphs, show the evolution of periodic characteristics. The modulation instability is used to investigate the stability of the obtained solutions. Additionally, the development of the fusion soliton is examined, as well as the fusion phenomenon in the traveling wave solution is described in the physical discussion.  For this evolution equation, the study indicates new mechanical structures and various characteristics. The derived results back up the model that was proposed. These discoveries open up a new avenue for us to investigate the concept further.

‎Let $\{Y_i; i = 1,\ldots,n \}$ be a length-biased sample from a population with cumulative distribution function $F(\cdot)$‎. If the probability of an item selected in the sample is proportional to its length‎, ‎then the distribution of the observed length is known as the length-biased distribution‎.‎We consider the kernel-type estimator $F_n^s(\cdot)$ of $F(\cdot)$‎. ‎Under suitable conditions‎, ‎the extended Glivenko-Cantelli theorem for $F_n^s(\cdot)$ is proved‎.

For a graph $G$, the third neighborhood degree index of $G$ is defined as: $$ND_3(G)=\sum_{ab\in E(G)}\delta_G(a)\delta_G(b)\Big(\delta_G(a)+\delta_G(b)\Big),$$ where $\delta_G(a)$ represents the sum of degrees of all neighboring vertices of vertex $a$. In this short paper, we establish a new lower bound on the third neighborhood degree index of trees and characterize the extremal trees achieving this bound.

A Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. Using character theory, it is proved that the Frobenius kernel is a normal subgroup of its Frobenius group. In this paper, we present some group-theoretical proofs that the Frobenius kernel is a subgroup of its Frobenius group under certain conditions.

‎    This paper introduces a modified version of the Variational Iteration Method, incorporating $\mathbb{P}$-transformation. We propose a novel semi-analytical technique named the modified variational iteration method   for addressing fractional differential equations featuring tempered Liouville-Caputo derivatives. The modified variational iteration method emerges as a highly efficient and powerful mathematical tool, offering exact or approximate solutions for a diverse range of real-world problems in engineering and the natural sciences, specifically those expressed through differential equations. To assess its effectiveness and accuracy, we scrutinize the modified variational iteration method by applying it to three problems related to the heat-like multidimensional diffusion equation with a fractional time derivative in a tempered Liouville-Caputo form.

This paper focuses on investigating the equivalence problem for fifth-order differential operators (FODOs) on the line under general fiber-preserving transformations. Utilizing the Cartan method of equivalence, the study specifically addresses the gauge equivalence problem, seeking to establish the conditions for two FODOs to be related by a fiber-preserving transformation. By analyzing the properties of these operators, the research aims to identify conditions for their transformation while maintaining the fiber structure. The systematic approach of the Cartan method is employed to derive the necessary conditions for gauge equivalence between these FODOs. The study aims to enhance understanding of the equivalence problem for FODOs and shed light on fiber-preserving transformations that uphold gauge equivalence.