In this paper, we introduce the concept of the Rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’ s contraction principle, the Kannan’ s fixed-point theorem and the Chatterjea’ s fixed-point theorem. Also we give an application to the fixed-circle problem.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating Rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

In this article, a queuing system with finite capacity, referred to as M/M/m/K, is analyzed for m ≥ 2, where K represents the system's capacity and m indicates the number of servers. Initially, a function known as the system cost function is introduced. This function is based on the number of customers present in the queue and the number of servers available. The main objective is to identify the optimal number of servers, termed mOpt, that minimizes the system cost function. This optimal configuration, denoted as M/M/mOpt/K, is termed the optimal system. To illustrate the concept, a numerical example is provided, showcasing various values of K to determine the optimal systems. The analysis covers key performance metrics such as the average number of customers in the queue and the entire system, the average waiting time of the customers both in the queue and the system, and a metric referred to as the average degree of customer satisfaction within these queuing systems. Through this comprehensive approach, the study aims to provide valuable insights into optimizing queuing systems for better efficiency and customer satisfaction.

Genomic aspects of animal’ s hybrid zone are studding in the recent decade. Introgression of gene in the evolution process is a very challenging issue among scientists. Gene flow reduction is probably a consequence of the speciation genes involvement. In this study, the influence of different geographical factors on gene introgression in hybrid index (genomic cline) was analyzed. We investigated 127 D-Loop sequences containing 140 independent loci for analysis: 82 sequences from M. m. castaneus and 45 sequences from M. m. domesticus. Results of the Introgress and Barrier programs showed gene invasion of M. m. domesticus subspecies in genomic background of M. m. castaneus subspecies. So, M. m. domesticus subspecies acts as an invasive subspecies and M. m. castaneus as a genome receptor. Also, our results showed that environmental elements such as mounts, lakes and salt marsh play the role of the barrier between the two subspecies in the studied regions. The results of the genomic cline represent the asymmetric genomic influence.

Packing Rectangular shapes into a Rectangular space is one of the most important discussions on Cutting & Packing problems (C&P); such as: cutting problem, bin-packing problem and distributors pallet loading problem, etc. Assume a set of Rectangular pieces with specific lengths, widths and utility values. Also assume a Rectangular packing space with specific width and length. The objective function is, to pack the pieces into the space in Order to get the maximum sum of utility value of the packed pieces. To generate the related packing pattern this paper proposes a new formulation metl10dbased on the column generation, approach. In this method one each cycle of the algorithm; a one-dimensional pattern is generated based on the shadow prices 'Of the Simplex method. The set of generated one-dimensional patterns are used: to construct the two-dimensional packing pattern. Also, the proposed model and the present models in the.state-of-1beart have been compared.

In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called M-fuzzifying closure operators, and some properties of M-fuzzifying closure operators are discussed. The M- fuzzifying matroid induced by an M-fuzzifying closure operator can induce an M-fuzzifying closure operator. Finally, the characterizations of M-fuzzifying acyclic matroids are given.

In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer’s balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and their service- times follow exponential distribution. The number of servers in long run depends on the queue-length. We obtain equilibrium queue size distribution. The expression for expected number of customers in the system in the long run has been obtained. Some other performance measures have also been provided. In order to match our results with earlier work, special cases are discussed. The numerical results are presented to verify the validity of the proposed analytical method.

One main group of a transportation network is a discrete hub covering problem that seeks to minimize the total transportation cost. This paper presents a multi-product and multi-mode hub covering model, in which the transportation time depends on travelling mode between each pair of hubs. Indeed, the nature of products is considered different and hub capacity constraint is also applied. Due to the transport volume and related traffic, a new priority M/M/c queuing system is considered, in which products with high priority are selected for service ahead of those with low priority. The objectives of this model minimize the total transportation cost and total time. Besides, because of the computational complexity, a multi-objective parallel simulated annealing (MOPSA) algorithm is proposed and some computational experiments are provided to illustrate the efficiency of the presented model and proposed MOPSA algorithm. The performance of this algorithm is compared with two well-known multi-objective evolutionary algorithms, namely non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES)‎.‎