مجله پژوهش های نوین در ریاضی
پیاپی 26 (مهر و آبان 1399)

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress than corresponding Huang’s method. Also, these ABS-type models need less number of multiplications for a square system. In this paper, in order to economize and compress required space, we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches. we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches.

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense. The computational method is based on bilinear spline interpolation and finite difference approximation. The convergence order of the proposed method investigated in the mean square norm and the accuracy of proposed scheme is analyzed in the perspective of the mean absolute error and experimental convergence order. The proposed method is considered in determining statistical indicators of Gompertzian and Nicholson models. The fractional stochastic delay Gompertzian equation is modeled for describing the growth process of a cancer and the fractional stochastic delay Nicholson equation is formulated for explaining a population dynamics of the well-known Nicholson blowflies in ecology.

The concept mapping and the Vee diagram are important tools for improving the level of conceptual learning of mathematics in all educational levels that can play an important role in the learner's achievement. The purpose of this study is to use a concept mapping and Vee diagram, to calculate the volume of an object by the integral, includes the reaction of what a teacher really knows, the way of expressing them, introducing the time of using knowledge and ability to justify them. It also shows that being familiar with formal definitions and mathematical principles do not mean to fully understand the concepts, and their internal complexities, and teaching process. According to the fact that conceptual learning has a mutual impact on the teacher and the learner, then the concept mapping and the Vee diagram can play an important role in teaching, learning and evaluation.

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a universe. There are many studies on the relations between generalized rough set approximation and rough topological space. In this paper, We are defined some properties of an n-ary relation such as reflexive, symmetry, strongly symmetry, quasi-transitive, n- transitive and n-equivalence on a set . We introduce topological method to generalized rough set and study the relationship between topological theory and rough set theory. By using an n-ary tolerance relation and quasi-transitive relation, we define a topology on nonempty set . In the end, we prove some topological properties such as quasi-discreteness, connectivity, compactness, quasi-metric able, separateness.

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers .In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers .In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers .In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers .

Vendor performance plays a key role in price, quality, timely delivery and service in achieving the goals of the supply chain. Given this, today's supplier performance has become a critical element in the success or failure of a company. In this study, an idealized planning model with multi-criteria decision-making approach with network analysis tool based on the expansion of fuzzy quality function has been developed. Also, a new way of ranking, selecting, and assigning orders to suppliers is provided. To this end, the concept of expanding fuzzy quality function and network analysis are used to evaluate and rank suppliers and the math planning model for assigning orders to suppliers. The method presented in this paper is a feasible, practical, and useful method for identifying and ranking suppliers as well as assigning orders to them. The advantage of this model compared to similar methods in using QFD and ANP tools is to measure the priorities and needs of the company to rank suppliers, which can listen to the voice of the customer and take their demands, as well as integrate the two tools with planning Ideal for ordering a new approach. Based on the results of this research, technology and timely delivery are the most important features in order to evaluate contractor selection. Selection of contractors in such a way that at the same time returns from the supplier, delays and costs of supply are the least possible, are the most important results of this research.

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evolution equation of the first nonzero eigenvalue of the buckling problem on closed Riemannian manifold (compact and without boundary Riemannian manifold) along the unnormalized Ricci flow and normalized Ricci flow and by using them, we prove that the first nonzero eigenvalue and some quantities dependent to this eigenvalue are monotonic along the Ricci flow, under the some geometric conditions. Then, on special manifold such as homogeneous, 3- dimensional, 2-dimensional manifolds, we study the evolutionary behavior of this eigenvalue. Especially in the 2-dimensional state, depending on the value of the scalar curvature along the normalized Ricci flow, we find the quantities dependent on the first eigenvalue that are monotonic under the normalized Ricci flow. Finally, we give examples of soliton states and Einstein manifolds, and we obtain the evolution of the first eigenvalue of the buckling problem under the Ricci flow on these examples.

In this paper, we prove that a Banach-algebra A is 𝛙-amenableas Long as matrix Banach-algebra 𝐀 ⊗ 𝐌𝒏 is 𝛙 ⊗ 𝐈-amenable which 𝛙 is ahomomorphism form A into A. Morever, for Banach-algebras A and B, weshow that 𝛙-amenability of A and 𝛗-amenability of B are equivalent with𝛙 ⊗ 𝛗-menability of 𝛉-lau product 𝑨 ×𝜽 𝑩 in which 𝛗 is also ahomomorphism on B and 𝛉 is a character on B.

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matching integral claw-free graph and K_2 is the only connected matching integral graph with a perfect matching. In this work, we characterize mathching integral graphs according to their order. We determine all connected matching integral graphs on at most seven vertices. We show that there are exactly eight matching integral graphs up to seven vertices. In addition, we prove that any connected matching integral graph on eight vertices has a 3-matching and its size is fourteen. Finally, we characterize all connected matching integral graphs with maximum vertex degrees at most three.

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are reviewed.In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are reviewed.In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a

Data envelopment analysis (DEA) is a method for evaluating the relative efficiency of a set of firms in a production process. Estimation of cost efficiency is one of the branches of performance evaluation. Cost efficiency evaluates the ability of producing current output with minimum available cost. Now let's assume that there are several groups of firms that operate separately and have different technologies, but are centrally managed, or in other words, their source of raw materials is shared, but each of these groups has different costs for these resources. Traditional DEA models do not offer any suggestions for calculating the cost efficiency in such situations where firms are grouped into different technological groups and the input's costs are different. In this paper, using the concepts of cost efficiency and meta-frontier and using the rational relation between cost efficiency and technical efficiency, a method is proposed to calculate the cost efficiency of firms in different technological conditions. There is also a way to use the transfer of units to improve their performance. The method presented in this study is used in a numerical example and a real case application and their results are explained.

In this paper, a bi-objective pharmaceutical supply chain network under uncertainty demand and transportation costs is modeled and developed. To control the uncertainty parameters, the robust optimization method is considering. The main objective of this paper determines the number and location of potential facilities such as drug manufacture centers and drug distribution centers by considering the minimizing the total costs and minimizing the maximum unsatisfied demand for distribution of drugs to demand zones. In this paper, production time, delivery, and drug perishable time is also considered in modeling. To solve the model, an example is designed and the multi-decision TH method is used. The results obtained the model shows this method is effective in finding the Pareto front at the right time. The results obtained the model shows this method is effective in finding the Pareto front at the right time.The results obtained the model shows this method is effective in finding the Pareto front at the right time.

Data Envelopment Analysis (DEA) is an appropriate tool for estimating various types of efficiency including Cost Efficiency (CE). Identifying and identifying inefficiency resources plays an important role in analyzing unit performance in order to plan for improving the status of Decision Making Units (DMUs). Now , if information on the inputs and outputs and pricing information of the evaluated units is available, we can calculate the lack of profit and revenue and cost optimization with respect to their inefficiencies. In this paper, we intend to determine the production possibility set (PPS) a new price and a new cost, based on which a new inefficient source and a new source selection of price vectors in a non competitive environment (that is , in the event of a possible change of loss due to the incorrect in Input prices And outputs from the Decision Making Unit to other Decision Making Units (DMUs)).

In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value of this matrix is not greater than the number of variables of the problem. Then, using this double parameter scaled quasi Newton formula, an explicit formula for calculating the step length in the steepest descent method is presented and therefore, this method does not require the use of approximate methods for calculating step length. The numerical results obtained from the implementation of the algorithm in MATLAB software environment are presented for some optimization problems. These results show the efficiency of the proposed method in comparison with other existing methods.