JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2018 | Volume:3 | Issue:12 |Papers Count:10

Although the importance of locating in manufacturing and service companies is not a new issue, one of significance applications is to determine the appropriate location for warehouses in manufacturing workshops warehouses to the maintenance of materials or products. In any organizations, Finding the suitable site for warehouses establishments to increase customer service and efficiency is one of the most important and costly issues. The warehouse location is the main decision and structurally multi-criteria that includes quantitative and qualitative objectives. In this study, we apply an MADM technique to achieve the primary ranking for the proposed and potential warehouse locations of the company, and then put them as the input of the UTAStar, which is a new and more practical to inference utility functions from past decision data. We will investigate the utility of the results and define the desirability of ranked options for evaluating and selecting of warehouse space.

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, introducing the concept of the generalized embedding and the generalized injection, we study Császár product of generalized spaces in the category of generalized topological spaces. Using by the tools of category theory, we describe the results of classifying on the generalized injective spaces in which these spaces are characterized as generalized embedding of Császár product with the product topology of two points Sierpinski space. Finally, the generalized dual-injection spaces as the objects of a special subcategory of the generalized topological spaces are studied for which all singlepoint subsets are closed.

In this paper, we study the existence of the following optimum solution for the system of differential equation (1)        y’= Ay (t) + ¦(t, y (t))     t Î J = [0, T]    y (t0)=y2, (2)        y’= Ay (t) + g (t, y (t))   t Î J = [0, T]    y (t0)= y1 in a Hilbert spaces in which ¦, g: J×H®H are single-valued maps, {A (t)} tÎJ is a family of linear operators in H and y1 y2 Î H.We prove the existence of the pair (x, y) such that x , y are the solution of differential equation (1) and (2) and ||x-y||=||y1-y2||The pair (x, y) is called the optimum solution of the system of differential equation. Under suitable conditions on ¦, g and family of linear operators {A (t)}tÎJ. The results of the existence of the optimal solution are obtained by applying the best proximity points for the integral equation to the differential equation system.

Some of the parameters in issues of the reality world are uncertainty. One of the uncertain problems with the qualitative parameters is economic problems such as bankruptcy problem. In this case, there is a probability of dealing with imprecise concepts including the intervals regarding the official’s viewpoint, organizations’ managers. Accordingly, this article uses the concepts of data envelopment analysis (DEA) game theory’ applications that it is appeared in all areas of studies, and combining it with uncertainty models like intervals, assess bankruptcy and specify the pessimistic and optimistic interval for bankruptcy assessment that hep us to assess uncertain concepts in economics and in the problems that we have certain, converting to interval programming a, is studied problems simply.

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equations of the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral equation to the solution of a system of algebraic equations. The precision and error analysis have been carefully and structurally studied and it has been emphasized that the proposed method for a variety of linear two-dimensional linear Fredholm linear integral equations with continuous kernel of polynomial type is completely accurate and error-free. On the other hand, with the help of the Maple Math Software, it is very easy to calculate the Boubaker polynomial coefficients of the solution. Also, we compared the results of present method with the results of other available methods to provide the validity, accuracy and efficiency of the technique.

In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate solutions of nonlinear differential equations. The developed convergence has been shown and its details are discussed. Additionally, a convenient method is considered for selecting an optimal value of the auxiliary parameter, via minimizing the residual error over the domain of problem. The effectiveness of the method and the accuracy of the proposed algorithm are illustrated by the implementation of physical problems such as Sturm-Liouville problem, Airy equation, and Quantum mechanical harmonic oscillator problem. The numerical results and obtained demonstrate clearly reflect the accuracy of the method and its convergence.

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed with fuzzy graphs or bipolar graph. With definition of fuzzy n- polar sets this problem was resolved. But all of this information is partly true and partly false. So this information can not be shown as well with n- polar fuzzy graphs. In this article introduces n-polar intuitionistic set and then we define n-polar intuitionistic graph the extension of the n- polar fuzzy graph. Also, some basic concepts such as the cartesian product, composition, union and join in the graph with proving theorems and examples are also provided.

In this paper, to solve a linear one-dimensional Volterra integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space. Then we obtain the solution of integral equation in terms of the basis functions. The examples presented in this paper show validity of the method. But this method does not provide results for nonlinear onedimensional Volterra integral equations of the second kind. In this case for calculation Fourier cofficients the new method should be given. Thus the next focus on providing a method for calculating Fourier cofficients in the nonlinear mode. Also we think that this method can be generalized to linear two-dimensional Volterra integral equations of the second kind and we worked on this in the another paper.

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace. Thus every permutation matrix over ℂ is a quasi-permutation matrix. For a given finite group  G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field ℚ, and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. Thus, c(G) ≤ q(G) ≤ p(G). In this paper, we investigate the relationship between these quantities for finite nilpotent groups. In fact, we show that if G is a nilpotent group with no direct factor of order 6 and G = p1 × ⋯ × pr is a decomposition of G as a direct product of nontrivial Sylow subgroups, then c(G) = c(P1) + ⋯ + c(pr). In particular as a consequence, we show that if G is a nilpotent group of odd order, then c(G) = q(G) = p(G).

In this paper some properties of the complement of a new graph associated with a commutative ring R are investigated .This new graph, denoted by  W*(R), is an undirected graph whose vertex set is the set of all nontrivial ideals of R and two distinct vertices I and J are adjacent if and only if J. Ann (I)=(o) or I. Ann (J)=(o). Then, while studying some properties of graph complement W*(R), we provide a necessary and sufficient conditions for reduced rings R so that W*(R) has no isolated vertices. Moreover, the rings R are characterized for which W*(R) is planar. In addition, some bounds for domination number of aforementioned graph are presented.