مجله پژوهش های نوین در ریاضی
پیاپی 36 (خرداد و تیر 1401)

Cross-efficiency method is a useful tool for efficiency evaluation of decision-making units in data envelopment analysis. The issue of non-uniqueness of optimal weights in the cross-efficiency evaluation has reduced the usefulness of this powerful method. This paper introduces a new method for selection of weights profiles as the secondary goal in cross-efficiency with stochastic data. The issue of zero-weight which implies the exclusion of some variables from the assessments, is also addressed in the new proposed method. The provided weights selection method also reduces the weight disparity in the achieved weights profile. In the peer-restricted stochastic cross-efficiency evaluation, the new approach guarantees that different DMUs should not attach very different weights to the same variables. As the result, a common set of weights using the idea of similarity between sets of weights is achieved in the proposed computation method. Some numerical examples are also used for illustration and comparison purposes.

In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of hybrid functions. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations. Convergence analysis and some numerical results are presented to illustrate the effectiveness and accuracy of the method.

In this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory.

Fuzzy regression is a generalized regression model that shows the relationship between independent and dependent variables in the fuzzy environment. Fuzzy linear regression analysis is the generalization of regression models that is appropriate using all data based on a specific criterion. This paper uses an adaptive neural fuzzy inference system to analyze and predict a non-parametric fuzzy regression function with non-fuzzy inputs and symmetrical trapezoidal fuzzy outputs. To this end, a new hybrid algorithm is proposed in which fuzzy minimum squares and linear programming are used to optimize secondary weights. Algorithms are applied by multi layer validation to validate models. More precisely, the accuracy of the algorithms with simulations is fully confirmed. Finally, two simulation examples were used to examine the efficiency of the model, in which the data were defined as trapezoidal numbers and by teaching them and specifying the number of rules used, the unknown parameters were estimated.

In data envelopment analysis (DEA) models, the weak disposability axiom has been used for undesirable outputs such as environmental pollutants in many cases. Considering this axiom, different models are exhibited to assess the efficiency of units under evaluation. In this paper, we express duality in weak disposability models proposed by Kousmanen (2005) and Amirteimoori et al. (2017). In the following, economical interpretations of dual are represented in the abovementioned technologies. Also, projection points for inefficient units will be introduced; then, proposed methods will also be explained in an application that includes different designs for the production line of a company.

In this paper, we consider the Brato differential equation, in which the boundary condition values ​​are fuzzy values and the purpose is to calculate the approximate Solution. For this, first, using arithmetic operations on fuzzy data, we convert the Bratu differential equation into three sets of differential equations with exact value, and then, using the Tamimi and Ansari method (TAM), the approximate solution of the differential equation can be calculated. Finaly, two examples to express efficiency and simplicity by finding an approximate solution have been presented. Matmetica software has been used for all calculations and plots.

A new method for solving n-order fuzzy differential equation by using polynomial interpolationA new method for solving n-order fuzzy differential equation by using polynomial interpolationGiven the importance of the role of fuzzy differential equations in science and engineering,in this paper, we study a numerical method for solving N th order fuzzy differential equations under generalized differentiability. In this method a solution of fuzzy differential equation is approximated by fuzzy polynomial in the form of piece wise fuzzy polynomials in eachsub interval of interval solution. In special case, for solving second order fuzzy differential equation under generalized differentiability, according to the type of differentiability, four cases are considered, then fuzzy polynomial approximation in each cases for solving fuzzy differential equation were constructed. The order of the piece wise fuzzy polynomial in each sub interval of solution is two .Finally this method is illustrated by solving two second order fuzzy differentialequations under generalized differentiability.

In this paper, a semi-analytic approach is proposed to solve the oxygen diffusion problem.First, we discretize the partial differential equation of the oxygen diffusion problem in temporal direction using the backward finite difference Euler method. We achieve a sequence of free boundary problems in the form of ordinary differential equations (ODEs) in the spatial direction. The ODEs are then solved analytically and a recursive formula is presented to compute the solutions of the ordinary differential equations. The problems of finding unknown boundaries are reduced to nonlinear algebraic problems. Finally, the nonlinear algebraic problems are solved using the root-finding methods such as the false position method. The method proposed in this paper is easy to implement and a comparison with other numerical methods shows that the proposed approach is very efficient and gives very accurate numerical results.Some tables and figures are included to show the efficiency and effectiveness of the proposed technique.

Let G be a finite group and Z(G) be a subgroup of it. Suppose that for the finite group G, Pi_e(G) denotes the set of orders of elements of G. Then G is an EPPO-group if the orders of its elements are non-negative powers of primes. Also, for a subset A of G, let r_G(A) be the number of conjugacy classes of G that intersect A non-trivially. The purpose of this paper is to classify all finite EPPO-groups with the property r_G(G-Z(G))=7. We first verify the case where Z(G)=1. Then we verify the case where G/Z(G) is abelian. After that, we consider the case where G/Z(G) is non-abelian. We verify this case in three subcases where G/Z(G) is a p-group, a Frobenius group or a 2-Frobenius group. In fact, we show that the only groups which satisfy the intended property are the groups that are attained in the case Z(G)=1 and all of these groups are Frobenius groups.

In the last few decades there has been lots of discussion in the literature regarding robust optimization. Since Epsilon constraint is one of the most important technique in interactive problems, therefore in this paper, due to the importance of robust optimization and multi-objective programming problems, we consider Multi-Objective Linear Fractional Programming (MOLFP) problem in the presence of box-uncertainty in the coefficients of the objective functions. We propose an approach based on ε-constraint and Charnes-Cooper methods to obtain weakly robust efficient solutions, that have special importance in the literature, for a MOLFP problems in the presence of uncertain data. Charnes-cooper method is applied to reduce a fractional programm to a non fractional programm. At the end we write the robust counterpart of the UMOLFP model in the presence of the box-uncertainty and it's equivalent linear programming problem: Finally a numerical example is used to show the usefulness of the proposed approach.

 We establish new sufficient conditions which guarantee existence of solutions of equilibriumProblems:Let K be a nonempty subset of a topological space E and f . The problem of interest, called equilibrium problem, is defined as follows:Find x such that f(x,y)>0 for all y: This problem is very general in the sense that it includes, as special cases, complementarityproblems, fixed point problems, minimax problems, Nash equilibrium problem in non-cooperative games, optimization problems and variational inequality problems, to name a few. As a matter of fact, this formulation unifies these problems in a convenient way, and many of the results obtained.Our results are without making any convexity and monotonicity assumptions on the underlying problem data. Our results are based upon the relation between the KKM principle and equilibrium problems through constructing a certain family of subsets of a given Hausdorff topological vector space. We also illustrate our developments and describe applications by adapting our existence results for non-convex minimization problems.

In this paper we introduce the bi-VB groupoid and representation of double Lie groupoids, using the concept of vector bundle object in the category of Lie groupoids or Lie groupoid object in the category of vector bundle. A bi-VB groupoid is a bi-vector bundle object in the category of Lie groupoids. By a bi-vector bundle, we mean that a manifold by two vector bundle structures over two manifolds. We study some properties of the representation of double Lie groupoid as a cochains and smooth groupoid cohomology. We can show that there exists a one to one corresponding between a representation of a double Lie groupoid and two continues degree one operator which the space of normalized cochains, satisfying graded Leibniz identity and vanished their square. We study some properties and some example of bi-VB groupoids. And then we show that any representation of double Lie groupoids induced a bi-VB groupoid structure on its action groupoid.

This article first provides a brief overview of the structure of the classical Grassmann manifold(Grassmannian) and how the universal Grassmann manifold is constructed using maps. Also, the underlying topological space and its sheaf structure are introduced to some extent in a theorem. Then, we enter the topic of super-geometry and a new type of supergrassmannian is introduced by applying odd involution in super ringed space and gluing superdomains. In a similar way to the normal case, the next infinite supergrassmannians and the canonical super vector bundle on it are introduced in the supergeometry. Here our tools mainly include multilinear algebra between supermatrices and their induced mappings, the direct limit in the topology of the underlying spaces and the inverse limit in the structural sheaf of the spaces. Finally, we show that the resulting super bundle is a global member of the category of the super vector bundle; Structures that are used in the classification of super vector bundles and are in proportion to the homotopy classification.

Let H_μ=(h_(n,k) )_(n,k≥0) be the Hausdorff matrix associated with the probability measure . Graham Bennett in 1996 established the following extension of Carleman's inequality[sumlimits_{n = 0}^infty {prodlimits_{k = 0}^n {{{left| {{x_k}} right|}^{{h_{n,k}}}}} } le {e^{int_0^1 {|log theta |dmu (theta )} }}sumlimits_{n = 0}^infty {left| {{x_n}} right|} .,,,,,,,(1)]In this paper we show that the Hausdorff matrix in (1) can be replaced by any lower triangular matrix [A = {left( {{a_{n,k}}} right)_{n,k ge 0}}]for which the sum of each rows is one, provided that the constant in the right hand side, be replaced by[left( {mathop {inf }limits_{p > 1} left| A right|_p^p} right)]. . . . . . . . . As a consequence, we apply our results to Norlund matrices and weighted mean matrices to establish some new inequalities. Further, we show that being equal to 1 is an essential condition for the rows sum of A.

In a unit disk graph two vertices are adjacent if the distance between them is less than or equal to one with a two-dimensional Euclidean meter. The size of the maximal independent set in a graph G is called the independent number denoted by α(G). The size of the minimal connected dominating set in a graph G is called the connected domination number denoted by γ_c^((G)). A subset S of vertices in a graph is called a dominating set if every vertex is either in the subset or adjacent to a vertex in the S. A dominating set is connected if it induces a connected subgraph. A connected dominating set is often used as a virtual backbone in wireless sensor networks to improve communication and storage performance. Clearly the smaller virtual backbone gives the better performance.However computing a minimal connected dominating set is NP-hard. In other hand relation between the size of the minimal connected dominating set in a graph G is very important. The aim of this paper is to determine two better upper bounds of the independence number dependent on the connected domination number for a unit disk graph. Further we improve the upper bound to obtain the best bound with respect to the upper bounds obtained thus far.