مجله پژوهش های نوین در ریاضی
پیاپی 27 (آذر و دی 1399)

The relative efficiency of a set of decision makers with multiple inputs and outputs is obtained by analyzing data coverage. One of the main assumptions of the classic models of data envelopment analysis is to consider each decision maker as a black box. Also, the independence of inputs and outputs is relative to each other. In this paper, the performance of subway stations in Tehran is determined by considering the two stage network structure in which the first stage indicates efficiency and the second stage demonstrates its effectiveness, and then, with regard to the presence of indicators, the input depends on In the first and second stages, the two stage models were modified and the resulting model was used for 71 metro stations in Tehran, and finally, 3 effective stations and 2 stations were effective. In total, of the 71 stations, no one of the metro stations have been operating efficiently.

The unit disk graph is used to model a wireless sensor network when all sensors have the same communication radius. Hence, the following two optimization problems have been investigated by the researchers: maximal independent set in the network and minimal network dominating set. Since these problems are Np-hard, several algorithms have been presented for their approximation. In this paper, we have presented a honeycomb graph and algorithmic matrix methods for approximating the maximal independent set in the network. Finally, we have confirmed the validity of the algorithm and its complexity and studied it with a numerical example. Keywords: Wireless network, Independent set, Dominating set, Algorithm, Honeycomb network E. Leeuwen, Approximation Algorithms for Unit Disk Graphs, technical report, institute of information and computing sciences, utrecht university, (2004), UU-CS-2004-066. N. Bourgeois, F. Della Croce, B. Escoffier. V.Th. Paschos, Fast algorithms for min independent dominating set, Discrete Applied Mathematics 161, (2013), pp. 558-572

Many issues are expressed in terms of various applied sciences such as physics, chemistry, and economics, which are concerned with the examination of variations of one or more variables, by differential equations. The prediction of climate, quantum mechanics, wave propagation and dynamics of the stock market is some of these examples, whose quick and accurate solution will have tremendous effects on human life, and therefore several methods have been proposed for solving differential equations.The main objective of this study was to investigate the applicability of the antler colony genetic algorithm to the production of experimental solutions and improve them to produce numerical analytic-numerical solutions of various types of ordinary differential equations. An antler colony optimization algorithm (ACO) has an appropriate algorithm with high convergence accuracy and speed for finding approximate solutions for solving optimization problems using probability function dependent on the amount of residual effect of anti-movement. Genetic algorithm is also an optimization method based on mutated and intersect operators with a wide search area that prevents the algorithm from trapping in the local response. The combination of these two algorithms creates an algorithm with maximum efficiency. Examining various examples in the final section of the article will highlight the speed and accuracy of the proposed method.

In the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local fractional partial differential equation on a cantor set. The non-differentiable exact and approximate solutions are obtained for kind of local fractional linear and nonlinear equations. It is shown that the used method is an efficient and easy method to implement for linear and nonlinear problems arising in science and engineering. In this article, we emphasize on the LFYLVM method which is a combination form of local fractional variational iteration method and Yang-Laplace transform. Most of the obtained solutions from this method are in series form that converge rapidly to exact or approximate solutions. Illustrative examples demonstrate that the method is able to reduce the volume of computation compared to the existing classical methods.

Let G be a simple graph with vertices v_1,..., v_n. The adjacency matrix of G denoted by A(G) is an n×n matrix whose the entry (i,j) is 1 if v_i and v_j are adjacent and is zero otherwise. By the eigenvalues of G we mean the eigenvalues of A(G). Let λ_1 (G)≥λ_2 (G)≥⋯≥λ_n (G) be the eigenvalues of G. In this paper we obtain some results related to graphs with at most three non-negative eigenvalues. We obtain all non-connected graphs with this property. In addition, we find some families of connected graphs with this property. In particular we study two following families of graphs:1. Graphs such as G with exactly two positive eigenvalues and one zero eigenvalues. In other words graphs such as G with λ_1 (G)>0 , λ_2 (G)>0 , λ_3 (G)=0 and λ_4 (G)0 , λ_2 (G)>0 , λ_3 (G)>0 and λ_4 (G)

Let $Delta$ be the open unit disc in the complex plane $mathbb{C}$, i.e. $Delta={zin mathbb{C}:|z|< 1}$ and $mathcal{H}(Delta)$ be the class of functions that are analytic in $Delta$.Also, let $mathcal{A}subset mathcal{H}(Delta)$ be the class of functions that have the following Taylor--Maclaurin series expansionbegin{equation*} f(z)=z+sum_{n=2}^{infty} a_nz^nquad(zinDelta).end{equation*}Thus, if $finmathcal{A}$, then it satisfies the following normalized conditionbegin{equation*} f(0)=0=f'(0)-1.end{equation*}The set of all univalent (one--to--one) functions $f$ in $Delta$ is denoted by $mathcal{U}$. Also, we denote by $mathcal{LU}subset mathcal{H}$ the class of all locally univalent functions in $Delta$. Let $f$ and $g$ belong to class $mathcal{H}(Delta)$. Then we say that a function $f$ is subordinate to $g$, written bybegin{equation*} f(z)prec g(z)quad{rm or}quad fprec g,end{equation*}begin{linenomath}if there exists a Schwarz function $w$ with the following propertiesbegin{equation*} w(0)=0quad{rm and}quad |w(z)|0}$, $varpi(0)=1$ and $varphi'(0)>0$.

In this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusionsIn this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusions

In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica. In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica.

Let S be a simplicial affine semigroup of dimension r and R=K[[S]] be the semigroup ring assigned to S, where K is a field. Then R is a Noetherian ring of krull dimension r. When r=1, S is a numerical semigroup whose assigned semigroup ring is a one dimensional Cohen-Macaulay ring. In this case, all each set of S is a finite set, and the number of its maximal elements with respect to the natural relation, is equal to the type of R. But in general, when r>1, the Apery sets of S are not necessarily finite. In this paper, we introduce r Apery sets of S whose intersection is a finite set and determines the type and the canonical module of R. This set coincides with an Apery set, when r=1. In particular, we extend the known facts about canonical module of numerical semigroups to all Cohen-Macaulay simplicial affine semigroups.

In this paper, we first define the notions of orbitally continuous and orbitally complete on a C*-algebra-valued metric space. We show that if T is an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d), where X is a nonempty set and A is a C*-algebra with the relation ⪯ and if T orbitally complete and satisfies some conditions, then for any x∈X the iterated sequence {Tn (x)} converges to a fixed point of T. Also, we prove that an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d) under conditions has a periodic point. It is prove that an orbitally continuous self-map on a C*-algebra-valued b-metric space (X,A, d) under which conditions has at least a fixed point. In additions, if (X,A, d) be a complete C*-algebra-valued metric space and T has some property. Then T has a fixed point in X provided that there exists x0∈X such that T2 (x0)≠x

In this paper, as motivated by a work of Daffer et al. [6], we state and prove some theorems for set valued mappings and by them we conclude the existence of coincidence points and fixed points of a general class of set valued mappings satisfying a new generalized contractive condition which extends some well-known results in the literature. For this reason, firstly, by using a recent work of Eshaghi et al [11], we define the notion of orthogonal sets and by the notion, we consider our results in strongly orthogonal complete metric spaces (not necessarily complete metric spaces). In addition, this article has a new and different view on the subject and consists of several non-trivial examples which signify the motivation of such investigations. Also, in the end of this paper, by using our examples, we show that our results are real generalization of the previous results in the literature.

Let , and be nonempty subsets of a matric space . Then the mapping is called cyclic if , and . Consider the following optimization problem Let , certainly if the condition be true for some then it is best answer for optimization problem , that we called it triple best proximity point of .In this paper‎, first ‎we introduce the notion of 3-cyclic summing Meir-Keeler contractions as a generalization of 3-cyclic summing contractions, then we obtain the conditions for the existence of a triple best proximity point for these class of mappings in the metric spaces with property UC‎. Our results in this paper are true for a n-cyclic summing Meir-Keeler contraction just we work with order 3 for the simplicity of proofs. Note that, our results are generalizations of some existing theorems with shorter and simpler proofs. Note that, our results are generalizations of some existing theorems with shorter and simpler proofs.

A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc. -------------- A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc.

Data Envelopment Analysis (DEA) is a relatively new data oriented approach for evaluating the performance of a set of peer entities called Decision-Making Units (DMUs) which convert multiple inputs into multiple outputs. In a relatively short period of time DEA has grown into a powerful quantitative, analytical tool for measuring and evaluating performance. DEA has been successfully applied to a host of different types of entities engaged in a wide variety of activities in many contexts worldwide. The issue of measuring the cost efficiency in manufacturing and economic systems is one of the most important issues in the world. In the real world, there are manufacturing and economic systems that are composed of independent units. One of the ways to measure the cost efficiency for economic and production systems is the DEA technique. This paper presents two network DEA models to measure the cost efficiency of a network model with identical processing components taking into account the individual processing functions in the network structure. In this paper, we examine the cost efficieny model of Färe et al., and through modifying the model of Färe et al., a model has been developed to measure the cost efficiency in economic and manufacturing networks.