JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2016 | Volume:2 | Issue:7|Papers Count:10

This paper represents a technique for finding optimal paths with multiple indexes in a graph. Up to the present time, all optimal paths have been determined upon one index, say, distance for which an evaluation method exists. In this paper firstly we define multiple indexes for each edge in such a way that anyone can treat the factor for assigning an optimal path. Here, we use Data Envelopment Analysis (DEA) technique for designing a model that can identify optimal paths with multiple indexes, and separate them from the other paths.

A 2-rainbow dominating function (2RDF) of a graph G is a function F from the vertex set V(G) to the set of all subsets of the set {1, 2} such that for any vertex v Î V(G) with f(v)=Æ the condition ÈuÎN(v)f(u)={1, 2}is fulfilled, where N(v) is the open neighborhood of v. A maximal 2-rainbow dominating function on a graph G is a 2-rainbow dominating function f such that the set {wÎV(G)|f(w)=Æ} is not a dominating set of G. The weight of a maximal 2RDF f is the value w(f)=SvÎV|f(v)|. The maximal 2-rainbow domination number of a graph G, denoted by gmr(G), is the the minimum weight of a maximal 2RDF of G. In this paper, we continue the study of maximal 2-rainbow domination number. We characterize all graphs G of order n whose maximal 2-rainbow domination number is equal to 2 or 3. Finally, we characterize all graphs G of order n with g(G)³5 for which gm2r=n-2.

The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different economical and political elements. In order to earn the best model, at first we study the effectiveness of different stochastic differential equations models and then using the daily OPEC oil price in years 2003 to 2016, according to the high oscillation of oil price due to the various economical and political creases, we divide the data to four parts and estimate the unknown parameters of the equations in these time periods using the General Method of Moment. At last, the best model can be defined by attention to the main price chart and numerical simulations.

Computing the exact ideal and nadir criterion values is a very ‎ important subject in ‎ multi- ‎ objective linear programming (MOLP) ‎ problems ‎‎. In fact ‎, ‎ these values define the ideal and nadir points as lower and ‎ upper bounds on the nondominated points ‎. ‎ Whereas determining the ‎ ideal point is an easy work ‎, ‎ because it is equivalent to optimize a ‎ convex function (linear function) over a convex set which is a convex optimization problem ‎, ‎ but the problem of computing ‎ the nadir point in MOLP is equivalent to solving a nonconvex optimization ‎ problem whose solving is very hard in the general case ‎. ‎‎ In this paper ‎, ‎ a bi-level linear programming problem is presented for obtaining the nadirpoint in MOLP problems which can be used in general to optimize a ‎ linear function on the nondominated set ‎, ‎ as well ‎. Then ‎, ‎ as one of the solution methods of this problem ‎, ‎ a ‎ mixed-integer linear programming problem is presented which obtains ‎ the exact nadir values in one stage.

In conventional DEA, measures are classified as either input or output. However, in some real cases there are variables whose status is not known as input or output before assessment. These variable are known as flexible measures. One of the most important economic dimensions for ensuring the success of a company is the efficiency with which it uses its resources. Therefore, centering on Assessment costs and profit of financial institutions is an important issue. Aware of the importance of this subject, we propose the cost and profit efficiency model in presence of flexible measures due to the many application of these variables in real world. The proposed models determine the status of each flexible measure as an input or output statue and simultaneously maximize profit/ minimize cost in profit/cost model.In order to evaluate the capability model the proposed model are applied to a real-life data set of 50 U.S. banks.

Non-parametric DEA is a technique on the basic of mathematical programming to determine the efficiency of homological decision making units. DEA models changes in demand cause changes in variations in output levels and also will cause changes in a firm’s inefficiency. Often a firm can adjust input influencing on the output level. Models designed with technique on DEA that considers changes in demand and with a short-run capacity planning method quantifies the effectiveness of a firm’s production system under demand uncertainty.The DEA is assumed that accurate data input, output and demand. In some cases data observed with a difference or mistake, so the uncertainties involved in achieving predetermined goals. To measure the effectiveness of the techniques DEA data is important in the evaluation of uncertainty. Data input, output and demand can be interval and probable and order, ect. This paper focuse uncertain data that it is interval and models will be propone for calculation effectiveness and the effect of uncertain demand with interval data.

The problem of generalized equilibrium problem is very general in the different subjects. Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequality problem and fixed point problem. In this article, a new iterative algorithm is introduced based on theextragradient method. Under suitable conditions, a weak convergence theorem for finding a common solution of a generalized equilibrium problem, a variational inequality problem and the set of fixed points of a finite family of strictly pseudo contraction mappings is proved. Our results improve and generalize some recent results in the literature. Finally, we give a numerical example to show the validity of the results.

Data envelopment analysis which is a nonparametric technique for evaluating relative efficiency of the decision making units with multiple inputs and outputs, has been a very popular method among researchers. While this nonparametric technique is popular, it has some drawbacks such as lack of discrimination in efficient units and weights dispersion. The present study, which is a model based on a multi-criteria data envelopment analysis has been proposed to moderate the homogeneity of weights dispersion by using goal programming. The proposed model minimized variances of input and output weights. The result shows that the dispersion of input and output weights has been balanced. Furthermore, the power of discrimination has been improved in DEA.

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing the quadratic cost functional. In addition for greater precision, the included integrals in Volterra integral equation and the cost functional are approximated using Legendre-Gauss-Lobatto nodes and weights. These nodes are considered as collocations points. The optimal control problem is reduced to a minimization so that the control vector and the state vector are considered as an approximation of solution vectors based on radial basis functions. Two numerical examples are presented and results are compared with the analytical solutions to demonstrate the applicability and accuracy of the proposed method.

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties. We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.