مجله پژوهش های نوین در ریاضی
پیاپی 8 (زمستان 1395)

Design of assembly line is done in order to more coordinate a collection of some consecutive work stations for the aim of obtaining more productivity from the work stations and workers. The stations are arranged in a way to have a continuous and constant material flow. In this paper a multi-objective formulation for assembly line balancing is introduced. As a solution approach a two-step approach is proposed. In the first step the problem in a fuzzy environment is converted to a crisp problem and in the second step an efficient solution of the crisp problem is found by fuzzy programming approach. The efficiency of the proposed approach is shown by a numerical example.

Data Envelopment Analysis (DEA) deals with evaluating a set of decision-making units (DMUs) based on nonparametric mathematical approaches. In classical DEA models, the given set of factors of DMUs is divided into two categories, inputs and outputs, while in some practical problems there are some measures whose membership to these categories is unclear. It means these factors treat different input or output roll for various DMUs. This kind of factors is known as a flexible measure. The proposed models for this purpose are DMU-oriented in which each DMU evaluate its efficiency and classify flexible measures for all other DMUs regards to its benefit. This classification may not be optimal for every DMUs. In this paper, we present a model based on a common set of weights (CSW). The advantage of the proposed model is to classify flexible measures uniquely for all DMUs. At the end of paper, the proposed model is applied in an example of wind power farms.

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three examples of the effectiveness of the proposed method was evaluated. In all the calculations and diagrams of the software, Mathematica is used.
The advantage of the proposed method is that the algorithm is simple, appropriate and consistent with the exact solution provides a numerical answer. Examples and results presented in the previous section suggest this claim. A fast algorithm for the numerical solution for converting n fuzzy partition is also provided. The speed and simplicity of the algorithm allow any author to obtain a numerical answer with the help of this method it used to take.

Although discriminating between all efficient decision making units (DMUs) with identical efficiency is a very important subject in data envelopment analysis (DEA), it may not be an easy task, particularly when the decision maker wants to select one and only one efficient DMU among all. There are some papers that have proposed methods for finding an efficient DMU as the most efficient one but have some difficulties when used in practice. This paper points out the difficulties of the methods presented in two articles [Amin, G. R., (2009). Comments on finding the most efficient DMUs in DEA: An improved integrated model. Computers and Industrial Engineering 56, 1701-1702; Toloo, M., Nalchigar, S., (2009). A new integrated DEA model for finding most BCC-efficient DMU. Applied Mathematical Modelling, 33, 597-604]. In fact, in the present paper, it is proved by some examples that although some methods have principally been proposed in order to determine a single efficient DMU as the most efficient one, they may be unable to detect these DMUs.

In this article we survey the existence of best proximity points for a class of non-self mappings whichý satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [ýAý. ýAbkarý, ýMý. ýGabelehý, Best proximity points of non-self mappingsý, ýTopý, ý21, (2013)ý, ý287-295]ý which guarantees the existence of best proximity points for nonexpansive non-self mappings in the setting of uniformly convex Banach spaces.
We also introduce a new notion, ý called relatively asymptotic center, on a nonempty, bounded,ý closed ýand ýconvex ýpair ýof ýsubsets ýof aý ýHadamardý ýmetric space and ýas a result of our main conclusions, we will show that the asymptotic center of any sequence in a nonempty, bounded, closed and convex subset of a Hadamard space is singleton. Moreover, we obtain the other existence results of best proximity points for generalized nonexpansive mappings using the appropriate geometric properties of Hadamard spaces. Finally, we provide some examples to illustrate our main results.

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 and also if d(x,y)=2 then |f(x)-f(y)|1. The smallest positive integer k, for which there exists a coloring of G is denoted by . In 1993, Giriggs and Yeh conjectured that for every graph G, with maximum degree . In this paper, we give some upper bounds for coloring of graphs and we confirm this conjecture for squared graphs, line graphs and graphs without minor of K4 and K5.

In the global economy, crude oil is among the most important strategic goods that affects the performance of local and international markets. Prediction of the oil price has always been an important challenging topic in the global economy and producers and consumers have constantly been trying to improve their roll in the oil price changes and for many years OPEC has been one of the key players in this field of economy. Oil is considered as one of the most important financial resources for providing the budget of the OPEC country members. Oil price fluctuations, is one of the major causes of many economical crises among these countries. By applying the statistical models one can improve the performance of the oil price prediction dramatically and obtain results with less errors and higher precision. Therefore, in this paper, the nonlinear autoregressive model with a semi-parametric method is implemented to predict the oil price.

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kamei introduced the notion of the relative operator entropy and Furuta introduced the notion of the parametric relative operator entropy as a generalization of the notion of the relative operator entropy. These concepts can be described by the notion of perspective of some elementary functions and this description makes simplifier their verification. The relative operator entropy is concave and the parametric relative operator entropy is also concave for some suitable parameters. In this paper, we study some properties of the parametric relative operator entropy including its bounds. These bounds generalize the calculated bounds of the relative operator entropy by other authors and in particular the previous results will achieve.

The optimum use of the upstream resources, production corresponding to the market demands, and structural constraints for the optimum production with the less wastes during the most rapid time required by the market which finally result in the more profit for the shareholders are considered as the major objectives of this research.
In this research, for the purpose of increasing the efficiency and optimum production, a model with a sequence proportional to the constraints of the problem is proposed by use of zero–one, integer programming based on the operational research science. The gained mathematical model is studied and verified with the actual data of Jam Polypropylene Co. and executed during monthly periods with one year planning horizon that the expected results of this research will realize during the term of study and assessment will result in increase of net profit, decrease in product storage, the faster responding the market demand corresponding to the profit of the company by taking the structural constraints of the factory and production into account.

In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve cryptography system is proposed. The presented scheme, safe and efficient manner is able to meet the needs of a digital signature system meet the blind. Analysis and evaluation of the efficiency of the Protocol presented in comparison with that in the past has been raised, the superiority of the proposed method.