JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2017 | Volume:3 | Issue:10|Papers Count:10

A new approach or model to the dynamic DEA, referred to as the adjusted dynamic DEA, is proposed in this study. Adjusted dynamic DEA optimizes the production activity of DMUs by introducing adjustment variables to modify the interconnecting activities between consecutive terms, solving conflicts that arise between terms and between management and shareholders. The non-oriented SBM model is used as a base model and is extended to the adjusted dynamic framework, where adjustment variables are introduced. In order to examine the applicability of the proposed method, the model is applied to evaluate the efficiency of ten branches of ten branches of an Iranian bank during three consecutive terms. The adjusted dynamic SBM model under variable return to scale (VRS) is solved and reference units for each inefficient DMU are identified. In addition, the slacks and adjustment variables are analyzed and further suggestions about the efficient conditions to the management are provided.

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixedcharges) to satisfy the demand of each customer. As the problem is NP-hard, a moderate sized instance of this problem becomes intractable for general-purpose solvers. In order to overcome this difficulty, a Lagrangian relaxation approach is proposed. The computational experiments show that the Lagrangian relaxation algorithm is able to solve large sized problems with optimality gap compared to general-purpose solvers.

In this paper, we introduce the notion of sesquilinear map on B (H). Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality. In particular, we prove that if F is a quadratice map, A, B ∈ B (H) and p, q > 1 with 1/p + 1/q = 1, p ≤ q, then F(A - B) + F(1−p) A− B) ≤ pF(A) + qF(B).

In this paper, parametric technology display and a mathematical model of technology spillover as a different approach based on the technology changes would be discussed. The recently action that will be accomplished through formation matrices of technological changes, measure of technology spillover and other concepts along with a variety of matrices types. Several examples are given and the result would be helpful in mathematics, management and technology fields.

It is essential for most organizations and financial institutes to be able to evaluate their decision-making units (DMUs), when there is only a ratio of inputs to outputs (or vice versa) available. In this paper, we will propose our two-stage DEA-R models, which are a combination of data envelopment analysis and ratio data, based on value efficiency. Integrating value efficiency into data envelopment analysis would lead to identification of units with the highest productivity, from the manager’s perspective. Considering the managers’ opinions in DEA models in order to measure value efficiency would be an interactive method of DMU evaluation. generally, this study will suggest some two-stage DEA-R models, introducing the most productive units from the managers’ viewpoints. In the end, the obtained value efficiency will be our criterion for evaluation of DMUs in two-stage networks with ratio data.

Let ℳ be a family of monomorphisms in the category A. To study mathematical notions in a category A, such as injectivity, tensor products, flatness, with respect to a class M of its (mono) morphisms , one should know some of the categorical properties of the pair (A, M). In this paper we take A to be the category Pos-S of S-partially ordered sets and M=Mpo to be a particular class of monomorphisms, to be called partially ordered regular pure (po-pure)} monomorphisms paper In this. we investigate some categorical properties such as limits and colimits for this class.

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractional derivative, which has not been undertaken before. By using the function approximations based on the Bernstein basis and mentioned operational matrices, the optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative is reduced to a system of algebraic equations that easily solvable by Newton’s iteration method. We apply the proposed method for solving two examples. The numerical results show that present method is simple in implementation and the approximate solutions are in high accuracy. Some comparisons with other method guarantee that the results are reasonable. Also, the obtained solutions approach to classical solutions as the order of the fractional derivatives approach to 1, as expected.

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lower- C 2 functions. The class of proxregular functions covers all convex functions, lower- C 2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal sub-differential. Then, the definition of prox-regular functions have been developed in Banach and Hilbert spaces. In this paper, the parametric proxregular functions are defined using limiting sub-differentials. Also, a partial second order sub-differential is defined here for extended real valued functions of two variables corresponding to its variables through coderivatives of first-order partial sub-differential mappings. Then, relations between maximal monotonicity of the partial first-order sub-differentials of these functions and the positive semi definiteness of the coderivatives of partial first order sub-differential mapping are investigated. Finally, we present necessary and sufficient conditions for ¶ -proxregular functions to be convex based on positive-semi definiteness of the partial second-order sub-differentials mappings.

Cost efficiency measures the cost of resource by output production. While conventional cost efficiency models set targets separately for each DMU, There are cases where the Central decision making is seeking the above targets, and at the same tries to obtain the target of Min cost efficiency for the total consumption. In this paper we consider that there is a centralized decision maker (DM). In such case, the DM has an interest in minimizing the cost efficiency of individual units at the same time it wants that total input consumption is reduced or output production is increase. We proposed new centralized resource cost efficiency model measurement on the base of Farrell cost efficiency model and Centralized resource allocation of Lozano and Villa model that will reduce resource allocation total cost efficiency, however it is possible for some inputs to increase. The preferences and advantages of this model are present some examples.

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an ultra-group over a group, there exists a normal subgroup of that certain group. Moreover, by proving this feature that a monomorphism in groups preserve the ultra-groups over groups, we show that, corresponding to any monomorphism in groups, there is an ultragroup homomorphism on the subgroups of those groups. Finally, we prove isomorphism theorems for ultra-groups. These theorems connect three notions subultra-group, normal subultra-group, quotient ultra-group, and directly, similar to the isomorphism theorems in group theory and module theory are proved.