مجله پژوهش های نوین در ریاضی
پیاپی 15 (پاییز 1397)

The classic overall profit needs precise information of inputs, outputs, inputs and outputs price vectors. In real word, all data are not certain. Therefore, in this case, stochastic and fuzzy methods use for measuring overall profit efficiency. These methods require more information about the data such as probability distribution function or data membership function, which in some cases may not have sufficient information to estimate them, and only we have knowledge about the parameters so that they change in a convex space that is closed and bounded. Therefore, in this paper, we consider a budget uncertainty model in the robust optimization problem that able to adjust the conservative degree. The robust model by the input and output price vectors is proposed to compute overall profit efficiency measure. To illustrate the application of the proposed method, a numerical example is presented and the results show that the robust overall efficiency of the decision making units is higher than the optimistic model.

In assessing the relative efficiency of decision-maker units by classical Data Envelopment Analysis (DEA) models, the status of the data is determined from the input or output points of views. In real issues, there are some data whose statuses are debatable. Some decision making units consider them as input to achieve higher efficiency while some other decision making units consider them as output, but these data are known as flexible variables. Thus, these data are known as flexible variables. Several parametric and non-parametric models have been introduced for categorizing such data. In most of the status-oriented models (input or output based) introduced to determine the status of flexible data, different statuses of a model can produce different results in determining the statuses of the flexible variable. In non-status models, the value of M is also used to select the main constraint and to remove the waste constraints. In these models, by choosing different values for M, different results are achieved in determining the status of the flexible variable, the efficiency and return to scale of decision-making units. To solve these problems in DEA, a non-status model is proposed which, in addition to determining the status of the flexible variable, can obviate the computational error, and the problems caused by the presence of M in the model. The advantages of the proposed model are compared with other models with an empirical example.

Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring, named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. generically Gorenstein) and is generically maximal Cohen-Macaulay (resp. a generically canonical module), then is generically Cohen-Macaulay (resp. generically Gorenstein). We also defined the notion of generically quasi-Gorenstein ring and we investigate when is generically quasi-Gorenstein. In addition, it is shown that is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions. Finally it is shown that if R is approximately Gorenstein, then is approximately Gorenstein.

In this paper, the notion ofgraph operationsdisjunction and symmetric difference on bipolar fuzzy graphs are defined and it is proved that the new graph is a bipolar graph. Furthermore,the new concepts of bipolar fuzzy graphs calledupperstrong and lower strongbipolar fuzzy graphare introduced and some related properties investigated. Finally, an application of bipolar fuzzy graph is explnaid.

The Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs‎. ‎In Data Envelopment Analysis (DEA)‎, ‎it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS‎. ‎Although DEA models can determine the efficiency of a Decision Making Unit (DMU)‎, ‎but they cannot present efficient frontiers of PPS completely‎. ‎The notion of defining hyperplanes is crucial to marginal discussions‎, ‎marginal rates‎, ‎marginal rates of substitution‎, ‎sensitivity analysis‎, ‎returns to scale‎, ‎and in particular‎, ‎the efficiency analysis of DMUs‎. ‎In this paper‎, ‎we propose a new method to determine all strong efficient(Pareto-efficient) DMUs and strong defining hyperplanes of the PPS with variable returns to scale which strong efficient DMUs are located on them‎. ‎Furthermore‎, ‎we apply the proposed method to find the normal vectors or gradient of the strong defining hyperplanes of the PPS including strong efficient DMUs‎. ‎Consequently‎, ‎the equations of these hyperplanes are determined‎. ‎To illustrate the ability of the proposed method‎, ‎some numerical examples are finally provided‎. ‎Our method can be easily implemented using existing packages for operation research‎, ‎such as GAMS.

Next, we study the stability of this type of functional equation. Clearly, the function - holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate these spaces of holomorphic functions on the upper half plane from a new aspect which has not been considered up to now. Indeed we prove that without any necessary condition on a weight such as restricting the rate of growth from below or above (constructing the upper bound or lower bound) or limit condition (except the continuity on the upper half plane) any weighted spaces of holomorphic functions on the upper half plane has a special subspace which can be written as countable intersection of closed sets

In ‎this ‎paper, ‎we ‎study ‎the ‎relation ‎between ‎the ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎with ‎the ‎lattice theory. ‎We ‎introduce ‎the ‎concepts ‎of ‎the ‎lattice ‎of ‎soft ‎sets, ‎full ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎and next, we ‎verify ‎some ‎properties ‎of ‎them. We ‎prove ‎that ‎the ‎lattice ‎of ‎the ‎soft ‎sets ‎on ‎a fixed parameter set is isomorphic to the power set of a set with respect to set inclusion. In ‎particular, ‎we ‎characterize ‎the ‎atoms ‎in ‎the ‎lattice ‎of ‎the ‎soft ‎sets and the lattice of full soft Lie algebras. ‎After that, ‎we ‎introduce ‎the ‎compact ‎elements in the full soft Lie algebras ‎and ‎we present the necessary and sufficient conditions for the compactness and atomicness ‎of the lattice of full soft Lie algebras. We show that if a full soft Lie algebra is a compact element of the ‎lattice ‎of full soft Lie algebra then the parameter set is finite and the Lie algebra is finitely generated. In the sequel, we study the relationship between prime ‎and ‎maximal ‎ideals in Lie algebras and the prime ‎and ‎maximal ‎elements in the lattice of soft Lie algebras.

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability of fuzzy dynamical systems, vector Lyapunov like functions are defined. Then, by using these vector Lyapunov-like functions together with the new comparison theorem which is presented before, we will get results for some concepts of stability (eventual stability, asymptotic stability, strong stability, uniform stability and their combinations) for impulsive fuzzy delayed system of differential equations. Moreover, some theorems for practical stability in terms of two measures are introduced and are proved. Finally, an illustrating example for stability checking of a system of differential equations with fuzziness and time delay in states is given.

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones.

In this paper, a new class of a weighted quadrature rule is represented as where is a weight function, are interpolation nodes, are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as that and we obtain the explicit expressions of the coefficients using the q-binomial theorem. We give an error analysis for the introduced formula and finally we illustrate its application with some numerical examples.

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second vertex-edge Wiener indices of them with each other. Also, we compute these polynomials and indices for some well-known graphs. Then, we study the relation between the vertex-edge Wiener polynomials of Cartesian product of graphs with the Wiener polynomial and vertex-edge Wiener polynomials of the primary graphs and apply the results to compute the vertex-edge Wiener indices of Cartesian product of graphs. As applications of these results, we present exact formulas for computing the first and second vertex-edge Wiener indices of rectangular grids, C4-nanotubes, C4-nanotori, Hamming graph, and hypercubes.

In Evaluating Performance, Selecting a Subset from a Set of Solutions with Limited Resources is Essential. If There Is More Than One Input and Output, the Data Rnvelopment Analysis Optimization Models Are Evaluated and Performance Measurement Based on the Weighted Output Is Divided Weighted Input. In This Research, Two Models of Optimization with Limited Resources Present from Data Envelopment Analysis Models. Each Project Produces a Set of Outputs Using Different Input Sources. In This Method, a Subset of Projects Is Selected that Can be Applies to the Resource Constraints as a Composite Project. These Composite Projects Are Defined and Evaluated by Available Projects and with Production Technology in Data Envelopment Analysis. In Fact, Evaluation and Selection Are Combined in the New Model, which is Done by Inserting a Data Envelopment Analysis Model into a Binary-Hybrid Linear Programming. The Second Model, Involves Choosing a Set of the Best or Most Preferred Places for New Facilities. Again, the Second Proposed Model Also Relates to Choices with Limited Resources.