مجله پژوهش های نوین در ریاضی
پیاپی 33 (آذر و دی 1400)

Basic models of Data Envelopment Analysis intrinsically evaluate the decision making units with an optimistic point of view, in the sense that the efficiency status of each unit is evaluated by means of calculating its distance from the efficiency frontier. The efficiency frontier is in fact composed of all units indicating the best practice, in the sense that for each one there exist no other (virtual) unit with a better performance. A unit located on this frontier is called fully efficient and non-efficient, otherwise. In order to provide a more precise assessment, one can evaluate units with a pessimistic point of view, in the sense that a frontier consisting of the worst performance, called the in-efficient frontier is formed and then each unit is evaluated with respect to its distance from this frontier, in a way that the closer the unit to the in-efficient frontier, the more in-efficient it is. In this paper, assuming that the production technology is non-convex, we perform efficiency and in-efficiency evaluation and then, based on the optimal value of the corresponding (in-) efficiency model, we partition all units in two subsets called (in-)efficient and non- (in-)efficient units. Then we investigate the concept of stability of the obtained partitions, by means of presenting related multi objective programs. In the next step, assuming that the input and output data of all units are real intervals, we deal with the efficiency and in-efficiency analysis of units and partition them into three subsets, in each case.

In this paper, we consider the first-order Painleve differential equation, which variables and coefficients are real but are known boundary conditions and fuzzy numbers. The goal is to calculate the approximate answer for it. Given the boundary conditions fuzzy, it is obvious that the approximate answer function must be a fuzzy function. For this purpose, first, by applying arithmetic on fuzzy data with three components of central index, left ambiguity and right ambiguity, it converts Painleve differential equation into three sets of differential equations (central index, left ambiguity and right ambiguity) with accurate data. do . Then, using the Tammy and Ansari (TAM) method, we calculate the approximate solution of each of the three transformed differential equations and arrive at the fuzzy approximate solution of the Painleve differential equation. Finally, by giving an example, we show the suitability of the method by calculating the error and convergence by finding the approximate solution.

The non-abelian tensor product of groups has it's origin in K-algebraic theory and topology and was first introduced by R. Brown and J.L. Loday in 1987 .One of the first topics which was studied on G⊗G is that whether the properties of G⊗G inherited from G or not? For instance, Bacon in 1994 determined an upper bound for the number of minimal generators of G⊗G in terms of the number of minimal generators of G.Let G be a group and Autz (G) be the group of It's central automorphisms, which is a normal subgroup of Aut(G). Our goal is to obtain an estimate for the number of minimal generators of G⊗Autz(G). For this, we first identify it's minimal generators. Then, when both G and Autz(G) are nilpotent groups of class two, we give an upper bound for d(G⊗Autz(G)) in terms of d(G) and d(Autz(G)), where d(X) is the minimal number of generators of X.

First, using triangular norms and fuzzy sets, we define fuzzy k - normed spaces and then we study the stability of a class of differential equations. We apply a fixed point theorem to prove our stability results. Radu was the first mathematician who applied the fixed point method to prove the stability of functional equations both in normed spaces and random normed spaces. We consider the differential equation υ ʹ (ν ) = Г(ν, υ(ν)),which the related integral equation is υ (ν) = υ (m) - ∫_m^ν Г(τ, υ(τ)) dτ.In this article, by a fuzzy control function, we make stable the pseudo integral equation related to the differential equation. Next, we get an approximation for the pseudo integral equation by using the fixed point method. These results prove‎ Hyers - Ulam - Rassias stability and Hyers - Ulam stability in fuzzy k- normed spaces via fixed point method‎.

The (2+1)-dimensional Kundu-Mukherjee-Naskar (2D-KMN) equation that addresses the propogation of soliton dynamics in optical fiber communication systems is investigated in the present paper. The intended purpose is accomplished by applying a traveling wave hypothesis for reducing the 2D-KMN equation in a 1-dimensional domain and solving the resulting ODE using the exp_a and Jacobi elliptic function methods. As an accomplishment, optical solitons and other solutions of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation are extracted, confirming the outstanding performance of the methods.The (2+1)-dimensional Kundu-Mukherjee-Naskar (2D-KMN) equation that addresses the propogation of soliton dynamics in optical fiber communication systems is investigated in the present paper. The intended purpose is accomplished by applying a traveling wave hypothesis for reducing the 2D-KMN equation in a 1-dimensional domain and solving the resulting ODE using the exp_a and Jacobi elliptic function methods. As an accomplishment, optical solitons and other solutions of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation are extracted, confirming the outstanding performance of the methods.

In this paper, At first we define Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability and then by using the fixed point method, we prove the Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability for the first order delay differential equation of the form I can not transfer formulae here. Which F is a bounded continuous function and Τ is a fixed real number.For interval I, suppose that F is a continuous function such that satisfy the following conditionI can not transfer formulae here.Now suppose that the function F satisfy the following conditionI can not transfer formulae here.which Eq is Mittag-Leffler function. In this case there exists a unique function such that we have I can not transfer formulae here.for all... and ....In the other words, the function F is Mittag-Leffler-Hyers-Ulam stable. By changing in the conditions of F we can prove that the delay differential equation is Mittag-Leffler-Hyers-Ulam-Rassias stable.

Multi-parametric programming theory is a valuable tool for decision making under uncertainty and has been an active area of research. Although multi-parametric programming with uncertainty in the objective function coefficients and right-hand side of constraints has been extensively discussed and various methods have been proposed for this, uncertainty in the coefficients matrix (i.e. left-hand side uncertainty) have been less considered. In this work, a new method for solving multi-parametric mixed-integer linear problems (mp-MILP) with uncertainty in constraints is presented. This procedure consists of two steps, which in the first step, the bounds of the bilinear terms are improved by using tightening piecewise McCormick relaxations and secondly, based on these improved bounds and estimating bilinear terms, an approximate model of mp-MILP is obtained. The performance of the presented method is investigated by two examples. To do this, the approximation of the problem has been done in different partitioning factors and computational requirements to solve them have been compared.

One of the effective method for solving the multi-objective optimization problems is the ε-constraint method which, unlike the weighted sum method is able to find non-dominated points in non-convex parts of the non-dominated frontier. The main disadvantages of this method are finding similar non-dominated points for choosing different parameters and thus increasing the computational complexity of the algorithm and reducing its overall performance, which is not cost-effective in terms of time and cost. In this paper, a modified is made to ε-constraint method, which, due to the intelligence of the algorithm, the unnecessary areas that lead to the production of the same non-dominated points are eliminated from the beginning. Therefore, additional computational efforts are eliminated to produce the same non-dominated points. Discussions and details of the proposed method, with its algorithm, are presented and in the numerical examples section, the efficiency of the proposed method is compared with the ε-constraint method.

The purpose of this paper is to introduce a more integrated and specialized approach to address the challenging issues known as the "Last-Mile Transportation" and to provide a conceptual-mathematical framework for making a synergy and integration between theoretical concepts and classic urban logistics optimization issues. This is a two-echelon routing-location network consisting of an urban distributor (or warehouse), customers and potential locations to install two types of facilities (automated parcel locker and micro-distributor). After ordering based on their desirability, customers are able to receive their product at the door or at 24-hour parcel locker. A modified Bender decomposition algorithm is used to solve the proposed model, which is amplified by the strategy of rounding of master problem’s variables and local search. To prove the efficiency, we compared the properties obtained from the proposed algorithm with the results obtained from the epsilon-constraint method in the Python software environment, the CPLEX library and ILOG CPLEX Optimization Studio and the results confirms the absolute dominance of this method in large-sized instances. The results of the sensitivity analysis of the role of automated parcel lockers on the network’s cost and produced pollution indicate the efficiency and validity of the proposed model.

Let G be a simple connected finite graph. A graph invariant (also known as topological index or molecular descriptor) of graph G is a real number with the property that for every graph H isomorphic to graph G, Top(H) = Top(G). The sum of cubes of vertex degrees of graph G was revived by Furtula and Gutman under the name of forgotten topological index. The Forgotten index F(G) of a simple graph G can also be expressed asF(G)=∑_(uv∈E(G))▒(〖〖〖d_u〗^2+d〗_v〗^2 ) whered_u denotes the degree of the vertex u of G. In this paper, we compare the F-index with some graph parameters such as order, size, radius, minimal vertex degree and maximal vertex degree and some well-known molecular descriptors consisting of first Zagreb index and second Zagreb index, first modified Zagreb index and second modified Zagreb index, Harmonic index, Eccentric connectivity index, hyper-Zagreb index, Geometric-Arithmetic index and inverse sum indeg index.

For a finite group $ G $, let $ { rm n s e } ( G ) $ be the set of the number of the elements of the same order in$ G $. In this paper, we first study the set $ n s e $ of a Frobenius group , the set $ { rm n s e } $ of a $ 2 $- Frobenius group and the set $ { rm n s e } $ of a nilpotent group. Then, we show that for the finite non-solvable Frobenius group $ G $ with the certain structure and an arbitrary group $ L $ , if $ {rm n s e } ( G ) = { rm n s e } ( L ) $, then $ G ≅ L $. Also, a new criterion is presented to recognize nilpotent groups by their $ {rm n s e }$.

In this paper, a special case of the finite difference method which is called non-standard finite difference method is studied for the numerical solution of a mathematical model of epidemic diseases. The constructed non-standard finite difference schemes have the main properties of the continuous model such as positivity, boundedness, and stability. The stability of the equilibrium points of the system is investigated. The proposed non-standard finite difference schemes are convergent to the equilibrium points of the system. In solving nonlinear problems, one of the important advantages of this method is that nonlinear term discretized with nonlocal approximations. In most cases, non-standard finite difference schemes are stable even when large step sizes are considered. Therefore, using non-standard method will be cost-effective in dynamical systems that are studied over a large time interval. Numerical examples confirm the accuracy and efficiency of the non-standard finite difference method.

Predicting stock price is an important issue in both theoretical and practical aspects. Researchers develop prediction methods to get more accurate forecasting and investors try to find best investing program which depends on future prediction of their markets. The aim of this paper is comparing artificial neural network (ANN), nonlinear autoregressive exogenous model (NARX) and grey model (GM) for predicting stock price. The stock prices of insurance companies in Tehran Stock Exchange are considered in the period 7-10-2009- 9-10-2017. The variables 5 days simple moving average (MA-5), 20 days simple moving average (MA-20), moving average convergence divergence (MACD), gold price, oil price and exchange rate are considered for the prediction. Based on these variables, the models GM(1,1), GM(1,4) and GM(1,7) are selected for the prediction. The results show that ANN and NARX are in the same performance level while grey models have lower performance. The numerical simulations demonstrate that ANN and NARX provide reasonably good prediction with the average error RSME=2.04.

The element free Galerkin method is a well-known method for solving partial differential equations. Applying essential boundary conditions in this method, that based on moving least squares approximation, have some complexities. Since the shape functions of the moving least squares approximation do not satisfy the property of Kronecker delta function, therefore imposing essential boundary conditions is not as trivial as in the finite element method and we need some modifications of the Galerkin weak form of the equation. In this paper we propose a new approach to apply essential boundary conditions in element free Galerkin method for solving elliptic PDEs. This approach is based on interpolating moving least square method. First we apply the essential boundary conditions in the moving least square approximation of the function then the approximation is used in element free Galerkin method. Thus the essential boundary condition is applied directly. In this paper we first introduce the interpolating moving least squares approximation, and then describe how to apply the boundary conditions. Finally, some different examples show the accuracy and efficiency of the method.

The purpose of this study was to determine and evaluate the efficiency of decision making units with classical model and goal programming data envelopment analysis and output correlation with statistical methods in Ghavamin Bank.

In this paper, data envelopment analysis model based on output- oriented BCC was used to determine the efficiency of provincial branch management in the Ghavamin Bank. As well as to increase the discrimination power of decision-making units more efficient from the inefficient, first models of the default goal programming data envelopment analysis model was examined, then the output models of default as part of the input goal programming data envelopment analysis model was used. Finally, Pearson correlation coefficient was used to evaluate the correlation between the classical model and goal programming model in the outputs.

According to output amounts output- oriented BCC model all of decision-making units is efficient and value their efficiency is equal to one, then to discriminate higher than the goal programming data envelopment analysis model was used, the results showed that the 32 management 21 units are efficient and the rest are inefficient. The results also showed that there is a significant correlation between the classical model and the goal programming model.

The results showed that goal programming data envelopment analysis model in discriminating efficient decision making units from inefficient has higher discrimination power than output- oriented BCC model.