مجله پژوهش های نوین در ریاضی
پیاپی 16 (زمستان 1397)

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression models, and then convert the two models into Ax = y, in which A is the linear regression coefficient and x is the independent variable and y variable It Depends, where A is the linear regression coefficient and x is independent variable and y is dependent variable. Finally, to minimize this device, we use the total sum of squared error based on distance d. In two examples, the proposed method is compared with the only available method.

One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (introduced by Second the author in ) introduces a family of generalized Euler type constants, and a test for their convergence. Then the existence of such constants is proved, and it is shown that the existence test presented by J. Sandor that was published in Journal of Mathematical Analysis and Applications in  is one of its corollaries, and that generalized Euler type constants include a vaster spectrum of them. Also, some relationships between the topic and the Gamma-type functions (a class of functions satisfied the difference functional equation ----------- will be considered.

Economics depends on the economic scale of planning. Economists study the characteristics of the production function, while community operating management focuses on demand realization, so that loss of sales or inventory prevents cost reductions and maximizes profits. However, companies with a lack of capacity need to achieve economies of scale and demand to realize them simultaneously, especially when corporate demand is fluctuating. But always the customer's demand is not equal to output, the demand level may be less than the  maximum output level of the highest productivity scale (MPSS), between the highest output level of the MPSS and the maximum output level, or greater than the maximum output level. In this paper, we intend to find the highest level of productivity in relation to the demand for active insurance companies in 1396 in all three scenarios. In fact, we will examine the applicability of Lee's (2016) paper in insurance companies in Iran.

The present context of the electric industry, characterized by competitive markets, privatization, and regulatory of technical requirements forces the power utilities to optimize their asset management practices and develop the requisite decision plans techno-economically. Practically approaching, this paper devises a new support tool based on a multiattribute decision making (MADM) framework in combination with analytical hierarchical process (AHP) to determine the most critical components of power transmission systems. Measure of system-wide reliability performance, outage cost, Locational marginal prices demonstrative of market fairness, and network losses are among the attributes considered in this paper for component criticality assessment. With the frequent existence of qualitative and quantitative attributes, the proposed approach can effectively help to deal with the existent uncertainty and conventional judgment vagueness. As verified in a case study on the IEEE Reliability Test System (IEEE-RTS), the proposed framework introduces its applicability and efficiency for the practical asset management optimizations in electric utilities.

In the today’s world wherein every routine is based on economic factors, there is no doubt that theoretical sciences are driven by their capabilities and affordances in terms of economy. As a mathematical tool, data envelopment analysis (DEA) is provided to economics, so that one can investigate associated costs, prices and revenues of economic units. Data Envelopment Analysis (DEA) is a linear programming technique used for measuring the relative efficiency of decision making units based on input and output data. One of the applications of this technique is calculation of  revenue efficiency. Methods of revenue efficiency calculation in DEA are generally presented for obtaining maximum revenue from output selling, these methods are not sufficiently efficient for evaluation of all system including network systems due to ignoring the internal structure of units and their middle products. Therefore, in this article, in addition to introduction of inverse linear programming in DEA and its application in calculating   revenue efficiency, a new method is presented which considers the network structure of units, the ability to determine the optimal price and appropriate costs for efficiency of the unit. The proposed numerical examples demonstrated the superiority of the proposed methods over the traditional data envelopment analyses.

‎In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For each of these numbers, some results have been obtained in the structure of groups, the most well-known of which is Stallings theorem providing the structure of groups with more one ends as the amalgamated free product or HNN extension. Specifically, it was proved that group with exactly two ends is a virtually Z group. After that, we introduce the trivial end of the graphs and show that the trivial end is exactly the same as the special type of infinite path. Finally, we prove that the existence of trivial end for Cayley graph of a group is equivalent to being a free group, and this implies that the Cayley graph of a group has a trivial end if and only if all of its ends are trivial.

Decision Neural Network is a new approach for solving multi-objective decision-making problems based on artificial neural networks. Using inaccurate evaluation data, network training has improved and the number of educational data sets has decreased. The available training method is based on the gradient decent method (BP). One of its limitations is related to its convergence speed. Therefore, decision makers can simply guess the necessary data. In this paper, for increasing the Decision Neural Network training efficiency, a conjugate gradient based method has developed for network training. The key point in decision neural network training is to keep the same structures and parameters of the two sub network (multilayer perceptron) through training process. The efficiency of the proposed method is evaluated by estimating linear and nonlinear utility function of multi-objective decision problems. The results of the proposed method are compared with previous existing method and show that in the proposed method, convergence is faster than previous methods and the results are more favorable.

In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differential equations.

Theobjective in this paper to study and present a new iterative method possessing high convergence order for calculating the polar decompostion of a matrix. To do this, it is shown that the new scheme is convergent and has high convergence. The analytical results are upheld via numerical simulations and comparisons.

In  this  paper a  non-linear  model  with  fractional  order  is  presented  for  analyzing  and  controlling the  spread  of  HIV virus.  Both  the  disease-free  equilibrium and the endemic equilibrium are  found  and  their  stability is  discussed. The basic reproduction number , which is a function of the constant parameters in the model, plays an essential  role in the stability of  the above model. In more precise expression, When  the disease-free  equilibrium is attractor, but when ,  is unstable and the endemic  equilibrium    exists  and  it  is  an  attractor.  Finally  numerical  simulations  are also established  to  investigate  the influence  of  the  parameters in the model  on  the  spread  of  the  disease.

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem is reduced to a set of algebraic equation. Finally we use some numerical examples to show that this method include to demonstrate the validity and applicability of technique.

In this work “How the technology interacts with the mathematical model and their parametric characteristics” is a fundamental question. Technologies are mutually effective and impressive. These effects are very evident in various fields, especially engineering and management, and its applications in industry, services and economics. Therefore, in the same way as other fields of action and reaction presented in the mathematical logics, the development of measurment of technology will be of particular importance.

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to explain it. For this purpose, he obtained a combination of Ricci tensor and Ricci scalar through Bianchi identity, which its covariant derivative is zero and is known as Einstein tensor. The main purpose of this paper is to classify Einstein left-invariant metrics of signature (2,2) on four-dimensional Lie groups. Recently, four-dimensional Lie groups equipped with left-invariant metric of neutral signature has been investigated extensively and a complete list of them has been presented. Now we study Einstein structures on these Lie groups. Then some geometric properties of these spaces, such as Ricci-flatness will be considered.

In this paper, we define the concept of compatible and weakly compatible mappings in b-metric spaces and inspired by the Ciric and et. al method, we produce appropriate conditions for given the unique common fixed point for a family of the even number of self-maps with together another two self-maps in a complete b-metric spaces. Also, we generalize this common fixed point theorem for a sequence with together an even numbers of self-maps in complete b-metric spaces.