مجله پژوهش های نوین در ریاضی
پیاپی 38 (مهر و آبان 1401)

The trend of population growth and development of cities in recent decades has led to the use of vehicles, both private and public. Meanwhile, public transportation has attracted a lot of attention due to its economic viability. Therefore, urban planning officials and municipalities try to solve problems such as; Environmental pollution, heavy traffic congestion, insecurity on some roads, severe accidents on some roads and excessive consumption of fuel suitable for vehicles (including oil - diesel and gasoline) are to consider appropriate measures. Data envelopment analysis with appropriate mathematical solutions can be an accurate and comprehensive tool to investigate such situations, so that managers can use it to make the best decision and remove existing barriers. Our goal in this article is to determine the efficiency, satisfaction and productivity (productivity in efficiency, productivity in satisfaction) of public vehicles, specifically 10 bus lines in Mashhad, so that their productivity in three consecutive years 91, 92 and 93 has been evaluated and the ratio of productivity in satisfaction to productivity in efficiency of each line has been calculated.

In this paper, we introduce the concept of stabilizers of a set in UP-algebras and introduce a new class of UP-algebras. Then we introduce and study their properties and the relationships between the left and right stabilizers of a set in UP-algebras and provide equivalent conditions for easier and faster study of new UP-algebras. We also show that, by adding a condition, the left stabilizer of a set is a UP-filter, while the right stabilizer of a set is not. In the following, we define the concepts of coatom and strong coatom on UP-algebras and examine its properties. In addition, we provide equivalent conditions for easier study of coatoms in UP-algebras.We show that for a UP-algebra A, Coatom (A)=A- {0} if and only if each subset of A contains 0, is a UP-filter of A. We also examine the relationship between coatoms and stabilizers. Finally, we introduce the generalized co-annihilator set G relative to F and study its properties.

Selecting the optimal stock portfolio is one of the most important issues in the field of financial research, which tries to choose the optimal combination of assets in order to create maximum utility for the investor, Given that the return on securities in the real world is often vague and inaccurate, one of the most important investment challenges is uncertainty about the future. In this paper the problem of selecting and optimizing securities portfolios with different modeling goals has been solved and compared. The designed models have considered both the nature of the portfolio selection issue and the considerations considered by the shareholder in the portfolio selection. The uncertainty quality of the future return of a given portfolio is estimated using fuzzy LR numbers, while its return torques are measured using possibility theory. The most important purpose of this paper is to solve the problem and compare portfolio selection models with simultaneous optimization of two, three, and four objectives. For this purpose, the NSGA-II genetic algorithm is used and the mutation and intersection operators are designed specifically to generate possible solutions to the cardinality constraint of the problem. Finally, the efficiency and performance of the models in case of using fuzzy logic and not using it have been compared and it has been determined that the use of fuzzy logic and possibility theory leads to the formation of portfolios with higher performance and higher efficiency.

‎In this paper‎, ‎we introduce the neighborhood of each element x ‎of the Jleli_Samet's generalized metric space (X,d) ‎and ‎we ‎study ‎some ‎properties ‎of ‎the collection T_d of all unions of such neighborhoods which is called generalized topology in the sence of Csaszar. We show that some of the elementary properties on the metric spaces dose not happen on the generalized metric space in the sense of Jleli_Samet. Moreover the generalized topology T_d need not to be compatible. Also we give a sufficient condition to show that any point of the generalized metric space in the sense of Jleli_‎Samet‎, ‎has zero self-distance‎. ‎We introduce the statistical generalized metric space by replacing the concept of convergence with statistical convergence on the definition of generalized metric space in the sense of Jleli_ Samet and we show that two generalized metric spaces are equivalent.||| ||| ||| ||| ||| ||| ||| ‎

Data envelopment analysis (DEA) is a nonparametric method for measuring the efficiency of decision-making units (DMUs) with multiple inputs and outputs. This research used the original DEA model and extended it to solve the DEA efficiency measurement problem, specifically for unseparated shared inputs. The consideration of this context aims to establish a new DEA approach to explore bank branch performance in different activities based on the optimal usage of unseparated shared inputs. In this study, in the first stage, the efficiency score is calculated from several activities using graph efficiency, and then, a maximum efficiency score pertaining to each DMU is applied to propose a new model. In the second stage, the efficiency score, which is calculated by the new approach on unseparated shared inputs, is defined as a new constraint based on shared inputs on the CCR model. This approach is implemented on the real data of 25 branches of a private bank in Iran. In fact, the efficiency of each branch is calculated, and enhancement guidelines are presented considering the three activities of production, electronic banking, and intermediation. Presenting one real efficiency score for each DMU, instead of the traditional efficiency score, leads to more robust decisions based on a more transparent performance evaluation in bank branches.

Nowaday, steganography as an art or technique for hiding data in various media, has a wide variety of applications in information management. steganography can be used to convey a confidential message, enhance information security, categorize information, store specific information, and more . Image is one of the most popular media used in data hiding process and there are various methods for hiding information in images, the most common of which is the method of embedding information in low-value bits of the image and for which various algorithms and methods have been developed. One of these methods, which has a mathematical basis, is to use the calculation of the difference between the values of two adjacent pixels in order to identify suitable points for embedding confidential information. In this paper, two new methods for data embedding in images are proposed based on calculating the differences in the values of adjacent pixels in 4*4 blocks and tested on different images using the Mean Squares of Errors, Peek signal-to-noise ratio and structural similarity criterias has been studied and analyzed. Evaluations show that the first proposed method is optimal due to better results.

Fuzzy optimization issues have been discussed by many authors in recent articles, inspired by the concepts of generalized Hukuhara difference and generalized Hukuhara differentiability for one-dimensional functions from R to E, and have made considerable progress. In this paper, the concept of total generalized differentiability is introduced by using the concept of generalized difference from R^n to E for multi-dimensional mappings. Furthermore, the total generalized differentiability of the above is also examined and then the concept of directional generalized differentiability and partial generalized differentiability for fuzzy multi-dimensional mappings is defined and discussed in detail. In addition, directional generalized differentiability and partial generalized differentiability are expressed in terms of level-wise generalized differentiability. Also, the properties and the relationship between them are discussed. Finally, the relationships between total generalized differentiability, directional generalized differentiability and partial generalized differentiability are shown to illustrate the power and ability of relationships between them by mentioning some examples.

In this paper, a new class of absolute value equations is studied as follows:Ax-B|x|-b=o, ( B≠I, σ_"max" (|B|)<σ_"min" (A) ), This new class of absolute value equations, the single value absolute matrix B is less than the single value matrix A and the matrix B is not exclusively the identity matrix..Therfore the power of choice is wider than other methods of the absolute value equations and all matrices are arbitrary and this new class of absolute value equation is the NP hard problem..We solve this new class using a generalized Newton method and also convergence and numerical stability. Also, by testing the numerical examples of the efficiency and effectiveness of the solution method for the new class, it has been studied with other works that have been done including Lotfi and Zainali and Mangasarain and Khaksars method.Eceptthis new class and Lotfi and Zainali method are quadratic convergence, the rest methods are linear convergence.

This article is concerned with non-smooth/nonconvex robust multi-objective optimization problems involving uncertain inequality and equality constraints. Employing some advanced tools of variational analysis such as the approximate extremal principle and the weak fuzzy sum rule for the Frechet subdifferential, we first drive a fuzzy necessary optimality condition of a non-smooth/nonconvex multi-objective optimization problem without any constrained qualification in the sense of the Frechet subdifferential. Then by exploiting the obtained fuzzy optimality condition, the non-smooth version of Fermat’s rule and formulae for the limiting subdifferential of an infinite family of non-smooth functions, we establish a necessary optimality condition in terms of the limiting subdifferential for weakly robust efficient solutions of the reference problem. Further,we present an example to illustrate this condition for an uncertain multi-objective optimization problem involving equality and inequality constraints.Finally sufficient conditions for weakly robust efficient solutions and robust efficient solutions of the problems are provided by presenting new concepts of generalized convexity.

Let n , k be positive integers such that n ≥ 3, k < n/2. Let q be a power of a prime p and F _ q be a finite field of order q. Let V(q,n) be a vector space of dimension n over F_q. We define the graph S( q , n , k )as a graph with the vertex set V = V _ k ⋃ V _ (k+1), where V _ k and V _ (k+1) are subspaces in V( q , n )of dimension k and k+1 respectively, in which two vertices v and ware adjacent whenever v is a subspace of w or w is a subspace of v. It is clear that the graph S(q , n , k )is a bipartite graph. In this paper, we study some properties of this graph. In particular, we determine the spectrum of the graph S(q,n,k).

American trading options are a way to manage risk in the commodity exchange. This method can be applied before maturity. The valuation of the American trading option in the finite difference method is less complicated than other methods and its calculation time is relatively short, and also with increasing the sample and increasing the volatility, the parameters are not disturbed. In this research, using the mentioned method, the American option for two products of wheat and rapeseed meal has been done and specified according to the data of Iran Commodity Exchange: A) The value of the American option for wheat and rapeseed meal is very small and negligible from the binomial tree method and the finite difference method calculated using the algorithm presented in the research and coding in MATLAB software. B) The American option value for wheat is higher than soybean meal for both options. The main reason for this is the high volatility (σ) of the base price of wheat stocks compared to rapeseed meal. C) The result of the effect of volatility change and price change on the value of the option, is in favor of volatility change. This indicates the importance of the volatility parameter in the valuation of options. Finally, it is suggested that considering that the American option is capable of applying before maturity ,in the iranian stock exchange for agricultural commodities is presented as one of the tools of risk management .

The layout of a graph is finding a linear order for the vertices of the graph such that each of its edges is assigned to exactly one of the stacks (resp. queues) based on the properties of the stack (resp. queue). In this paper, we find a relationship between the stack layout and the queue layout of a graph. In particular, we provide an algorithm for converting a 1-stack layout of any graph into a 2-queue layout of the same graph, and we prove the correction of our algorithm. This method obtains the queue layout from a given stack layout without considering the graph itself and its properties. We hope by generalizing and developing this method one would achieve a queue number (i.e., the smallest number of the queues required by the queue layout of the graph) for some graph categories with almost the same upper and lower bound on their stack number.