مجله پژوهش های نوین در ریاضی
پیاپی 21 (آذر و دی 1398)

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdirection by the Levenberg-Marquardt direction. The descent property of the direction generatedby new algorithm in each iteration is established. Also, the global convergence of such a methodare established under some mild assumptions. Some numerical results are reported.In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdirection by the Levenberg-Marquardt direction. The descent property of the direction generatedby new algorithm in each iteration is established. Also, the global convergence of such a methodare established under some mild assumptions. Some numerical results are reported.

Let A be a Banach algebra and (B,B_*) be a dual Banach algebra. A linear map φ:A⟶B is said to be a δ - homomorphism map if ‖‖φ(a_1 a_2)-φ(a_1)φ(a_2)‖‖≤δ‖‖a_1‖‖ ‖‖a_2 ‖‖ for every a_1,a_2∈A. In this paper, we study the δ - homomorphism maps from A into B. Among other things, we prove that if φ:A⟶B is a δ - homomorphism map and B_* is multiplicative on the algebra generated by φ(A), then φ is bounded and ‖‖φ‖‖≤1+δ. Let A be a Banach algebra and (B,B_*) be a dual Banach algebra. A linear map φ:A⟶B is said to be a δ - homomorphism map if ‖‖φ(a_1 a_2)-φ(a_1)φ(a_2)‖‖≤δ‖‖a_1‖‖ ‖‖a_2 ‖‖ for every a_1,a_2∈A. In this paper, we study the δ - homomorphism maps from A into B. Among other things, we prove that if φ:A⟶B is a δ - homomorphism map and B_* is multiplicative on the algebra generated by φ(A), then φ is bounded and ‖‖φ‖‖≤1+δ.

The TOPSIS process is one of the most comprehensive systems designed for decision making with multiple criteria, since this technique enables formulation of the problem as decision matrix, as well as the possibility of considering different quantitative and qualitative criteria in the problem. Fuzzy TOPSIS methods have been introduced to make fundamental decisions that make decisions decisions in these ways, including the lack of precision in fuzzy calculations, which can be attributed to the lack of use of the principle of "Zadeh” in the definition of operators. For example, the multiplication of two triangular fuzzy numbers will not necessarily be triangular fuzzy. However, in most of the fuzzy TOPSIS methods, this is assumed. In this paper, we attempt to first define the ideal vector of false algebra, then two functions are designed for this purpose, then the optimal of these functions can be found using GA. All steps are based on the principle of "Zadeh”".

Nonlinear programming problems belong to the realm of commonly used optimization problems. In most cases, the objective function of such problems is non-convex. However, to guarantee global convergence in the algorithms proposed based on Newton's method to solve these problems, a convexity condition is generally required. Meanwhile, the quasi-Newton techniques are more popular because they use an approximation of the Hessian matrix or its inverse. However, in these algorithms, only gradient information is used to approximate this matrix. One of the most applicable quasi-Newton algorithms in solving nonlinear programming problems is the BFGS method. This paper presents a new idea for a linear search in the BFGS method. It proves that using this technique will lead to global convergence for general problems without the need for any additional conditions. Finally, the performance of the proposed algorithm is evaluated numerically.

One of the most important concerns of investors in financial markets is choosing a share or stock portfolio that is optimal in terms of profitability. To this end, there are many ways in which the stock portfolio has been chosen. The optimal portfolio selection is a portfolio management goal. In this dissertation, the DEA technique has been used as a new and reliable way to select the stock optimal stock. In this thesis, the risk of different orders, average returns, return variances, higher torque are considered as output variables. It will also be possible to take into account the priorities for increases in risk ignored by DEA in applied studies but discussed in economic theory. Finally, in this research, 278 companies were evaluated in 50 stock portfolios during the 5-year period, which is evaluated by 3 models, one for higher returns, one for lower risk and one for a combination of these two methods has meant greater returns and less risk. Also, baskets number 6 and 8 ranked best in the first, second and third models. .

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].

In this paper, the problem of sequencing machines in the final assembly line with regard to the supply of parts has been investigated. For this reason, a basic integer linear programming model has been developed and based on this, the problem-solving algorithm is developed in accordance with the reaction-based approach based on the renewal of the sequence of operations. Also, due to the Np-hardness of the problem, a meta-innovative method based on the variable-neighborhood search algorithm is presented. To evaluate the proposed solution method, a sample of library issues was used and to simulate the disruption event, test questions were designed in large, medium and small dimensions. The results show that, in three categories of problems, the proposed meta-innovation method is approaching it in a very appropriate way compared to the best available method. In addition, due to the solving time, it is much more efficient than the optimal solution method and is responsive. The immediate needs are to update the sequence of operations in the face of disturbances created in the car production line.

Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a rigid body with a fixed point in the gravitational field. This Mechanical systems is usually know as symmetric heavy top. Then we show that the extracted equations by this theory coincide with the known equations of heavy top. Finally, as an infinite dimensional example, we study the Camassa-Holm equations on Bott-Virasoro group at the presence of potential. Bott-Virasoro group is the product of the group of diffeomorphisms of the circle of Sobolev class by the real line and by a potential on a Lie group G we mean a differentiable function from G to the real line R.

Today, neuroscientists are interested in discovering human brain functions through brain networks. In this regard, the evaluation of dynamic changes in functional connectivity of the brain regions by using functional magnetic resonance imaging data has attracted their attention. In this paper, we focus on two model-based approaches, called the exponential weighted moving average model and the dynamic conditional correlation model, to estimate the dynamic correlation between the two brain regions. Initially, the performance of these two models is evaluated using two new simulations. According to the results, in these simulation studies, the dynamic conditional correlation model has better performance than the exponential weighted moving average model. Therefore, a dynamic conditional correlation model is used to estimate the dynamic functional connectivity of two brain regions (the anterior cingulate cortex and the posterior cingulate cortex) for three Iranian addicted to methamphetamine in a resting state functional magnetic resonance imaging. The dynamic conditional correlation model has a good performance in assessing the dynamic functional connectivity of these addicted to methamphetamine. In addition, the dynamic functional connectivity varies between subjects.

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances from new facilities to the radius distance of clients and sum of weighted distances between new facilities is minimized. Since in the most instance there dose not exist the location of a new facility such that its distance to each Customers be exactly equal to given radiuses, so we try to minimize the sum of the weighted square errors. We model the problem and propose an iterative method (weiszfeld like algorithm) for solving the presented problem. Then a discussion about convergence of presented method and some numerical examples are given. We show that the optimal solution lies in an extended rectangular hull of the existing points.

This paper describes two proposed strategies for involving families in mathematics education and forming a mathematical association for parents with the aim of involving parents in their children's mathematics education, implemented at one of the Tehran schools, describing the outcomes and performance of students before and after school. They were analyzed using Data Envelopment Analysis (DEA).Data Envelopment Analysis (DEA) is a linear programming method whose main purpose is to compare and evaluate the efficiency of a number of similar decision-making units, to compare and analyze them with different amounts of inputs and outputs.In this research, inputs on various aspects of cultural, social, and economic conditions (such as family income, physical and mental health of family members, parents' occupation, etc.) of families of sixth grade elementary school boy students in TALAYEDARAN school, district 4 of Tehran, and outputs The success of the math test is the interest of the students in these math activities in math lessons and ethical discipline

Let n  1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1  k  n. The hyper-star graph B(n;k) is the subgraph of Qn induced bylayers Lk and Lk+1; 0 < k < n. In this paper, we determine the spectrum of the hyperstargraph B(n;k) and L(B(n;k)), where L(B(n;k)) is the line graph of the graphB(n;k). In particular, we show that the graph L(B(n;k)) is an integral graph, that is,all of its eigenvalues are integers. In this paper, we investigate some of the algebraic properties of the graph B(n;k) andits line graph L(B(n;k)). In particular, we determine the spectrum of these graphs.