JOURNAL OF NEW RESEARCHES IN MATHEMATICS
Year:2021 | Volume:7 | Issue:31|Papers Count:16

This paper is devoted to the existence of infinitely many solutions for a forth order elliptic Kirchhoff problem involving Multi-singular inverse square potentials in a bounded domain using the methods in nonlinear analysis, precisely the variational methods. Nonlinear analysis is a powerful tool for solving many physical models and a technique for proving the solvability of them. Among the methods can be considered in nonlinear analysis, variational methods can prove the existence and multiplicity of solutions without finding the exact value of them. Accordingly, we shall be told, perhaps, that we can find in this field of analysis one of the most applications of analysis in solving the real models of natural problems. The most important feature of the problem proposed in this article, is the existence of singular points in the domain. Using the critical point theory, we prove that there exists an interval in which, the problem has a sequence of distinct weak solutions. In other word, the existence of infinitely many solutions for this problem can be proved. This problem is of the type time independent Poison-Schrodinger equation appearing in an interesting physical context.

In the present study, we first examined and identified the psychological-individual factors and considered the following components for each: psychological-individual factors included personality traits, lifestyle, motivation, learning, resistance against change; values included hedonic and utilitarianism values, self-concept and authenticity; Then, the effect of these factors on nostalgic behaviors, like tendencies, sentiments and nostalgic intensity were examined. Later on, the effect of nostalgic behaviors on need for belonging, consumption conditions, brand heritage, brand attitudes, levels of feeling and emotions is examined, and the effects of these factors and nostalgic behaviors on purchase intention (PI) were investigated, and finally, the effect of PI on actual purchases were measured. Conceptual model that extraction of literature and testing the sample size of participants. The methodology of had two stages: stage one was examined using Exploratory Factor Analysis and the second stage using structural equations. Highlights to finding this research and present articles aims to provide managerial implications for customer nostalgia behavior via Exploratory Factor Analysis (EFA)& Structural Equation Modeling (SEM). The analytical results showed the psychological-individual factors affect Nostalgia behaviors. Nostalgia behaviors, need for belonging, consumption conditions, levels of feeling and emotions brand attitudes, affect purchase intention, but brand heritage is not significantly related purchase intentions. Finally purchase intentions are significantly related purchase behavior.

A set of second-order differential equations (the initial value problem) is used to analyze the vibrations of structures. This method is based on changing the second-order differential equations to the eigenvalue problem, which is usually used for modal analysis of structures. This problem involves a matrix equation with mass and stiffness as coefficient matrices. Changes in some stiffness matrix arrays change eigenvalues and eigenvectors, and changes in stiffness matrices indicate damage to one or more structural members. Therefore, identifying modified arrays is very useful for monitoring the health of structures. Modified stiffness array arrays can be obtained by comparing new eigenvalues and eigenvectors with old ones. The Stubbs Index (Modal Strain Energy) Stubbs (MSE) uses only special vectors to identify injuries. In the improved modal strain energy method (IMSE) proposed by Lee et al., In addition to special vectors, special values are also entered in relation to the damage index. In this research, a new injury index is presented with the development of the above two indicators, which show more accurate results than them. In this study, the health monitoring of a template platform structure of Forouzan Persian Gulf oil field is compared to compare the accuracy of these three indicators. The results show that the new method is more accurate than the Stubbs and IMSE indices, especially in the presence of multiple injuries.

The main reason for conducting the present study is to design and explain the credit crunch risk test model of the banking industry under macroeconomic scenarios. In addition to the use of documents and reports related to the banking industry, the panel data related to the annual reports and datasets of the banking industry were used. In the present study, in order to perform econometric analyzes, E-Views software was used and Matlab artificial intelligence environment was used to design an intelligent system. Then, based on the GARCH method, the regression statistics related to the GARCH model for the fluctuations between the research objective function and GDP growth rate, interest rate, unemployment rate, inflation rate and per capita income growth rate are calculated equal to 0. 927, which indicates very high predictive power. The econometric model of research is. One of the most important results of the present study is that according to the calculations performed, the bank's credit portfolio to reduce the probability of default is exactly 91 percent (the fifth level of system output is excellent).

Let S denote the (initial) set of black vertices of graph G. The color-change rule converts the color of a vertex from white to black if the white vertex u is the only white neighbor of a black vertex v. The set S is said to be a zero forcing set of G if all vertices of G will be turned black after fi nitely many applications of the color-change rule. The zero forcing number of G is the minimum of |S| over all zero forcing sets S ⊆ V (G). In this paper, we study the zero forcing number and maximum nullity of Mycielski’ s construction in some graphs. In particular, we show that the zero forcing number of some graphs with this construction equals to maximum nullity. Also we calculate the zero forcing number and maximum nullity of Mycielski graphs μ (K_n)، μ (C_n) and connected graphs of order at least 4.

For a connected open subset Ω of the plane and n a positive integer, let B_n (Ω ) be the Cowen-Douglas class of operators. In this article, for a special case of Ω , we show that if T∈ B_n (Ω ) and its canonical model is a Von Neumann operator, then T is reflexive. In the main theorem of this paper we assume that the adjoint of the canonical model associated with g. B. K is a Von Neuman operator. We may replace this by the assumption that ‖ M_P ‖ ≤ c‖ P‖ _Ω or ‖ M_P ‖ =c‖ P‖ _Ω for every polynomial P. Actually K is the reproducing kernel for a coanalytic functional Hilbert space K on which we can define the operator M_z^* of multiplication byz. Note that if K is stricly positive kernel function on Λ , it gives rise to a functional Hilbert space on Λ with reproducing kernel K. A bounded linear operator T is said to be Von Neumann if the C^*-algebra generated by T is a Von Neumann algebra. We must point out that the operators of Cowen-Douglas class is not reflexive in general, since every operator of this class is unitarily equivalent to the adjoint of non-reflexive operator multiplication by Z ̅ . We need to impose the additional conditions for reflexivity of T.

For a locally compact group G, let A(G) be the Fourier algebra and let A_M (G) be the completion of this algebra in its multiplier algebra. In this paper, we show that A(G) is an abstract Segal algebra in A_M (G). Also, a necessary and sufficient condition for equality of these two algebras is given. Then we prove that A_M (G) is an ideal in its second dual if and only if G is discrete. We show that if G is a discrete group, then A_M (G) is a BSE algebra if and only if G is M-weakly amenable. As a corollary, it is proven that A_M (F_2 ) is a BSE algebra while A(F_2 ) is not. Finally, we examine our results for the Lebasque-Fourier algebra and also give a completely new proof for equality of the character space of A(G) and A_M (G).

The theory of α-resolvent families was developed as a generalization of the classical theory of strongly continuous semigroups and cosine operator families, to study the fractional evolution equations with Caputo derivative of order α . An important problem in semigroup theory and also for cosine operator families is to discuss different type of boundedness (in terms of their generator) for these families. In this paper, we study polynomially bounded α-resolvent families. We impose conditions on the resolvent of a closed and densely defined linear operator to be the generator of an α-resolvent family. We also show that these conditions are necessary in the case of Hilbert spaces. This generalizes the result by T. Eisner on polynomially bounded semigroups. Moreover, since α-resolvent families describe the solutions to fractional evolution equations, with this generation result, we discuss the existence and stability of solutions to these problems at the same time.

The concept of approximately biprojective Banach algebras has been introduced by Pourmahmood-Aghababa [15], O. Ya. Aristov [2] and Y. Zhang [19] in different aspects of approximation. Here we follow the definition provided by Pourmahmood-Aghababa that is more general with an abundant amount of various interesting examples, and less restrictive conditions. In this paper, some hereditary properties of this notion are investigated. Indeed, we show that approximate biprojectivity of the second dual of a Banach algebra A (equipped with Arens product) implies approximate biprojectivity of A. This concept is also investigated on amalgamated Banach algebras that are genuine generalization of the direct sum of Banach algebras and includes the unitization, the Lau product, the semidirect product, and the module extension Banach algebras. We prove that the first summand in an approximately biprojective amalgamated Banach algebra is approximately biprojective, while for approximate biprojectivity of the second summand some additional hypothesis are necessary.

In today’ s world, intrinsic complexity in numerous decision making conditions, decides the need of utilizing decision making methods more than previously. On the other hand, the present modern organization have turned out to be so widespread, which one doesn’ t capable to oversee them. In this manner, this issue of multi attribute group decision making is considered as an organizational problem. In multi attribute group decision making problems, according to the different attributes in decision matrix, knowing the coefficient of importance or weight of each attribute in decision making is essential. As the weight of each attribute express its relative importance to the others and the conscious and correct selection of weights is a great help in achieving the desired goal. The purpose of this paper is to introduce a linear programming model to determine the weight of each attribute in multi attribute group decision making problems with intuitionistic fuzzy data. As good as, decision makers are prevented from making eventual mistakes in determining the weight of attributes. Finally, using the obtained weights, a new method for ranking the alternatives based on ELECTRE III method, is presented. A numerical applied example is provided to illustrate the details of the proposed method.

In this paper, first we introduce the properties and theorems of the multi groups. After, we describe the results of the isomorphisms in multi groups, We show that how a multi group can be generated another non constant multi group under a proper binary operator, , call it t n norm. In fact, under an arbitrary t n norm to a multi group, we obtain the other multi group and examine their interactions. We use this process to generate a non constant multi group of a multi set relation under an arbitrary t n norm. We also present at the end an application of the concepts presented for generating usage encryption.

Control and reduction in environmental pollutants are of a great importance in all countries. In this paper, pollutant gases in the cement industry are analyzed and then prioritized for purposes of control and filtration based on DEA models. Two new radial and non-radial DEA models are proposed to prioritize reduction in total costs and in the effects of pollutant gases. Then, another non-radial model is provided for prioritizing reduction in costs and in the effects of pollutant gases. This prioritization is carried out using free disposal hull (FDH) and central resource allocation (CRA) models considering the types of disease caused by the pollutant gases and the medical treatment costs incurred. Finally, the results of the prioritization of Fars cement industry pollutant gases by all three proposed models are compared with those given by Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS) method and by FDH models.

Nowadays, evaluating the efficiency of entities and knowing how resources should be organized is a significant aspect in order to achieve optimal results. One of methods for the performance evaluation is data envelopment analysis (DEA). Also, one of the important DEA topics is the most productive scale size (MPSS) estimation. Due to the presence of undesirable factors in the production systems, models are suggested in this paper for evaluating MPSS and determining the largest and smallest MPSS (nearest and farthest points of MPSS) while undesirable outputs with weak disposability are available. Models proposed determine the role of environmental factors in the performance estimation of units. These models can be used in factories, hospitals and as well as environmental protection for continual monitoring on the environmental situation affected by industrial activities and also showing the impact of environmental factors in measuring the efficiency. We use data from the Chinese industry to present the theoretical results.

In this paper, we solve the Cooper-Schmidt equation in a way that is consistent with Jacuzzi and Airfoil foundations. This PDE equation is one of the most important equations in physics and chemistry. This nonlinear equation in mechanical engineering appears as a wave phenomenon, and in plasma physics discusses systems that are composed of positive and negative charged particles that can move freely. Comparison of the level of hot electron production and its surface causes the harmonic emission of some source signals and the heat electrons in the plasma are radiated spherically [1]. The Cooper-Schmidt equation plays an important role in nonlinear wave scattering. Individual waves are propagated in the nonlinear scattering of media. These waves maintain a stable shape. Due to the dynamic equilibrium and nonlinearity of this equation, an approximate solution has been proposed in many papers [12, 13]. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be obtained that can be obtained by the method. Solved nonlinear systems, such as Newton's iterative method. The existence, uniqueness of the answer, and convergence of methods are examined.

In many applications, there are some fixed costs for constructing the common platform of an organization which must be shared by all decision making units (DMUs). It is important how one should allocate such costs among all competing DMUs. Data envelopment analysis (DEA), which is a useful tool to evaluate the relative efficiency of DMUs, has been successfully used in allocating fixed costs among DMUs. Two main approaches have been proposed to allocate fixed costs that are based on maintaining or improving the relative efficiency of DMUs. In fixed costs allocation, one however needs to take into account both competitive and cooperative aspects among all DMUs. Therefore, it seems more reasonable to apply a peer-evaluation method in evaluating the efficiency of DMUs. To this end, we use cross-efficiency evaluation in DEA to allocate fixed costs between DMUs. Using cross-efficiency method and some concepts of game theory, we propose a new fixed costs allocation approach to share costs between DMUs such that the vector of cross-efficiency scores of DMUs after allocation is Pareto. We use a real application to more illustrate the proposed method and compare it with some of the existing methods.