مجله پژوهش های نوین در ریاضی
پیاپی 28 (بهمن و اسفند 1399)

The role of some factors is not completely clear as an input or an output in many real applications of Data Envelopment Analysis (DEA). In other words, some Decision Making Units (DMUs) can use a factor as an input while it may play an output role in other DMUs. This type of factors is called flexible factors. In this paper, a model is proposed to develop models of flexible factors type in the DEA model. This model, at the same time, minimizes the inputs contraction factor and maximizes the outputs expansion factor in the Russell efficiency measure, in presence of flexible factors. The proposed measure in objective function is linear. In the other words, the relation between the factors is suggested as an additive function. In fact, the proposed model, in contrast the Russell measure is not nonlinear. By an illustrated example, the proposed model is compared with the existing models.

Let 𝑅 be a commutative ring with identity and 𝑀 be a unitary 𝑅-module,and let 𝐼(𝑅)* be the set of all nontrivial ideals of 𝑅. The complement ofthe 𝑀-intersection graph of ideals of 𝑅, denoted by Γ𝑀(𝑅), is a graphwith the vertex set 𝐼(𝑅)* , and two distinct vertices 𝐼 and 𝐽 are adjacentif and only if 𝐼𝑀∩𝐽𝑀={0}. In this paper, for every multiplication𝑅-module 𝑀, the diameter and the girth of Γ𝑀(𝑅) are determined. Also,we show that if 𝑚,𝑛>1 are two integers and ℤ𝑛 is a ℤ𝑚-module, thenthe complement of the ℤ𝑛-intersection graph of ideals of ℤ𝑚 is weakly perfect.

Patterns are found everywhere and the past fifty years studies have advanced our understanding of the mechanisms . In this paper, we study those systems that develop temporary patterns. Special emphasis is made on Turing instabilities as one of the most common sources of pattern formation. Gierer-Meinhardt model acts as one of prototypical reaction diffusion systems describing pattern formation phenomena in natural events. Bifurcation analysis, including theoretical and numerical analysis, is carried out on the Gierer-Meinhardt activator-substrate model. The effects of diffusion on the stability of equilibrium points is investigated. It shows that under some conditions, diffusion-driven instability, i.e, the Turing instability, about the equilibrium point will occur, which is stable without diffusion. These diffusion-driven instabilities will lead to the occurrence of spatially nonhomogeneous solutions. Consequently, some pattern formations, like stripe and spots solutions, will appear. To illustrate theoretical analysis, we carry out numerical simulations. These diffusion-driven instabilities will lead to the occurrence of spatially nonhomogeneous solutions. Consequently, some pattern formations, like stripe and spots solutions, will appear. To illustrate theoretical analysis, we carry out numerical simulations.

Graph coloring is one of the issues that has been most noticed among combinatorial optimization issues. Many useful utility issues can be modeled as graph coloring issues. The general form of this application is to form a graph with nodes representing our favorite parts. The main problem of coloring the graph is the grouping of vertex graphs in small groups, so that no two heterogeneous vertices are in the same group. An important part of the application of graph coloring problem in management science is. The concept of traffic lights includes controlling the system of a traffic light so that a safe level of safety can be obtained. Modeling the problem of traffic lights has been proposed as a problem of assignment in combinatorial theory. This problem is also modeled as a graph coloring problem. In this paper, we have tried to model these problems in practical examples as the problem of staining the fuzzy graph and compare them with the proposed methods.

‎In this paper, for a discrete group ‎$G=mathbb{Z}‎astmathbb{Z}_n‎‎‎$‎ and a weight function of polynomial‎$‎‎‎omega_‎alpha‎‎$‎,‎ we show that the Burling algebra ‎$‎ell^1(G‎‎, ‎‎‎omega_‎alpha)‎$‎ is not weakly amenable ‎and ‎dihedral group‎ ‎$D_‎infty=mathbb{Z}_2astmathbb{Z}_2‎‎‎$ ‎is‎ amenable.‏ We also show that for a continuous weight function ‎$‎‎‎‏‎‎omega‎$ ‎under certain conditions ‎on group ‎$‎‎‎‎‎‏‎G‎$‎, if the Burling algebra $‎ell^1(G‎‎, ‎‎‎omega‎)‎$‎ is weakly amenable‎ then ‎$‎‎omega‎‎$‎ is bounded.‎In this paper, for a discrete group ‎$G=mathbb{Z}‎astmathbb{Z}_n‎‎‎$‎ and a weight function of polynomial‎$‎‎‎omega_‎alpha‎‎$‎,‎ we show that the Burling algebra ‎$‎ell^1(G‎‎, ‎‎‎omega_‎alpha)‎$‎ is not weakly amenable ‎and ‎dihedral group‎ ‎$D_‎infty=mathbb{Z}_2astmathbb{Z}_2‎‎‎$ ‎is‎ amenable.‏ We also show that for a continuous weight function ‎$‎‎‎‏‎‎omega‎$ ‎under certain conditions ‎on group ‎$‎‎‎‎‎‏‎G‎$‎, if the Burling algebra $‎ell^1(G‎‎, ‎‎‎omega‎)‎$‎ is weakly amenable‎ then ‎$‎‎omega‎‎$‎ is bounded.‎In this paper, for a discrete group ‎$G=mathbb{Z}‎astmathbb{Z}_n‎‎‎$‎ and a weight function of polynomial‎$‎‎‎omega_‎alpha‎‎$‎,‎ we show that the Burling algebra ‎$‎ell^1(G‎‎, ‎‎‎omega_‎alpha)‎$‎ is not weakly amenable ‎and ‎dihedral group‎ ‎$D_‎infty=mathbb{Z}_2astmathbb{Z}_2‎‎‎$ ‎is‎ amenable.‏ We also show that for a continuous weight function ‎$‎‎‎‏‎‎omega‎$ ‎under certain conditions ‎on group ‎$‎‎‎‎‎‏‎G‎$‎, if the Burling algebra $‎ell^1(G‎‎, ‎‎‎omega‎)‎$‎ is weakly amenable‎ then ‎$‎‎omega‎‎$‎ is bounded.

T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p

In a graph G=(V,E), an independent set I(G) is a subset of the vertices of G such that no two vertices in I(G) are adjacent. Any maximum independent set of a graph is called a diagonal of the graph. Let c be a proper (r+1)-coloring of an r-regular graph G. A vertex v in G is said to be rainbow with respect to c if every color appears in the closed neighborhood N[v]=N(v)∪{v}. Given a diagonal I of G, the coloring c is said to be silver with respect to I if every v∈I is rainbow with respect to c. G is called silver if it admits a silver coloring with respect to some diagonal. In [1], the authors introduced silver coloring and the following question is raised “Find classes of r-regular graphs G, that G is a silver graph". This paper is aimed toward study this question for the generalized Petersen graphs. In this paper we show that, if n≡0 (mod4) and k is odd, then P(n,k) is a totally silver graph. Also, for every natural number n, the existence of silver coloring for generalized Petersen graphs P(n,1), P(n,2) except for n=5, this is well-known petersen graph, P(n,3) except for n=10,14 and 26. Also, for any k>2,P(2k+1,k), and for any k>3,P(3k+1,k), and for any k>3, k ≠5,9 P(3k-1,k) are silver graphs.

Suppose that σ(n) is the sum of the divisors of n. This paper focuses on the Erdos-Serpinsky conjecture, which expresses the set of solutions of equation σ(n+1)=σ(n) is infinite. In present paper, we review some research on solutions of equations involving σ. As a generalization of equation σ(n+1)=σ(n), we investigate solutions of equation σ(n+1)=σ(n) under various conditions. For example, by using the representation of perfect numbers, we show that for a prime number n, n is a solution of equation σ(n+1)=2σ(n), if and only if n is equals to 5. Consequently, we conclude that for a prime number n≠5, n is a solution of equation σ(n+1)=kσ(n) if and only if n+1 is a k-perfect number. Also, we show that the only solution of equation σ(n+1)=2^r σ(n) which is presented as n=p ,n+1=2q_1 q_2…q_s ,where s≤r and q_1 ، q_2،…، q_s and p are odd and prime numbers, is (n,r)=(5,1)

One of the main challenges of performance evaluation in organizations and all systems is the irrationality and inaccuracy of the methods and criteria used. Traditional performance evaluation methods are mostly one-level, so they usually fail to provide sufficient feedback to identify inefficient units. Data envelopment analysis is a mathematical programming technique that compares the relative efficiency of several decision-making units based on observed inputs and outputs expressed by a variety of different scales. In practice, since many decision-making units are subdivided into smaller parts, with standard data envelopment analysis models that consider the organization as a whole, logical results are not obtained. Therefore, it would be better to use developed models like the two-stage DEA model to more accurately evaluate under investigation units in these conditions. Moreover, in cases that there are a large number of inputs and outputs, traditional DEA is not very efficient and it may consider a large number of units as efficient one. To deal with the problem, this study uses PROMETHEE method to rank criteria. After that, the efficiency evaluation problem is continued with most important inputs and outputs. Since the available information is usually incomplete and inaccurate, the problem is solved in the gray environment. The findings indicate a significant decrease in the number of identified efficient units which shows the improvement in discrimination power of DEA method. Additionally, the use of uncertain environment has led to more accurate estimates than previous definite models.

In this paper, based on the results and theorems of C^*-algebra valued S_b-metric spaces, we solve one type of matrix operator equations in L(H) defined by X-∑_(n=1)^∞▒〖A_n^* XA_n=Q〗, in which H is a Hilbert space and L(H) is the set of linear and bounded operators on H. Also, we prove that the Kannan contraction mapping has a unique fixed point in C^*-algebra valued S_b-metric spaces. Furthermore, we prove that the Chatterjea-type contraction mapping has a unique fixed point in C^*-algebra valued S_b-metric spaces. Finally, by using the Banach contraction principle in C^*-algebra valued S_b-metric spaces that has previously been studied by the authors of this article and by using the results of the above theorems, we solve the above matrix operator equation in C^*-algebra valued S_b-metric spaces. As well as, we show that this matrix operator equation has a unique solution in L(H), and this solution is a Hermitian operator.

The performance and resources allocation in large organizations such as banks, universities, and airports are one of the most important indicators in organizational management science. In this paper, by data envelopment analysis, which is a very powerful method of evaluating the efficiency of organizations, we analyze and review the performance and resource allocation. The optimal allocation of resources in organizations is considered to be the most important tool for implementing a long-term strategy and program for them, and the policies and objectives of the organization's plan are reflected in resources allocation of the activities. Indeed, given the importance of future organizations' performance, managers, taking into account the efficiency of each unit, provide strategies for target setting and how to allocate resources, including human resources, financial costs, technological facilities, and so on. On the other hand, given that actual data in organizations are usually random and stochastic, this paper addresses methods for allocating resources with stochastic data. Also, in line with this research, we will devise strategies for allocating resources as well as confronting limited resources in stochastic data, which will result in a new model for data envelopment analysis. In this model, stochastic data are presented with probability distribution due to probability. One of the most valuable achievements in this paper is to resolve the problem of allocating appropriate and optimal limited resources with stochastic data. Finally, with numerical results, the advantages of the new model are shown in relation to the previous models with stochastic data.

We know that ameromorphic function, is an analytic function on domain D such that,its single singular points on domain D, are of pole type. These functions are also called regular functions. Recently, meromorphic convex functions of order α have been defined and their properties have been investigated. In this paper, at first we introduce the meromorphic convex functions of inverse order α. In fact, convex functions of order revers α are a special class of analytic functions on unit open disk U that satisfy the following property:R(1+(f^' (z))/(zf^'' (z)))

In this paper we will give the definition of almost multiplicative linear functionals on commutative Banach algebras and investigate the closeness of these linear functionals with multiplicative linear functionals (AMNM property) . Several Banach algebra has this property, but not all of them. Due to relationship between the spectrum of an element of a complex Banach algebra and multiplicative linear functionals. Thus this investigation about almost multiplicative linear functionals give us some information about the spectrum of an element of a Banach algebra. In this paper We will give a very helpful theorem, for this investigation. Also we will show that, if in two commutative Banach algebras A and B, near any almost multiplicative linear functional, there is a multiplicative linear functional, then A×B also has this property and vice versa. We investigate this property for finite product of commutative Banach algebras. Also we will refer to some of the sequential spaces.

In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them. In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them. In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them. In this paper, the concepts of m-complete parts in a hyperring are introduced and its connection with complete parts of a hyperring are investigated. Moreover, ε_m-complete hyperrings are defined based on ε_m-relation in hyperrings, and a characterization is obtained by m-complete parts for them.

Let B(H) denotes the C*-algebra of all bounded linear operators on a complex Hilbert space H together with the operator norm. Suppose A is a Banach *- subalgebra of B(H) , Ω a compact Hausdorff space equipped with a Radon measure μ and α:Ω→[0,1] is an integrable function. We first introduce the space L^p consists of all operator-valued functions from Ω to A which have finite norm related to a L^p-norm. Next, it is proved that if p and q are conjugate exponents, for every two elements belongs to L^p and L^q with almost synchronous property for the Hadamard product, then we will have a new operator Chebyshev type inequality involving the Hadamard product. Also using some properties of positive linear functional "tr", we introduce a semi-inner product for square integrable functions of operators in L^2. Using the obtained results, we prove the Schwarz and Chebyshev type inequalities dealing with the Hadamard product.

In a proactive secret sharing scheme, a set of secrets are distributed among a set of participants in such a way that: 1) the participants’ shares could be renewed in certain time periods without the aid of the dealer, and 2) while some specific subsets of the participants, called authorized subsets, are able to reconstruct the secrets, other subsets could not obtain any information about the secrets. To the best of our knowledge, there exists only one proactive multi-secret sharing scheme in the literature. This scheme can be considered as the combination of a well-known proactive (single) secret sharing scheme and the one-time-pad encryption system. This scheme is only weakly secure meaning that the disclosure or reconstruction of one of the secrets in this scheme would be lead to the disclosure of all the secrets. In addition to being weakly secure, this scheme reconstructs all the secrets at once and does not provide gradual reconstruction of the secrets. To solve these problems, we use Lagrange interpolation and the Chinese remainder theorem in this paper and propose a new proactive multi-secret sharing scheme. The proposed scheme is a strongly secure proactive multi-secret sharing scheme. It allows gradual reconstruction of the secrets in a predetermined order and provides verifiability using the intractability of discrete logarithm problem.

In this paper, the notion of C_v-injectivity of monoid acts is studied. The behavior of C_v-injectivity with respect to products, coproducts and direct sums is investigated. We characterize monoids over which all acts are C_v-injective and show that any act over such monoids is vitally injective. The class of acts satisfying C_v-injectivity is determined. By means of the notion of C_v-injectivity, we find conditions over which any projective act is injective. Also, it is shown that on a left reversible monoid, any C_v-injective act with zero is C-injective. We prove that if any C_v-injective act on monoid S is vital injective, then monoid S is left leversible. Using the concept of vitally injective envelope, a class of C_v-injective acts is obtained. Moreover, we consider the notion of M_v-injectivity as a generalization of CC-injectivity and study when the factor act of an M_v-injective act is M_v-injective. As a result, we show that any factor of a principally weakly vital injective act is principally weakly vital injective.