مجله پژوهش های نوین در ریاضی
پیاپی 30 (خرداد و تیر 1400)

This paper presents a simultaneous optimization model of location and server allocation for a company that enters into a competitive market. The goal is company's profit maximization. Customers are likely to select the facility based on price, travel time and queue time. Furthermore, as a contribution to the literature, it is assumed that customer awareness of the levels of waiting times in the facilities will increase in stages and over the successive uses of the facilities network. Demand is defined elastic and as a function of the customer's desirability of network’s design and the cost of delivering service at a facility is defined as a function of its demand attraction. An improved differential evolution algorithm has been developed to solve the model and sample problems to demonstrate its efficiency have been solved.

We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).We study the relation between homomorphisms of Banach algebras A and B with that of 𝒜⊗̂ ℬ. Then, we investigate 𝜎− weak amenability of (𝒜⊗̂ ℬ).

The purpose of this research is to present a method based on DEA-TOPSIS for ranking the DMUs in group decision making. In the proposed method, after creating an expert team and determining their weights, the DMUs, inputs and outputs are determined and ranked in three stages. In the first stage, by using Euclidean Distance, the matrix of each expert is normalized and consequently, the DEA models corresponding to each expert are solved. The DMUs are divided into two groups, the first group consists of DMUs where at least one experts’ opinion is inefficient and the second group consists of DMUs where the views of all experts are efficient. In the second stage, the rank of the DMUs of the first group is determined by calculating the weighted arithmetic average. In the third stage, the rank of the DMUs of the second group is determined using the TOPSIS method for each expert, consequently, the final rank of the DMUs is calculated using the Weighted Borda Scoring Method. Then the proposed approach was implemented to rank the six-paths of the Blue Ocean Strategy of the IRAFA industry and management group. The IRAFA team of experts, consisting of seven senior experts, was formed, and their weights were determined. It was also found that six paths to restructure the Blue Ocean Strategy (DMUs) are effective on IRAFA Value Innovation, and the DEA model has four outputs (utility, price, cost, and acceptance). The results of solving the DEA model of each expert showed that there are four paths in the first group and two paths in the second group. Applying the Weighted Borda Scoring Method to rank the DMUs of the second group shows that creating a functional-emotional orientation for the organization's customers is the top priority of IRAFA

Lusternik schnirelmann category and topological complexity are important invariant of topological spaces, now a days a lot of mathematician are interested to work in this area. In this paper in order to detect properties of spaces, we will compute Lusternik schnirelmann category and topological complexity of some of these spaces by computing the cup-length and zero-cup-length. These include the manifolds that we will calculate for the topological complexity and Lusternik Schnirelmann category are some of the Gressmannian manifolds, such as G_2 (R^4), and the products of manifolds, especially the products of the real projective spaces and their wedge products. Let TC(X) denotes the topological complexity of the path connected topological space X, and also cat(X) denots the Lusternik Schnirelmann category of topological space X. In the calculation of these numbers, we will first compute the upper and lower bounds of these invariants for considerable spaces, and we will try to approximate the boundaries with the methods and techniques to get the exact number. In this paper, we will use the cup-length and zero divisors cup length of spaces as the lower bounds for calculating TC and cat that are important computational tools for calculating these numbers.

Given a graph Г, we denote the kth iterated line graph of Г by LK(Г) and LK(Г)=L(LK-1(Г)). In particular, L0(Г)=Г and L1(Г)=L(Г) is the line graph of Г. The toroidality (and projectivity) index of a graph Г is the smallest integer k such that the kth iterated line graph of Г is non-toroidal (and non-projective). We denote the toroidality index of a graph Г by ξT and the projectivity index of a graph Г by ξP. If LK(Г) is toroidal (and projective) for all k≥0, we define ξT=∞ (and ξP=∞). Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by 𝔍R, is defined as a simple graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 - xy is not a unit of R. In this paper, we study the toroidality and projectivity indices of Jacobson graphs. We give full characterization of this graph with respect to its toroidality and projectivity indices. Moreover, the toroidality and projectivity index of Jacobson graph is either infinite or two.

Injectivity with respect to some subclasses of monomorphisms in a category has been studied. In this article, we define the notion of regular poprime monomorphism in the category of S-posets with a monotone action of a pomonoid S on them and study M-injectivity where M is a subclass of regular poprime monomorphisms. More ever, we characterize their behaviour considered constructions such as the product, coproduct, direct sum, pullbacks, and pushouts of S-posets. The main purpose of this paper is to find a relation between regular poprime injective and poprime extensions of S-posets.

There has been many researches in the field of combinational commutative algebra; however, what makes this research distinct from the previous ones is its focus on monomial ideals and their connection to graphs. The present study aims at various goals one of which is analyzing the existence of linear resolution of such ideals. Concerning combinatorial commutative algebra there are numerous methods for creating connection between combinational objects and algebric objects‎. ‎This article is to study such objects through corresponding monomial ideals with graphs and simplicial complexes‎. ‎The most significant treatable ideals of simplicial complex include edge ideal and Stanly-Reisner ideal‎. Let r be a positive integer. A monomial ideal I is said to be linear in the first r steps, if for some integer d , β_(i.i+j) (I)=0 for all 0≤i

Let A be a dual Banach algebra, and let φ be a w^*-continuous homomorphism from A to C.In this paper we study the projectivity of C_φ as a A-bimodule as well as a WAP〖(A^*)〗^*-bimodule.Let A be a dual Banach algebra, and let φ be a w^*-continuous homomorphism from A to C.In this paper we study the projectivity of C_φ as a A-bimodule as well as a WAP〖(A^*)〗^*-bimodule.Let A be a dual Banach algebra, and let φ be a w^*-continuous homomorphism from A to C.In this paper we study the projectivity of C_φ as a A-bimodule as well as a WAP〖(A^*)〗^*-bimodule.Let A be a dual Banach algebra, and let φ be a w^*-continuous homomorphism from A to C.In this paper we study the projectivity of C_φ as a A-bimodule as well as a WAP〖(A^*)〗^*-bimodule.Let A be a dual Banach algebra, and let φ be a w^*-continuous homomorphism from A to C.In this paper we study the projectivity of C_φ as a A-bimodule as well as a WAP〖(A^*)〗^*-bimodule.

Our main objective in this paper is to analyze Bayesian Shrinkage Estimators of the parameter of two-parameter Exponential Distribution Scale under General Entropy Loss Function based on the prior conjugate distribution and Progressive Type-II Censored Data in the presence of the location parameter. To this end, in the present paper, firstly, we present Shrinkage Estimator of scale parameter based on the Bayesian estimator that obtained under General Entropy Loss Function, and prior conjugate distribution, and then investigate the efficiency of the proposed estimator with other estimators, such as maximum likelihood estimator, Bayes estimator, empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator. The method used in this paper to compute empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator is guessing. Using simulated data based on Monte Carlos’ method, under six censorship schemes and with two prior distributions of Jeffrey and Hartigan, the effectiveness of estimators is compared. Finally, using actual data, the efficiency of the proposed estimators will be examined.

If a matrix is square and nonsingular namely its rows (or columns) are linear independent, it is said that the matrix is invertible. In recent years, in various fields of applied mathematics, there has been a need to find the inverse of singular and rectangular matrices. Therefore, an inverse was defined that founds the inverse for larger class of nonsingular matrices while still having some properties of conventional inverse which gives the same inverse when the matrix is nonsingular. This inverse is called generalized inverse or quasi-inverse. In this paper, the most common types of such inverse are investigated.

Let be a simple and undirected graph, consists of a set of vertices and a set of edges If the vertices and are connected by an edge then we write . For any vertices , the degree of a vertex in , denoted by , is the number of edges of incident with . A topological index is a numerical quantity related to a graph which is invariant under graph automorphisms, Let be a topological index of a graph , for every graph isomorphic to , we have . The first of topological indices, which based on degree of vertices of graphs are first and second Zagreb indices. In this paper we study on another kind of this graph invariants called total irregularity. The total irregularity of G is a graph invariant and defined as the follows, . In this paper, we introduce two kind of transformations on polyomino chains and by using these transformations obtain upper and lower bounds of the total irregularity of polyomino chains. Moreover, we prove that the linear chain and zigzag chain are extremal polyomino chains with respect to total irregularity.

In this paper, we introduce the decomposition property on locally compact groups and we give a multi-norm structure based on the Fourier and Fourier-Stieltjes algebras on locally compact groups with this property. We show that compact groups have the decomposition property. This construction generalizes the known multi-norm structure of L1-algebras on compact abelian groups. Also, we study some special multi-bounded maps on the Fourier algebras and improve some results in this theory.

In home health care (HHC) problem, the assignment of medical teams to patients and scheduling medical members are done manually, which is a time-consuming process and sometimes are not optimized. In this article, we examine the scheduling assignment of medical teams to the patients with a new innovative approach based on resource constrained project scheduling problem. Advantages of proposed approach can be included the use of theorems, standard benchmark problems, and various (meta-innovative) scheduling methods to improve assignment quality, as well as determining the minimum number of human resources required to cover all medical services requested by patients. In this approach, we solve the HHC problem by defining a dynamic priority rule and using the parallel scheduling scheme. Evaluation criteria for evaluating the quality of feasible solutions resulting from scheduling include minimizing the travel time of medical team members, reducing overtimes, maximizing the number of human resources which are used, and so on. The set of feasible solutions satisfy to some constraints such as the total working time in the contracts, the hardware time window of each job, the mandatory breaking time, and the optimal assignment of the medical team to patients (according to the type of service requested by the patient). The numerical results obtained from calling the proposed algorithm on the Kolisch’s benchmarks are presented to evaluate the performance of proposed approach. Based on the results, the proposed algorithm has a high ability to solve the HHC problem.

In this paper, we introduce the notion of state extended ideal associated to a subset of state MV-algebras ‎‎and‎‎‎‎‎‎ investigate the related properties. A characterization of this state extended ideal in a state MV-algebras is given‎. In addition, we study the relation between state extended ideals and state prime ideals, state maximal ideal in a state MV-algebra. We show that if f:A→B is state homomorphism MV-algebra such that f(A^' )=B', then we have (1) If I is a state stable relative to B'⊆B, then f^(-1) (I) is a state stable relative to A'⊆A. (2) If f is an onto and I is a state stable relative to A'⊆A, Ker(f)⊆I, then f(I) is a state stable relative to B'⊆B. ‎In ‎finally, ‎we define state stable ideals and we show that the ‎class ‎‎‎S(B)‎ of ‎all ‎state stable ‎ideals ‎relative ‎to ‎‎ B⊆A ‎is ‎also a‎ ‎complete ‎Heyting ‎algebra, ‎for ‎a state ‎‎MV‎-algebra ‎‎(A,σ).

Let G be a finite group. We denote by n_{p}(G) the number of Sylow p-subgroup of G, that is, n_{p}(G)=|mathrm{Syl}_{p}(G)|. Denoted by m_{i}(G) the number of elements of order i of G. Given a positive integer n and a prime r, we write n_{r} to denote the full r-part of n, so we can factor n=n_{r}m, where m is not divisible by r. Now fix a prime p. We say that a positive integer n is a strong Sylow number for $p$ if for every prime q, the full q-part n_{q} of n satisfies n_{q}equiv 1 (mod p). Note that if n is a strong Sylow number for p, then nequiv 1 (mod p), and thus n is not divisible by p. Note also that the set of strong Sylow numbers for p is closed under multiplication. Let S be a nonabelian simple group that is not isomorphic to L_2 (r), where r is a Mersenne prime and let p be the greatest prime divisor of |S|. In [1, Conjecture E] A. Moreto conjectured that if a finite group G is generated by elements of order p and G has the same number of elements of order p as S, then G/(Z(G))≅S. In this paper, we verify the conjecture for the sporadic simple groups.