مجله پژوهش های نوین در ریاضی
پیاپی 39 (آدر و دی 1401)

The need for integration has long been the focus of researchers and industry managers. Therefore, some researchers sought to coordinate and integrate production, maintenance and repair. The issues of integrating production planning, maintenance and repair and quality control with other parts of production and industrial systems reduce costs and increase the profitability of production organizations. Accordingly, in this research, integration and continuity in simultaneous planning of production areas and support in production organizations have been discussed. These areas include the schedule of production, maintenance and preventive maintenance, and human resources. Therefore, the mathematical optimization model is presented with the aim of manpower planning and increasing the volume of the company's production by considering the limitations of human resources. In this model, personnel skills, equipment usage rate and equipment failure rate in case of uncertainty with fuzzy method are used in the model parameters. The purpose of the proposed model is to minimize the labor force deficit over production efficiency. The results obtained from the implementation in a production organization by comparing the indefinite and meta-innovative solution show the improvement in the company's production with the least reasonable time, provide answers with the least possible error. Sensitivity analysis shows that the rate of equipment failure in the intervals before and after the preventive maintenance process has a great impact on the value of the objective function of the mathematical model.

In a unit disk graph two vertices are adjacent if the distance between them is less than or equal to one with a two-dimensional Euclidean meter. The size of the maximal independent set in a graph G is called the independent number denoted by α(G). The size of the minimal connected dominating set in a graph G is called the connected domination number denoted by γ_c^((G)). A subset S of vertices in a graph is called a dominating set if every vertex is either in the subset or adjacent to a vertex in the S. A dominating set is connected if it induces a connected subgraph. A connected dominating set is often used as a virtual backbone in wireless sensor networks to improve communication and storage performance. Clearly the smaller virtual backbone gives the better performance.However computing a minimal connected dominating set is NP-hard. In other hand relation between the size of the minimal connected dominating set in a graph G is very important. The aim of this paper is to determine two better upper bounds of the independence number dependent on the connected domination number for a unit disk graph. Further we improve the upper bound to obtain the best bound with respect to the upper bounds obtained thus far.

The common ways for analyzing the nonlinear autoregressive models are based on normality assumption of errors, whereas in many practical situations, the residuals show a nonnormal structure. The use of these methods leads to misleading and unreliable forecasts. Also, in these conditions, parametric and nonparametric methods do not have the necessary efficiency in estimating the nonlinear regression function. In this paper, a first-order nonlinear autoregressive model with dependent skew normal errors is introduced and a semiparametric method is proposed to estimate the nonlinear part of model. The parameters are estimated by the maximum likelihood (ML) method using Expectation-Maximization (EM) algorithm. The performance of the proposed model is investigated by a simulation study and analysis of a real data set of daily data on the exchange rate of the euro to the dollar.

In this paper, we focus on a new autoregressive stochastic frontier model based on the nonlinear function of the exogenous variable in the panel data. In classical financial models, the technical inefficiency is considered uncorrelated, which is often not satisfied in empirical cases. In the proposed autoregressive stochastic frontier model, the error consists of two components, statistical error, and technical inefficiency, so that technical inefficiency is assumed to be autocorrelated. Autocorrelated technical inefficiency can be interpreted as the technical inefficiency of a company at the current time depends on the extent of the company's previous technical inefficiency and its current transient inefficiency. The semiparametric method for estimating the nonlinear function of the exogenous variable is calculated through a two-step process with Taylor series expansion and nonparametric adjustment factor. The expectation-maximization approach is used to estimate the parameters of the model and the estimation performance is evaluated by Monte Carlo simulation.

Let R be a ring and M be an R-R bimodule. R is called left quasi-morphic if for every a∈R, there exist elements b,c∈R such that l_R (a)=Rb and l_R (c)=Ra. Besides, R is said to be left morphic whenever in the above definition b and c can be chosen the same. In this paper, we investigate conditions under which the trivial extension R⋉M of R by M is (quasi-)morphic. We present some examples showing that neither R nor M inherits the (quasi-)morphic property from R⋉M, and vice versa. So, we obtain several necessary and sufficient conditions under which R⋉M is (quasi-)morphic. For instance, we show that left quasi-morphic property of R⋉M implies that M_R is divisible. Moreover, we prove that if R⋉M is left quasi-morphic and there exists x∈M such that either r_R (x)=0 or l_R (x)=0 then (_R^ )M is cyclic. In particular, if R is commutative, then M≃R and R is also quasi-morphic. In addition, we investigate the (quasi-)morphic property of R⋉M whenever M is free as a left (right) module over R. Consequently, we prove the following theorem which is the main outcome of this paper: if R is an integral domain and (_R^ )M is free, then R⋉M is left (quasi-)morphic if and only if R is a division ring and (_R^ )M≃(_R^ )R . As an application of this theorem, the result which is proved by Lee and Zhou, and also by Van An and et al., in 2007 and 2016, respectively, is deduced.

Although fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. The convexity is an assumption which lead to converting of modular space to the normed space so relaxing this assumption lead to stronger theorems. But as we know much theorems are proved on convex modular spaces.In this paper, we introduce the modular-like definition which is a generalization of modular space. And common fixed point of generalized weakly contraction mappings are proved. We focus on convexity and boundedness of modular-like in fixed point results taken from the literature for generalized weakly contractive mappings. So our results, generalized fixed point theorems in many acpects. Afterwards we present examples and an application to a particular form of integral inclusions to support our main results.