مجله پژوهش های نوین در ریاضی
پیاپی 37 (امرداد و شهریور 1401)

In this paper, the problem of estimating unknown parameters is investigated when lifetime data following Poisson-exponential distribution under classical and Bayesian frameworks based on progressively type-II hybrid censored data. We compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimators of model using Expectation-Maximization (EM) and Stochastic Expectation-Maximization (SEM) algorithms under classical approach, these algorithms are easily implemented. We compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using different loss functions namely squared error, LINEX as well as general entropy in Bayesian framework. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods. Finally, we present a conclusion.

Performance appraisal is essential for any bank to plan and control. And considering the role of banks in the country's economy, measuring its efficiency is very important, so it is necessary to use appropriate models to assess the efficiency of banks. One of these models is data envelopment analysis. Due to the multi-stage structure of banks, conventional data envelopment analysis models cannot be used, because conventional models do not pay attention to internal structure, intermediate products or communication activities And provide an estimate of the quality of performance. Also, conventional models pay less attention to the nature of inputs and outputs and have a radial nature, so the aim of this study is to provide a new model of NDEA with SBM model and FDH model for eliminating the weakness of conventional DEA models and Have a higher resolution. Also, for experimental study, to evaluate the performance of 20 branches of a commercial bank by considering the indicators, number of personnel and staff working hours as input and free deposits (free of charge and costly deposits) and facilities as intermediate indicators (intermediaries). And the indicators of overdue receivables and received fees have been considered as output and the ranking the branches , and finally efficient and inefficient branches have been identified. And the necessary strategies were given to improve the performance of inefficient branches.

The Best-Worst Method (BWM) is one of the latest methods in Multiple Attribute Decision Making (MADM) problems. The mentioned method determines the optimal solution by forming and solving a Non-Linear Programming Model (NLPM). In respect to the difficulties of solving the relevant NLPM, some attempts have been made to provide Linear Programming Models (LPM) or Equivalent Mixed Linear Programming Models. But there are some deficiencies in each of the proposed models. In this paper, by removing the mentioned deficiencies, an algorithm was proposed to estimate the solution of BWM NLPM with an acceptable error by forming and solving Mixed Integer Linear Programming Models (MILPMs). In the suggested algorithm, first, the equivalent model of NLPM (ENLPM) was formed. Then by Piecewise Linear Approximation (PLA) using the SOS2 method, the non-linear sentences of ENLPM were approximated and the first MILP model was formed and solved. If the error of solution is not acceptable, improving the PLA of the ENLPM nonlinear sentences, the forming of new MILPMs, and its solving continues until a solution with acceptable error obtained. To investigate the reliability of the algorithm, a new method for generating samples was proposed. Then using this method, 128 samples with three and five attributes were generated. The results of implementing the proposed algorithm to solve generated samples showed the performance and efficiency of the proposed algorithm. In this regard by forming and solving a maximum of three MILPMs of the samples, an estimation of the solution with 1% error was obtained.

In this study, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved using a series based analytical techniques Parameterized Perturbation Method (PPM). The concept of this method is briefly introduced, and its application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of PPM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate ( ) and permeation Reynolds number ( ) on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.

To face uncertainty in the real world, the two value logic has gradually replaced the fuzzy logic. In some real world problems, accurate determination of membership value is difficult and decision- making is associated with uncertainty and hesitation. This new perspective manages the uncertainty caused by hesitation. Generalized trapezoidal hesitant fuzzy numbers (GTHFN), whose membership degree is expressed by several trapezoidal fuzzy number, is best suited to solve the decision-making problem in real life than real numbers. In this paper, we refer to a new concept called 'generalized trapezoidal hesitant fuzzy numbers' and its combination with data envelopment analysis. Using this information, we consider the deviation and the score values as input and output of the data envelopment analysis model in two stages respectively; then we used the result to construct a paired comparison matrix and eventually we prioritize the receivers decision making units. To use some concepts in the proposed decision making method, we first present some definitions of concepts such as the score and deviation functions from the generalized trapezoidal hesitant fuzzy numbers. Finally, a numerical example is presented for the proposed method to confirm its applicability, and the ranking result is compared with the methods of AP, TOPSIS with GTHF number and the weighted geometric operator in [7].

In this paper, we propose an estimate of reliability in a multicomponent stress-strength system. The reliability of such a system is obtained when strength and stress variables are given by Gompertz distribution with common scale parameter λ and different shape parameters α and . The system reliability is estimated using maximum likelihood estimation (MLE) and the best observational percentile estimation (BPE) methods in samples drawn from strength and stress distributions. Also, the asymptotic confidence interval for system reliability is obtained. The reliability estimators obtained from both methods are compared using mean squares error criteria and confidence interval length via Monte Carlo simulation. In the end, using two real data sets we illustrate the procedure. Before analyzing the data, we first show that the Gompertz distribution is fitted to this data sets using the Kolmogorov-Smirnov goodness-of-fit test statistic. In general, the simulation results show that due to the increase in sample size, the average mean, mean squares error and length of confidence interval in the maximum likelihood method is decreasing compared to the best percentile estimator method. This indicates that the maximum likelihood method is more efficient. Also, in this paper, it was shown that the one out of three component system reliability is more than the one out of two component system reliability for both methods of estimation.

Performance evaluation is one of the important tasks of management in order to better understand the ‎past successes of a manufacturing unit and plan for its future development. The goal is to determine ‎whether the unit can be expected to increase its output with current input, or while maintaining the ‎current production output, how much savings in input can be made merely by increasing efficiency. A ‎system is usually composed of multiple parts, each with a specific function. When we are interested in ‎the performance of the system as a whole unit, where only inputs coming into the system and outputs ‎going out of the system are considered, it is called whole unit or black box analysis, because how ‎inputs are converted into outputs through intermediate products is not considered. The whole unit ‎analysis provides a general idea of the performance of a unit. However, since the system usually ‎consists of several interrelated parts, ignoring the functions of constituent parts may cause misleading ‎results. To properly evaluate the performance of a system, this article proposes a set of additive ‎models. The proposed models measure the inefficiency slacks of a system from both optimistic and ‎pessimistic views. Therefore, an overall performance evaluation for each system is obtained. An ‎example of the banking industry in Iran is offered to explain how to calculate the inefficiency slacks ‎of the system and processes.‎

Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essential. In this paper we present a numerical method based on the transferred Legendre polynomials to solve multiple pantograph delay differential equations. In this method we use the Legendre-Gauss-Lobato collocation points to discretize the problem and turn the problem into a nonlinear programming problem. From solving this nonlinear programming problem we get an approximate solution for the the main multiple pantograph delay differential equation. We analyse the feasibility of the nonlinear programming problem and the convergence of the obtained approximate solution to the exact solution. In addition by solving several numerical examples and comparing the method with other methodsWe show the efficiency and the capability of the proposed method.

Let v be a henselian valuation on a field K, and v ̃ be its unique extension to the algebraic closure K ̃ of K. An element α∈K ̃K has a distinguished pair if the corresponding set M(α,K) (defined as the following) has a maximum elementM(α,K)={v ̃(α-β)┤β in K ̃,[K(β) ∶K]<[K(α) ∶K]}.In this case, a pair (α,β) of elements of K ̃ is a distinguished pair for α whenever β is an element of smallest degree over K such that deg⁡α>deg⁡β and v ̃(α-β)=supM(α,K). In this paper, we first present some results about distinguished pairs of algebraic elements of arbitrary degree over henselian valued fields. Then considering the importance of algebraic elements of prime degree in the extensions of valued fields, we concentrate on such elements. In particular, for α∈K ̃ of prime degree over K, we give a necessary and sufficient condition for the existence of the maximum of the corresponding set M(α,K) by using the minimal polynomial of α over K.

In the paper, we introduce the notins of PMV-norm on pseudo MV-algebras and study some it’s algebraic properties. We also show that there is a contrvariant functor of pseudo MV-algebras to category of semigroups. We define (para) topological pseudo MV-algebras and find the connection between them and PMV-pseduo norms. Finally, we define filter topology on this algebraic structure and show that it is a paratopological pseudo MV-algebra.