فصلنامه مدل سازی پیشرفته ریاضی
سال یازدهم شماره 3 (پاییز 1400)

In this article, we first investigate some extensions of Kullback-Leibler information and theirproperties. Then, we consider the moment constraints for the maximum distribution of cumulative residualentropy and investigate the relationship between the cumulative residual Kullback-Leibler information(CRKL) and cumulative residual entropy (CRE). We also discuss the methods for estimating the scaleparameter of Rayleigh distribution and provide two estimation methods. In the following we use cumulativeresidual Kullback-Leibler information as a goodness of fit test statistic. Then we compute the criticalvalues and the power of proposed tests and compare the power values with with the power of other tests.Finally, we apply the tests for a real data set.

In this paper, we classify three-dimensional super-Einstein Lorentzian Lie groups as homogeneous manifolds. For this, at first level we present a complete classification of Einstein Lorentzian Lie groups, then we complete this classification by super-Einstein condition. For some of the geometric descriptions of the classification, we study the Einstein-like conditions, that is, the Killing and Codazzi conditions, on the three-dimensional super-Einstein Lorentzian Lie groups. Finally, we present the three-dimensional super-Einstein curvature homogeneous Lorentzian manifolds of order one, for non-homogeneous examples.

In spatio-temporal data analysis, the most common way to consider the spatio-temporal correlation structure of data is to use the covariance function, which is usually unknown and estimated based on observations. This method requires constraints such as stationarity, isotropy and separability for the random field. Although the acceptance of these hypotheses facilitates the fitting of valid models to the spatio-temporal covariance function, they are not necessarily realistic in applied problems. In this paper, to expedite the calculation of spatio-temporal prediction for a non-stationary and non-separable random field, a possible model based on spatial-temporal covariance tensor analysis based on Tucker analysis is investigated. Then, we show the proposed method for predicting wind energy based on spatio-temporal wind speed data at 31 weather stations in Iran.

In this paper, a nonparametric time series model based on fuzzy observations is presented.Fuzzy prediction values are estimated using the generalization of the Nadaraya-Watson method in a fuzzy environment. An algorithm for achieving autoregressive order and optimal bandwidth is stated and then criteria are introduced to evaluate the prediction values. In the following, the performance of the proposed model is examined and analyzed using real data. The effectiveness of the proposed model is also compared with the other time series models with fuzzy data.

In this work, we propose a novel technique for solving the nonlinear fractional Volterra-Fredholm integro-differential equations (FVFIDEs). This method approximates the unknown function with the Legendre wavelets. To do this, the Legendre wavelets are used in conjunction with the quadrature rule for converting the problem into a linear or nonlinear system of algebraic equations which can be easily solved by applying the mathematical programming techniques. Furthermore, the existence and uniqueness of the solution are proved by preparing some theorems and lemmas. Also, the error estimate and convergence analysis of the method will be shown. Moreover, some examples are presented and their results are compared to the results of Chebyshev wavelet, modification of hat functions, NystrÖm and Newton-Kantorovitch methods to show the capability and accuracy of this scheme.

Pathogenic factors can affect several groups of an epidemic. In this paper, by using the Brownian motion, an Ito stochastic differential equation is presented to express the stochastic behavior of an infected disease based on mean and variance. The model includes different species of population with the presence of suspected, exposed, infected and immune types. The model covers all the previous models including SI, SIS, SIR, SEIR, and SIRS. Also, the incubation, an important period in the epidemic, is considered. Finally, a few numerical examples of this model's behavior are presented.

In this paper, statistical inference is considered for k-component coherent systems, when the system lifetime data is progressively type-II censored. In these coherent systems, it is assumed that the system structure and system signature are known and the component lifetime distribution is exponential. Pivotal and Bayesian methods are introduced for point estimation of the component lifetime parameter, and these methods are compared with the maximum likelihood and the least squares methods existing in the literature. Pivotal confidence interval, Bayesian confidence interval and confidence interval based on the likelihood ratio test are computed. Using Monte Carlo simulations, different point and interval estimates are compared and it is observed that pivotal and Bayesian methods perform better than other existing estimation methods.

This research proposes a two-phase algorithm whose main idea is based on meta heuristic algorithms, Big Bang and Black Hole. In the first phase of this algorithm, the artificial ants scan the reticulated rectangular region in parallel directions. The best points in the ant’s navigations are used as starting points for the second stage of this algorithm. Big Bang and Black Hole algorithms, as an exploitation phase, try to investigate more accurate answers in the neighborhood of the starting points by reducing the neighborhood radius. Numerical examples confirm that this algorithm is capable to achieve an optimal solution with the desired accuracy and low computational costs.

The purpose of this paper is to present a new method for solving multi-commodity and bounded transportation networks in optimization problems.Multi-commodity and bounded transport networks with the aim of minimizing the total cost of transporting goods in the network, is an important and widely used issue in optimization problems.Two very important and key features of multi-commodities and bounded are examined in different articlesand have provided algorithms to solve it.We are ,based on the network simplex method, offer an innovative method without any complexity to obtain the solutions of multi-commodity and bounded transportation networks problems. At the end, , the efficiency of this method is shown with some numerical examples.

In this study, we consider the statistical inference of multicomponent stress-strength reliability when stress and strength variables follow power Topp-Leone distributions. This system has independent and identically distributed strength components and each component is exposed to a common stress and is reliable if at least out of strength variables exceed the stress variable. The reliability of the system is estimated in view of classical and Bayesian in two cases. In the first case, we suppose that the first shape parameters are same and second shape parameters are different and in the second case, it is assumed that the common first shape parameter is known. Finally, a simulation study is performed to compare the performances of the estimators and one data set is presented for the application of methods.

Let‎ $H(mathbb{D})‎$ ‎be ‎the ‎space ‎of ‎all ‎analytic ‎functions ‎on‎ ‎$mathbb{D}‎$. ‎For ‎‎$‎u,vin H(mathbb{D})‎$ ‎and ‎self-map ‎‎$‎psi‎(‎psi(mathbb{D}‎)subset ‎mathbb{‎D}‎‎)‎$‎‎‎ the‎ Stevi' c-Sharma ‎type ‎operator ‎is ‎defined ‎as ‎follows‎‎begin{align*}‎‎T_{u‎, ‎v‎, ‎psi}f(z) = u(z) f{(psi(z))}‎+ ‎v(z) f'(psi(z))‎ ,‎quad fin H(mathbb{D} )‎, ‎quad zin mathbb{D}‎.‎end{align*‎}‎‎In ‎this ‎paper, ‎we ‎study ‎boundedness ‎and ‎compactness ‎of‎ Stevi' c-Sharma ‎type ‎‎operator ‎from Besov space into Zygmund ‎space ‎and ‎we ‎obtain ‎some ‎equivalence ‎conditions ‎for‎ boundedness ‎and ‎compactness ‎of ‎such ‎operator.

Ranking of efficient two-stage decision-making units (DMUs) is one of the most important issues in network data envelopment analysis (DEA), which hitherto many methods have been presented in this context. However, each of these methods has at least one of these drawbacks: Non-linearity, High computational complexity, Lack of distinction between strong and weak efficient two-stage DMUs, Measuring different efficiencies for each of two-stage DMUs, Failure to consider the internal structures of two-stage DMUs in calculating efficiency and ranking them, and Assigning the same ranks to the efficient two-stage DMUs. Hence, to tackle these problems, this study proposes a network DEA-based method to rank the extremely efficient two-stage DMUs with a series structure. The proposed method is based on eliminating these efficient two-stage DMUs from the reference set and evaluating the efficiency of inefficient two-stage DMUs using the Euclidean norm. Finally, two numerical and empirical examples are presented to illustrate the use of the proposed method.