فصلنامه مدل سازی پیشرفته ریاضی
سال نهم شماره 1 (بهار و تابستان 1398)

In this paper, we consider a general linear model where missing data may occur in response and covariate variables. We propose a new test based on Ramsy's test to identify goodness of fit for general linear model with missing data. We show that under the null hypothesis, our test functions for complete case analysis follow a Fisher distribution and the other test function used for analysis with available data converges in distribution to Quasi-Fisher distribution. Furthermore, we compare proposed test functions by using some simulation studies. Also, we apply our methods in analyzing a real data set.

The climatic and environmental conditions in each region contribute to the outbreak of certain diseases. Therefore, providing a map of the event rate of a disease or mortality from various diseases on a geographic area is one issue of concern for physicians and health experts. Considering that gastric cancer is the most common cancer in Gilan province, Iran, in this paper, we study the impact of some risk factors on the rate of this cancer for the cities of Gilan province by using two auto-binomial and auto-beta-binomial Bayesian spatial models. The other purposes of this study are providing the gastric cancer rate prediction map and comparing the performance of the two proposed models. We used a dataset from the Razi Educational Center of Rasht in which the data were collected for sixteen cities of Gilan during the period of 2012-2017. We fitted the proposed models for these data by using an approximate Bayesian approach, called the integrated nested Laplace approximation (INLA). Based on the results, it was found that prediction of the rates of cancer in most of the cities of Gilan are similar by using of both models; in cities where there is a difference, the auto-binomial model predicts a higher rate than the auto-beta-binomial model. The reason for this is also that the auto-binomial model is over-fitted, which reduces its ability to predict.

In this paper, a constrained optimization problem is formulated and solved to determine the smallest joint confidence region for Pareto parameters based on the progressively Type-II censored samples. The objective function is the area of the confidence region and the problem constraint is the specified confidence level. The proposed joint confidence ‎region is also valid for the complete samples and right censored samples. The area of the smallest proposed confidence region and the area of the balanced confidence region are compared. Finally, two numerical examples are presented to describe the proposed optimization method.

Suppose that a system is exposed to a sequence of shocks that occur randomly over time, and δ_1 and δ_2 are two critical levels such that 0 < δ_1

We consider a two-state network consists of n components and assume that the failure of components occur according to a nonhomogeneous Poisson process. Some networks have the property that after the failure, some of the components remain unfailed. The remaining unfailed components might be resumed from the network and be used again in a new network. In this paper, we explore some aging properties and stochastic comparisons of the residual lifetime of remaining unfailed components of the failed network.

In this paper, a new and effective optimization algorithm is proposed for solving the nonlinear time fractional convection-diffusion equation with the concept of variable-order fractional derivative in the Caputo sense. For finding the solution, we first introduce the generalized polynomials (GPs) and construct the variable-order operational matrices. In the proposed optimization technique, the solution of the problem under consideration is expanded in terms of GPs with unknown free coefficients and control parameters. The main advantage of the presented method is to convert the variable-order fractional partial differential equation to a system of nonlinear algebraic equations. Also, we obtain the free coefficients and control parameters optimally by minimizing the error of the approximate solution. Finally, the numerical examples confirm the high accuracy and efficiency of the proposed method in solving the problem under study.

In this paper, it is focused on a specific category of hybrid optimal control problems with autonomous systems. Because of existence of continuous and discrete dynamic, the numerical solutions of hybrid optimal control are not simple. The numerical direct and indirect methods presented for solving optimal control of hybrid systems have drawbacks due to sensitivity to initial guess and the inability of finding a global minimum solution. Meta-heuristic methods have been proposed. In this method, Meta-heuristic methods (e.g. using PSO) is used to determine the mode sequence, and by the attention to the prescribed the mode sequence, a problem with a determinate mode sequence is obtained, and then the switching times, the optimal value of the target function and the state and control are estimated by using the direct approach. Actually, using the proposed model, we will eliminate basic challenges of solving optimal control of hybrid autonomous systems problems, in which the number of switches and mood sequence are unknown .Finally, numerical results for solving an example presented.

In the past decades, in the area of mathematical ecology, the dynamical properties occurring in the predator-prey models have been studied. Moreover, the stability and boundedness of the solution for population model such as cyclic, delayed and etc. have been studied. In the present paper, a nonlinear cyclic predator-prey system with sigmoidal type functional response is analyzed. Indeed, a model of four species predator-prey system has been investigated and the sufficient conditions for stability and boundedness of the solutions of predator-prey system have been presented. For this purpose, the differential inequality theory is employed and finally, by constructing a suitable Lyapanov function the existence and uniqueness of asymptotically periodic solution which is globally asymptotically stable are proved.

In this article we introduce and study the concept of -almost semi Artinian modules. Using this concept we extend some of the basic results of -almost Artinian modules to -almost semi Artinian modules. Moreover we introduce and study the concept of -semi Krull modules. We show that if M is an -semi Krull module, then the perfect dimension of M is either or +1.

Let be a non-Archimedean normed space of real numbers. In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second order linear differential equations with non-constant coefficients, where are given continuous functions, in the non-Archimedean normed space . In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second order linear differential equations with non-constant coefficients, where are given continuous functions, in the non-Archimedean normed space .