فصلنامه مدل سازی پیشرفته ریاضی
سال یکم شماره 1 (بهار و تابستان 1390)

Stochastic differential equations (SDE) play a relevant role in many application areas such as collision, population and polymer dynamics, genetic regulation, investment finance and biology. The procedure of collision among particles was modeled by an infinite dimensional differential system (in the discrete case) and a nonlinear partial integro-differential equation (in the continuous case). The discrete case may be approximated with a parabolic partial differential equation. In this paper, using the Monte-Carlo method, we obtain an approximation for solving the parabolic differential equation in the continuous form.

In this article we have introduced and studied the notation of α-loewy modules (0-loewy modules is just a loewy module). Using this concept we extend some of the basic results of loewy modules to α-loewy modules and we find a universal upper bound for Krull dimension over ߙ- loewy rings. In particular, we show that module M has Krull dimension α if and only if each factor module of M is lambda-loewy modules for some lambda <=α and has finite Goldie dimension.

Presenting a new method for simultaneous determination of the control and trajectory functions in an optimal control problem governed by a vibrating circular surface system, is the main purpose of this paper. First, by identifying the form of the trajectory function, doing discretization and using the properties of measure, the problem is linearized. Then, by doing some approximation steps, the nearly optimal pair of trajectory and control with the optimal value of the objective function are obtained via solving a finite linear programming problem. A numerical example is also presented.

In the present research, inter-provinces immigration and its determinants in a 40 years period in Iran was investigated, using the latent class regression. The analyzed data were extracted from reliable governmental resources (Iran statistical center, ministry of industry and mining and ministry of agriculture). According to obtained results, Iran’s provinces were classified in two migrator and immmigrator categories. The pattern of immigration during 1345 to 1385 showed that the Tehran, Isfahan, Quem, Mazandaran, Boushehr, Semnan and Yazd provinces were immigrator. The most important related predictors were: civilization level, level of education, sex ratio, family dimension, Industrial development coefficient, unemployment rate. Accordingly, the obtained results in this study can be used for developing suitable strategy in order to managing immigration and diminishing its side effects.

In this paper, we discuss minimaxity of Generalized Bayes estimator of the shape parameter of Generalized Exponential (GE) distribution under Weighted Square Error Loss (WSEL) function. A common approach to the prior uncertainty in Bayesian analysis is to choose a class of prior distributions and look for an optimal decision within this class. This is known as robust Bayesian methodology. We obtain Posterior Regret Gamma Minimax estimator of the shape parameter of GE distribution under WSEL function.

The aim of this research was to find the structural model of learner knowledge based on designing instructional objectives of Second Order Non-Homogeneous Linear Differential Equations. To do this, the instructional objectives of purposed subject were designed and their integrity was confirmed by three members of academic staff who teach this course for more than 10 years. In a pilot study, a test consists of 25 questions was given to thirty-one science and engineering students who were chosen randomly. Analyzing data with attention to Cronbach’s Alpha (0.834) confirmed that designed questions verified with mentioned instructional objectives of goal-content’s table. By using difficulty index, discrimination index and loop method unfit questions removed and 15 questions remained. engineering students who were chosen by cluster sampling. The empirical model of learner’s knowledge was compiled and results showed that there are meaningful relationships between ‘knowledge of definitions’ and ‘knowledge of method of undetermined coefficients’; ‘knowledge of method of variation of parameters’ and ‘knowledge of special methods’; and ‘knowledge of special methods’ and ‘knowledge of definitions’.

This paper concerned with the testing of homogeneity of mean vectors against ordered restriction in multivariate normal distribution. Three different cases for covariance matrices are considered. First when covariance matrices are known, second when it is assume that covariance matrices have an unknown scale factor and third when the covariance matrices are completely unknown and equal. In two first cases the critical values of test statistic are computed for bivariate and trivariate normal distribution. The power and p-value of the test statistic are estimated by simulation method. When the covariance matrices are completely unknown and equal some tests are presented which the computation of those probabilities can be used as the upper bonds of p-values.