فصلنامه مدل سازی پیشرفته ریاضی
سال دوم شماره 1 (بهار و تابستان 1391)

A hybrid censoring is a mixture of type-I and type-II censoring schemes. It is categorized to type-I and type-II hybrid censored based on how the experiment set to terminate. In this paper, we describe the type-I hybrid censoring where lifetime variables have a two-parameters exponential distribution. Bayes estimation of unknown parameters under squared error loss function is developed. Among several methods of constructing the optimal procedures in the context of robust Bayesian methodology, we obtain posterior regret gamma minimax estimation of unknown parameters under squared error loss function. Finally, we discuss minimaxity and admissibility of the generalized Bayes estimator under squared error loss.

Up to now, Adomian Decomposition Method (ADM) has been widely employed in solving different kinds of differential equations. However, in many cases it is observed that the ADM has a lower precision in comparison with other methods, especially that of Homotopic ones. ADM is a relatively general and powerful method for finding analytical approximate results from different equations. In this paper, we seek to raise Optimal Adomian Decomposition Method (OADM) precision by employing the standard pattern of ADM. The main character of this repetitive method is based on employment of a controlling parameter in convergence, which resemble the parameters used in Homotopy Analysis Method (HAM). This parameter is indicated in such a way to reasonably increase the precision of obtained results. To indicate the optimizing parameter, the Least Squares Method has been used. The presented examples demonstrate that, how the above mentioned method has validity, applicability and a high degree of precision in solving differential equations of fractional order so that it can be generally used in solving differential equations.

In this paper the application of marching scheme and mollification approach to solve a one dimensional inverse moving boundary problem for the heat equation is investigated. The problem is considered with noisy data. A regularization method based on marching scheme and discrete mollification approach is developed to solve the proposed problem and the stability and convergence of numerical solution is proved. To show the ability and efficiency of the proposed method, some numerical experiments are investigated.

In this article, we study the Artin-Rees property in C(X), in the rings of fractions of C(X) and in the factor rings of C(X). We show that C(X)/(f) is an Artin-Rees ring if and only if Z(f) is an open P-space. A necessary and sufficient condition for the local rings of C(X) to be Artin-Rees rings is that each prime ideal in C(X) becomes minimal and it turns out that every local ring of C(X) is an Artin-Rees ring if and only if X is a P-space. Finally we have shown that whenever XZ(f) is dense C-embedded in X, then C(X)f is regular if and only if Xz(f) is a P-space.

In this paper, using mathematical techniques, we are going to model some of the important financial markets. Due to the close relations between stock exchange and derivatives markets, we introduce models which also indicate the collaboration between mathematicians, statisticians, computer and finance researchers. Moreover, in this way, the weakness of the old models has been compensated, thus the new and modern models have been generated to improve financial and mathematical relations for new researches. The aim of this article is not to present the solution of new models, but it is to introduce one of the applied mathematics branchs in finance science. Finally, we make a model with three important problems in financial instruments, which transfer he partial-integral differential equations. Depending on market, application of inverse problems and free boundary value problems in finance science is being explained.

In this paper we consider a delayed mathematical model of cell cycle. Adding drug toxicity، the model is modified and developed. A proper Lyapunov function is suggested for stability analysis. Furthermore، by obtaining a criterion for appropriate control، it is shown that any treatment strategy which satisfies the criterion، causes the system converge to tumor free equilibrium point.