Journal of Advanced Mathematical Modeling
Shahid Chamran University,Ahvaz





Vol. 2
, No. 1 

Bayesian Inference Based on typeI Hybrid Censored Data from a TwoParameter Exponential Distribution
Abstract
A hybrid censoring is a mixture of typeI and typeII censoring schemes. It is categorized to typeI and typeII hybrid
censored based on how the experiment set to terminate. In this paper, we describethe typeI hybrid censoring where lifetime
variables have a twoparameters 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.
Keywords: Admissible Estimator, Bayes Estimator, Minimax Estimator



1 




Optimization of the Adomian Decomposition Method for Solving Differential Equation with Fractional Order
Abstract
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 AdomianDecomposition 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.
Keywords:
Adomian Decomposition Method, differential equations
with fractional order, Approximate analytical methods,
Optimization 


27 




A Stable Numerical Solution of an Inverse Moving Boundary
Problem of Heat Conduction Using Discrete Mollification Approach
Abstract
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.
Keywords: Heat Conduction, Inverse Problem, Moving Boundary Problems,Stefan Problem, Marching Scheme 


47 





Pspaces and ArtinRees Property
Abstract
In this article, we study the ArtinRees property in, in the rings of fractions of and in
the factor rings of.
We show that C(X)/(f) is
an ArtinRees ring if and only if Z(F) is an open
Pspace. A necessary and sufficient condition for the
local rings of to
be ArtinRees rings is that each prime ideal in becomes
minimal and it turns out that every local ring of is an
ArtinRees ring if and only if
is a Pspace. Finally we have shown that whenever X \
Z(f) is dense Cembedded
in , then C(X)f is regular if and only if X \ Z(f) is a Pspace.
Keywords:
ArtinRees property, Pspace, rings of fractions
of ,
local rings of ,
Cembedded, regular 


61 





Three Critical Models inMathematical Finance
Abstract
In this paper, using mathematical techniques, we are going to model some of the important financial markets.Due tothe 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, thusthe 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 partialintegral differential equations. Depending on market,application of inverse problems and free boundary value
problemsin finance science is being explained.
Keywords: Financial Modeling, Financial Derivative, Free Boundary Value Problem, Inverse Problem, Stochastric Volatility



78 





Extension of Cell Cycle Model
Abstract
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.
Keywords: Delay differential equations, Equilibrium point, Mathematical modeling of cancer,Lyapunov stability criterion 


97 



