Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

Background: The bone mineral density of the lumbar vertebra has been assessed according to the results of the Dual-Energy X-Ray Absorptiometry (DEXA). Although anemia is known to affect bone mineral density, at the present time, it is not clear which vertebra is more affected by this disease. Objective: To evaluate the effects of anemia on the bone mineral density of the lumbar vertebra in comparison with a normal subject and determine which part of the lumbar vertebra is more affected by anemia. Methods: All 205 participants in this study complained of bone pain (90 males and 105 females). 95 patients, including both sexes, suffered from anemia. Additionally, the study included 110 seemingly healthy volunteers as the control group

Abstract

The research Compared two methods for estimating fourparametersof the compound exponential Weibull - Poisson distribution which are the maximum likelihood method and the Downhill Simplex algorithm. Depending on two data cases, the first one assumed the original data (Non-polluting), while the second one assumeddata contamination. Simulation experimentswere conducted for different sample sizes and initial values of parameters and under different levels of contamination. Downhill Simplex algorithm was found to be the best method for in the estimation of the parameters, the probability function and the reliability function of the compound distribution in cases of natural and contaminateddata.

The study aimed to identify the use of the electronic concept maps method in learning some of the skills of the floor exercises in the artistic gymnastics for third graders ,as well as to identify the best group between the two research groups (experimental And the officer to learn and retain some of the skills of the floor exercises in the artistic gymnastics of the research subject , and the experimental method was used and included the sample research on students of the collage of Physical Education and Sports Sciences/University of Baghdad, third grade, and has selected (10) Students for each group of The experimental and controlling groups randomly by lottery and after the completion of the period of implementation of the experiment wh

The Boltzmann transport equation is solved by using two- terms approximation for pure gases and mixtures. This method of solution is used to calculate the electron energy distribution function and electric transport parameters were evaluated in the range of E/N varying from . 172152110./510.VcmENVcm
The electron energy distribution function of CF4 gas is nearly Maxwellian at (1,2)Td, and when E/N increase the distribution function is non Maxwellian. Also, the mixtures are have different energy values depending on transport energy between electron and molecule through the collisions. Behavior of electrons transport parameters is nearly from the experimental results in references. The drift velocity of electron in carbon tetraflouride i

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of B