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

Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Background:Hydrocephalus is dilatation of the ventricular system due to excessive production and/ or obstruction of cerebrospinal fluid (CSF) pathways. Different surgical procedure are used to treat this disease. Ventriculo peritoneal shunt is by far the most popular technique for CSF diversion..
Objective;To compare the programmable and non-programmable valves regarding the complications of both types
Methods:This study was conducted in the Neurosurgical hospital of Baghdad/Iraq over a period of 3 years from July 2008 to August 2011.
A special inclusion criteria has been tabulated for the selection of patients..
Results:.Fifty cases with hydrocephalus admitted and diagnosed by CT scan and treated by ventriculoperitoneal shun

Background : The aim of this work is to study the clinical features and causative fungi of tinea pedis in diabetic and non-diabetic patients. Result : Tinea pedis was estimated to be the second most common skin disease in the United States, after acne. Up to 15% of the U.S., population may have tinea pedis. Across Europe and East Asia, prevalence rates reach 20 %. Methods: The Complete history taking regarding: age, sex, occupation, residency, history of diabetes and diabetic profile (fasting blood sugar and post prandial).and Clinical examination of the feet Aim of the study : The aim of this work was to study the clinical features and causative fungi of tinea pedis in diabetic and non-diabetic patients Conclusion : Tinea pedis is more

The process of selection assure the objective of receiving for chosen ones to high levels more than other ways , and the problem of this research came by these inquires (what is the variables of limits we must considered when first preliminaries selections for mini basket ? and what is the proper test that suits this category ? and is there any standards references it can be depend on it ?) also the aims of this research that knowing the limits variables to basketball mini and their tests as a indicators for preliminaries for mini basketball category in ages (9-12) years and specifies standards (modified standards degrees in following method) to tests results to some limits variables for research sample. Also the researchers depends on (16)

The aim of this paper is to approximate multidimensional functions by using the type of Feedforward neural networks (FFNNs) which is called Greedy radial basis function neural networks (GRBFNNs). Also, we introduce a modification to the greedy algorithm which is used to train the greedy radial basis function neural networks. An error bound are introduced in Sobolev space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result is published in [16]).

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.