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

The study problem is about the role of Shaqra University in building the mental image of the Kingdom’s 2030 vision among its female students. The study aims to examine the university’s role in providing information about the Kingdom’s 2030 vision, its role in shaping the vision’s image, the university’s role in the behavioral aspect of the vision, along with studying the extent of differences in answers of the sample individuals towards the study themes attributed to the personal variables. The researcher adopted the descriptive survey method. A sample of (1399) female students was used to achieve the study objectives. The results showed that university’s role in building the mental image of the Kingdom’s 2030 vision, among

Manufacturing industries are at the beginning of the thinking of those who put economic policies in developed countries and also more in developing countries, where manufacturing is the engine of industrial and economic development through its performance and its effective role in the formation of GDP, as well as the great advantages that characterize this sector and affect Largely on sustainable development, as well as its importance in its influential role in protecting national industry through increased exports and reduced imports.

      Iraq is one of the countries that rely on its oil economy to rely entirely on the provision of needs and requirements of the state, and this

Summed up the idea of this research in an attempt to find the establishment of the knowledge convergence to show the features of verbal acts that occurred a prime location in the lesson deliberative theory book unique contract ( IbnAbdRabbaAndalusian ) to prove that Arabic was the old literary studies included many of the features of this theory in both theoretical and practical

A simplified parallel key was presented in this work for the Taxa of Stackys L. wildly grown in Iraq. Three records within this genus were newly recorded to our country in the present work and they are S. kermanshahansis Rech S. setifera C.A. Mey. subsp setifera, S. setifera ssp iranica (Reck.) The characteristics of these new records were also given with some representative specimens.

       It has become clear to see the role of the small and medium enterprises in the economy, and for the continuity of these projects it is necessary to supply finance from the banks, How ever the latter suffers risk of lending.                                                                          

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Reconstruction project management in the cities of Mosul, Anbar, and Tikrit, in Iraq still faces major obstacles that impede the comprehensive performance of these projects. It is thus necessary to improve the arising challenge estimation in the implementation of reconstruction projects and evaluate their components: time, cost, quality, and scope. This study used the Analytical Hierarchy Process (AHP) to prioritize major and minor criteria in the influential causes of challenges and formulate a mathematical model to help decision-makers estimate them. Using the Super Decisions software, the final results indicated that changes in scope reached 40.8%, which is the greatest difficulty, followed by changes in cost at 27.6%, changes in

Background: Since the periodontal disease Index of Ramfjord (Ramfjord index) can potentially shorten the examination time by almost half, many studies evaluated Ramfjord teeth in predicting full-mouth periodontal status of an adult population. The aim of this study was to evaluate the benefit of Ramfjord teeth in predicting the full-mouth clinical attachment level of an adult population in patients attending the college of dentistry- Baghdad University. Materials and methods: The study participants were 100 patients with age range from 30-60 years old which represent group zero. The patients were divided into three main groups according to the age of the patients. Group I and group II each of them composed of 30 patients while group III co