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 Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
In the present study, semi – batch experiments were conducted to investigate the efficiency of ozone microbubbles (OMBs) in the treatment of aqueous dye solutions methylene orange under different reaction conditions such as effect of initial solution pH , ozone generation rate and initial MO-concentration. The results showed that the removal of MO by OMBs were very high at the acidic and alkaline media and upon increasing the generation rate of ozone from 0.498 to 0.83 mg/s, the removal efficiency dramatically increased from 75to 100% within 15 min. The rate of oxidation reaction followed a pseudo first- order kinetic model. The results demonstrated that OMBs is efficient in terms of the decline of methylene orange c
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The teacher is the most able to achieve the goals of education in education because he has the ability to affect the behavior of the disciples testified and its actions and appearance and other actions that convey pupils with it sometimes in a manner unconscious or unconscious , and the importance of the role of the teacher in the educational process , it is necessary to compromise the care and attention to the extent that commensurate with the important role that the rise in the preparation of youth and composition , and as a result is needed to continue efforts to improve the quality of teacher preparation so that it can be more effective and positive in the educational process .
First - Research Goals -<
The e-commerce is one of the best achievements of the twentieth century, since the conduct commercial transactions via the Internet may be the consumer easy selection process and purchase convenient manner different from traditional methods, and with the beginnings of the new millennium impose the emergence of e-commerce term significant challenges to the insurance industry as an important economic sectors Generally, and insurance companies in particular as a result of scientific development, which has led to a reduction in costs and innovation in the production, which led to intense competition on both levels local or global. The insurance industry is a vital part of the economy and it has a varied impact to the community and individual
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The current research aims to identify the level of organizational relaxation among the employees of educational directorates in the Sultanate of Oman. The descriptive approach was used, as well as a questionnaire of two parts to collect data. The questionnaire consists of (15) items divided into three themes about the relaxing level. It was applied on a sample of (406) male & female employees of the educational directorates who were randomly selected. The results of the study showed that the level of organizational relaxation was low. The study results also found that there were no statistically significant differences at the level of significance (α ≤ 0.05) of the study sample in the level of org
... Show MoreThe slums one of the main problem plaguing the city of Baghdad in general and
the unity of municipality of New Baghdad, especially, where the characteristics of the study
area a prominent role in population growth and the emergence of slums where a private,
although the region suffer from the housing crisis is the lack of the number of housing units
compared to the number of families in which, With high land prices and the level of rent
which was accompanied by the absence of the law, which was followed by the year 2003, has
become the study area and one of the most municipalities of the city of Baghdad Contain
slums which took fills abandoned buildings and acquires vacant land agricultural ones and
allocated to d
Abstract
The Umayyad poets tried to invest all artistic tools in order to achieve a measure of creativity in their texts. The phenomenon of visual composition is breaking the familiar writing system, with the aim of increasing the number of possible connotations. The visual in the Umayyad poetry tries to replace it through expression with the visual image, and its manifestations were manifested by the multiplication of punctuation marks in the body of the poetic text and the tearing of the single poetic line by cutting it into several sentences or repetition.
Keywords: visual formation, poetic writing, Umayyad poetry, recipien
Preserving the Past and Building the Future: A Sustainable Urban Plan for Mosul, Iraq
In this research, the multi-period probabilistic inventory model will be applied to the stores of raw materials used in the leather industry at the General Company for Leather Industries. The raw materials are:Natural leather includes cowhide, whether imported or local, buffalo leather, lamb leather, goat skin, chamois (raw materials made from natural leather), polished leather (raw materials made from natural leather), artificial leather (skai), supplements which include: (cuffs - Clocks - hands - pockets), and threads.This model was built after testing and determining the distribution of demand during the supply period (waiting period) for each material and completely independently from the rest of the materials, as none of the above mate
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