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.
Abstract:
The achievement of economic and social welfare for individual is the main target to all policies that adopted by all countries worldwide either were economic, social, political or others. The obtaining of education by individuals and especially the higher education is one of the most important determinates in achieving the wellbeing and lasted economic development. This is because via the higher education new fields can be opened in front of individuals in order to get adequate jobs associated with their scientific specialization. This is allowing educated individuals gain higher income that can reduce the gap of income inequality.
Thus, this paper aims to analysis the n
... Show MoreAt the beginning of 1935 theMinistry of (Yasin AL-Hashimi) was formed which was the result of the (Sulayikh)Conference .The new ministys policy was towards the authority of the one party and the exclusivity of power.The policy of (Yasin AL-Hashemi)has faced severe campaigns from the AL-Ekhaa and AL-Ahaly newspapers.The new ministry like its predecessor ministries . When it faces criticism from opposition newspapers .its shutting down newspapers and not accepting requests for them. Some opposition newspapers named Yassin AL-Hashemi (the dictator).Iraqi opposition newspapers have been neglected and deprived of press freedom although they were the main factor in educating the community and representing the public opinion of people . Lt appe
... Show MoreThe primary aim of this study was to identify the effect of using the simultaneous electronic presentations strategy in teaching basic skills of basketball to second-grade intermediate students. The present study had a parallel group, pre-post experimental design. In the present study the students of the Salah al-Din Intermediate School for the academic year 2020-2021 constituted the research community. A total of 75 students were present in the research community. Out of 75 students 16 students were selected as the participants for the study. The students falling within the age group of 13-14 years were recruited as the study participants, making up a percentage of 21.33 of the total number. Based on the results of th
... Show MoreThis study focuses on the slab-beam interaction in one-way systems. In the context of this study, slab-beam interaction means how beam deflection can affect moment distribution in one-way slabs. This interaction is usually neglected in the traditional approximate analysis that is adopted in engineering practice and design codes. Slab positive moments have been considered as indicators on the accuracy of approximate methods, as they overestimate negative moments while underestimating positive moments.
After proposing of effecting parameters in slab-beam interaction including of panel length and width, beam dimensions, and slab thickness, Buckingham’s theorem has been adopted to transform the dimensional-mo
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In this search, we examined the factorial experiments and the study of the significance of the main effects, the interaction of the factors and their simple effects by the F test (ANOVA) for analyze the data of the factorial experience. It is also known that the analysis of variance requires several assumptions to achieve them, Therefore, in case of violation of one of these conditions we conduct a transform to the data in order to match or achieve the conditions of analysis of variance, but it was noted that these transfers do not produce accurate results, so we resort to tests or non-parametric methods that work as a solution or alternative to the parametric tests , these method
... Show MoreThe analysis of the orientations of Iraqi art commodification contributed to the discovery of deliberation, which was founded in the deliberative discourse in the trends towards commodification in the Iraqi art, since the important transformations in social structures and relations produced a dictionary with new vocabulary and tools that replaced the traditions and norms that have been in circulation for a century. Deliberation and commodification have become more prevalent in the mechanics and trends of the art where the pace of change is becoming increasingly frantic towards the market. The general market for art constitutes one of the most effective phenomena within contemporary art, that there has been a proliferation of sales auctio
... Show MoreThe house flies Musca domestica )Diptera:musidae) are the primary carrier of many pathogens such as cholera, typhoid, anthrax, and others. The use of chemical pesticides as a basic method of control leads to many problems at the environmental and health level. The use of safe alternatives to chemical pesticides has become an urgent necessity. The research aims to find biological alternatives that are environment-friendly and non-pathogenic to humans in controlling house flies through the possibility of extracting and diagnosing some secondary metabolites produced by the fungus Metarhizium anisopliae and testing their effects on the second larval stage of house flies using different treatment methods that include
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