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 study aims at building a mathematical model for the aggregate production planning for Baghdad soft drinks company. The study is based on a set of aggregate planning strategies (Control of working hours, storage level control strategy) for the purpose of exploiting the resources and productive capacities available in an optimal manner and minimizing production costs by using (Matlab) program. The most important finding of the research is the importance of exploiting during the available time of production capacity. In the months when the demand is less than the production capacity available for investment. In the subsequent months when the demand exceeds the available energy and to minimize the use of overti
... Show MoreThis research introduce a study with application on Principal Component Regression obtained from some of the explainatory variables to limitate Multicollinearity problem among these variables and gain staibilty in their estimations more than those which yield from Ordinary Least Squares. But the cost that we pay in the other hand losing a little power of the estimation of the predictive regression function in explaining the essential variations. A suggested numerical formula has been proposed and applied by the researchers as optimal solution, and vererifing the its efficiency by a program written by the researchers themselves for this porpuse through some creterions: Cumulative Percentage Variance, Coefficient of Determination, Variance
... Show MoreFreshwater mussels are a guild of stationary, suspended-feeding species; they perform significant ecological functions like nitrogen cycling, bioturbation that gives oxygen and habitat that other creatures need to survive, and increasing water clearance by filtration. Knowledge of the freshwater mussel Unio tigridis Bourguignat, 1852, distribution, and molecular study in Iraq was inadequate. In the current study, this species of freshwater Mussels belonging to the family Unionidae was collected from different locations in the Greater Zab River, from April 2022 to November 2022. The average water temperature of the site was arranged between (17.8 to 36.1 C°). All previous studies in the Kurdistan Region and Iraq were based on morphologic
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Research topic: (The Epistemological Foundations for Comparison of Religions by al-Amiri)
The research sought to study the topic with: a descriptive methodology by investigating the components of al-Amiri's approach to the interfaith comparison. And analytical, by showing the applied perception of an objective model in the comparison of religions to answer two questions: What are the cognitive foundations of al-Amiri? And what is his approach to establishing an objective comparison between religions?
The research started by introducing Abu al-Hassan al-Amiri, and then presented four topics: An introduction to al-Amiri's efforts in the interfaith comparison, his knowledge foundations, an applied model
... Show MoreAccounting changes have taken place in either the local or international level has led to more disclosure from companies, and that many of the economic units in order to attract investors to negotiate on its shares price in the stock market require amendments with respect to the information disclosed, Thus, the objective of this research is to analyze whether companies were research sample disclose contingent assets and liabilities and provisions in their annual financial reports with what brought him International Accounting Standards. It has been used descriptive analysis of annual financial reports for a sample of (50) listed company on the Iraq Stock Exchange were identified companies that disclose contingent assets and liabi
... Show MoreBMMAM Saleh, EUROPEAN ACADEMIC RESEARCH, 2016
Sovereign wealth funds have attracted the attention of the governments of the oil and non-oil countries alike, with a variation of the size of those funds to those states, based on the size of the financial surpluses resulting from Alriadat oil or foreign reserves, or state revenues for other sovereign assets. Raj use these funds remarkably during the financial crises the world has seen, including the crisis of 2008-2007., And Iraq is a oil-producing countries, which has the third largest reserves of crude oil (Crude Oil) at the level of the Arab world and of 140 300)) million barrels after Saudi Saudi Arabia and the Islamic Republic of Iran, and the fourth reserves of crude oil in the world after issued Venezuela to the reserve
... Show MoreCovalent modification of protein by drugs may disrupt self-tolerance, leading to lymphocyte activation. Until now, determination of the threshold required for this process has not been possible. Therefore, we performed quantitative mass spectrometric analyses to define the epitopes formed in tolerant and hypersensitive patients taking the β-lactam antibiotic piperacillin and the threshold required for T cell activation. A hydrolyzed piperacillin hapten was detected on four lysine residues of human serum albumin (HSA) isolated from tolerant patients. The level of modified Lys541 ranged from 2.6 to 4.8%. Analysis of plasma from hypersensitive patients revealed the same pattern and leve
The Audit evedances represent the reconciliation tools between the Financial data shown on financial statements, and the level of satisfaction level of the Auditor about these statements. According that, the Auditor try to achieve the highest quantity of These evidances, and the most satisfactive of it…, but that will be so hard sometimes, when the internal controlling system is not good, and when the Auditor had some satisfied evidences, but not sharp… So, this research comes to inspect the relation between the quantity, and the level of satisfaction, and argument to prove that evidences gives. This research assumes that getting enough evidences leads to reduce faults, improves the auditing operation, and avoids risks. The research
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