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:
This study deals with the influence of the industrial buyer behavior in Channels of distribution. It concentrates on one section of management levels in the company. Which is that of administrative managers The research problem is attempt to study and analysis the influence of industrial buyer behavior in channels of distribution.. The aiming at achieving a number of applicable goals depending on one major hypotheses I set a questionnaire in collecting the data and information relating to the study، which was distributed to sample of ( 30) department manager heads of section states company . In order to process the data resorted to many statistical methods such as arithmetic means the sta
... Show MoreThe objective of this research is to analyze the content of science textbook at the elementary level, according to the dimensions of sustainable development for the academic year (2015-2016). To achieve this goal has been to build a list with dimensions of sustainable development to be included in science textbooks in primary school, after seeing the collection of literature and research and studies, as has been reached to the list of the dimensions of the three sustainable development and social, economic and environmental in the initial image consisted of (63) the issue of sub-divided the three-dimensional, the menu and offered a group of arbitrators and specialists in curriculum and teaching methods, and thus the menu consiste
... Show MoreThe term “non-violence” is a means of political, social, and advocacy that excludes force in reaching its objectives, and lacks infringement of the rights of non-violence. The policy of non-violence is a beautiful logic of the whole of Islamic creation, in that it is an integral part of the whole structure of Islam and it is a policy of brilliant and brilliant saying in the Almighty: `` Neither level nor good or bad, pay what is better, If that between you and him enmity as if he were intimate guardian (Suratvsalat, verse: 34. Has According to the prophet of Islam, it means that God gives to kindness (kindness) what does not give to violence (Sunan Abu Dawood, 4/255). These terms accurately communicate what is meant by violence and n
... Show MoreA field experiment is conducted to study the effect of different levels of peat (0, 25, 50, 75, and 100 Mg ha-1 to uncropped and cropped soil to wheat. Soil samples are taken in different period of time (0, 3, 30, 60, 90, 120, and 180 days after cultivation to determine (NaHCO3-Exteractable P at 3 different depths (0-10, 10-20, and 20-30 cm). Field Experiment is conducted in a randomized complete block design (RCBD) with four replicates. Wheat, Al-Rasheed variety, is cultivated as a testing crop. The entire field is equally dived in two divisions. One of the two divisions is cultivated to wheat and the second is left uncropped. The effect of five levels of peat namely 0, 25, 50, 75, 100 Mg ha-1 is investigated. Soils are fully analyzed
... Show MoreGumbel distribution was dealt with great care by researchers and statisticians. There are traditional methods to estimate two parameters of Gumbel distribution known as Maximum Likelihood, the Method of Moments and recently the method of re-sampling called (Jackknife). However, these methods suffer from some mathematical difficulties in solving them analytically. Accordingly, there are other non-traditional methods, like the principle of the nearest neighbors, used in computer science especially, artificial intelligence algorithms, including the genetic algorithm, the artificial neural network algorithm, and others that may to be classified as meta-heuristic methods. Moreover, this principle of nearest neighbors has useful statistical featu
... Show MoreTheoretical and experimental investigations of the transient heat transfer parameters of constant heat flux source subjected to water flowing in the downward direction in closed channel are conducted. The power increase transient is ensured by step change increase in the heat source power. The theoretical investigation involved a mathematical modeling for axially symmetric, simultaneously developing laminar water flow in a vertical annulus. The mathematical model is based on one dimensional downward flow. The boundary conditions of the studied case are based on adiabatic outer wall, while the inner wall is subjected to a constant heat flux. The heat & mass balance equation derived for specified element of bulk water within the annulu
... Show MoreThe aim of this study is to estimate the parameters and reliability function for kumaraswamy distribution of this two positive parameter (a,b > 0), which is a continuous probability that has many characterstics with the beta distribution with extra advantages.
The shape of the function for this distribution and the most important characterstics are explained and estimated the two parameter (a,b) and the reliability function for this distribution by using the maximum likelihood method (MLE) and Bayes methods. simulation experiments are conducts to explain the behaviour of the estimation methods for different sizes depending on the mean squared error criterion the results show that the Bayes is bet
... Show MoreThe primary objective of this study was to identify the obstacles and problems encountered in the work of sports clubs according to the reality of the application of administrative automation. The present study was conducted in the sports club headquarters of Baghdad within the timeframe of October 2021 to December 2021. In the present study, a descriptive approach was used by the researchers in an analytical style according to the nature of the problem to be studied. The research community of the current study was composed of 100 sports clubs in the governorate of Baghdad. A total of 80 questionnaires were filled by the sample participants, who represented a percentage of 80% of the research community. After processin
... Show MoreThis research deals with a shrinking method concernes with the principal components similar to that one which used in the multiple regression “Least Absolute Shrinkage and Selection: LASS”. The goal here is to make an uncorrelated linear combinations from only a subset of explanatory variables that may have a multicollinearity problem instead taking the whole number say, (K) of them. This shrinkage will force some coefficients to equal zero, after making some restriction on them by some "tuning parameter" say, (t) which balances the bias and variance amount from side, and doesn't exceed the acceptable percent explained variance of these components. This had been shown by MSE criterion in the regression case and the percent explained v
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