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
We produced a study in Estimation for Reliability of the Exponential distribution based on the Bayesian approach. These estimates are derived using Bayesian approaches. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .we derived bayes estimators of reliability under four types when the prior distribution for the scale parameter of the Exponential distribution is: Inverse Chi-squar
... Show MoreEminent figures in Quranic studies in the fourth century of the Hegira, in his
copacity as the founder of the essentials of the indicative approach in interpretation
which is based on the consideration of research principles in interpretation science.
Al-Qushayri participated in clarifying the promotions of this approach in his
works which represent this approach. The mast distinguished of these works is
Tafseer Lataef Al-Isharat. The researcher examined the characteristics of this
approach and its effect on the interpretative movement in Al-Qushayri age an come to
employ them as a practical example for the indicative approach in studying the
interpretation mebods in Islamic sciences.
An innovative two-step noncatalytic esterifcation technique was proposed to synthesize alkyl esters from free fatty acids simulated in waste cooking oil, as a pretreatment process for biodiesel production, without adding any catalyst under normal conditions of pressure and temperature. The efect of methanol:oil molar ratio, reaction time, mixing rate, and reaction temperature were investigated. The results confrmed that the conversion of the reaction was increased when increasing the methanol molar ratio and decreased in prolonged reaction temperature. High conversion (94.545%) was successfully achieved at optimized conditions of 115:1, 65:1 methanol:oil molar ratio in the frst step and second step, respectively, other conditions i
... Show MoreThe game theory has been applied to all situations where agents’ (people or companies) actions are utility-maximizing, and the collaborative offshoot of game theory has proven to be a robust tool for creating effective collaboration strategies in a broad range of applications. In this paper first, we employ the Banzhaf values to show the potential cost to waste producers in the case of a cooperation and to reduce the overall costs of processing non-recyclable waste during cooperation between producers. Secondly, we propose an application of the methodology to study a case for five waste producers' waste management in the Al-Mahmudiya factory with the aim of displaying the potential cost to waste producers in case of cooperatio
... Show MoreThe present study aims at finding out the (effect of the Caroll’s pattern on the second intermediate class pupils' achievement in geography)
The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (74) female pupils. The sample is divided into two groups (38) experimental group and (36) control one. The sample is selected from first intermediate class pupils ( Am Salama Secondary School for girls) \ Baghdad\ Al-karkh-1, for academic year 2015-2016.
The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scor
... Show MoreIn this work, the occurrence conditions of both local Bifurcation and persistence were studied, Saddle-node bifurcation appears near fourth point, near the first point, the second point and the third point a transcritical bifurcation occurred but no pitchfork bifurcation happened near any of the four equilibrium points. In addition to study conditions for Hopf-bifurcation near positive stable point that is the fourth point. Besides discuss persistence occurrence as globally property of the food chain of three species include prey, first predator and top predator with impact of toxin in all species and harvesting effect on the predator’s only. Numerical results for the set of hypothe
The Diwan of Imam Al-Shafi’i acquires great importance, as Al-Shafi’i is an authority in the language, and when I saw that no one had preceded me in exploring its depths, I took my tool and turned my face towards it intending to study the triple verb in it. I stop at these verbs and the student pauses for their morphological forms, looking at the significance of the triple verb more with one letter, two letters, and three letters, and I found that they are many, and such research cannot contain them all, so the choice came to choose the triple verb more with one letter, and the significance of the increase in it, as the increase in The building necessitates an increase in the meaning, and from here the study was limited to the triple
... Show MoreSimple, cheap, sensitive, and accurate kinetic- spectrophotometric method has been developed for the determination of naringenin in pure and supplements formulations. The method is based on the formation of Prussian blue. The product dye exhibits a maximum absorbance at 707 nm. The calibration graph of naringenin was linear over the range 0.3 to 10 µg ml-1 for the fixed time method (at 15 min) with a correlation coefficient (r) and percentage linearity (r2%) were of 0.9995 and 99.90 %, respectively, while the limit of detection LOD was 0.041 µg ml-1. The method was successfully applied for the determination of naringenin in supplements with satisfac
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