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.
The importance of the research lies in preparing an experimental curriculum according to a scientific method that will contribute to the development of the special strength(endurance the strength of arms) in order to contribute to the attempt to develop the basic skills of the national team players with the goal ball for the blind As for the research problem, it lies in the weakness of the strength endurance of the national team players with the goal ball for the blind, as the research problem is clearly evident in the last minutes of the match, as well as the former studies in the field of goal ball game for the blind at the country level The research aims to prepare special exercises for endurance of strength as well as t
... Show MoreSurface drip irrigation is one of the most conservative irrigation techniques that help control providing water directly on the soil through the emitters. It can supply fertilizer and providing water directly to plant roots by drippers. One of the essential needs for trickle irrigation nowadays is to obtain more knowledge about the moisture pattern under the trickling source for various types of soil with various discharge levels with trickle irrigation. Simulation numerical using HYDRUS-2D software, version 2.04 was used to estimate an equation for the wetted area from a single surface drip irrigation in unsaturated soil is taking into account water uptake by roots. In this paper, using two soil types were used, namely
... Show MoreUrban planning include the creation of strategies as well as the management of metro regions, municipalities, and cities. In this study, the importance of applications of remote sensing and GIS in urban planning will be studied. The distribution of educational destitution cases in cities will be considered. A study area (Baghdad city) will be adopted, and the spatial analysis of the distribution will be according to population densities. In this study, the focus was on the importance of the sustainable distribution of urban educational institutions and the spatial appropriateness of this distribution according to the study areas and the available information. Distribution maps were pr
The distribution of chilled water flow rate in terminal unit is an important factor used to evaluate the performance of central air conditioning unit. A prototype of A/C unit has been made, which contains three terminal units with a complete set of accessories (3-way valve, 2-way valve, and sensors) to study the effect of the main parameters, such as total water flow rate and chilled water supply temperature with variable valve opening. In this work, 40 tests were carried out. These tests were in two groups, 20 test for 3-way valve case and 20 test for 2-way valve case. These tests were performed at three levels of valve opening, total water flow rate and water supply temperature according to the design matrices establis
... Show MoreThis paper develops a nonlinear transient three-dimensional heat transfer finite element model and a rate independent three-dimensional deformation model, developed for the CO2 laser welding simulations in Al-6061-T6 alloy. Simulations are performed using an indirect coupled thermal-structural method for the process of welding. Temperature-dependent thermal properties of Al-6061-T6, effect of latent heat of fusion, and the convective and radiative boundary conditions are included in the model. The heat input to the model is assumed to be a Gaussian heat source. The finite element code ANSYS12, along with a few FORTRAN subroutines, are employed to obtain the numerical results. The benefit of the proposed methodology is that it
... Show MoreThe parameter and system reliability in stress-strength model are estimated in this paper when the system contains several parallel components that have strengths subjects to common stress in case when the stress and strengths follow Generalized Inverse Rayleigh distribution by using different Bayesian estimation methods. Monte Carlo simulation introduced to compare among the proposal methods based on the Mean squared Error criteria.
The importance of the research lies in knowing the effect of the exercises of the reciprocal method in developing some physical abilities in learning the performance of the players for the effectiveness of the long jump in an economical manner in terms of time and effort and knowing their positive impact and the extent of their impact in creating the required learning for students, and the research aims to prepare reciprocal style exercises in developing some abilities The researchers used the experimental method in the pre and post test for the experimental and control groups to suit the nature of the research, and the research community was identified for the long jump players, the Specialized School for Talent Care in the 2022 sports sea
... Show MoreThe importance of media coverage in the war remains dependent on many indicators for its success, the most important is to have qualified reporters who carry the war news professionally. The idea of this research is to determine the role played by war correspondents working on Iraqi satellite channels during the war against ISIS.
The researcher has chosen ( 40 ) reporters those who was able to contact them and prepared a questionnaire for them to study their situations. Also, he chose an intentional sample from Baghdad audience on condition they should be informed by the performance of the reporters in the satellite channels applying the hypotheses of the theory of depending upon media.
The most important results reached by the re