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 grey system model GM(1,1) is the model of the prediction of the time series and the basis of the grey theory. This research presents the methods for estimating parameters of the grey model GM(1,1) is the accumulative method (ACC), the exponential method (EXP), modified exponential method (Mod EXP) and the Particle Swarm Optimization method (PSO). These methods were compared based on the Mean square error (MSE) and the Mean Absolute percentage error (MAPE) as a basis comparator and the simulation method was adopted for the best of the four methods, The best method was obtained and then applied to real data. This data represents the consumption rate of two types of oils a he
... Show MoreThe aim of the research is to identify the percentage of success and failure of some compound offensive skills in joiner basketball. It was evident that development only occurred though the mastery of the basic single offence skills as well as the ability to perform compound skills accurately and consistently. Not paying enough attention to compound skills leads evidentially to weakness in the athlete's level that in turn leads to mistakes in performance. Six joiner games of the best four teams in Baghdad were filmed and analyzed. The results of analyzing the compound offence skills were as follows: There was some weakness in the athletes' ability in using compound offence skills specially receiving, dribbling and following through that
... Show MoreThis study was conducted to study the cytogenetic effect of both alcoholic and water extracts of propolis on mice. Three different samples of propolis were collected from three different regions of Iraq (Najaf, Arbil and Baghdad) to be used in this study. The cytotoxic effect of two different doses of each extracted sample was measured by employing cytogenetic analysis which included (mitotic index (MI), chromosomal aberrations (CAs), micronucleus index (MN) and sperm abnormalities). Results showed that significant increase in MI and significant reduction in MN, CAs and sperm abnormalities percentage were seen after treatment with both alcoholic and water extract of the three samples when compared with negative control, and alcoholic extrac
... Show Morel development in addition to environmental reform, which is not possible at its best, and from this the faculties of physical education and sports science realize the scale of the problem and its importance in the development of society that this all puts on the faculties of education Physical and sports sciences are a very difficult task and an end in holiness, for it is the responsibility of the human development service and its leadership, because the community leaders and its elites are those who value their direction and future more than others. The importance of this study comes from the goal of sustainable development to maximizing pain. The net gain from higher education while ensuring the preservation of the quality of reso
... Show MoreThe current investigation included study of leaf surface epidermis beside indumentum for the species Galium aparine L., G. ceratopodum Boiss, G. setaceum Lam., G. spurium L., and G. tricornatum Dandy, the study showed that paracytic type of stomatal complex is the only type occur in leaf. The indumentum compose of eglandular hairs vary in their apices, length and occurrence of different part of plant body
Potentiostatic polarization and weight loss methods have been used to investigate the corrosion behavior of carbon steel in sodium chloride solution at different concentrations (0.1, 0.4 and 0.6) M under the influence of temperatures ( 293, 298, 303, 308 and 313) K. The inhibition efficiency of the amoxicillin drug on carbon steel in 0.6 M NaCl has also been studied based on concentration and temperature. The corrosion rate showed that all salt concentrations ( NaCl solution) resulted in corrosion of carbon steel in varying ratio and 0.6 M of salt solution was the highest rate (50.46 g/m².d). The results also indicate that the rate of corrosion increases at a temperature of 313 K.. Potentiodynamic polarization studi
... Show MoreIn this study, the four tests employed for non-linear dependence which is Engle (1982), McLeod &Li (1983), Tsay (1986), and Hinich & Patterson (1995). To test the null hypothesis that the time series is a serially independent and identical distribution process .The linear structure is removed from the data which is represent the sales of State Company for Electrical Industries, through a pre-whitening model, AR (p) model .From The results for tests to the data is not so clear.
The research aims at determining the main reason for the deterioration of the services and determining the correct method of distributing the funds to the administrative and administrative units. The discrepancy between the size of the financial allocations and the municipal services was the main research problem. Therefore, the researcher identified the gaps in municipal services by the concerned departments and compared them with The percentage of funds obtained through the work of a checklist for each of the directorates concerned. The researcher studied the specific criteria for these services, which were approved by the Ministry of Construction, Housing, Municipalities, and Public Works, and compared them wi
... Show MoreThe research aims to study and definition of the concept of creative accounting and motives adopted by the management of companies to achieve their own goals and their impact on the reliability of the financial statements and the tax settling accounts and whether that tax administration is able to detect and limit the creative accounting practices and impose legal sanctions deterrent against companies The research has come to a set of conclusions, including:
- The administration motives in the use of creative accounting methods, some internal motives related to the interests of the administration in maximizing profits to increase incentives and rewards, others are external, such as the impact on stock prices or reduce the am
This research aims to identify the impact of the reciprocal reading strategy on developing the innovative reading skills of fifth-grade secondary school students/ scientific branch. To achieve the goal of the research, an achievement test to measure the academic achievement of fifth-grade secondary school students in Arabic language grammar was prepared, a sample of (60) female students from the secondary school of Al- Bawaba Al-Sharkey for Girls in Baghdad were chosen for the academic year (2019-2020). For the purpose of applying the experiment, the test was applied on a pilot sample consisting of (30) students from the same research community. The researcher herself had taught the three
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