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 research involved a rapid, automated and highly accurate developed CFIA/MZ technique for estimation of phenylephrine hydrochloride (PHE) in pure, dosage forms and biological sample. This method is based on oxidative coupling reaction of 2,4-dinitrophenylhydrazine (DNPH) with PHE in existence of sodium periodate as oxidizing agent in alkaline medium to form a red colored product at ʎmax )520 nm (. A flow rate of 4.3 mL.min-1 using distilled water as a carrier, the method of FIA proved to be as a sensitive and economic analytical tool for estimation of PHE.
Within the concentration range of 5-300 μg.mL-1, a calibration curve was rectilinear, where the detection limit was 3.252 μg.mL
The sports field is one of the fields that are concerned with the various methods and methods because of their positive impact on the development of actual training, the investment of the exerted effort in time, and through the follow-up of the researcher in the field and academic field, I noticed that there is a weakness in explosive ability, which affects performance and skill level during training and competition Therefore, the researcher decided to prepare maximum physical exertion exercises according to the anaerobic threshold as a principle of development in many physical and skill variables because good physical performance leads to reaching the best achievements and since the skill of shooting by jumping high - either constitutes a
... Show MoreThe research discusses the problem of salaries in the public sector in terms of the process of analyzing its structure and the possibility of benefiting from the information provided by the analysis process for the strategic planning process, and the General Authority for Groundwater has been adopted and one of the formations of the Ministry of Water Resources, which is centrally funded, to represent the salary structure of its employees (1117) employees be a field of research, as the salary structure in it was analyzed for the period between (2014-2019) using the quantitative approach to analysis and by relying on a number of statistical tools in the analysis process, including mathematical circles, upper limits, lower limits, p
... Show MoreWe have focused the research problem through an assessment of the applicability of the third pillar of the decisions of the Basel Committee 11 (market discipline) or not and its impact on both the adequacy of bank capital, supervisory oversight and banking risks and the statement weaknesses commitment banking institutions and which in turn lead to the stability of the financial system as a whole. .
The research is important statement on the importance of big capital in the banking business and the attributes of a role in the absorption of losses suffered by the bank, which reflects the willin
Besides the role of state institutions that come in the forefront of their priorities and obligations to provide security and development of the economy and reduce the unemployment rate and the reduction of inflation and improving education, health and others, the Community Partnership At frames what has become known as the institutions of society civil-with the state does not eliminate the role, but rather complements its role ; it is the role of civil society partner and an extension of the role of the state in the face of challenges and crises, but it may be sometimes a race role in addressing social, political and economic issues of the role played by the state, not complementary.
The highlighting the specificity of the relationsh
An analytical form of the ground state charge density distributions
for the low mass fp shell nuclei ( 40 A 56 ) is derived from a
simple method based on the use of the single particle wave functions
of the harmonic oscillator potential and the occupation numbers of
the states, which are determined from the comparison between theory
and experiment.
For investigating the inelastic longitudinal electron scattering form
factors, an expression for the transition charge density is studied
where the deformation in nuclear collective modes is taken into
consideration besides the shell model space transition density. The
core polarization transition density is evaluated by adopting the
shape of Tassie mod