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 investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
The ligand 4-(2-aminmo-5-nitro-phenylazo)-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one derived from 4-aminoantipyrine and 4-nitroaniline was synthesized. The synthesized ligand was characterized by 1HNMR, FT-IR, UV-Vis spectra and (C.H.N) analysis. Complexes of (YIII and LaIII ) with the ligand were prepared in aqueous ethanol with a 1:2 M:L ratio and at optimum pH. The prepared complexes were characterized by using flame atomic absorption, FT-IR, UV-Vis spectra,(C.H.N) analysis and conductivity measurement. The stoichiometry of complexes was studied by the mole ratio and job methods. A concentration range (1×10-4 - 3×10-4 M) obeyed Beer's law, the complex solutions show high values of molar absorption. On the basis of physicochemical
... Show MoreThe ligand 4-(2-aminmo-5-nitro-phenylazo)-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one derived from 4-aminoantipyrine and 4-nitroaniline was synthesized. The synthesized ligand was characterized by 1HNMR, FT-IR, UV-Vis spectra and (C.H.N) analysis. Complexes of (YIII and LaIII ) with the ligand were prepared in aqueous ethanol with a 1:2 M:L ratio and at optimum pH. The prepared complexes were characterized by using flame atomic absorption, FT-IR, UV-Vis spectra,(C.H.N) analysis and conductivity measurement. The stoichiometry of complexes was studied by the mole ratio and job methods. A concentration range (1×10-4 - 3×10-4 M) obeyed Beer's law, the complex solutions show high values of molar absorption. On the basis of physicochemical
... Show MoreBumpiness in the atmosphere is the vertical movement of air, whether
upward or downward movement and the bumpiness is accompanied by areas
of unrest in the air and wind. And contribute to each of the coups thermal
fronts, wind, wind and thunderstorms. Moreover, bumpiness is net of the
reasons that lead to circumstances is appropriate to cut the wind, and this
contributes to the formation of bumpiness in the atmosphere. The study found
that the noon of the times, which is expected to occur where clear-air
bumpiness during flights because of the warmth of the earth's surface. The
study found increased incidence of air hole during the summer, especially
July, due to increased incidence of coup surface, while the s
Knowing the nature of the relationship in federal systems lies in studying the political, social, economic and cultural forces, for their role in laying the foundations and the federal system. No matter how important the pillars of that system are, and through this research, we will learn how the political elites were able to crystallize this unique system, until it became one of the political systems that some countries seek to copy and apply its experience.
The first section of this research discussed the manner of the research from many sides like the problem it faces, importance of it , its targets ,boundaries, the way to collect and get information's and its assumption.
When the second chapter discussed the press – manufacturing and the development ,importance and types of newspapers, also its merits and weaknesses.
The third chapter talked about the scientific side and how to choose an assumption for the research . as it talked also about the apparent honest and stability tests that help in analyzing the research until getting results and so the right assumption for the research will be chosen.
And finally, the fourth chapter put highlight on the be
... Show MoreThe research aims to develop a proposed mechanism for financial reporting on sustainable investment that takes the specificity of these investments.
To achieve this goal, the researcher used (what if scenario) where the future financial statements were prepared for the year 2026, after completion of the sustainable project and operation, as the project requires four years to be completed.
The researcher relied on the results of the researchers collected from various modern sources relevant to the research topic and published on the internet, and the financial data and information obtained to assess the reality of the company's activity and its environmental, social, and economic i
... Show MoreThe aim of the research is to demonstrate the importance of leadership empowerment in its dimensions (knowledge, participation in decision-making, incentives, trust between the leader and subordinate, delegation of authority and communication) and its impact on enhancing the effectiveness of the company in its dimensions Represented by (achievement of objectives, quality of insurance service, adaptation to work environment and job satisfaction), by adopting the questionnaire as a main tool in collecting data from officials in the National Insurance Company, numbering (56) surveyed in job sites (section manager, division official and unit official) Their answers were analyzed using the SPSS statistical program in calculating the a
... Show MoreThe scholars differed very much in determining the grammatical doctrine of Ibn Qaysan. It was said that he confused between the two sects and took the two groups(1) and that he took from Abu Abbas the fox and Abu al-Abbas almabrd(2).He was descended from the two sheikhs almbrad and fox(3), This research to find out his grammatical opinions in the tools and grammatical words that appeared in the Book of Resonance of Multiplication to the many reported by Ibn Hayyan in it, he has seen the books of Ibn Kisan did not reach us.
The collection of these opinions and analysis is important for the scholars. Because the books of Ibn Kaysan specialized in grammar have lost their most important, the books that are similar to the book of Ibn al-Ha