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 Problem

We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

In order to improve the effectiveness, increase the life cycle, and avoid the blade structural failure of wind turbines, the blades need to be perfectly designed. Knowing the flow angle and the geometric characteristics of the blade is necessary to calculate the values of the induction factors (axial and tangential), which are the basis of the Blade Element Momentum theory (BEM). The aforementioned equations form an implicit and nonlinear system. Consequently, a straightforward iterative solution process can be used to solve this problem. A theoretical study of the aerodynamic performance of a horizontal-axis wind turbine blade was introduced using the BEM. The main objective of the current work is to examine the wind turbine blade’s perf

Improvisation is that spontaneous automatic achievement which is formed by a new cognition that is not based on something prior to it or a previous cognition. It is instantaneous. Whereas in art, improvisation also inters in all types of applied and performance arts as a foundation for launching and initiating it in music, painting, cinema, television and theater. In order to study the improvisation of the actor, the researcher put forward a theoretical study that included two sections. The first section is (the improvisation concept) and the second section is (improvisation in the show). The researcher, in the research procedures, took an intentional sample that was represented by the theatrical show (Rehearsal in Hell Play) and after t

Deposits with the Industrial Bank, together with loans received from others, are non-financial financial resources, which are sources of supply to the Industrial Bank of funds that allow the Bank to expand the granting of loans. The increases in this resource indicates that the bank is practicing comprehensive banking, which is consistent with the nature of the transformation of the banking system towards multiple businesses. Therefore, the research comes to highlight the causality of the trend between total deposits and total loans. And if the causality is found, is it one-way or two-way? How long is the impact?

The study aimed to prepare rehabilitation exercises using some rubber ropes for people with partial rupture of the anterior cruciate ligament, to recognize their effect on the recovery of motor tides and to reduce the pain of those with partial rupture of the anterior cruciate ligament of the knee joint, and adopted the experimental method by designing the experimental and controlled groups on a sample of those with partial rupture of the anterior cruciate ligament of men (30-35) One year of those who attend the Physiotherapy Center/Rafidain University College of 12 injured were deliberately selected from their community of origin by (100%), and after determining the measuring tools and preparation of exercises applied with rubber r

Abstract

      The research aims to identify the mediator role of  workplace spirituality in the  relationship between psychological capital and entrepreneurial  behavior: field research to a sample opinions from employees at the center of the Iraqi ministry of Oil . The importance of the current research emerged from paucity of studies that have attempted to identify and know the nature of the relationship between the variables as well as trying to find the current address and realistic problem directly affects the performance of employees in the Iraqi oil sector.

 In order to achieve the goal of research the use of the analytical method (quantitative)

This research aims to test the causal relationship long-and short-run between the price of gold the global crude oil price and the exchange rate of the dollar and how you can take advantage of the nature of this relationship, particularly in the Arab oil states that achieve huge surpluses, including Iraq and how to keep on the purchasing power of these surpluses or reduce the levels of risk.

The problem is that the Arab oil countries, adversely affected, as a result of that relationship, due to the fact that its role confined to the sale of crude oil only. They do not have control in the dollar, then they are not able to take advantage of its impact on the price of gold the fact that gold is effective pr

In this research, the X-ray diffraction pattern was used, which was obtained experimentally after preparation of barium oxide powder. A program was used to analyze the X-ray diffraction lines of barium oxide nanoparticles, and then the particle size was calculated by using the Williamson-Hall method, where it was found that the value of the particle size is 25.356 nm. Also, the dislocation density was calculated, which is equal to1.555 x1015 (lines/nm2), and the value of the unit cell number was also calculated, as it is equal to 23831.