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

In this study used three methods such as Williamson-hall, size-strain Plot, and Halder-Wagner to analysis x-ray diffraction lines to determine the crystallite size and the lattice strain of the nickel oxide nanoparticles and then compare the results of these methods with two other methods. The results were calculated for each of these methods to the crystallite size are (0.42554) nm, (1.04462) nm, and (3.60880) nm, and lattice strain are (0.56603), (1.11978), and (0.64606) respectively were compared with the result of Scherrer method (0.29598) nm,(0.34245),and the Modified Scherrer (0.97497). The difference in calculated results Observed for each of these methods in this study.

Fire incidences are classed as catastrophic events, which mean that persons may experience mental distress and trauma. The development of a robotic vehicle specifically designed for fire extinguishing purposes has significant implications, as it not only addresses the issue of fire but also aims to safeguard human lives and minimize the extent of damage caused by indoor fire occurrences. The primary goal of the AFRC is to undergo a metamorphosis, allowing it to operate autonomously as a specialized support vehicle designed exclusively for the task of identifying and extinguishing fires. Researchers have undertaken the tasks of constructing an autonomous vehicle with robotic capabilities, devising a universal algorithm to be employed

The Planning and Resource Development Department of the Iraqi Ministry of Health is very interested in improving medical care, health education, and village training programs. Accordingly, and through the available capabilities of the ministry, itdesires to allocate seven health centers to four villages in Baghdad, Iraq therefore the ministry needs to determine the number of health centers allocated to each of these villages which achieves the greatest degree of the overall effectiveness of the seven health centers in a fuzzy environment. The objective of this study is to use a fuzzy dynamic programming(DP) method to determine the optimal allocation of these centers, which allows the greatest overall effectiveness of these health centers

A new Ni(II) nanostructured chelating system (DHN) was introduced for selective optical heavy-metal ion sensing in an aqueous medium. The cooperative chelating system comprising 8-hydroxyquinoline (8-HQ) and dimethylglyoxime (DMG) has been developed for the first time in association with fibre optic sensing for selective optical heavy-metal ion sensing in an aqueous medium. The Ni(II) nanocompound fluoresces upon 578 nm excitation, showing a highly sensitive optical response with a linear calibration curve in the range 0–100 ng/mL. The regression equation of the calibration curve is y = 0.0035x + 0.9990, which indicates very good linearity, implying R2 = 0.999 with high sensitivity (calibration slope of 0.0035) and low baseline noise (bla

Arts acts to reduce and exclude everything that is not necessary in the delivery of meaning, especially representative performance, which is based on the intensification of the physical and vocal actions, and in drawing the dimensions of the character. And because that, the artistic staff, among others in the ministry of education, are considered the cornerstone, in the development of theatrical activities in schools, this research came to find out the extent to which teachers in primary schools, in secondary schools and artistic supervisors rely on shorthand mechanisms in the representative performance.
The current research relied on the descriptive approach, in analyzing his sample, which was deliberately chosen, Among the most imp