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

A lotic ecosystem is considered a source of carbon dioxide (CO2) in the atmosphere where it becomes supersaturated with CO2, which contributes to the global carbon cycle. To enhance our comprehension of the roles of CO2 in rivers, an outdoor experiment was designed with controlled carbon source inputs to investigate the roles of the dissolved organic carbon (DOC) and dissolved inorganic carbon (DIC) in the phytoplankton community. Plastic enclosures were installed in the Tigris River within Baghdad for that goal. Samples were collected on the first day, as well as on the 5th and the 12th days from 14 enclosures. The enclosures were treated by artificial glucose (C6H12O6) (10, 20, 30mg/ l) as DOC sources, while sodium bicarbonate (NaHCO3) (1

 Represent choices Behaviorism available to the Managerial leaders one of the prerequisites to run any beginnings of a psychological or dilemmas Managerial barriers to working in the field of work has been varied these options until it had taken several kinds of which contributed to the left different impacts on the alleviation of these problems, which prompted the researcher to raising the problem of study within the framework of questionable content how to contribute to that shown by Choices Behaviorism accredited to the Managerial leaders in the management of frustration

Documentary Credit passes through many practical phases starting from Opening credit and matching documents and payment of the amount of credit……etc.  It is worthy to mention that there are several aspects that are varied and differed from Bank to another one which can offer Competitive Advantage for the bank …This will be shown in this research.

For the purpose of achieving the objective of this research within the theoretical aspect, the researcher had seen and briefed several books and researches which are mainly related to the subject of the research.

As for the practical aspect, has included Questionnaire which included many questions that are fit and suitable to the hypotheses.

Research sample has

This study has been undertaken to postulate the mechanism of impact test at low velocities. Thin-walled tubes of 100Cr6 were deformed under axial compression. In the present work there are seven velocities (4.429,4.652,5.240,5.600,5.942,6.264, 6.569) m\sec were applied to show how they effect the load, change in length, also the kinetic energy. However, the comparison between the obtained results and the other studies (Alexandar[3] , Abramowicz[4], Ayad[5]) was made the present work and Ayad data show good agreement. Load, change in length, kinetic energy were determined to understand the impact test.

The research aims to extrapolate the repercussions of the use of expert systems in the work of the external auditor on the quality of audit, as the research problem was that despite the use of these techniques in audit work, there is a problem related to the efficiency and effectiveness of these technological systems used in audit work, the feasibility of their use and the extent of their impact: The quality of the audit process.

The researchers adopted the questionnaire as a tool for collecting study data from a community composed of auditors in auditing offices and companies in Iraq, and the auditors of the Iraqi Federal Financial Supervision Bureau. The number of recovered and valid qu

The economical design of plate loaded by pressure can be obtained by using stiffeners instead of increasing the thickness of plate. The main subject of this work is to obtain the effect of stiffener height on the maximum stress in the plate subjected to pressure load. Different plate-stiffener sets are selected to find the effects of stiffener thickness, plate dimensions and pressure, on the optimum stiffener height. The models under consideration are square plates clamped rigidly from four edges. Finite Element method is used to analyze 160 different models by using the Finite Element software package ANSYS version 11. Another analysis method based on maximum stress equation is used to analyze 30 models. The graphical comparison of results

Direct measurements of drag force on two interacting particles  arranged in the longitudinal direction for particle Reynolds numbers varying from J O to 103 are conducted using a micro-force measurement system. The effect of the interparticle distance and Reynolds number on the drag forces  is examined. An empirical equation is obtained to describe the effect of the interparticle distance (l/d) on the dimensionless drag.