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

This paper develops a nonlinear transient three-dimensional heat transfer finite element model and a rate independent three-dimensional deformation model, developed for the CO₂ laser welding simulations in Al-6061-T6 alloy. Simulations are performed using an indirect coupled thermal-structural method for the process of welding. Temperature-dependent thermal properties of Al-6061-T6, effect of latent heat of fusion, and the convective and radiative boundary conditions are included in the model. The heat input to the model is assumed to be a Gaussian heat source. The finite element code ANSYS12, along with a few FORTRAN subroutines, are employed to obtain the numerical results. The benefit of the proposed methodology is that it

The calculation. of the nuclear. charge. density. distributions. ρ(r) and root. mean. square. radius.( RMS ) by elastic. electron. scattering. of medium. mass. nuclei. such. as (⁹⁰Zr, ⁹²Mo) based. on the model. of the modified. shell. and the use of the probability. of occupation. on the surface. orbits. of level 2p, 2s eroding. shells. and 1g gaining. shells. The occupation probabilities of these states differ noticeably from the predictions of the SSM. We have found. an improvement. in the determination. of ground. charge. density. and this improvement. allow. more precise. identification. of (CDD) between. (⁹²Mo- ⁹⁰Zr) to illustrate the influence of the extra

Augmented reality technology is a modern technique used in all fields, including: medicine, engineering and education, and has received attention from officials in the educational process at present; The focus of this research is on the degree of use of augmented reality among field experience students in the project's optimal investment program for teaching staff and their difficulties, applied to a sample of 75 students, through a questionnaire prepared by the researcher as a tool to determine the degree of use, as well as difficulties. The researcher addressed the subject through two main axes to determine the degree of use, as well as the difficulties preventing teachers and learners from using this technique. The results of the rese

Metal-organic frameworks (MOFs) have emerged as revolutionary materials for developing advanced biosensors, especially for detecting reactive oxygen species (ROS) and hydrogen peroxide (H₂O₂) in biomedical applications. This comprehensive review explores the current state-of-the-art in MOF-based biosensors, covering fundamental principles, design strategies, performance features, and clinical uses. MOFs offer unique benefits, including exceptional porosity (up to 10,400 m²/g), tunable structures, biocompatibility, and natural enzyme-mimicking properties, making them ideal platforms for sensitive and selective detection of ROS and H₂O₂. Recent advances have shown significant improvements in detection capabilities, with limit

This research aims to know the impact of leadership integrity as explanatory variable including its dimensions (courage, asceticism, justice, rationality, and humanity) on organizational conflict as responding variable. This research depended on the descriptive- constructive approach through the responses of a sample of (79) employees from (Real Estate Office of The State) in Al-Najaf province. The analyzing of the study done by using (Smart PLS) program to calculate (R^2, t, p). Many results concluded and one of them, there is significant impact correlation of the leadership integrity on organizational conflict. There are many suggestions have been reached depending on the results reached and one of them is the necessity of de

The present study aims at representing the importance of Quranic readings in the interpretation of the meaning of the Holly Quran in Imam Al Wahidi’s interpretation “Al Wasiet”, declaring its meaning, and eliminating of the paradox which takes place when trying to understand the intention of the Almighty Allah in His Holly book. The study aims at:

1- Defining the paradox linguistically and in terminology according to the formatives or the fundamentalists, the scientist of interpretation and of the Quranic sciences.

2-Reasoning paradox in the Quranic readings: Believing in matters that disagree with the Holly Quran and Sunnis, variety of the subjects in the verses, disagreement of the place and the place for the vers

The reason for my choice of the topic (what Imam Al-Tirmidhi mentioned in his book Al-Sunan regarding the provisions of sales) is that he mentioned many topics that affect people's lives, which are represented by commercial transactions and the exchange of benefits between them, so it became clear to them what is forbidden and what is not, aiming not to fall into the prohibited, and to achieve their interests, and relieve them of embarrassment. What we will see in the research.

Electrical distribution system loads are permanently not fixed and alter in value and nature with time. Therefore, accurate consumer load data and models are required for performing system planning, system operation, and analysis studies. Moreover, realistic consumer load data are vital for load management, services, and billing purposes. In this work, a realistic aggregate electric load model is developed and proposed for a sample operative substation in Baghdad distribution network. The model involves aggregation of hundreds of thousands of individual components devices such as motors, appliances, and lighting fixtures. Sana’a substation in Al-kadhimiya area supplies mainly residential grade loads. Measurement-based