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

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environme

Background: Radiopacity is one of the prerequisites for dental materials, especially for composite restorations. It's essential for easy detection of secondary dental caries as well as observation of the radiographic interface between the materials and tooth structure. The aim of this study to assess the difference in radiopacity of different resin composites using a digital x-ray system. Materials and methods: Ten specimens (6mm diameter and 1mm thickness) of three types of composite resins (Evetric, Estelite Sigma Quick,and G-aenial) were fabricated using Teflon mold. The radiopacity was assessed using dental radiography equipment in combination with a phosphor plate digital system and a grey scale value aluminum step wedge with thickness

Objective:Fluorid-containing dental alginate impression materials can exert a considerable reduction in
enamel solubility. The objective was to evaluate the effect of fluoride addition on the setting time and
compressive strength of alginate impression materials.
Methodology: 60 samples were constructed from alginate impression material (30 samples for setting
time test and 30 samples for compressive strength test).Specimens of each test divided into three
subgroup. Group A: 10 specimens of alginate were mixed with distilled water [control], Group B: 10
specimens of alginate were mixed with100-ppm fluoride and Group C:10 specimens of alginate were
mixed with 2%Naf.
Results: the result of setting time test showed t

The current research is concerned with methods of formation and their effect on the sintering process of ceramic materials. The research is divided into a number of chapters. The first chapter addressed the research structure (the research problem, importance, objective, limits, and it also defined the terms used in the research). The second chapter addressed the theoretical framework, where the theoretical framework has been divided into three sections. The first section dealt with methods of formation of ceramic materials including: Plasticizing method 2- semi-dry pressing method 3- dry pressing method 4- extrusion method 5- casting method.
The researcher found that there is a clear difference between the methods through her formati

The Tigris River is one of the main rivers and an important resource for the population of Iraq. The present study aimed to quantify the concentration of surface-active substances in the Tigris River and to investigate the dynamics of this ecosystem. Five sampling sites were selected along the river within Baghdad city (Al-Muthanna Bridge, Al-Greaat Bridge, Al-Sarrafia Bridge, Al-Jadriyah Bridge, and Al-Za'franiya Area) for the period from July 2020 to April 2021. The study examined the relationship between the concentrations of surface-active materials (surfactants, including anionic and nonionic types) and their potential interaction with nutrients—nitrate (NO₃⁻), phosphate (PO₄), and sulfate (SO₄²⁻)—as well as the

Background: Radiopacity is one of the prerequisites for dental materials, especially for composite restorations. It's essential for easy detection of secondary dental caries as well as observation of the radiographic interface between the materials and tooth structure. The aim of this study to assess the difference in radiopacity of different resin composites using a digital x-ray system. Materials and methods: Ten specimens (6mm diameter and 1mm thickness) of three types of composite resins (Evetric, Estelite Sigma Quick,and G-aenial) were fabricated using Teflon mold. The radiopacity was assessed using dental radiography equipment in combination with a phosphor plate digital system and a grey scale value aluminum step wedge with thickness