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

Surface runoff is considered one of the most significant water resources in arid and semi-arid environments. Estimating the volume of surface runoff through the application of Geographic Information Systems (GIS), along with maps detailing the geomorphological and geological characteristics of the Wadi Haran basin, is an essential process. This estimation is supported by mathematical equations based on the Soil Conservation Service Curve Number method (SCS-CN), which is among the most widely used approaches for calculating runoff volume. The study area, Wadi Haran basin, covers approximately 1,895 km². The Curve Number (CN) was found to be 92, with runoff volume (QV) values ranging between 582.71 m³ and 12.85 m³. The total surfa

This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

In real conditions of structures, foundations like retaining walls, industrial machines and platforms in offshore areas are commonly subjected to eccentrically inclined loads. This type of loading significantly affects the overall stability of shallow foundations due to exposing the foundation into two components of loads (horizontal and vertical) and consequently reduces the bearing capacity.

Based on a numerical analysis performed using finite element software (Plaxis 3D Foundation), the behavior of model strip foundation rested on dry sand under the effect of eccentric inclined loads with different embedment ratios (D/B) ranging from (0-1) has been explored. The results display that, the bearing capacity of st

      In this study, simple, low cost, precise and speed spectrophotometric methods development for evaluation of sulfacetamide sodium are described. The primary approach contains conversion of sulfacetamide sodium to diazonium salt followed by a reaction with p-cresol as a reagent in the alkaline media.  The colored product has an orange colour with absorbance at λmax 450 nm. At the concentration range of (5.0-100 µg.mL^-1), the Beer̆ s Low is obeyed with correlation coefficient (R²= 0.9996), limit of detection as 0.2142 µg.mL^-1, limit of quantification as 0.707 µg.mL^-1 and molar absorptivity as 1488.249 L.mol^-1.cm^-1. The other approach, cloud point extraction w

The researcher attempts to examine Barman model in acquiring the historical concepts among fourth-grade students at literary classrooms. To this end, the researcher held the null hypothesis, there is no significant difference between the experimental groups who was taught based on Barman model and the control group that taught based on the traditional method in acquiring the historical concepts on the post-test. To testify the effectiveness of Barman model, the researcher administered a questionnaire included (60) items on bunch of female-students who were selected from al-khamaeal preparatory school in al-hurriyah district in Baghdad. The author utilized different statistical tools to analyze the collected data.    &

   In this paper, a mathematical model for the oxidative desulfurization of kerosene had been developed. The mathematical model and simulation process is a very important process due to it provides a better understanding of a real process. The mathematical model in this study was based on experimental results which were taken from literature to calculate the optimal kinetic parameters where simulation and optimization were conducted using gPROMS software. The optimal kinetic parameters were Activation energy 18.63958 kJ/mol, Pre-exponential factor  2201.34 (wt)^-0.76636. min^-1  and the reaction order 1.76636. These optimal kinetic parameters were used to find the optimal reaction conditions which