The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Abstract

                 The research aimed to test the relationship between the size of investment allocations in the agricultural sector in Iraq and their determinants using the Ordinary Least Squares (OLS) method compared to the Error Correction Model (ECM) approach. The time series data for the period from 1990 to 2021 was utilized. The analysis showed that the estimates obtained using the ECM were more accurate and significant than those obtained using the OLS method. Johansen's test indicated the presence of a long-term equilibrium relationship between the size of investment allocations and their determinants. The results of th

Shadow detection and removal is an important task when dealing with color outdoor images. Shadows are generated by a local and relative absence of light. Shadows are, first of all, a local decrease in the amount of light that reaches a surface. Secondly, they are a local change in the amount of light rejected by a surface toward the observer. Most shadow detection and segmentation methods are based on image analysis. However, some factors will affect the detection result due to the complexity of the circumstances. In this paper a method of segmentation test present to detect shadows from an image and a function concept is used to remove the shadow from an image.

The process of identifying the region is not an easy process when compared with other operations within the attribute or similarity. It is also not difficult if the process of identifying the region is based on the standard and standard indicators in its calculation. The latter requires the availability of numerical and relative data for the data of each case Any indicator or measure is included in the legal process

Introduction: This study was designed to examine the effects of addition of the combination of polymerized polymethyl methacrylate (PMMA) and zirconia (ZrO2) particles to heat cure PMMA resin on impact strength, surface hardness, and roughness. Methods: The 70% (w/w) of polymerized PMMA powder (particle size: 0.70mm) was mixed with 30% (w/w) of zirconia powder (ZrO2) (1mm) to produce PMMA-ZrO2 filler. Ninety acrylic specimens created were divided into three groups containing 0% wt (Control group), 2% wt, and 4% wt, PMMA-ZrO2 filler. Ten specimens were used for impact strength, surface hardness and roughness test, blindly. Data were analyzed via oneway ANOVA and the Tukey post hoc test using R 3.6.3. Results: There was statistically signific

Background: The PMMA polymer denture base materials are low in thermal and strength properties. The aim of the study was to investigate the change in glass transition temperature, E-Moudulus and coefficient of thermal expansion of acrylic denture base material by addition of Al2O3, TiO2 and SiO2nano-fillers in 5% by weight. Materials and methods: The type of polymerization is free radical bulk polymerization. one hundred twenty (120) specimens were prepared , the specimens were divided into four groups according to the material had been added (one control and three for Al2O3, TiO2 and SiO2nanocomposite) each group was subdivided in to three groups according to the test had been done on it, the degree of transition (Tg) was measured by The d

The research aims at the possibility of measuring the technical and scale efficiency (SE) of the departments of the College of Administration and Economics at the University of Baghdad for a period lasting 8 years, from the academic year 2013-2014 to 2018-2019 using the method of Applied Data Analysis with an input and output orientation to maintain the distinguished competitive position and try to identify weaknesses in performance and address them. Nevertheless, the research problem lies in diagnosing the most acceptable specializations in the labor market and determining the reasons for students’ reluctance to enter some departments. Furthermore, the (Win4DEAp) program was used to measure technical and scale efficiency (SE) and rely on