In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

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

Objectives: The purpose of this in vitro study was to compare the effect of adding a poloxamer surfactant to the irrigant solutions on its cleaning efficiency. Design: In this study the roots of extracted permanent premolar teeth were used and evaluated by using Scanning Electronic Microscopy (SEM). Materials and Method: 72 human single tooth of permanent premolar (8 for each group) were used in this in vitro study. Roots after sectioning at cervical area to get 15 mm were embedded in a plastic container filled with impression silicon, then instrumented with ProTaper rotary instruments till size F4. Each group (8 root) were irrigated with one of the nine solutions used in study: three concentrations of NaOH [5% (A1), 2.5%(A2), 0.5%(A3)], th

In the present work, nanocomposite of poly (vinyl alcohol) (PVA) incorporated with functionalized graphene oxide (FGO) were fabricated using casting method. PVA was dispersed by varying content of FGO (0.3, 0.5, 0.8, 1 wt %). The PVA- FGO nanocomposite was characterized by FT‐IR, FE-SEM and XRD. Frequency dependence of real permittivity (ε’), imaginary (ε’’) and a.c conductivity of PVA/FGO and PVA/GO nanocomposite were studied in the frequency range 100 Hz- 1 MHz. The experimental results showed that the values of real (ε’) and imaginary permittivity (ε’’) increased dramatically by increasing the FGO content in PVA matrix. PVA/ FGO (1 wt %) nanocomposite revealed higher electrical conductivity of 6.4×10-4 Sm-1 compared to

The structural, optical properties of cupper indium gallium selenite (CuIn1-xGaxSe) have been studied. CuIn1-xGaxSe thin films for x=0.6 have been prepared by thermal evaporation technique, of 2000±20 nm thickness, with rate of deposition 2±0.1 nm/sec, on glass substrate at room temperature. Heat treatment has been carried out in the range (373-773) K for 1 hour. It demonstrated from the XRD method that all the as-deposited and annealed films have polycrystalline structure of multiphase. The optical measurement of the CIGS thin films conformed that they have, direct allowed energy gap equal to 1.7 eV. The values of some important optical parameters of the studied films such as (absorption coefficient, refractive index, extinction coeffici

In order to study the effect of inoculation with mycorrhiza and fertilization with plant residues on the growth of plants, we used two factors: the first two levels of mycorrhiza inoculation, Glumus mossea (0 and 10 g.pot-1) and the second factor, four levels of plant residues (10 g.pot-1) celery plant residues, 10 g pot-1 mint residues, and 10 g pot-1 black bean seed residues. Mychorrizal treatment (10 g pot-1) increased the number of mycorrhiza spores and the infection percentage of mycorrhizal by 917.44% and 13088.23%, respectively; celery treatment (10 g.pot-1) increased the chlorophyll index in the leaves and height of the chard plant by 31.34% and 94.04%, respectively; and black seed treatment (10 g.pot-1) increased the percen

In order to study the effect of inoculation with mycorrhiza and fertilization with plant residues on the growth of plants, we used two factors: the first two levels of mycorrhiza inoculation, Glumus mossea (0 and 10 g.pot^-1) and the second factor, four levels of plant residues (10 g.pot^-1) celery plant residues, 10 g pot^-1 mint residues, and 10 g pot^-1 black bean seed residues. Mychorrizal treatment (10 g pot^-1) increased the number of mycorrhiza spores and the infection percentage of mycorrhizal by 917.44% and 13088.23%, respectively; celery treatment (10 g.pot^-1) increased the chlorophyll index in the leaves and height of the chard plant by 31.34% and 94.04%, re

An investigation was conducted for the improvement of viscosity index of light lubricating oil fraction (40 stock)
obtained from vacuum distillation unit of lube oil plant of Daura Refinery, using solvent extraction process.
In this study furfural solvent was used to extract the undesirable materials which reduce the viscosity index of raw
lubricating oil fraction.
The studied effecting variables of extraction were extraction temperature range from 70 to 110°C, and solvent to oil
ratio range from 1:1 to 4:1 (wt/wt).
The n-d-M method was used for calculation of carbon distribution and structural group analysis of the raffinate
produced from furfural extraction.
Also the three component phase diagram for a mixed-ba

   In this research the effect of grain size and effect of La2O3 doping on densification  rate for the  initial and intermediate  stages of sintering were studied .The experimental results for α – cristobilite powder are modeled using ( L2-Regression ) technique in studying  the effect of grain size and La2O3 doping using  three particles size (6.12, 8.92, 13.6 ) µm, with undoped  initial powder and with La2O3 doping . The mathematical simulation showes that the densification rates increase as the initial particles sizes decrease and vice versa. This shows that the densification depends directly on the initial compact density which reflects the contacts area between the particles . How

     In this study, cadmium oxide (CdO) was deposited on glass bases by thermal chemical spraying technique at three concentrations (0.05, 0.1, 0.15) M and then was irradiated by CO₂ laser with 10.6 μm wave length and 1W power. The results of the atomic force microscope AFM test showed that the surfaces of these CdO thin films were homogenous and that the laser irradiated effect resulted in decreasing the roughness of the surface as well as the heights of the granular peaks, indicating a greater uniformity and homogeneity of the surfaces. The optical properties were studied to determine laser effect. The results of optical tests of these thin films showed that the photoluminescence spectra and absorption s