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.
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 alternating direction implicit method (ADI) is a common classical numerical method that was first introduced to solve the heat equation in two or more spatial dimensions and can also be used to solve parabolic and elliptic partial differential equations as well. In this paper, We introduce an improvement to the alternating direction implicit (ADI) method to get an equivalent scheme to Crank-Nicolson differences scheme in two dimensions with the main feature of ADI method. The new scheme can be solved by similar ADI algorithm with some modifications. A numerical example was provided to support the theoretical results in the research.
A legal discourse in the Qur’an and Sunnah is almost devoid of the use of one of the general formulas, and due to its frequent rotation in the tongue of the legislator, the formulas may overlap their members in apparently contradictory provisions, which makes the individual from the general members appear to the beholder to be covered by two contradictory provisions, and this research came to present what might happen to him The legal text interpreter of weighting between the two opposing texts is the strength of the generality that is established by the generality formula, so the two strongest formulas in the inclusion of its members outweigh the weaker of them and precede them, and the research decided that the formulas vary
... Show MoreNumerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th
... Show MoreAs a result of the entry of multinationals companies in Iraq for investing in the joint projects through conducting agreements and contracts for work on important and strategic projects to get the necessary funds and various experiences which characterize the foreign participant sides that Iraq currently needs them and because of the non-applying the accounting processing stipulated in the unified accounting system in addition to the absence of a local accounting bases as well as the default of the participant contracts on indicating the accounting methods about those projects which are considered one of the bases that enables auditors in the public sector to depend on it, thus the research paper deals with studying an
... Show MoreLimestones have considerable commercial importance because they are used as building stones and are widely used for flooring and interior and exterior facings. On the other hand, the reserve calculation reveals the economic effectiveness of the investigation. This study aims to calculate the reserve of the middle Miocene limestone for engineering purposes. The limestone beds of the Nfayil Formation in Central Iraq have been studied over 15 outcrop sections. The Nfayil bed has an average thickness of about 1.64 m, while the overburden has an average of about 0.93 m. The average bulk density of limestone is 2.1 gm/cm3 . Kriging and triangulation method has been adopted and used in the calculation and assessment of reserve. The industrial laye
... Show MoreBoth traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a
... Show MoreAlmost all thermal systems utilize some type of heat exchanger. In a lot of cases, evaporators are important for systems like organic Rankine cycle systems. Evaporators give a share in a large portion of the capital cost, and their cost is significantly attached to their size or transfer area. Open-cell metal foams with high porosity are taken into consideration to enhance thermal performance without increase the size of heat exchangers. Numerous researchers have tried to find a representation of the temperature distribution closer to reality due to the different properties between the liquid and solid phases. Evaporation heat transfer in an annular pipe of double pipe heat exchanger (DPHEX) filled with cooper foam is investigated numerical
... Show MoreThe internet is a basic source of information for many specialities and uses. Such information includes sensitive data whose retrieval has been one of the basic functions of the internet. In order to protect the information from falling into the hands of an intruder, a VPN has been established. Through VPN, data privacy and security can be provided. Two main technologies of VPN are to be discussed; IPSec and Open VPN. The complexity of IPSec makes the OpenVPN the best due to the latter’s portability and flexibility to use in many operating systems. In the LAN, VPN can be implemented through Open VPN to establish a double privacy layer(privacy inside privacy). The specific subnet will be used in this paper. The key and certificate will
... Show MoreAZ Khalaf, M kassim Haidir, LK Jasim, Iraqi Journal of Science, 2012