In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.
In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
... Show MoreIn this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.
The semiempirical (PM3) and DFT quantum mechanical methods were used to investigate the theoretical degradation of Indigo dye. The chemical reactivity of the Indigo dye was evaluated by comparing the potential energy stability of the mean bonds. Seven transition states were suggested and studied to estimate the actually starting step of the degradation reaction. The bond length and bond angle calculations indicate that the best active site in the Indigo dye molecule is at C10=C11. The most possible transition states are examined for all suggested paths of Indigo dye degradation predicated on zero-point energy and imaginary frequency. The first starting step of the reaction mechanism is proposed. The change in enthalpy, Gibbs free energ
... Show MoreThe tax system, like any other system, as a set of elements and parts that complement each other and are interrelated and interact to achieve specific goals, and is a natural reflection of the economic, social and political conditions prevailing in society, and therefore the objectives of tax policy formulated in line with the objectives of economic policy in general, which means that any change in economic policy clearly affects fiscal policy measures and fiscal policy in particular.
The problem of searching for the impact of foreign direct investment in the Iraqi tax system was focused on the study the of foreign direct investment and therole played in developing and improving the economic reality and its implicatio
... Show MoreLibraries, information centers, and everything related to organizing and preparing information need to be periodically re-evaluated in order to stand on the level of quality, which means improving the general reality of these institutions to ensure sufficient satisfaction from beneficiaries of the services provided. This is what was worked on in this research, as one of the most important quality standards in libraries and information centers, LibQUAL+®, was applied in one of the most important and oldest central university libraries, namely the Central Library of the University of Baghdad at its two locations, Al-Jadriya and Al-Waziriya. The sample of beneficiaries to whom the questionnaire was distributed reached 75 beneficiaries distrib
... Show MoreThe primary objective of this paper is to improve a biometric authentication and classification model using the ear as a distinct part of the face since it is unchanged with time and unaffected by facial expressions. The proposed model is a new scenario for enhancing ear recognition accuracy via modifying the AdaBoost algorithm to optimize adaptive learning. To overcome the limitation of image illumination, occlusion, and problems of image registration, the Scale-invariant feature transform technique was used to extract features. Various consecutive phases were used to improve classification accuracy. These phases are image acquisition, preprocessing, filtering, smoothing, and feature extraction. To assess the proposed
... Show MoreIn the present research, a crane frame has been investigated by using finite element method. The damage is simulated by reducing the stiffness of assumed elements with ratios (10% and 20 %) in mid- span of the vertical column in crane frame. The cracked beam with a one-edge and non-propagating crack has been used. Six cases of damage are modeled for crane frame and by introducing cracked elements at different locations with ratio of depth of crack to the height of the beam (a/h) 0.1, 0.20. A FEM program coded in Matlab 6.5 was used to model the numerical simulation of the damage scenarios. The results showed a decreasing in the five natural frequencies from undamaged beam which means
... Show MoreIn the past two decades, maritime transport traffic has increased, especially in the case of container flow. The BAP (Berth Allocation Problem) (BAP) is a main problem to optimize the port terminals. The current manuscript explains the DBAP problems in a typical arrangement that varies from the conventional separate design station, where each berth can simultaneously accommodate several ships when their entire length is less or equal to length. Be a pier, serve. This problem was then solved by crossing the Red Colobuses Monkey Optimization (RCM) with the Genetic Algorithm (GA). In conclusion, the comparison and the computational experiments are approached to demonstrate the effectiveness of the proposed method contrasted with other
... Show MoreThis paper presents a study of wavelet self-organizing maps (WSOM) for face recognition. The WSOM is a feed forward network that estimates optimized wavelet based for the discrete wavelet transform (DWT) on the basis of the distribution of the input data, where wavelet basis transforms are used as activation function.