This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.
In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.
The ground charge density distributions (CDD), elastic charge form factors and proton, charge, neutron, and matter root mean square (rms) radii for stable 40Ca and 48Ca have been calculated using single-particle radial wave functions of Woods-Saxon (WS) and harmonic-oscillator (HO) potentials. Different central potential depths are used for each subshell which is adjusted so as to reproduce the experimental single-nucleon binding energies. An excellent agreement between the calculated rms charge radii and experimental data are found for both nuclei using WS and HO potentials. The calculated proton rms radii for 40Ca are found to be in good agreement with experiment data using both WS and HO potentials while the results for 48Ca showed an ov
... Show MoreWith the aim of developing potential antimicrobials, a series of new 5-fluoroisatin derivatives incorporated with different secondary amines (piperidine, morpholine, pyrrolidine, dimethylamine, and diphenylamine) for monomer, and (piperazine) in case of dimer Mannich bases, separately in presence of formaldehyde to obtain Mannich bases of 5-fluoroisatin derivatives, which then each Mannich derivatives reacts with phenylhydrazine to form Schiff bases as final products. The resulting compounds were characterized by two spectroscopic analyses; (Fourier- transform infrared) FT-IR and proton nuclear magnetic resonance spectroscopy (¹H-NMR). In addition, the in vitro antibacterial and antifungal activities were tested against some human pathogen
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The conflict between the fundamentalist and news theory in the methodology that each of the two schools pursued with the Twelver Shi'a Imamiyyah in deriving the legal rulings from the sources of legislation, especially in the second source, which is the noble hadith and narration after the Holy Qur’an, which is the first source has gone through multiple and complex stages that led This struggle to excess, stress, exaggeration, negligence, neglect and indulgence by each of the two schools in dealing with the noble hadith and narration and in the manufacture of rules and laws and fundamentalist and juristic theories of the process of jurisprudential development of legal rulings where every school believed and proceed
... Show MoreThe study aimed to explaining the concepts of water footprint and virtual water and how these two concepts could use to achieve water savings at the local level to meet the water supply deficit in Iraq, which is expected to increase in the coming years and influence of that on food security in Iraq by using these concepts when drawing production, irrigated and import plans in Iraq. The study aimed to studying the water footprint and virtual water and their impact on the foreign trade for wheat and rice crops during the period 2000-2022 and estimating the most important indicators of virtual water and the water footprint of the study crops due to the importance of these criteria in det
Recording an Electromyogram (EMG) signal is essential for diagnostic procedures like muscle health assessment and motor neurons control. The EMG signals have been used as a source of control for powered prosthetics to support people to accomplish their activities of daily living (ADLs). This work deals with studying different types of hand grips and finding their relationship with EMG activity. Five subjects carried out four functional movements (fine pinch, tripod grip and grip with the middle and thumb finger, as well as the power grip). Hand dynamometer has been used to record the EMG activity from three muscles namely; Flexor Carpi Radialis (FCR), Flexor Digitorum Superficialis (FDS), and Abductor Pollicis Brevis (ABP) with different le
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