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
Todays, World is faced an energy crisis because of a continuous increasing the consumption of fuels due to intension demand for all types of vehicles. This study is one of the efforts dealing with reduce the weight of vehicles by using a new material of sandwich steel, which consists of two skin steel sheets with core of a polymer material. Resistance spot welding (RSW) can be easily implemented on metals; however a cupper shunt tool was designed to perform the resistance welding of sandwich steel with DP800 cover sheets to resolve a non-conductivity problem of a polymer core. Numerical simulations with SORPAS®3D were employed to test the weldability of this new material and supported by many practical experiments. In conclus
... Show MoreNanostructural cupric oxide (CuO) films were prepared on Si and glass substrate by pulsed laser deposition technique (PLD) using laser Nd:YAG, using different laser pulses energies from 200 to 600 mJ. The X-ray diffraction pattern (XRD) of the films showed a polycrystalline structure with a monoclinic symmetry and preferred orientation toward (111) plane with nano structure. The crystallite size was increasing with increasing of laser pulse energy. Optical properties was characterized by using UV–vis spectrometer in the wave lengthrange (200-1100) nm at room temperature. The results showed that the transmission spectrum decreases with the laser pulses energy increase. Sensitivity of NO2 gas at different operating temperatures, (50°C,
... Show MoreIn 1939, the Japanese scientist Michio Takaoka first mentioned resveratrol from Veratrum grandiflorum O. Loes. Majority of plants, such as grapes, berries, and peanuts, are significant sources of resveratrol, a well-known polyphenolic. resveratrol (RV) is noted for its links to several health care benefits, including glucose metabolism, anti-aging, cardioprotective, neuroprotective, antitumor, antidiabetic, and antioxidant effects. Importantly, there have been reports of promising therapeutic qualities in atherosclerosis, dementia, and various malignancies. These properties are controlled through a number of cooperative techniques, which control inflammation besides the effects of oxidative stress and cell death. However, circulating resver
... Show MoreCopper nanoparticles (CuNPs) were prepared with different diameters by sonoelectrodeposition technique using Electrodeposition process coupled with high-power ultrasound horn (Sonoelectrodeposition). The particle diameter of the CuNPs was adjusted by varying CuSO4 solution acidity (pH) and current density. The morphology and structure of the CuNPs were examined by X-ray diffraction (XRD) and Scanning Electron Microscopy (SEM). It was found that the size of the produced copper nanoparticles ranged between 22 to 77 nm, where the diameter of CuNPs increases with reduction the solution acidity from 0.5 to 1.5 pH and increasing the current density of the deposition from 100 to 400 nm. Finally the produced CuNPs were pressed to fabricate disc
... Show MoreIn this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex.
This study deals with a prominent critical term - poetics - in critical studies as an area related to uncovering the laws of creative and aesthetic discourses (Preaching)، and the various functions that accompany it in literary texts. So، the study employs the pioneers' works of this theory specially the eastern theorists in making a parallel comparing study of the text book of " the Magic and Poetry” by Al-Lisan Al-Din bin Al-Khatib (776 AH). It displays the utility of the concept of poetics in the referred book pointing to the illumination of various functions that، in turn، reflected the
A new results for fusion reactivity and slowing-down energy distribution functions for controlled thermonuclear fusion reactions of the hydrogen isotopes are achieved to reach promising results in calculating the factors that covered the design and construction of a given fusion system or reactor. They are strongly depending upon their operating fuels, the reaction rate, which in turn, reflects the physical behavior of all other parameters characterization of the system design
The purpose of this paper is to find the best multiplier approximation of unbounded functions in –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.
Studies from our laboratory have shown that Δ9-Tetrahydrocannabinol (THC), an ingredient found in marijuana plant Cannabis sativa, can attenuate acute lung injury induced by Staphylococcus enterotoxin B (SEB). In the current study, we investigated the role of THC on the metabolism of SEB-activated lymphocytes. To this end, we determined metabolic potential of SEB-activated lymphocytes treated with vehicle or THC by performing the Cell Mito Stress Test. The oxygen consumption rate (OCR) in THC-treated cells was decreased when compared to vehicle-treated group whereas the extracellular acidification rate (ECAR) was similar in both the groups. Specifically, electron transport chain inhi