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
اسهم تطور ادوات الاسواق المالية والتغيرات العالمية كالعولمة المالية وتحرير الاسواق المالية العالمية في احداث العديد من الازمات ومنها الازمة المالية الدولية التي تعد من اكثر الظواهر ملازمة للاسواق المالية على الرغم من التطورات التي تشهدها تلك الاسواق نتيجة تطور ادواتها المالية وانفتاحها على بعضها البعض. وتتعرض الاسواق المالية الدولية والناشئة (Emerging Market) منها بشكل خاص ا
... Show MoreOsteoblast and osteoclast activity is disrupted in post-menopausal osteoporosis. Thus, to fully address this imbalance, therapies should reduce bone resorption and promote bone formation. Dietary factors such as phyto-oestrogens and Zn have beneficial effects on osteoblast and osteoclast activity. However, the effect of combinations of these factors has not been widely studied. We therefore examined the effect of coumestrol, daidzein and genistein in the presence or absence of zinc sulphate (Zn) on osteoclast and osteoblast activity. Osteoclast differentiation and bone resorption were significantly reduced by coumestrol (10- 7 m), daidzein (10- 5 m) and genistein (10- 7 m); and this direct anti-osteoclastic action was unaffected by Zn (10-
... Show MoreThis work involves the preparation of high yield iminochalcon compounds (B1-B15) through two parts. The first part involves the preparation of 2,4-dihydroxy Chalcone (A1-A15) by the condensation of 2,4-dihydroxy acetophenone with aryl aldehyde in the presence of sodium hydroxide (40%) as a catalyst. The second part includes the preparation of iminochalcon from the condensation of p-hydroxy aniline with 2,4-dihydroxy chalcone derivatives )A1-A15) in the presence of some drops of conc. H2SO4. Thin-layer chromatography ((TLC) was used to control the chemical reaction . These new derivatives were characterized by using FT-IR and 1H-NMR spectroscopy. These synthesized
... Show MoreThe influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr
... Show MoreA modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the va
... Show MoreThe synthesis, characterization and mesomorphic properties of two new series of triazine-core based liquid crystals have been investigated. The amino triazine derivatives were characterized by elemental analysis, Fourier transforms infrared (FTIR), 1HNMR and mass spectroscopy. The liquid crystalline properties of these compounds were examined by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). DSC and POM confirmed nematic (N) and columnar mesophase textures of the materials. The formation of mesomorphic properties was found to be dependent on the number of methylene unit in alkoxy side chains.