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
Modern asphalt technology has adopted nanomaterials as an alternative option to assert that asphalt pavement can survive harsh climates and repeated heavy axle loading during service life and prolong pavement life. This work aims to elucidate the behavior of the modified asphalt mixture fracture model and assess the fatigue and Rutting performance of Hot Mix Asphalt (HMA) mixes using the outcomes of indirect Tensile Strength (IDT), Semicircular bend (SCB) and rutting resistance; for this, a single PG (64−16) nanomodified asphalt binder with 5 % SiO2 and TiO2 have been investigated through a series of laboratory tests, including: Resilient modulus, Creep compliance, and tensile strength, SCB, and Flow Number (FN) to study their potential
... Show MoreThe paper is highlighting the athletics and heroic sports which encouraged and played at Greek and Islamic period. The paper is identifying the Islamic athletics and heroic sport and compare them with Greek sports, as it is the model of sports while the sport during the Islamic period was not undertaken by scientific researches or articles even in Wikipedia. Although, this period was encouraged and practice many sports such as archery, sword grappling and wrestling, equestrianism, jogging and running whereas there are many Arabic references revealed during the Islamic 610 A.D. while the Greek and Olympic was known at 732 A.D. The paper is followed the literature review and historical to shied a light scientifically about traditional sports
... Show MoreThe paper is highlighting the athletics and heroic sports which encouraged and played at Greek and Islamic period. The paper is identifying the Islamic athletics and heroic sport and compare them with Greek sports, as it is the model of sports while the sport during the Islamic period was not undertaken by scientific researches or articles even in Wikipedia. Although, this period was encouraged and practice many sports such as archery, sword grappling and wrestling, equestrianism, jogging and running whereas there are many Arabic references revealed during the Islamic 610 A.D. while the Greek and Olympic was known at 732 A.D. The paper is followed the literature review and historical to shied a light scientifically about tradition
... Show MoreIn this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E1 , E2 , E3) of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the
... Show MoreCircular data (circular sightings) are periodic data and are measured on the unit's circle by radian or grades. They are fundamentally different from those linear data compatible with the mathematical representation of the usual linear regression model due to their cyclical nature. Circular data originate in a wide variety of fields of scientific, medical, economic and social life. One of the most important statistical methods that represents this data, and there are several methods of estimating angular regression, including teachers and non-educationalists, so the letter included the use of three models of angular regression, two of which are teaching models and one of which is a model of educators. ) (DM) (MLE) and circular shrinkage mod
... Show MoreFour electrodes were synthesized based on molecularly imprinted polymers (MIPs). Two MIPs were prepared by using the diclofenac sodium (DFS) as the template, 2-hydroxy ethyl metha acrylate(2-HEMA) and 2-vinyl pyridine(2-VP) as monomers as well as divinyl benzene and benzoyl peroxide as cross linker and initiator respectively. The same composition used for prepared non-imprinted polymers (NIPs) but without the template (diclofenac sodium). To prepared the membranes electrodes used different plasticizers in PVC matrix such as: tris(2-ethyl hexyl) phosphate (TEHP), tri butyl phosphate (TBP), bis(2-ethyl hexyl) adipate (BEHA) and tritolyl phosphate (TTP). The characteristics studied the slop, detection limit, life time and linearity range of DF
... Show MoreIn this paper, analyzing the non-dimensional Magnesium-hydrodynamics problem Using nanoparticles in Jeffrey-Hamel flow (JHF) has been studied. The fundamental equations for this issue are reduced to a three-order ordinary differential equation. The current project investigated the effect of the angles between the plates, Reynolds number, nanoparticles volume fraction parameter, and magnetic number on the velocity distribution by using analytical technique known as a perturbation iteration scheme (PIS). The effect of these parameters is similar in the converging and diverging channels except magnetic number that it is different in the divergent channel. Furthermore, the resulting solutions with good convergence and high accuracy for the d
... Show MoreCharacterization of the heterogonous reservoir is complex representation and evaluation of petrophysical properties and application of the relationships between porosity-permeability within the framework of hydraulic flow units is used to estimate permeability in un-cored wells. Techniques of flow unit or hydraulic flow unit (HFU) divided the reservoir into zones laterally and vertically which can be managed and control fluid flow within flow unit and considerably is entirely different with other flow units through reservoir. Each flow unit can be distinguished by applying the relationships of flow zone indicator (FZI) method. Supporting the relationship between porosity and permeability by using flow zone indictor is ca
... Show MoreOndansetron HCl (OND) is a potent antiemetic drug used for control of nausea and vomiting associated with cancer chemotherapy. It exhibits only 60 – 70 % of oral bioavailability due to first pass metabolism and has a relative short half-life of 3-5 hours. Poor bioavailability not only leads to the frequent dosing but also shows very poor patient adherence. Hence, in the present study an approach has been made to develop OND nanoparticles using eudragit® RS100 and eudragit® RL100 polymer to control release of OND for transdermal delivery and to improve patient compliance.
Six formulas of OND nanoparticles were prepared using nanoprecipitation technique. The particles sizes and zeta potential were measured
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