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 debate on the methodology of media and communication research is no longer subject to the logic of the contradiction between the quantitative and the qualitative approach, nor the logic of the comparison between them. The nature of the topics presented for research, the problems they raise, the goals to be achieved from the research, and the epistemological positioning of researchers are among the critical factors that dictate the appropriate approach or methodological approaches to conduct their research. This positioning means the implicit philosophical principles upon which any researcher relies and which determine the path he/ she takes to produce scientifically approved knowledge. The method of the researcher's access to the phe
... Show MorePreparation and Identification of some new Pyrazolopyrin derivatives and their Polymerizations study
Schiff bases, named after Hugo Schiff, are aldehyde- or ketone-like compounds in which the carbonyl group is replaced by imine or azomethine group. They are widely used for industrial purposes and also have a broad range of applications as antioxidants. An overview of antioxidant applications of Schiff bases and their complexes is discussed in this review. A brief history of the synthesis and reactivity of Schiff bases and their complexes is presented. Factors of antioxidants are illustrated and discussed. Copyright © 2016 John Wiley & Sons, Ltd.
The present study was undertaken to study the effect of apigenin and luteolin on physiological and histological changes in rats treated with cytarabine drugs. Thirty-five albino healthy male adult rats with equal age weighing 250 -300g were enrolled. Rats were randomly divided into seven groups according to the treatment. Group “1” was treated with normal saline and served as the control group. Groups “2,3 and 4” received cytarabine, apigenin, and luteolin respectively, while groups 5, 6, and 7 received a combination of “apigenin + cytarabine”, “luteolin + cytarabine”, and “apigenin + luteolin + cytarabine”, respectively. After one week of treatment, all seven groups of rats were
... Show MoreIt is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.
... Show MoreOver the past few decades, the global usage and applications of different kinds of complementary and alternative medicine are greatly exaggerated among the general population, this requires improving the knowledge of all health care provider including pharmacists toward proper and safe use of different complementary and alternative medicine modalities. The current study aims to assess the Iraqi pharmacists' knowledge, use, and recommendation toward complementary and alternative medicine A cross-sectional pilot survey was done on a convenient sample of Iraqi pharmacists. Data were collected using a pretested
Dam and powerhouse operation sustainability is a major concern from the hydraulic engineering perspective. Powerhouse operation is one of the main sources of vibrations in the dam structure and hydropower plant; thus, the evaluation of turbine performance at different water pressures is important for determining the sustainability of the dam body. Draft tube turbines run under high pressure and suffer from connection problems, such as vibrations and pressure fluctuation. Reducing the pressure fluctuation and minimizing the principal stress caused by undesired components of water in the draft tube turbine are ongoing problems that must be resolved. Here, we conducted a comprehensive review of studies performed on dams, powerhouses, a
... Show MoreIn this study, successive electrocoagulation (EC) and electro-oxidation (EO) processes were used to minimize some of the major pollutants in real wastewater, such as organics (detected by chemical oxygen demand (COD)), and turbidity. The wastewater utilized in the present study was collected from the Midland Refinery Company in Baghdad-Iraq. The performance of the successive batch EC-EO processes was studied by utilizing Graphite and Aluminum (Al) as monopolar anode electrodes and stainless steel (st.st.) as the cathode. The Taguchi experimental design approach was used to attain the best experimental conditions for COD reduction as a major response. Starting from chemical oxygen demand COD of (600 ppm), the effects of current density (C
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