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
In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data sets
Research summary
Muslim scholars have established fundamental rules for deriving rulings to be a methodology for every mujtahid who wants to extract rulings from his reliable sources, and one of the most prominent fundamental rules on which many rulings are built is the permissible and the many rulings related to it.
Leaving what is permissible on its own terms sometimes causes embarrassment and distress in some cases, so we need something that restricts it. In our Islamic law, many legal rulings are embodied in which the restriction of what is permissible is in the public interest, or to relieve embarrassment in public.
Because of the importance of this fundamentalist rule, and the difference in some
... Show MoreCopper Telluride Thin films of thickness 700nm and 900nm, prepared thin films using thermal evaporation on cleaned Si substrates kept at 300K under the vacuum about (4x10-5 ) mbar. The XRD analysis and (AFM) measurements use to study structure properties. The sensitivity (S) of the fabricated sensors to NO2 and H2 was measured at room temperature. The experimental relationship between S and thickness of the sensitive film was investigated, and higher S values were recorded for thicker sensors. Results showed that the best sensitivity was attributed to the Cu2Te film of 900 nm thickness at the H2 gas.
In our work present, the application of strong-Lensing observations for some gravitational lenses have been adopted to study the geometry of the universe and to explain the physics and the size of the quasars. The first procedure was to study the geometrical of the Lensing system to determine the relation between the redshift of the gravitational observations with its distances. The second procedure was to compare between the angular diameter distances "DA" calculated from the Euclidean case with that from the Freedman models, then evaluating the diameter of the system lens. The results concluded that the phenomena are restricted to the ratio of distance between lens and source with the diameter of the lens noticing.
Nanoparticles are defined as an organic or non-organic structure of matter in at least one of its dimensions less than 100 nm. Nanoparticles proved their effectiveness in different fields because of their unique physicochemical properties. Using nanoparticles in the power field contributes to cleaning and decreasing environmental pollution, which means it is an environmentally friendly material. It could be used in many different parts of batteries, including an anode, cathode, and electrolyte. This study reviews different types of nanoparticles used in Lithium-ion batteries by collecting the advanced techniques for applying nanotechnology in batteries. In addition, this review presents an idea about the advantages and d
... Show MoreObjective: To determine the effectiveness of hypothermia on renal functions for patients undergoing
coronary artery bypass graft CABG surgery.
Methodology: A purposive (non-probability) sample of (50) patients undergoing Isolated coronary artery
bypass graft surgery consecutively admitted to the surgical ward, and they were followed up in the
intraoperative, Intensive Care Unit (ICU) and in the postoperative (surgical ward). Post-operative renal function
test (glumeruler filteration rate (GFR) by using the Crockroft-Gault formula and serum creatinine level) was
determined first week post operative and post operative renal function was classified on the base of peak of
the serum creatinine level and decline of glomeru