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
Nano crystalline copper sulphide (Cu2S) thin films pure and 3% Bi doped were deposited on glass substrate by thermal evaporation technique of thickness 400±20 nm under a vacuum of ~ 2 × 10− 5 mbar to study the influence of annealing temperatures ( as-deposited, and 573) K on structural, surface morphology and optical properties of (Cu2S and Cu2S:3%Bi). (XRD) X-ray diffraction analysis showed (Cu2S and Cu2S:3%Bi) films before and after annealing are polycrystalline and hexagonal structure. AFM measurement approves that (Cu2S and Cu2S:3%Bi) films were Nano crystalline with grain size of (105.05-158.12) nm. The optical properties exhibits good optical absorption for Cu2S:3%Bi films. Decreased of optical band gap from 2.25 to 2 eV after dop
... Show MoreThis research was based on two pillars. The first is a comparison between of research done and the result of a particular variable of research indebendently in the united state, and second, knowledge and determine the effect of managers practices on the contributions of personnel. The manager and staff are considered to be the most important elements in the organization and all of them have a duty towards the others which governed by the relationship rules of procedure of the ministry researched, on the one hand and the interests of the organization and hence employees , whether executives or employees within management formations that the availability of an acceptable level of good pract
... Show MorePolymer electrolytes systems compose of (PEO+KI+I2) and (PEO+RbI+I2) with different concentration, and a fixed amount of ethylene carbonate (EC) and propylene carbonate (PC) over temperatures range 293-343 K prepared by solution cast me
... Show MoreAdolescent pregnancy is common health problem still found in both developed and developing countries; as adolescent may have early sexual practice or early marriage. Adolescent mothers face substantially higher maternal and perinatal morbidity and mortality than adult women. This is a randomized prospective clinical study conducted at Al-Elwiya Maternity Teaching Hospital, Baghdad, Iraq. The objective of this work is to assess the adverse maternal, fetal and neonatal outcomes in early and late teenage pregnant mothers. Study sample consisted of 220 primigravid women with a singleton, cephalic, viable fetus and no congenital abnormality that gave birth at Al-Elwiya Maternity Teaching Hospital, Baghdad, Iraq. The 1stgroup: early teenage (46 w
... Show MoreGaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db
... Show Moreالخلاصة لقد شكل المحافظون الجدد وهم بالأساس نخبة من المثقفين ومن السياسيين الأمريكيين كتلة ضغط كبيرة التأثير على الإدارة في عهد الجمهوريين. حمل هؤلاء المحافظون مشروعاً إيديولوجياً البسوه لسلطة الجمهوريين وهو يهدف إلى جعل أمريكا سيدة العالم من دون منازع خاصة بعد انهيار الاتحاد السوفييتي ونهاية الحرب الباردة. واكب هذا الحدث التاريخي الكثير من الأفكار ومنها (نهاية التاريخ)، وصراع الحضارات، وكذ
... Show MoreThere is no doubt that development is a human necessity and an urgent technical imperative that science imposes on all aspects of societal life. Especially in the field of graphic design, as logos are among the most prominent graphic achievements of an interactive nature with the requirements of the technical and functional era to serve the recipient and the continuity of interaction with him through a visual message sent to him constantly to remind him of what he interacted with in advance, which is known as visual identity, and during the process of developing logos especially And by providing designs that suit the contemporary technical and functional development, we often see the logo lose its visual identity. Therefore, the research
... Show MoreReceipt date:9/1/2020 accepted date:11/24/2020 Publication date:12/31/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
the Nile River and the Renaissance Dam is one of the most prominent factors that had an important role in the nature of relations between Egypt - Ethiopia, as they contributed to building a relationship that has common characteristics through the nature of the i
... Show More