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
A total of 48 experiments were conducted to investigate the impact of slit weir dimensions and locations on the maximum scour depth and scour area created upstream. The slit weir model was a 110 mm slit opening, and it was installed at the end of the working section in a laboratory flume. The flume was 10.0 m long, 30 cm wide, 30 cm deep, and almost middle. It includes a 2 m working section with a mobile bed with 110 mm in thickness. In the mobile bed, two types of nonuniform sand (with a geometric standard deviation of 1.58 and 1.6) were tested separately. The weir dimensions and location were changed with flow rates. Then dimensions of the slit weir were changed from 60 x 110 mm to 60 x 70 mm (width x height), while th
... Show MoreBackground: This in vitro study compares a self-etch primer (SEP) to an etch-and-rinse (EaR) for bonding sapphire brackets by evaluation of the enamel etch-pattern, shear bond strength, amount of remnant adhesive and enamel surface damage following thermal and fatigue cyclic loading. Material and Methods: Ceramic (sapphire) brackets were bonded to 80 extracted human premolars using two enamel etching protocols: conventional EaR using 37% phosphoric acid (PA) gel (control), and a SEP (Transbond Plus). Each group was subdivided into two subgroups (n=20 teeth) according to the time of bracket debonding: after 24 h water storage or following 5000 thermo-cycles plus 5000 cycles fatigue loading, to determine the shear bond strength (SBS), adhesiv
... Show MoreThe principle of rights and duties is part of the reform project of the Commander of the Faithful Ali ibn Abi Talib, to build a state of institutions whose foundations have been built on Quranic rules, a prophetic biography, and his diligence in doing so in accordance with the requirements of interests and evil, and his certainty in determining the most important and important, and research analytical study of speeches Imam Ali and his career, in this study (the principle of rights and duties) of the ruler and the parish because of their role in the reform process, which depends on the demolition and construction together, as it is the responsibility of the ruler to demolish all constructed corrupt and contrary to the principles of Islam
... Show MoreBackground: The present study aimed to assess the distribution, prevalence, severity of malocclusion in Baghdad governorate in relation to gender and residency Materials and Methods: A multi-stage stratified sampling technique was used in this investigation to make the sample a representative of target population. The sample consisted of 2700 (1349 males and 1351 females) intermediate school students aged 13 years representing 3% of the total target population. A questionnaire was used to determine the perception of occlusion and orthodontic treatment demand of the students and the assessment procedures for occlusal features by direct intraoral measurement using veriner and an instrument to measure the rotated and displaced teeth. Results a
... Show MoreBACKGROUND: Femoral shaft fracture is a common fracture in pediatric age group reaching 62% of all fracture shaft femur in children in spite of rapid union rate and successful conservative treatment but some cases need surgical intervention and one of the methods using plate and screw by the lateral approach. AIM: This study aims to compare functional outcome fixation of mid-shaft femur fracture in children by plate and screws between (subvastus lateralis and transvastus lateralis) regarding infection, union, and limitation of knee movement. PATIENT AND METHOD: The study was done on 30 children who had diaphyseal fracture femur in Al-Kindy Teaching Hospital in period (April 2018–April 2020) with 6 months follow-up, and the pa
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The most famous thing a person does is talk. He loves and hates, and continues with it confirming relationships, and with it, too, comes out of disbelief into faith. Marry a word and separate with a word. He reaches the top of the heavens with a kind word, with which he will gain the pleasure of God, and the Lord of a word that the servant speaks to which God writes with our pleasure or throws him on his face in the fire. Emotions are inflamed, the United Nations is intensified with a word, and relations between states and war continue with a word.
What comes out of a person’s mouth is a translator that expresses the repository of his conscience and reveals the place of his bed, for it is evidence of
... Show MoreA novel Schiff base ligand [N1-benzylidenebenezene-1,2-diamine(L) = C20H16N2] was prepared through intensification of benzaldehyde (C6H5CHO) and O- amino aniline O-C6H4(NH2)2 in ethanol with 8-Hydroxyquinoline (8HQ) . Formed compounds were acquired of 1:1:2 molar proportion reactions for metal ions and ligands (L) and 2(8HQ) during reaction for MCl2 .nH2O salt products complexes conformable into the forms [M(L)(8HQ)2] ,where M = Mn(II),Co(II) and Ni(II). Whole the compounds were identified during the basis of their; FT-IR and U.V spectrum, melting point, molar conduct, identify of the percentage from the metal at the complexes via flame (AAS), C, H and N content of the Schiff base (L) and metal complexes were analysis and magnetic susceptib
... Show MoreBreast cancer is a disease in which cells in the breast grow out of control. CD200 is a cell surface glycoprotein expressed on many cells, it belongs to the immunoglobulin family (Ig) and have a great role in the regulation of inflammation in autoimmunity. CD200 is the ligand for CD200R1 receptor. To determine if serum level of CD200 and its receptor CD200R1 can be used as a diagnostic and prognostic marker in patients with breast cancer.This case control study was carried out at Oncology Teaching Hospital – Medical city in Baghdad. Six groups were enrolled, four groups were confirmed with breast cancer stage (I, II, III and IV), fifth group (benign) and sixth group was control (healthy individual). Serum is divided to me
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