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 poetic text, being an artistic product, is achieved during the moment of inspiration. However, this inspiration does not come from a vacuum. Rather, it needs a good environment capable of pushing the poetic text to the surface after its formation in the poet's mind, with the images and ideas it contains, expressed in his own language and style. Distinguished, and we must not overlook that language is not just words and meanings, but rather those feelings and emotions that are the essence of creativity (()), including musical, sentimental and imaginative aspects with colors of suggestion and symbols (()), because the poetic language is distinguished from others in that it (Symbols for psychological states are the substance of thought)
... Show MoreThe aim of the research is to identify the losses resulting from the terrorist operations and then find a proposed accounting treatment for the losses resulting from the terrorist operations and to indicate their impact on disclosure in the financial statements by reviewing the international standards and local rules and the unified accounting system and not dealing with these losses, Of the financial statements and therefore adversely affect the accounting disclosure as well as the weak commitment of economic units to apply the requirements of accounting measurement and disclosure of losses of terrorist operations in a manner consistent with local and international standards to achieve the Reliability in the financial statement.
The optimum separators operating pressure is determined by using flash calculations and equilibrium ratios. In this study, the optimum separator size for Jambur field is calculated by using equations introduced by Arnold and Stewart and API12J Specification [1]. Because Jambur field has a high production rate two conditions are taken in the study to determine separator size, first based on production rate 80,000 bbl/day and second based on split the production between two banks A and B (40,000 bbl/day for each bank). The calculation resulted in optimum separator pressure for the first stage of 700 psi, and the second stage of 300 psi, and the third stage of 120 psi. The results show that as the number of stages increased above three-stag
... Show MoreThis work deals with the separation of benzene and toluene from a BTX fraction. The separation was carried out using adsorption by molecular sieve zeolite 13X in a fixed bed. The concentration of benzene and toluene in the influent streams was measured using gas chromatography. The effect of flow rate in the range 0.77 – 2.0 cm3/min on the benzene and toluene extraction from BTX fraction was studied. The flow rate increasing decreases the breakthrough and saturation times. The effect of bed height in the range 31.6 – 63.3 cm on benzene and toluene adsorption from BTX fraction was studied. The increase of bed height increasing increases the break point values. The effect of the concentration of benzene in the range 0.0559 – 0.2625g/
... Show MoreBackground:: Infertility is a very common condition affecting approximately 13-14% of couples in the reproductive age. In general population; about 85% of couples have achieved conception within a year. Intrauterine insemination is one of the procedure which have a role in the treatment of infertile couple.Objectives:is to confirm that the use of ovulation induction in the course of intrauterine insemination elevates the pregnancy success rate.Method:This study had been conducted between December 2013 till December 2014 in AL-Elwiyah maternity hospital and AL-Samaraii hospital / Baghdad.On history and clinical examination; the chosen couple had the following criteria; primary infertility for more than one year, no previous IUI trials, hu
... Show MoreA good performance of reinforced concrete structures is ensured by the bond between steel and concrete, which makes the materials work together, forming a part of solidarity. The behavior of the bond between the reinforcing bar and the surrounding concrete is significant to evaluate the cracking control in serviceability limit state and load capacity in the ultimate limit state. In this investigation, the bond stresses between reinforcing bar and reactive powder concrete (RPC) was considered to compare it with that of normal strength concrete (NSC). The push-out test with short embedment length is considered in this study to evaluate the bond strength, bond stress-slip relationship, and bond stress-crack width relationsh
... Show MoreIn light of accelerating environmental degradation, the transition to a green economy is an imperative for achieving sustainable development. This study provides a critical analysis of the international legal and institutional framework governing this transition, revealing a significant gap between normative developments and the institutional framework on one hand, and their practical implementation on the other. The transition faces legal obstacles, including reliance on non-binding voluntary commitments and conflicts between environmental obligations and global trade and investment rules. It also reveals a significant financing gap, as financial flows to developing countries continue to lag behind commitments, in add
... Show MoreA total of four types of instant dry yeast
We study clusters in warm dark matter (WDM) models of a thermally produced dark matter particle 0.5 keV in mass. We show that, despite clusters in WDM cosmologies having similar density profiles as their cold dark matter (CDM) counterparts, the internal properties, such as the amount of substructure, show marked differences. This result is surprising as clusters are at mass scales that are a thousand times greater than that at which structure formation is suppressed. WDM clusters gain significantly more mass via smooth accretion and contain fewer substructures than their CDM brethren. The higher smooth mass accretion results in subhaloes which are physically more extended and less dense. These fine-scale differences can be probed by strong
... Show More