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 provision of safe water for people is a human right; historically, a major number of people depend on groundwater as a source of water for their needs, such as agricultural, industrial or human activities. Water resources have recently been affected by organic and/or inorganic contaminants as a result of population growth and increased anthropogenic activity, soil leaching and pollution. Water resource remediation has become a serious environmental concern, since it has a direct impact on many aspects of people’s lives. For decades, the pump-and-treat method has been considered the predominant treatment process for the remediation of contaminated groundwater with organic and inorganic contaminants. On the other side, this tech
... Show MoreA new Schiff base of HL has been synthesized from amoxicillin drug and 4- Chlorobenzophenone. Cr (III), Fe (III), Co (II), Ni (II), Cu (II), Cd (II) and Hg (II) mixed ligands complexes of Schiff base and Nicotinamide. Diagnosis of synthesis ligand and its complexes are done by 1HNMR, 13CNMR and thermal analysis for HL ligand, FTIR, UV-visible, molar conductance, CHN analysis, magnetic susceptility and atomic absorption. Octahedral geometries have been suggested for all complexes. All compounds under study were tested antimicrobial activity against four type of bacteria such as Pseudomonas aeruginosa, Escherichia coli, Staphylococcus aureus Bacillis subtilis in nutrient agar.
Despite efforts to contain and manage the SARS-CoV-2 outbreak which was declared a public health emergency of international concern in January 2020 by the World Health Organization (WHO), the COVID-19 pandemic still remains a major global challenge. Patients who display the classical symptoms of the infection are easily identified, tested, isolated and monitored. However, many cases of infected asymptomatic patients have been documented. These patients are not easily identified even though many evidences suggest that they can spread the virus to others. How and why these COVID-19 asymptomatic presentations occur remain unclear. The many theories and views are conjectural, and supporting evidences are still needed. In this review, we
... Show MoreAlopecia areata is considered as a major health problem, its importance is attributed to its
recent increased incidence in our population. Till now, there is no exact cause for alopecia areata
although researchers thought it's an autoimmune disease.
This clinical study was designed to evaluate the role of trace elements (zinc and copper) in patients
with alopecia areata. Twenty patients were diagnosed as having alopecia areata with an age range
(10-40 years) were involved in this study. Normal subjects of the same age group were also
evaluated as control. The level of serum Zn and Cu were measured by flame atomic absorption
spectrophotometry in both control and patient group. And the ratio of Zn/Cu was also estimated
Shell-and-double concentric tube heat exchanger is one of the new designs that enhance the heat transfer process. Entransy dissipation is a recent development that incorporates thermodynamics in the design and optimization of heat exchangers. In this paper the concept of entransy dissipation is related to the shell-and-double concentric tube heat exchanger for the first time, where the experiments were conducted using hot oil with temperature of 80, 100 and 120°C, flow rate of cold water was 0.667, 1, and 1.334 kg/m3 respectively and the temperature of inlet cold water was 20°C. The entransy dissipation rate due to heat transfer and to fluid friction or pressure drop was studied.
Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers, Muhammad and his family
The good and pure and after his companions
God Almighty said: ( ) Do they not contemplate the Qur’an? If it had been from other than God, they would have found in it much discrepancy. God Almighty has made the well-being of people and their lives linked to faith in it. So what is the need of people today to return to the Book of their Lord so that they may return to the right path that God intended for His servants so that they may attain sustenance? Security and the good life. How could it not be, when many of the nations of the world no longer see security or stability because their leaders and politic
... Show Moreلخلاصة تشغل قضايا الهوية محور اهتمام الكثير من الباحثين والدارسين في بنية المجتمعات ومستقبل الدول, وفي كثير من الدراسات التي كتبها هؤلاء كان هناك ميل نحو دراسة الهوية وعلاقتها بحركة الدول تقدما وتراجعا ,فهناك من عزا تقدم دولة ما إلى نجاح نخبها السياسية في صناعة هوية جامعة لحالة التنوع الذي يميز مجتمعها, ويمكن ان تشير الى الولايات المتحدة الامريكية كأنموذج للنجاح في هذا الاطار.وهناك من ارجع
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