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 scholastic view of public religion differed, and this difference was on two extremes. All economic schools agreed that public debt is a monetary liquidity that was unjustly deducted from the income and output cycle as a result of the imbalance in the economic balance and the departure from the conditions of balance between aggregate demand and aggregate supply. Debt is a waste of financial resources allocated to productive accumulation. Except for the Keynesian school, which considers public debt to be an addition to aggregate demand after the decline in the role of the private sector in investment as a result of pessimistic expectations that warn of signs of economic contraction. Public debt is linked to the ex
... Show MoreThis research investigates the meanings and significance of the verse and the concluded educational purports. The expression “And in the heaven is your provision” signifies the deism of Allah. This research introduces the what have been said by Quran Explainers about meaning of Heaven & Provision. It introduces also the meaning of the sentence “which you are promised” and its concluded educational purports. This research discuses the role of educational institutions as well as the family and mosques in connecting Muslims and their children with the promise given by Allah.
Provision is guaranteed for all people if moral and material causes have been considered.
Key Words:
Purports – Educational – Co
... Show MoreThe current study aims to examine the level of problems faced by university students in distance learning, in addition to identify the differences in these problems in terms of the availability of internet services, gender, college, GPA, interactions, academic cohort, and family economic status. The study sample consisted of (3172) students (57.3% females). The researchers developed a questionnaire with (32) items to measure distance learning problems in four areas: Psychological (9 items), academic (10 items), technological (7 items), and study environment (6 items). The responses are scored on a (5) point Likert Scale ranging from 1 (strongly disagree) to 5 (strongly agree). Means, standard deviations, and Multivariate Analysis of Vari
... Show MoreA square experimental arena with vegetation on one interior side was deployed in a Sharjah, United Arab Emirates desert. Individual darkling beetles (Coleoptera, Tenebrionidae) Akis subtricostata Redtenbacher, 1850 and Trachyderma philistina Reiche and Saulcy, 1857 were placed inside the arena at temperatures ranging between 27 - 49°C. Whether they chose the vegetated side of the arena or not was recorded, as well as how long it took for them to reach the vegetated side, if they chose it. Both species preferred the vegetated side at all temperatures, and the chance of them choosing the vegetated side increased significantly with increasing temperature (logistic regression, p = 0.0096 and p = 0.0003 for
... Show MoreIn this research investigation, a total of eighteen diverse tetra- and penta-lateral cyclic compounds were synthesized. These included 1,3,4-thiadiazole, thiazolidin-4-one (via an alternative method), 1,2,4-triazole, carbothioamide, thiazole-4-one, azetidin-2-one, and oxazole. The synthesis procedure entailed a sequence of reactions. The thiazolidine-4-one 1 was obtained by reaction p-aminobenzoic acid with thiosemicarbazide, followed by treatment with p-tolualdehyde to produce Schiff base 2. Reaction Schiff base 2 with mercaptoacetic acid in dry benzene was carried out to produce thiazolidine-4-one 3. In another synthesis pathway, the esterification of p-nitro benzoic acid with ethanol in the presence of sulfuric acid was
... Show MoreThis study aimed new indications that may clarify the relationships between the total and standard lengths, and the length of the otolith, as well as the thickness and weight of these bones compared to the body weights of two different species of invasive fish in the Iraqi aquatic environment, the common carp
Many international studies indicated that the polymorphisms of some genes disturbed the folate homocysteine (Hcy) metabolism and increased the vulnerability to Down syndrome (DS). We aimed to measure the serum levels of folate and Hcy in DS children and compare the levels with age and sex-matched apparently normal healthy children. We also aimed to study the A80G polymorphism of the gene reduced folate carrier (RFC1) in the DS children as a risk factor. Forty children with DS (24 were boys, and 16 were girls) with the age range between 5-13 years, and 26 normal healthy children (16 boys and ten girls) were included in this study. The results show that the highest genotype in the control group was AG (53.85%) followed by AA and GG (30.
... Show MoreIn this study, dead and live anaerobic biomass was used in biosorption of Pb(II), Cr(III) and Cd(II) ions from a synthetic wastewater. The biosorption was investigated by batch adsorption experiments. It was found that, the biosorption capacities were significantly affected by biosorbent dosage. The process follows Langmuir isotherm (regression coefficient 0.995, 0.99 and 0.987 for Pb(II), Cr(III) and Cd(II) ions, respectively, onto dead anaerobic biomass) model with uniform distribution over the biomass surface. The experimental uptake capacity was 51.56, 29.2 and 28 mg/g for Pb(II), Cr(III) and Cd(II), respectively, onto dead anaerobic biomass, compared with 35, 13.6 and 11.8 mg/g for Pb(II), Cr(III) and Cd(II), respectively, onto live
... Show MoreThe nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for some 1f-2p-shell nuclei, such as 58Ni, 60Ni, 62Ni, and 64Ni
isotopes have been calculated in the framework of the coherent fluctuation model (CFM) and expressed in terms of the weight function lf(x)l2 . The weight function (fluctuation function) has been related to the nucleon density distribution (NDD) of the nuclei and determined from the theory and experiment. The NDD is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of the l