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
Phosphorus is usually the limiting nutrient for eutrophication in inland receiving waters; therefore, phosphorus concentrations must be controlled. In the present study, a series of jar test was conducted to evaluate the optimum pH, dosage and performance parameters for coagulants alum and calcium chloride. Phosphorus removal by alum was found to be highly pH dependent with an optimum pH of 5.7-6. At this pH an alum dosage of 80 mg/l removed 83 % of the total phosphorus. Better removal was achieved when the solution was buffered at pH = 6. Phosphorus removal was not affected by varying the slow mixing period; this is due to the fact that the reaction is relatively fast.
The dosage of calcium chloride and pH of solution play an importa
Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe
... Show MoreSol-gel derived CuCo-oxide coatings as solar selective surfaces, synthesized onto aluminium substrates at various annealing temperatures, are analysed by correlating their structural, chemical bonding states, and surface morphological topographies. As the annealing progressed, all the coatings displayed a Cu0.56Co2.44O4 (ICSD 78-2175) phase with preferential orientation along (400) reflection plane. Rietveld refinement of X-ray diffraction (XRD) data indicate that residual stress and microstrains developed around the coating surfaces are reduced resulting in mechanically stable thin films. Enhancement of the crystallite size and preferred orientation of the surface were confirmed via XRD, field emission scanning electron microscopy (FESEM),
... Show MoreTill now, isatin derivatives have received a lot of interest in organic and medicinal chemistry due to their significant biological and pharmacological activities. Schiff’s and Mannich bases of isatins are an effective group of heterocyclic derivatives that play a significant role in medicinal chemistry as antimicrobial agents. In light of these facts, new Schiff bases and Mannich bases of isatin were synthesized. The monomer Mannich bases; 3(a-e) have been synthesized by reacting isatin with different secondary amines, piperidine, morpholine, and pyrrolidine, dimethylamine, diphenylamine, separately, and formaldehyde, while the dimer (5) formed by using piperazine and formaldehyde which then react separately with Phenylhydrazine
... Show MoreA field experiment was carried out at University of Baghdad, College of Agricultural Engineering Sciences during fall season of 2020 and spring season of 2021. This study was aimed evaluate the effect of the organic fertilizer and boron foliar on the yield of potatoes for processing. The factorial experiment (5*4) within RCBD and three replicates. The organic fertilizer as palm peat at four levels (0, 12, 24 and 36 ton. ha-1) in addition to the chemical fertilizer recommendation treatment. Boron at four Concentrations 0, 100, 150 and 200 mg. L-1 . The results revealed significant different among application of organic fertilizer at the level of 24 ton. ha-1 and the foliar application of boron at a concentration of 100 mg. L-1 in the
... Show MoreHashimoto Thyroiditis (HT) is the most common autoimmune thyroid disease and the commonest cause ofhypothyroidism. C-reactive protein (CRP) is synthesized in hepatocyte in response to autoimmune disorders;strongly induced by IL-6. This study aimed to estimate serum IL-6 and CRP levels in autoimmune and non-autoimmune hypothyroidism. The present study included 60 Iraqi female hypothyroid patients divided to 30autoimmune and 30 non-autoimmune, with age ranged between 24-50 years and 30 healthy controls withage ranged between 27-52 years. Serum samples were collected from study groups. The levels of thyroidhormones (TSH, T4 and T3) were determined by using automated Chemiluminescence Immunoassay (CLIA)analysis system. Detection the levels of t
... Show MoreBackground: The disc prolapse is a common condition especially in young adults. Different levels are affected in the lumber region; the L4/L5 disc is more susceptible to longitudinal load and is the most common site of lumbar disc prolapse. The L5/S1 disc is protected from torsion load by strong ilio-lumbar ligaments but it is more susceptible to axial compressive forces. Many factors affect the result and outcome of surgery in these levels.Objective: The aim of this study is to correlate operative data, short-term results, complications, and prognostic factors (age, gender, mobility, hospital stay, and level of pain) for one-level lumber discectomybetween different levels (L4–L5 vs. L5–S1).Methods In this prospective study, 32 patie
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