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
An agricultural waste (walnut shell) was undertaken to remove Cu(II) from aqueous solutions in batch and continuous fluidized bed processes. Walnut shell was found to be effective in batch reaching 75.55% at 20 and 200 rpm, when pH of the solution adjusted to 7. The equilibrium was achieved after 6 h of contacting time. The maximum uptake was 11.94mg/g. The isotherm models indicated that the highest determination coefficient belongs to Langmuir model. Cu (II) uptake process in kinetic rate model followed the pseudo-second-order with determination coefficient of 0.9972. More than 95% of the Cu(II) were adsorbed on the walnut shells within 6 h at optimum agitation speed of 800 rpm. The main functional groups responsible for biosorption of
... Show MoreExperimental results on harmonic distortions in 13.56 MHz RF Argon glow discharge using different grounded electrodes areas and electrodes spacing are presented. The experiment is carried out at four pressure values. RF power values used are between 20 and 90 watts. The results indicate significant increase in distortions at two specific values of the cone angle enclosing the two electrodes within its geometrical volume. The computation of the cone head angle gave the symmetry discharge or asymmetry as well as when the angle is small the condition is near symmetry discharge associated with decrease in the nonlinearity.
Knowledge of literature is an integral part of learning any spoken language. Learning literature expands the learner’s ability to understand the language studied. The field of literature is wide and cannot be limited to poems. It includes the etiquettes of a language and its environment, customs, and traditions etc. The Arabic language is among the languages with a centuries old history. It has achieved remarkable record accomplishments since the pre-Islamic era through to the present. This development is clear evidence of the great importance of literature in the revival of the Arabic language through different eras. As such, in Malaysia and other non-Arabic speaking countries, literature is taught in most schools, institutions and un
... Show MoreThis study aims to employ modern spatial simulation models to predict the future growth of Al-Najaf city for the year 2036 by studying the change in land use for the time period (1986-2016) because of its importance in shaping future policy for the planning process and decision-making process and ensuring a sustainable urban future, using Geographical information software programs and remote sensing (GIS, IDRISI Selva) as they are appropriate tools for exploring spatial temporal changes from the local level to the global scale. The application of the Markov chain model, which is a popular model that calculates the probability of future change based on the past, and the Cellular Automa
Abstract
In the present work, thermal diffusivity and heat capacity measurements have been investigated in temperature range between RT and 1473 K for different duplex stainless steel supplied by Outokumpu Stainless AB, Sweden. The purpose of this study is to get a reliable thermophysical data of these alloys and to study the effect of microstructure on the thermal diffusivity and heat capacity value. Results show the ferrite content in the duplex stainless steel increased with temperature at equilibrium state. On the other hand, ferrite content increased with increasing Cr/Ni ratio and there is no significant effect of ferrite content on the thermal diffusivity value at room temperature. Furthermore, the heat capacity of all sam
... Show MoreWheat (Triticum aestivum L.) is one of the Poaceae family (Gramineae). Is momentous for human nutrition, and the stresses can affect strongly on the phenotype characteristics of the plant. The aim of this study was to determine how electric shock on germinated grain (for 2.5, 5, and 7.5 mins.) and heat shock at ( 35 oC, 40 oC and 45 oC) applied after phase out the radical length of 2-5 mm, from the grain of two wheat Varieties: “Baghdad 1” and “Babylon 113”. The electric shock for 2.5 mins., lead to delay of flowering, from day to 50 % flowering was 93 day, as well as, gave lowest value of plant height 64.5cm and lowest spike length was 10.7 cm. While The highest flag leaf area was obtained by electric shock for 5 mins. was 56.6
... Show MoreThe high cost of chemical analysis of water has necessitated various researches into finding alternative method of determining portable water quality. This paper is aimed at modelling the turbidity value as a water quality parameter. Mathematical models for turbidity removal were developed based on the relationships between water turbidity and other water criteria. Results showed that the turbidity of water is the cumulative effect of the individual parameters/factors affecting the system. A model equation for the evaluation and prediction of a clarifier’s performance was developed:
Model: T = T0(-1.36729 + 0.037101∙10λpH + 0.048928t + 0.00741387∙alk)
The developed model will aid the predictiv
... Show MoreBackground: overweight and obesity are the fifth leadingrisk for global deaths. At least 2.8 million adults die eachyear as a result of being overweight or obese. Numerousstudies show that weight loss, even if only 5-10%,significantly improves dyslipidemia, hypertension, diabetesmellitus, risk for osteoarthritis and its symptoms and risk forselected cancers.Objectives: is to evaluate the effect of diet and exerciseprogram on anthropometric and biochemical status of adultobese patients.Methods: descriptive study. 124 adult obese patientsattending Al Kindy obesity research and therapy unit duringDecember 2012 were included. Measurement of Wt, heightHt and WC performed and BMI was calculated. Laboratorytest analysis, on the fasting state, w
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