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
This study offers the elastic response of the variable thickness functionally graded (FG) by single walled carbon nanotubes reinforced composite (CNTRC) moderately thick cylindrical panels under rotating and transverse mechanical loadings. It’s considered that, three kinds of distributions of carbon nanotubes which are uniaxial aligned in the longitudinal direction and two functionally graded in the transverse direction of the cylindrical panels. Depending on first order shear deformation theory (FSDT), the governing equations can be derived. The partial differential equations are solved by utilizing the technique of finite element method (FEM) with a program has been built by using FORTRAN 95. The results are calculat
... Show MoreRutting in asphalt mixtures is a very common type of distress. It occurs due to the heavy load applied and slow movement of traffic. Rutting needs to be predicted to avoid major deformation to the pavement. A simple linear viscous method is used in this paper to predict the rutting in asphalt mixtures by using a multi-layer linear computer programme (BISAR). The material properties were derived from the Repeated Load Axial Test (RLAT) and represented by a strain-dependent axial viscosity. The axial viscosity was used in an incremental multi-layer linear viscous analysis to calculate the deformation rate during each increment, and therefore the overall development of rutting. The method has been applied for six mixtures and at different tem
... Show MoreThe analysis of the classic principal components are sensitive to the outliers where they are calculated from the characteristic values and characteristic vectors of correlation matrix or variance Non-Robust, which yields an incorrect results in the case of these data contains the outliers values. In order to treat this problem, we resort to use the robust methods where there are many robust methods Will be touched to some of them.
The robust measurement estimators include the measurement of direct robust estimators for characteristic values by using characteristic vectors without relying on robust estimators for the variance and covariance matrices. Also the analysis of the princ
... Show MoreThe influence of adding metal foam fins on the heat transfer characteristics of an air to water double pipe heat exchanger is numerically investigated. The hot fluid is water which flows in the inner cylinder whereas the cold fluid is air which circulates in the annular gap in parallel flow with water. Ten fins of metal foam (Porosity = 0.93), are added in the gap between the two cylinder, and distributed periodically with the axial distance. Finite volume method is used to solve the governing equations in porous and non-porous regions. The numerical investigations cover three values for Reynolds number (1000 ,1500, 2000), and Darcy number (1 x10-1, 1 x10-2, 1x10-3). The comparison betwee
... Show MoreCox regression model have been used to estimate proportion hazard model for patients with hepatitis disease recorded in Gastrointestinal and Hepatic diseases Hospital in Iraq for (2002 -2005). Data consists of (age, gender, survival time terminal stat). A Kaplan-Meier method has been applied to estimate survival function and hazerd function.
The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the ana
... Show MoreThe inhibition of mild steel corrosion in 1.0M HCl by 1-propanol and the synergistic effect of potassium iodide (KI) was investigated using weight loss and polarization techniques in the temperature range (30 ‒ 50) ̊ C. A matrix of Doelhert to three factors was used as the experimental design, adopting weight loss results as it permits the use of the response surface methodology which exploited in determination of the synergistic effect as inhibition on the mild steel. The results were confirmed using electrochemical polarization measurements. Experimental results showed that the inhibition efficiency (IE%) increases with increase in concentration of inhibitor and with increasing of temperature. The addition iodide ions t
... Show MoreTriticale is being evaluated as a substitute for corn in animal feed and as a forage crop for Florida. Storage of triticale seed is difficult in Florida's hot and humid climate, and more information about the relationships between equilibrium moisture content (EMC) and equilibrium relative humidity (ERH) at constant temperature (sorption isotherms) of triticale is needed to develop improved storage methods. Therefore, the primary research objective was to measure the EMC for triticale seed at different ERH values at three different constant temperatures (5°C, 23°C, and 35°C) using six desiccation jars containing different saturated salt concentrations. The secondary objective was to determine the best fit equation describing these relati
... Show MoreThe equation of Kepler is used to solve different problems associated with celestial mechanics and the dynamics of the orbit. It is an exact explanation for the movement of any two bodies in space under the effect of gravity. This equation represents the body in space in terms of polar coordinates; thus, it can also specify the time required for the body to complete its period along the orbit around another body. This paper is a review for previously published papers related to solve Kepler’s equation and eccentric anomaly. It aims to collect and assess changed iterative initial values for eccentric anomaly for forty previous years. Those initial values are tested to select the finest one based on the number of iterations, as well as the
... Show MoreIn the present work experiments were conducted to study the effect of solid loading (1,5 and 9 vol.%) on the enhancement of carbon dioxide absorption in bubble column at various volumetric gas flow rate (0.75, 1 and 1.5 m3/h) and absorbent concentration (caustic soda)( 0.1,0.5 and 1 M ). Activated carbon and alumina oxide (Al2O3) are used as solid particles. The Danckwerts method was used to calculate interfacial area and individual mass transfer coefficients during absorption of carbon dioxide in a bubble column. The results show that the absorption rate was increased with increasing volumetric gas flow rate, caustic soda concentration and solid loading. Mass transfer coefficient and interfac
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