To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which shows the reliability and applicability of the proposed approach.
The fractional free volume (Fh) in polystyrene (PS) as a function of neutron -irradiation dose has been measured, using positron annihilation lifetime (PAL) method. The results show that Fh values decreased with increasing n-irradiation dose up to a total dose of 501.03× 10-2 Gy.
A percentage reduction of 2.14 in Fh values is noticed after the initial n-dose corresponding to a percentage reduction in the free volume equal to 42.14/Gy.
The total n-dose induces a percentage reduction of 7.26, corresponding to a percentage reduction of 1.45/Gy. These results indicate that cross -linking is the predominant process induced by n-irradiation.
The results suggest that n-irradiation induces structure changes in PS, causing cross-linking
Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl
The increasing demand for energy has encouraged the development of renewable resources and environmentally benign fuel such as biodiesel. In this study, ethyl fatty esters (EFEs), a major component of biodiesel fuel, were synthesized from soybean oil using sodium ethoxide as a catalyst. By-products were glycerol and difatty acyl urea (DFAU), which has biological characteristics, as antibiotics and antifungal medications. Both EFEs and DFAU have been characterized using Fourier transform infrared (FTIR) spectroscopy, and 1H nuclear magnetic resonance (NMR) technique. The optimum conditions were studied as a function of reaction time, reactant molar ratios, catalyst percentage and the effect of organic solvents. The conversion ratio of soybea
... Show MoreThe research aims to estimate missing values using covariance analysis method Coons way to the variable response or dependent variable that represents the main character studied in a type of multi-factor designs experiments called split block-design (SBED) so as to increase the accuracy of the analysis results and the accuracy of statistical tests based on this type of designs. as it was noted in the theoretical aspect to the design of dissident sectors and statistical analysis have to analyze the variation in the experience of experiment )SBED) and the use of covariance way coons analysis according to two methods to estimate the missing value, either in the practical side of it has been implemented field experiment wheat crop in
... Show MoreIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
... Show MoreIn recent years, there has been expanding development in the vehicular part and the number of vehicles moving on the road in all the sections of the country. Vehicle number plate identification based on image processing is a dynamic area of this work; this technique is used for security purposes such as tracking of stolen cars and access control to restricted areas. The License Plate Recognition System (LPRS) exploits a digital camera to capture vehicle plate numbers is used as input to the proposed recognition system. Basically, the developing system is consist of three phases, vehicle license plate localization, character segmentation, and character recognition, the License Plate (LP) detection is presented using canny Edge detection algo
... Show MoreThin a-:H films were grown successfully by fabrication of designated ingot followed by evaporation onto glass slides. A range of growth conditions, Ge contents, dopant concentration (Al and As), and substrate temperature, were employed. Stoichiometry of the thin films composition was confirmed using standard surface techniques. The structure of all films was amorphous. Film composition and deposition parameters were investigated for their bearing on film electrical and optical properties. More than one transport mechanism is indicated. It was observed that increasing substrate temperature, Ge contents, and dopant concentration lead to a decrease in the optical energy gap of those films. The role of the deposition conditions on value
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