This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
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... Show MoreIn this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel
... Show MoreThe aim of this study was to know ( the impact of education differentiated strategy to modify the alternative developments of geographical concepts when students first grade average) .
To achieve the goal of this study , researcher relied on the experimental design of a partial set , the design is ( the experimental group with a control group of post-test ).
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... Show MoreIn recent years, the positioning applications of Internet-of-Things (IoT) based systems have grown increasingly popular, and are found to be useful in tracking the daily activities of children, the elderly and vehicle tracking. It can be argued that the data obtained from GPS based systems may contain error, hence taking these factors into account, the proposed method for this study is based on the application of IoT-based positioning and the replacement of using IoT instead of GPS. This cannot, however, be a reason for not using the GPS, and in order to enhance the reliability, a parallel combination of the modern system and traditional methods simultaneously can be applied. Although GPS signals can only be accessed in open spaces, GP
... Show MoreThe radial wave functions of the generalise dWoods–Saxon (GWS) potential within the two-body model of (Core + n) have been used to study the ground-state density distributions of protons, neutrons and matter and the associated root mean square (rms) radii of neutron-rich 14B, 22N, 23O and 24F halo nuclei. The calculated results show that the radial wave functions of the generalised Woods–Saxon potential within the two-body model succeed in reproducing neutron halo in these exotic nuclei. Elastic electron scattering form factors for these nuclei are studied by combining the charge density distributions with the plane-wave Born approximation (PWBA).
This paper presents the syntactic dimension of ditransitive verbs in terms of the universal theory of Role and Reference Grammar (RRG). This theory is syntactic in nature, but it also covers the semantic as well as the pragmatic aspects of any linguistic phenomenon. It assumes a universal framework through which syntactic constructions can be analyzed. However, the morphological structure that each language enjoys renders the universal treatment more complicated and can question the universal nature of such a theory. In this paper, an attempt is made to check if the universal tenet of the theory is maintained over two typologically different languages: English and Arabic in respect of the way that double-object constructions (DOCs)
... Show MoreThe impact of television has made it an essential technology that can't be dispensed with in all circumstances and situations, measuring the society's need for it. Some argue that there is no stronger media than television in introducing people of the world to each other, as it has the most powerful impact and attracts millions of viewers.
Television is deemed as the most effective tool of media as it is designed to capture both sound and image. The image, in itself, has the ability to engage and interact with our thoughts. In light of the aforementioned, it is noticeable that this interactive medium (television) has significantly evolved over the years, thanks to modern technologies that have been introduced over time. These advancem