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.
Linear and nonlinear optical properties of epoxy/ Al2O3 nanocomposites system were studied for epoxy neat and (0.5, 1.5, 3, and 5) % Al2O3 nanocomposites.The band gap of epoxy and its nanocomposites was obtained at these weight ratios. Nonlinear optical properties experiments were performed using Q-switched Nd:YAG laser z-scan system.These experiments were carried out for different parameters: wavelengths (1064 nm and 532 nm), laser intensities (0.530, 0.679, and 0.772) GW/cm2 and weight ratio of Al2O3 nanocomposites. The results showed that the band gaps were decreased with increasing the weight ratio of nanoalumina except at 5wt% and the nonlinear refractive index coefficient is directly proportional to the incident intensities while o
... Show MoreThe Sacrament of Marriage in the Christian Religion
This research is concerned with the study of (the aesthetic of constructive relations in linear composition) with what distinguished Arabic calligraphy through the style and artistic method in its construction, and the specifications it carries that enabled it to pay attention to building formations to achieve in its total linear ranges aesthetic values and relationships. Through the research, the models and the exploratory study that he obtained, the researcher was able to raise the research problem in the first chapter according to the following question: What is the aesthetic of constructive relations in linear formation?
The importance of the research in achieving the aesthetics of the formations, which is a wide field according t
Magic is an attempt to affect people or events either by cheating and charlatanry means or by expecting devil powers in order to bring advantage or to avoid a harm or to bring harm to others or to for see the future and divition .
Magic is either real by the devil like writing majic works to prevent the marriage of someone and to depart the husband and his wife , causing someone to be distressed the physical and nervous diseases and stopping the stories and the project; majic can be artificial by being intellect and legerdemain and different types of triks and to cancel the magic by using magic or by protecting the self by using Talismans as well as presenting or offering sacrificers to the masters and th
... Show MoreABSTRACT Studying the positive and negative effects resulted from the industrial projects and laying down the comprehensive planning bases to the urban development projects which insure retaining the social, economic and environmental development, taking in to consternation the time factor within the planning process which is considered the most important factor that determine the extent of the efficient selection to the site and not interpenetrate in the industrial activities and efficiency and calculating its future expansions away from the residential areas. It is more favorable to plan the industrial areas of apparent pollution outside the bounds of the basic plan to limit the negative effects on the environment and providing
... Show MoreThe aim of the research is to clarify the role of service quality through its dimensions represented by (tangibility, reliability, safety, response, empathy) in tax compliance with taxpayers, i.e. performance of the duties and obligations of the taxpayer through its dimensions (registration, accounting, payment of the amount of tax), and to know For this role, a sample was taken from the taxpayers of the branches of the General Authority for Taxes spread in the governorate of Baghdad and its affiliated districts, which amount to (15) tax branches, as (215) questionnaires were distributed to know the impressions and reactions of the taxpayers regarding the level of service quality through the aforementioned dimensions. Using the statistic
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