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.
Since its establishment, cities have been looking for a special urban architectural language that distinguishes them from other cities and expresses their distinctive identity through continuous products through time and controls the totality of temporal and spatial changes through a bridging dialogue that manages the language of the city correctly, Which gives the stability of that language and its ability to adapt to the total changes that occur in the city over time, and thus the possibility of producing ideas integrated series and ideas are renewed overlapping with the legacy and bear multiple layers of meaning and signals and symbols create a total of two meanings The problem of research (not comprehensive studies to create a contem
... Show MoreMaterials with external dimensions of one or more nanometers are referred to as nanomaterials. These structures result from a number of manufacturing processes. They are used in many industries, including pharmaceuticals, which is the most significant one. Numerous variables, including size, shape, surface morphology, crystallinity, solubility, etc., affect physical properties. While new physical and chemical processes are being created constantly, the biological method is the ideal strategy for synthesizing nanoparticles since it is straightforward, safe, and economical. Different kinds of nanoparticles can be metabolically synthesized by a wide variety of biological sources, including plants, bacteria, fungi, and yeast. There are
... Show MoreThis study highlights the social concepts of the ‘night’ of the residents of Mesopotamia, who realized the nature of the universe, constellations, planets, stars, and the sun and the moon and their effect on the daily life. Moreover, they recognized the requirements of the day and the aspects of the night that impacted their life in one way or another. Through the cuneiform regarding day and night, we found that people had their special view concerning ‘night’ in terms of religious and secular dimensions. They had benefited from the appearance of stars and the moon and had related many events – social, religious, or military – to these phenomena. I chose to do this study in relation to ‘night’ due to its importance in the th
... Show MoreEconomics / University of Mosul
Abstract
The spread of the phenomenon of excessive buying in our society, especially for cosmetics, and at the same time increase the marketing deception by the organizations to take quick profit 'and accordingly was identified the problem of research in several questions, including:
Is there a significant effect of consumption culture on marketing deception? &n
... Show MoreVerbal Antonyms: A research in the relationship in meaning Between the words in Arabic language
Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing artificial TABU algorithm to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as sport, chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement.
The study sought to highlight the importance of applying the administrative control procedures which play an important role in assessing the performance of the employees of the tax administration and specifically the companies department by setting the standards and objectives of the department on the basis of which in the implementation of its work and identify deviations and errors and find appropriate solutions and evaluate the results according to appropriate solutions, The study of the problem of research, namely the extent to which the tax administration applied to the administrative control procedures in view of its importance in evaluating the performance of its employees and the extent of their application to the legislations an
... Show MoreThe primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o
... Show MoreThe primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent of the
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