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.
Abstract
Through social service tasks for the elderly, it natural for elder people to have some attitudes about the quality and nature of provided services, whether negative or positive. Accordingly, the current research is an attempt to investigate the attitudes of the elderly toward the social service provided to them in the nursery homes. The research sample included 60 elderly people chosen from the nursey home at Al-Karrada district and then a scale of attitudes was administered to them that had proved its reliability and validity. The study concluded with a set of recommendations and suggestions were.
Self is the main factor of personality and the acceptance of others where each of them are connecting and plays an important role in emotional maturation. The researches affirmed that the leading behavior depending on good human relations between the employers and the employees will enhance their goals and the goals of the institution at the same time . This study aims to measure the emotional maturation among the leactures of the university according to sex variable and identify the correlation between emotional maturation and the level of leading behavior among the lecturers of the university. The sample consists of two samples where the lst is to build the measwe consisting of (200)males and famales lecturers and the 2nd which is the
... Show MoreB Saleem, H Alwan, L Khalid, Journal of Engineering, 2011 - Cited by 2
The research shows the importance of orientation towards the formulation of the green strategy and its effect in determining the behavior of the green municipal institution in Babel governorate. The research highlighted the formulation of the green strategy as an important variable, especially today, the trend towards protecting the environment and minimizing the damage resulting from the delivery of services, and through it also the type of green behavior or performance adopted by the municipal institution and the emergence of the need for a strategy that is not harmful to the environment. The research took the sample intentionally comprehensive size of 222 personnel of municipal institutions and some formations concerned with t
... Show MoreNot necessarily to be malnutrition is a result of poverty and lack of food, it may be the outcome of the wrong food practices; and the lack of knowledge in nutrition basis and chronic diseases. Some studies have confirmed that the more the knowledge in nutrition basis increased, the more the child has well-balanced food.
Unhealthy eating habits spread among children at an early age, which is one of the negative factors affecting the nutritional status they have causing various disorders as a result of lack or increase of food or lack of balance. The signs and symptoms of these disorders can be simple or can lead to deadly diseases.
Training children on proper eating habits in different fields of life is considered the mos
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The aim of this research is to identify the general level of teachers’ curriculum expectations in (geography subject as a model), as well as the significance of the difference in the level of teachers’ curriculum expectations in light of the gender variables (male, female), the years of service (10 years or less - more than 10 years), the level of attitudes of fourth-grade literary students towards geography, the level of congruence between teachers’ curriculum expectations and the attitudes of fourth-grade literary students towards geography in light of the variables, the general level of congruence and the level of congruence between teachers’ curriculum expectations and the attitudes of studen
... Show MoreThe current research aims to adopt production quality decisions as the most important decisions , because they are accompanied by customer satisfaction through monitoring the quality of drinking water in iraq which reach through the pipeline network associated with water treatment projects of Tigris and Euphrates rivers. One of the indicators of quality control was the drawing of the C-chart by specifying the central line and the upper and lower limit of the control and the diagnosis of whether the production system as a whole within the scope of quality control or not and determine the strength and significance of the correlation between the quantities of water And actual needs for customers , the research has reached a number o
... Show MoreEmotions are part of the personality of the individual and affect many different aspects of the personality, and it is an important element of social and psychological adaptation, especially if it is within the limits of nature, and if the methods used to express them are appropriate and moderate.
Submission is one of the characteristics that express the way an individual relies upon in dealing with others and in dealing with matters of life. An individual who complies with instructions and orders and abides by them, and performs what is required of him without hesitation or delay. Adolescence is an important and accurate stage in the constructive development of an individual and in his psychological and social life.
The
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