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.
Conclusion and results
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In this research, the results of the Integral breadth method were used to analyze the X-ray lines to determine the crystallite size and lattice strain of the zirconium oxide nanoparticles and the value of the crystal size was equal to (8.2nm) and the lattice strain (0.001955), and then the results were compared with three other methods, which are the Scherer and Scherer dynamical diffraction theory and two formulas of the Scherer and Wilson method.the results were as followsScherer crystallite size(7.4nm)and lattice strain(0.011968),Schererdynamic method crystallite size(7.5 nm),Scherrer and Wilson methodcrystallite size( 8.5nm) and lattice strain( 0.001919).And using another formula for Schearer and Wilson methodwe obtain the size of the c
... Show MoreLocal communities are in need of self-resources so that they can perform their multiple functions which serve the objectives of the local development, and tax revenues are considered as important sources of their funding. However, despite the efforts of the state to reform the fiscal system and to improve the management in the local administration, tax collection can increase when the state adopts a more effective policy to combat tax evasion and tax fraud. Accordingly, this research aims to shed light on the role of local tax revenues in the local development. A set of conclusions are drawn; the most important one is that Algeria, in order to achieve local development, has taken a set of reforms, which are still valid until now. The mos
... Show MoreThe aims of this study to diagnose the role of the (relationship and impact) Academic driving practices dimensions (model the way, inspire a shared vision, challenge the process, enable others to act, encourage the heart ) in the activation of human capital (investment and development) for (knowledge, skills, expertise, creative and training capabilities) in a sample of university professors in Baghdad city(Baghdad University, Al Mustansiriya University, University of Technology). (367 )samples were distributed to (232 at the University of Baghdad, 97 at Al-Mustansiriya University and 38 at the University of Technology). The goals of descriptive analytical method research have been used, questionnaire has been a main tool for dat
... Show MoreThe adrenal gland is a vital endocrine gland that secretes many important hormones in the daily life of birds. It is located in the Iraqi Pterocles alchata bird on both sides of the aorta in the front and side of the cranial lobe of the kidney at the caudal end of the lungs, triangular shape with a creamy yellow color. The statistical analysis showed no significant differences between the weight and length of the right and left glands. Histologically the gland of the sandgrouse bird capsule contains autonomic nodes consisting of nerve cells and the average thickness of the capsule is 42.69±1.81μm, the parenchyma of the gland is divided into two areas; the cortex and medulla in addition to the blood sinuses. The cortex area is divided into
... Show MoreThe Psychologists have noticed, not long ago, that the man’s success and happiness in life do not only depend on his degree and education, which express on his mental intelligence but also they need another kind of intelligence called emotional intelligence. The research aims at identifying the emotional intelligence level of the top and administrative leaderships in the Federal Board of Supreme Audit by evaluating their emotional intelligence when the administrative and audit leaderships face emotional interactions by dealing with administrative and audit stuffs in the Board. The research problem is focused on the following question “Is the emotional intelligence of the top and administrative leaderships in the Fede
... Show MoreThis study aimed to determine the radioactivity and radiation hazard indicators of rice samples potentially for human consumption. Gamma spectroscopy was used to calculate the specific activity of natural and artificial radionuclides (238U, 232Th, 40K, and 137Cs) in local and imported rice samples collected from local markets in Baghdad Governorate, Iraq, in addition to various radiological hazard indices. The radionuclide concentrations in the samples varied from 2.123 ± 1.457 Bq/kg to 13.032 ± 3.610 Bq/kg for 238U, 2.906 ± 1.705 Bq/kg to 17.290 ± 4.158 Bq/kg for 232
Background: Gingival crevice fluid (GCF) is a mixture of substances derived from serum, leukocytes, and structural cells of periodontium and oral bacteria. These substances possess a great potential for serving as indicators of periodontal disease and healing after therapy the main purpose of this study was to find if there is a difference in albumin concentration between healthy and diseased periodontal tissues and to compare between diseased group according to pocket depth Materials and methods: total sample composed of 60 pockets found in 35 patients all of them had no history of any systemic disease, The samples were divided in to three main group that include two diseased groups divided according to the depth of the periodontal pocket
... Show MoreComputer simulations were carried out to investigate the dependence of the main perturbation parameters (Sun and Moon attractions, solar radiation pressure, atmosphere drag, and geopotential of Earth) on the orbital behavior of satellite. In this simulation, the Cowell method for accelerations technique was adopted, the equation of motion with perturbation was solved by 4th order Runge-Kutta method with step (1/50000) of period to obtain the state vectors for position and velocity. The results of this simulation have been compared with data that available on TLEs (NORD data in two line elements). The results of state vectors for satellites (Cartosat-2B, Gsat-14 an