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.
Praise be to God, who started his book with the praise of himself and prayers and peace be upon those who do not have a prophet after him and his family and companions and those who followed them with charity until the Day of Judgment. Either:
The research examines the meanings of the formulas of the increased verbs that were mentioned in Surat Al-Baqara, at the imam of the imams of the Islamic nation, namely, Al-Fakhri Al-Razi (d. 606 AH), may God Almighty have mercy on him. With the imams of Quranic scholars.
At a time of increasing human potential in the face of crises and risks through the use of technology on a large scale and steadily in various fields of life, and the vulnerability of business organizations as a result of mistakes. The failure of a sudden these errors or omissions or symptoms. Also, some crises occur outside the control of management, others caused by leakage of important information and sometimes secret may be a strategy or a new plan or new project occurs outside the organization to the opposite of what is planned. Therefore, the crisis management are critical to all organizations, because the active management of the crisis helps to ensure the continued prosperity of the organization. Here comes from the resea
... Show MoreGovernment-sponsored projects in Iraq significantly improve the economic situation and provide services but face high rates of troubling blocks. This work aims to identify indicative factors of the Troubled Project using periodic health check reports based on a literature review and interviews with Iraqi experts. As a result, a questionnaire was prepared that included four sections. The first is personal information; the second section is information about knowing the level of institutions’ implementation of project management through prepared documents. The third section is about indicative factors for the project's trouble, including 25 workers; the fourth section is about the questions in the periodic reports to che
... Show MoreIn this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami
... Show MoreThe treatment of migraine headache targets the neurovascular mechanism and involves the use of serotonin receptor antagonists. Some of these drugs are used for the treatment of acute attacks; while others are effective as prophylactic measures to decrease the duration and frequency of attacks. Pizotifen, a 5-HTA antagonist, is one of the prophylactic drugs for which the clinical use resulted in low outcomes in reducing migraine symptoms. Melatonin, a serotonin derived neurohormone, was reported to exert many functions like sleep induction, anti-inflammatory, neurovascular regulation, cytoprotection and modulation of neurotransmitter release. In the view of the involvement of serotonin in the pathophysiology of migraine a
... Show MoreThe study aimed to identify the perceptions of social studies teachers in the Governorate of Muscat about the importance of employing the skills of the twenty-first century in teaching. The study employed a qualitative approach. The two researchers used an analytical approach based on the Grounded Theory, the data was gathered through semi-structured interviews with (15) male and female teachers. The results indicated that social studies teachers relate the twenty-first-century skills more to improving students’ achievement level in the subject, while they see that these skills have less influence in developing students’ communication skills and cooperation with their peers. In light of the results of the study, the two researchers r
... Show MoreThe aim of this study was spot light to the possibility of confection between hepatitis C&G viruses in Iraqi patients. The groups was studied included two groups as follow: 1- first group: its (Infected group) the patients of this group have Anti-HCV abs in their serum by using Indirect ELISA technique. 2- second group: its (Control group) the persons of this group have no Anti-HCV abs in their serum by using indirect ELISA technique. The result of this study was observed there was two patients from the first group have Anti-HGVabs in their serum with infection percent 2.70%, also the same result was found in the second group wich mean there was two persons have Anti-HGVabs in their serum with infection percent 8.33% .So when we comparin
... Show MoreObjective(s): This study aims to evaluate the hardness of two commercially available cold cured acrylic resin material
(Vertex and PAN) when polymerized at different temperature in comparison to those polymerized by conventional
methods in air at 23C ± 5C.
Methodology: Eighty specimens, forty from cold cured acrylic (Vertex Type) and forty from cold cured acrylic (PAN
type) were prepared, flasking and packing procedure were done according to manufacturer direction and divided
according to processing as follow: 20 specimens (10 from Vertex type and 10 from PAN type) were processed in air for
two hours at 23C ± 5C under press (bench curing) as a control, and 60 specimens (30 from Vertex type and 30 from
PAN type) wer
The Histo-mrphology were directed on the pneumonic alveoli of 6 male goats. The respiratory portion is composed of typical cuboidal epithelial cells with Clara cell, however, alveolar ducts are lined by simple squamous epithelium and alveoli were generally circular structures that opened into the alveolar conduits and alveolar sacs or respiratory bronchioles. Alveoli were made out of two kinds of cells for example Type-I pneumocytes and Type-II pneumocytes. Previous framed the mainlining epithelial cells of alveoli which were squamous in sort having noticeable perinuclear territory and central found the core, while the last were cuboidal fit as a fiddle with the midway found core and periodically found among the Sort I cells in the
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