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.
This study showed that the lens in baloot muluki fish Chondrostoma regium is transparent, spherical shape, and solid in textures, while in the tree frog Hyla arborea savignyi, freshwater turtles Clemmys caspia caspia, white–eared bulbul Pycnonotus leucotis and brown rat Rattus norvegicus are transparent, soft and biconvex, it is very soft in white–eared bulbul. There are many significant differences have been recorded between the average weight lens and the total concentration of the protein in the lens all studied animals. Electrical migration process for lens proteins showed that there is one bundle of crystalline –? and one bundle also crystalline–? in all studied species, either crystalline–? may represent one bundle character
... Show MoreThe study introduces the twentieth century background where the image of teacher is shaped by various factors according to the wide emergence of new educational institutions in the aftermath of the Second World War. A group of writers mirrored the influence of the war on educational institutions and accordingly on the image of teacher in their novels whose main action is set in and around the campus of a university. The genre dates back to the nineteen forties. where they show the foibles of human nature and reactions to external pressures. One of the early examples of this genre is Lucky Jim (1954). The image of teacher is swinged in many shapes from the tyrant to the rebellion to the defiant. All is personified in the characters of these
... Show MoreBackground: Tooth extraction is one of the most commonly performed procedures in dentistry. It is usually a traumatic process often resulting in immediate destruction and loss of alveolar bone and surrounding soft tissues. Various instruments have been described to perform atraumatic extractions which can prevent damage to the paradental structures. The physics forceps is one of those innovations in dental extraction technologies that claim to provide an efficient means for atraumatic dental extractions. Materials and method: A randomized clinical trial was conducted to compare the physics forceps with the conventional forceps for the removal of 28 mandibular single rooted teeth under the following parameters: incidence of crown, root, b
... Show MoreThe study highlighted the transformation of value systems and educational patterns between past and present, especially with the introduction of modern variables and means, such as mobile phones, the internet, social media, and others. These factors have contributed both positively and negatively to the study. The study highlights the integral role of the school in collaboration with the family in guiding and educating children. It also emphasizes the active role of the school in developing students' abilities and skills, either attracting them to school or vice versa. This includes an examination of the essential skills required in education and their role in achieving a state of psychological well-being and systematically developing child
... Show MoreThis article discusses how women have significant abilities to cope with the difficulties of war times. They are not the weak and vulnerable victims who are thought to be. On the contrary, they have the power to control over many-sided fronts, like participating in the battlefield as nurses or activists for peace, or even fighters, as well as through the tasks and responsibilities assigned to them to protect and support their families during wartime. The researcher will examine the impact of war upon women. Like men, women suffer during wartime. They are being injured, tortured and killed. Yet, they are able to give examples of love and courage even in the difficult times of war. Hana is one of those women who lived during wartimes,
... Show MoreThe political movements of Islam are among the most prominent phenomena of the popular uprisings witnessed by the Arab world. However, this rise and the rise of some movements led to many problems on the political theses of Islam, especially those associated with the ideas of Islamic ideologues and their slogan Legitimacy and the authorities as the origin of the divine, and said the application to achieve the Islamic solution, and then became the state in theses of some Islamists a tool to apply the law and then the preservation of religion.