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 paper develops the work of Mary Florence et.al. on centralizer of semiprime semirings and presents reverse centralizer of semirings with several propositions and lemmas. Also introduces the notion of dependent element and free actions on semirings with some results of free action of centralizer and reverse centralizer on semiprime semirings and some another mappings.
يهدف البحث الحالي الى استكشاف علاقات التفاعل والتاثير بين الاحتكام للمكانة والتوجه للفردية– الجماعية والدمج التنظيمي مستنداً على مزج اختلاف القيم الشخصية مع افكار نظرية الهوية الاجتماعية لبلورة نموذج البحث. وفي ضوء هذا تم صياغة عدد من الفرضيات التي توضح علاقات التفاعل ما بين ابعاد الاحتكام للمكانة والتوجه للفردية– الجماعية للتنبؤ بوجود الدمج التنظيمي. جمعت البيانات باستخدام استمارة الاستبيان ووزع
... Show MoreAn experimental and numerical study has been carried out to investigate the heat transfer by natural convection and radiation in a two dimensional annulus enclosure filled with porous media (glass beads) between two horizontal concentric cylinders. The outer cylinders are of (100, 82 and70mm) outside diameters and the inner cylinder of 27 mm outside diameter with (or without) annular fins attached to it. Under steady state condition; the inner cylinder surface is maintained at a high temperature by applying a uniform heat flux and the outer cylinder surface at a low temperature inside a freezer. The experiments were carried out for an annulus filled with
glass beads at a range of modified Rayleigh number (4.9 ≤ Ra≤ 69), radiation
The multiple linear regression model is an important regression model that has attracted many researchers in different fields including applied mathematics, business, medicine, and social sciences , Linear regression models involving a large number of independent variables are poorly performing due to large variation and lead to inaccurate conclusions , One of the most important problems in the regression analysis is the multicollinearity Problem, which is considered one of the most important problems that has become known to many researchers , As well as their effects on the multiple linear regression model, In addition to multicollinearity, the problem of outliers in data is one of the difficulties in constructing the reg
... Show Morehe assignment model represents a mathematical model that aims at expressing an important problem facing enterprises and companies in the public and private sectors, which are characterized by ensuring their activities, in order to take the appropriate decision to get the best allocation of tasks for machines or jobs or workers on the machines that he owns in order to increase profits or reduce costs and time As this model is called multi-objective assignment because it takes into account the factors of time and cost together and hence we have two goals for the assignment problem, so it is not possible to solve by the usual methods and has been resorted to the use of multiple programming The objectives were to solve the problem of
... Show MoreLinear and mass attenuation coefficient of reactive powder concrete (RPC) sample ( of compressive strength equal to 70 Mpa) using beta particles and gamma ray with different energies have been calculated as a function of the absorber thickness and energy. The attenuation coefficient were obtained using NaI(Tl) energy selective scintillation counter with 90Sr/90Y beta source having an energy rang from (0.546-2.274) MeV and gamma ray energies (0.569, 0.662, 1.063, 1.17 and 1.33) MeV . The attenuation coefficient usually depends upon the energy of radiations and nature of the material. The result represented in graphical forms. Exponential decay was observed. It is found that the capability of reactive powder concrete to absorber beta particle
... Show MoreMass transfer was examined at a stationary rectangular copper electrode (cathode) by using the reduction of cupric ions as the electrochemical reaction. The influence of electrolyte temperature (25, 45, and 65 oC), and cupric ions concentration (4, 8, and 12 mM) on mass transfer coefficient were investigated by using limiting current technique. The mass transfer coefficient and hence the Sherwood number was correlated as Sh =
A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interac
... Show MoreMillions of pilgrims and visitors from numerous parts of the world flock to Karbala (one of the most prominent ideological and religious places in central Iraq) each year to visit the holy shrines in Karbala due to their sanctity. Many improvements have been made to the Two Holy Shrines (THS), the Shrines of Imam Husayn and Imam Abbas, and the area between them (ATHS), due to the high temperatures in this region and to improve pedestrian thermal comfort. Studies on improving outdoor thermal comfort in Karbala are scarce. Hence, this research aims to look into historical and current architectural changes and how they affect thermal comfort. On the hottest summer day, the ENVI-met software program was used to simulate the building des
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