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.
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Praise be to Allah, Lord of the Worlds, and peace and blessings be upon our master Muhammad and his good and pure family. At the end of this research, we summarize some of the most important findings of our research, namely:
Raising a child properly from childhood leads to integrity in the life of the individual society, and if the young raised bad education, this education will affect itself and society negatively, so on parents and government institutions in any country to take care of children, and Islamic countries Specifically to give the child great attention; he is raised on the Koran and watered from its fountains, and armed with a weapon of morality from a young age, and to understand the biography of Mustafa (peace be upon h
The typographical elements work significantly in engaging a recipient and attracting his attention to the idea and content of the printed work with all its types and goals for which<br /> it is designed. This is because of the fact that the typographical elements have tremendous expression capabilities that reflect the content of the artistic work in a simple way without any complexities. These elements have a special effect in achieving a clear, readable design, besides their effective contribution to the reception and understanding of the designs by the recipient. Accordingly, the designs of the electronic advertisement poster with their promoting goals of its products are considered among the graphic achieveme
... Show MoreEducation is the most powerful and important weapon in fighting poverty and unemployment because it provides students with new skills that appropriate the new market requirements and fair distribution of natural resources. It also transfers knowledge, skills, and ethics over generations. Education aims to create effective leaders who go under training and rehabilitation process, create a new human and instill faith, generate the creativity and innovation, and keep abreast with scientific process, updating curriculum, and finally, applying the technical education
The deliberation and exchanged of power is a matter of political importance For the Iraqi political system after 2003, The deliberation of power and its democratic transition and electoral integrity Is a good indicator of political stability and progress In the Iraqi parliamentary political system , The transfer of authority in terms of adopting the deliberative approach represents a structural and institutional dimension of the political process , it led the power to become Authority of the Foundation Exercised in accordance with the Constitution and the law not real power , And lead to the recognition of the existence of an official parliamentary opposition and its right to take political power later through the ballot box Makes the pr
... Show MoreIn this paper, the static analysis for finding the best location of boxes inside the composite wing-box structure has been performed. A software ANSYS (ver.11) was used to analyses the Aluminum wing to find the maximum stresses reached in. These results are used as a base for the composite wingbox to find the numbers of layers and location of the box beam and its dimensions so that the composite wingbox may carry the same loading conditions in the Aluminum wing. Analysis showed that a composite wingbox having two boxes is better than the single or triple boxes wing based on stress to weight ratio. Mass saving of (40%) had been achieved when composite wing-box is used instead of Aluminum wing.
The arts global digital marketing activity is one of the most prominent manifestations of the contemporary transformation in the circulation of cultural products, and that this event has become a new knowledge event that deserves to be a framework for the problem of our current research, while this phenomenon is growing and developing to compete with the traditional marketing of art through galleries, exhibitions, auctions and museums. It is still the preserve of certain civilized and knowledge environments, and from here this research comes with the aim of shedding light on the mechanisms of digitizing the contemporary art market that have been linked to the two variables of the growing idea of indirect marketing through the intermediar
... Show MoreThis study aims to discuss how English Language Textbook (ELT), used in Iraqi schools, can be developed. All Iraqi teachers in Iraq spend much time using ELT textbooks in classrooms, and most of the Iraqi students depend on these textbooks to learn and improve the English language, so choosing an appropriate ELT textbook is so essential. A suitable book must include critical components that fit teachers' and students' needs. The quality of ELT textbooks has been improved dramatically in recent years, even though these textbooks still do not meet students' needs, especially in language communication skills. This study seeks to investigate the most critical components that may make the ELT textbooks are more influential and interactive for Ir
... Show MoreLow incoming discharge upstream of Samarra-Al Tharthar System leads to sediment accumulation and forming islands, especially an island upstream of Al Tharthar Regulator. This island and the sedimentation threaten the stability of the structure and reduce the efficiency of the system. This study aims to hydraulically identify the sedimentation problem mentioned above, to find solutions of how to control the sediment problems, and to develop the capacity of
the system for 500 years return period flood of 15060 m3/s. Surface Water Modeling System (SMS10.1) with two dimensional depth average models (RMA-2) software were used to simulate and analyze the system. The results of analysis showed that the maximum permissible discharge through t
This study deals with Aphid predators of the genus Coccinella L. recognized in different
regions of the world. They have been arranged systematically according to Korschefsky’s
catalogue (1931). The list includes sites of study and the reference (works) that consider
Coccinellids as predator. The study has revealed that there are thirteen Aphid predator species
belonging to the genus Coccinella L. in different places of the world, although there might be
other species that were not recorded by this work.