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.
The expressive discourse, in the form of the rural singing, is considered one of the interactive framework and the metaphorical dialogues in creating the aesthetic climate that connects the circles of its basic elements, singing, playing music, expression, costumes, sham movements and so forth.
The rhetorical language in this field includes all those parts and turns them into an integrated idea within the culture of the musical science, specifically the heart of the rural singing. This research dealt with a number of topics of relevance in the expressive discourse for the form of the rural singing. The first chapter consists of the methodological framework of the research, represented by the r
... Show MoreSince the property in Islam is based on the principle of succession , "which made you Khalaúv land and raise yourselves above some degree of Iblukm with Atakm The Lord of the fast punishment and it is Forgiving, Merciful " [cattle : 165 ] and human only Mstkhalaf where " God promised you who believe and do good deeds for Istkhalvenhm Normans in the ground as those before them " [Nur : 55 ] , considering that King God alone any talk about having ownership in Islam in the contemporary sense of ownership , containing three rights are:
1- right to dispose of the right of usufruct tenure
2-The concept is ambiguous as long as that man Mstkhalaf does not have the right to dispose
... Show MoreThe Arab Islamic art was best known as pure abstraction or realism distorted from what is natural. The two styles, or one of them, was the most prominent in the Islamic arts, such as decoration, photography and architecture. The analogy that was prevalent in the non-Islamic world did not have a presence equivalent the aforementioned styles despite the great openness to the cultures of different countries, which characterized that stage, which resulted from the Islamic conquests, the conversion of many people to the Islamic faith, and their migration to the Islamic cities at the time, bringing with them their arts and methods of formulation. This makes us question the influential references that invite the Arab Muslim artist to follow the
... Show MoreBiodiversity, biological diversity, biological diversity, biological diversity, biological diversity, biological diversity, biological diversity (by developmental factors) environmental factors and environmental factors environmental factors and environmental factors and environmental factors Correlation between biology and the succession of geological and historical factors of living organisms and geological and historical factors to the site and what It is surrounded by natural and tourist attractions and the pursuit of scientific methods in order to advance the studies of biological diversity in the region .
Iraq has the distinction of being a great potential of non-renewable natural resources,
especially crude oil and natural gas. Since the discovery of crude oil at the beginning of the
twentieth century in Iraq. Although the different of investment types, it contributed to the oil
sector in the provision of financial resources to the state treasury , since that date until the
present time.
Search has been marked by division ((The foreign investment in the oil sector in Iraq after
2003)) into three sections. The first section included a brief history of the development of
Iraq's oil potential in terms of oil reserves, and oil fields, and the quantities of production and
export. The second section reviewed the investm
fashion designers who have benefited greatly from the mobilization of ancient aesthetic ideas in the heritage of the people and guaranteed in their productions so that there is no change In the aesthetic value created by the designers of the research in the ancient heritage to find new signs that reflect the connection of man to the present as the aesthetic value of all the man created by the designs of fabrics and fashion through the ages The problem of research was determined in the absence of a precise understanding of the nature of classical thought in fashion and the absence of a clear perception of the sustainability of this thought in contemporary fashion. He
... Show MoreThe problem of internal sulfate attack in concrete is widespread in Iraq and neighboring countries.This is because of the high sulfate content usually present in sand and gravel used in it. In the present study the total effective sulfate in concrete was used to calculate the optimum SO3 content. Regression models were developed based on linear regression analysis to predict the optimum SO3 content usually referred as (O.G.C) in concrete. The data is separated to 155 for the development of the models and 37 for checking the models. Eight models were built for 28-days age. Then a late age (greater than 28-days) model was developed based on the predicted optimum SO3 content of 28-days and late age. Eight developed models were built for all
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