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.
ABSTRACT Studying the positive and negative effects resulted from the industrial projects and laying down the comprehensive planning bases to the urban development projects which insure retaining the social, economic and environmental development, taking in to consternation the time factor within the planning process which is considered the most important factor that determine the extent of the efficient selection to the site and not interpenetrate in the industrial activities and efficiency and calculating its future expansions away from the residential areas. It is more favorable to plan the industrial areas of apparent pollution outside the bounds of the basic plan to limit the negative effects on the environment and providing
... Show MoreThis work aims to introduce the concepts of left and right derivations in an AT-algebra and discuss some interesting theorems of these concepts. Also, a fuzzy derivation of an AT-subalgebra, a fuzzy right (left) derivation ideal, a fuzzy derivation of AT-subalgebra, and a fuzzy right (left) derivation ideal are studied. Finally, a level derivation of AT-algebras is defined and some propositions are achieved.
The reason for studying (The secret of Repentance and Confession in Christianity) goes back to the deep roots of repentance in all religions, specially the three revealed religions, and those who adhere to them. The human psych by nature is incessantly demanding sins and the wrong deeds. It is in need of repentance which God has opened for them. Almighty God is happy when his creatures repent and refrain from sinning. This is the reason for success in life and the hereafter and the principle of the happiness. It is also a condition for the good course. Therefore, man should refrain from sinning and feel regret for committing sins forever.
Recent studies have tended to look at Mottagorat texts for seeking more of the information provided by the book for the reader, has been known by several terms Mottagorat texts, including thresholds, including the margins of the text and the parallel texts, and came this difference, according to researchers who ate the subject of research and investigation. Thus, the researchers assert that all these texts must be subjected to provide information even if propaganda of the text. Hence arose the importance of these texts in Informatics scientific material being wrapped body of the text as well as being propaganda material to evoke the recipient to read, and then to the importance of this topic, the search came on five chapters, the first c
... Show MoreThis research is concerned with the study of (the aesthetic of constructive relations in linear composition) with what distinguished Arabic calligraphy through the style and artistic method in its construction, and the specifications it carries that enabled it to pay attention to building formations to achieve in its total linear ranges aesthetic values and relationships. Through the research, the models and the exploratory study that he obtained, the researcher was able to raise the research problem in the first chapter according to the following question: What is the aesthetic of constructive relations in linear formation?
The importance of the research in achieving the aesthetics of the formations, which is a wide field according t
Linear and nonlinear optical properties of epoxy/ Al2O3 nanocomposites system were studied for epoxy neat and (0.5, 1.5, 3, and 5) % Al2O3 nanocomposites.The band gap of epoxy and its nanocomposites was obtained at these weight ratios. Nonlinear optical properties experiments were performed using Q-switched Nd:YAG laser z-scan system.These experiments were carried out for different parameters: wavelengths (1064 nm and 532 nm), laser intensities (0.530, 0.679, and 0.772) GW/cm2 and weight ratio of Al2O3 nanocomposites. The results showed that the band gaps were decreased with increasing the weight ratio of nanoalumina except at 5wt% and the nonlinear refractive index coefficient is directly proportional to the incident intensities while o
... Show MoreThe paper tries to explore the grammatical phenomenon of rankshift in Systemic Grammar, a functional grammar that establishes five units or the rank scale , : namely sentence, clause phrase, word and morpheme .Rankshift a Hallidayan term , occurs when a given unit is downgraded or shifted down the rank scale and operates further down its rank or a rank equal to itself as when a clause which has to operate in sentence structure operates at q “ qualifier” in a nominal group. The paper , quite significantly, introduces the systemic background that enunciates the systemic theory whose organising concept system rather than structure. The paper then, grammatically explores rankshifted elements, successive rankshifting, degrees of rankshifting
... Show MoreThe Present study aims to shed some light on the concept of authority of university students and to find statistically significant differences as regards this concepts in accordance with three variables gender (males, females),field of study(scientific ,humanities)and grade(second ,fourth). To accomplish the study a ( 7) level scale was developed for the concept of authority and it subjected to validity and credibility the scale was used with 590 student sample (237) males and (353) females Results show that male students show obedience to authority forms below the Avery e component with the theoretical Avery of the scale besides ,reinforcement was on the top of authority chain ,followed by person traits ,friends, affect punishment and t
... Show MoreIn order to reduce the losses due to evaporation in the stored crude oil and minimizing the decrease in °API many affecting parameters were studied (i.e. Different storage system, namely batch system with different types of storage tanks under different temperatures and:or different pressures). Continuous circulation storage system was also studied. It was found that increasing pressure of the inert gas from 1 bar to 8 bar over the surface of the crude oil will decrease the percentage losses due to evaporation by (0.016%) and decrease the change of °API by (0.9) during 96 hours storage time. Similarly using covering by surfactant (potassium oleate) or using polymer (polyurethane foam) decreases the percentage evaporation losses compare
... Show MoreThis study aims to discuss the projects of poultry in Wasit province in 2013 and geographical distribution according to the type and contrast on the level of administrative units representing Districts and The reasons for this discrepancy, as well as knowledge of the factors affecting the distribution by the analysis and reasoning and description This study divided to the four themes, The first of the statement of nutritional importance and economic Poultry focused on the importance of various poultry products, The second one shows the relative position of the province of Wasit between the provinces of Iraq in poultry and production of eggs and meat farming projects, and then followed by the third one (theme) as it ensures the geographic
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