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 archaeological and religious sites play a prominent role in the rest of the other tourist activities as cultural and spiritual needs that can not be dispensed with. Archaeological sites represent cultural origins of the nation. Religious sites represent the state of man's orientation to God in places of worship . The focus was on the city of Babylon because it is an ancient city and tourist because of its characteristics and elements. The importance of the city of Babylon is illustrated by highlighting its archeological and religious status through its geographical distribution. This gives the subject special importance for the purpose of knowing the city's important sites. And come out with a number of results and a set of recommend
... Show MoreThe influx of Arab Qahtani and Nizari tribes continued to the countries of Baluchistan and the Levant in pre-Islamic times until the Levant became open to the Arab-Islamic tide during the first century AH. The Islamic Orient until the early Islamic Arab Army reached the western borders of China. What we will see in the folds of the search.
The current report dealt with the effect of pesticides on the ecosystem through their impact on soil, water, and microorganisms and their impact on human health. As well as this study dealt with the biodegradation process of pesticides and the organisms involved in this process, even some previous studies proved that Bacillus spp. And Pseudomonas sp. Bacteria is the most efficient in the biodegradation of pesticides, at the same time, other previous studies dealt with the environmental factors that affect the biodegradation process of pesticides. It proved that each of the incubation periods, pH, and temperature have different effects on biodegradation. Most of the studies indicated that the best incubation period for biodegradation is 7-8
... Show MoreThe issue, the existence of God Almighty, and the creativity of the universes including the whale, and assets and how diversified, and faith in him and his lordship and divinity, is a delicate issue, and very important and dangerous, and it occupied human thought old and new, and still occupy it until God takes the land and on it. Many complex issues of thought, behavior, and ethics have resulted in the belief of many communities in the existence of the Almighty, having ruled their minds, depicting their beliefs and distancing their thoughts about slippage and abuse. When they looked at the wonders of creatures and the minutes of the assets, they thought about the planetary and astronomical motion systems. His existence was denied by ath
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Summary of the jurisprudence research
Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of the Messengers, our master Muhammad, and upon his pure family, and his ignorant and ignorant companions, and those who followed them in goodness until the Day of Judgment.
Then:
The many jurisprudential aspects that the Shafi’i imams said are of great importance, because these aspects are nothing but the opinions of venerable jurists who have reached a high degree of knowledge until they have become among the owners of faces. And among them are the Shafi’i jurists, the jurists may differ among themselves, either because there is no text about their imam in a
... Show MoreCUPPER(||)AND MERCURY (||)Complexes WITH SCHIFF BASE LIGAND FROM BENZIDIN WITH ISATIN AND BENZOIN:SYNTHESIS,SPECTRAL CHARACTERIZATION, THERMAL STUDIES AND BIOLOGICAL ACTIVITIES
This study is attempt to improve thermal isolation through measuring thermal conductivity composite of on polyester resin with fillers of (TiO2, ZnO, Acrylonitril, wood flour Coconut (Wf). The grain size of the fillers is 200 µm. The number of samples is (16) in addition to the virgin sample; these samples are prepared by cast molding method for polyester with filler volume fractions (5%, 10%, 15% and 20%). Shore hardness tests were used to measure the hardness and Lee disk method for thermal conductivity. The experimental results showed that the (20% ZnO) sample has the maximum value of thermal conductivity where (20% w.f) has minimum thermal conductivity .on the other hand (15% ZnO) sample give the maximum value of hardness where (20% w
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