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 study is conducted to verify the efficienecy of local Ninivite rock when used in the treatment of drinking water in plants operating currently in the country in order to develop the situation of these stations to cope with the increase in population. Also, this will limit the pollutian which are increasing in the country's rivers.
(Euphrates and Tigris). These rivers are the sources to feed all water treatment plants in the country. The idea is the develop or the modify these stations by replacing part of top layer of sand filters used in these stations with Ninivite rock to operate as filters composed of two medium. The efficiency of this rock is compared with other materials used successfully worldwide in this area, such a
... Show MoreIncreasing need for day after day to find ways and innovative means of
helping to educate and give children the skills of different kind, has found a
researcher on the subject of hats, six room to give children language skills
through the experience of field reconnaissance conducted on the three
children found that language skills improved, he decided to make these study.
Objectives of the study:
Understand the differences between the experimental group first (the way the
debate) and second (six caps) depending on the test post administration.
to identify the language skills of the second group according to the pre and
post test
Differences between males and females in the second group (Six Hats)
Search T
Agricultural lands have great importance in people's lives, and their exploitation has a great impact on strengthening the national economy. Therefore, countries have given great importance to this sector, and because of the importance of this sector, the state has given large areas of these lands to the farmers to invest in agriculture, and among these farmers are those who died and left behind children who took up crafts. Agriculture, for fear that these agricultural lands would be abandoned and turned into waste lands, a land system was introduced called (regular distribu- tion), which corresponds to (legitimate inheritance). Under this system, these lands were trans- ferred to the children of farmers who died so that the process of inve
... Show MoreThe scholastic view of public religion differed, and this difference was on two extremes. All economic schools agreed that public debt is a monetary liquidity that was unjustly deducted from the income and output cycle as a result of the imbalance in the economic balance and the departure from the conditions of balance between aggregate demand and aggregate supply. Debt is a waste of financial resources allocated to productive accumulation. Except for the Keynesian school, which considers public debt to be an addition to aggregate demand after the decline in the role of the private sector in investment as a result of pessimistic expectations that warn of signs of economic contraction. Public debt is linked to the ex
... Show MoreThis article describes how to predict different types of multiple reflections in pre-track seismic data. The characteristics of multiple reflections can be expressed as a combination of the characteristics of primary reflections. Multiple velocities always come in lower magnitude than the primaries, this is the base for separating them during Normal Move Out correction. The muting procedure is applied in Time-Velocity analysis domain. Semblance plot is used to diagnose multiples availability and judgment for muting dimensions. This processing procedure is used to eliminate internal multiples from real 2D seismic data from southern Iraq in two stages. The first is conventional Normal Move Out correction and velocity auto picking and
... Show MoreIn this research, the preparation of bidentate Schiff base was carried out via the condensation reaction of both the salicylaldehyde with 1-phenyl-2,3-dimethyl-4-amino-5-oxo-pyrazole to form the ligand (L). The mentioned ligand was used to prepare complexes with transition metal ions Mn(II), Co(II), Ni(II), Cu(II) and Zn(II). The resulting complexes were separated and characterized by FTIR and UV-Vis spectroscopic technique. Elemental analysis for Carbon, Hydrogen and Nitrogen elements, electronic spectra of the ligand and complexes were obtained, and the magnetic susceptibility tests were also achieved to measure the dipole moments. The molar conductivities were also measured and determination of chlorine content in the complexes and
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