Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Radial density distribution function of one particle D(r1) was calculated for main orbital of carbon atom and carbon like ions (N+ and B- ) by using the Partitioning technique .The results presented for K and L shells for the Carbon atom and negative ion of Boron and positive ion for nitrogen ion . We observed that as atomic number increases the probability of existence of electrons near the nucleus increases and the maximum of the location r1 decreases. In this research the Hartree-fock wavefunctions have been computed using Mathcad computer software .
Magnetic Abrasive Finishing (MAF) is an advanced finishing method, which improves the quality of surfaces and performance of the products. The finishing technology for flat surfaces by MAF method is very economical in manufacturing fields an electromagnetic inductor was designed and manufactured for flat surface finishing formed in vertical milling machine. Magnetic abrasive powder was also produced under controlled condition. There are various parameters, such as the coil current, working gap, the volume of powder portion and feed rate, that are known to have a large impact on surface quality. This paper describes how Taguchi design of experiments is applied to find out important parameters influencing the surface quality generated during
... Show MorePorosity is important because it reflects the presence of oil reserves. Hence, the number of underground reserves and a direct influence on the essential petrophysical parameters, such as permeability and saturation, are related to connected pores. Also, the selection of perforation interval and recommended drilling additional infill wells. For the estimation two distinct methods are used to obtain the results: the first method is based on conventional equations that utilize porosity logs. In contrast, the second approach relies on statistical methods based on making matrices dependent on rock and fluid composition and solving the equations (matrices) instantaneously. In which records have entered as equations, and the matrix is sol
... Show MoreThis work aims to investigate the tensile and compression strengths of heat- cured acrylic resin denture base material by adding styrene-butadiene (S- B) to polymethyl methacrylate (PMMA). The most well- known issue in prosthodontic practice is fracture of a denture base. All samples were a blend of (90%, 80%) PMMA and (10%, 20%) S- B powder melted in Oxolane (Tetra hydro furan). These samples were chopped down into specimens of dimensions 100x10x2.5mm to carry out the requirements of tensile tests. The compression strength test specimens were shaped into a cylinder with dimensions of 12.7mm in diameter and 20mm in length. The experimental results show a significant increase in both tensile and compression strengths when compared to cont
... Show MoreContemporary management is interested in the process of performance assessment because of its significance in the field of planning and controlling the multiactiveties to attain its goals and uncovering digression of virtual performance after comparing it with the plan or equitable performance.
Digression is analyzed to enable management control centers of authority.
Assessment process significance is closely related by setting definite categories to evaluate the economic activity to know the ability to achieves aims.
This study concentrated on the most important categories that used to evaluate company understudy with ather categories suggested to complete assessment process.
This study is in
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