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.
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 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 MoreWireless sensor networks (WSNs) are emerging in various application like military, area monitoring, health monitoring, industry monitoring and many more. The challenges of the successful WSN application are the energy consumption problem. since the small, portable batteries integrated into the sensor chips cannot be re-charged easily from an economical point of view. This work focusses on prolonging the network lifetime of WSNs by reducing and balancing energy consumption during routing process from hop number point of view. In this paper, performance simulation was done between two types of protocols LEACH that uses single hop path and MODLEACH that uses multi hop path by using Intel Care i3 CPU (2.13GHz) laptop with MATLAB (R2014a). Th
... Show MoreThe raw material soil of Al-Sowera factory quarry (quarry soil and mixture) used for building brick industry was tested mineralogically, geochemically and geotechnically. Mineral components of soil are characterized by Clay minerals (Palygoriskite and chlorite) and nonclay minerals like calcite, quratz, feldspar, gypsum and halite. The raw material is deficient in SiO2, Al2O3, K2O, Fe2O3 and MgO, while enriched in CaO. Loss on ignition and Na2O are in suitable level and appear to be concordant with the standard. Grain size analyses show that the decreasing sand and clay, and increasing silt ratio in both quarry soil and mixture caused decreasing in strength of brick during molding and after firing. The quarry soil is characterized by high p
... Show MoreThe cytotoxic effect of catechol was examined in two human cancer cell lines, Epidermoid larynx carcinoma (Hep- 2), Cerebral glioblastoma multiforme (AMGM-5) and Murine mammary adenocarcinomacell (AMN3) treated with half concentrations of catechol (1000, 500, 250, 125, 62.5 and 32.25 μM) for 72 hr. The get hold of results showed catechol have a toxic effect of the cell viability of three types of cell lines after 72h of exposure, the toxicity was dependent on catechol concentrations and/or autoxidation for quinines formation, there were a marked decreased of cell viability in a dose dependent manner in all cell line types. Inhibition concentration of catechol for 50% of cell viability (IC50) were calculated, they were at 581.5 μM, 478 μM
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