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.
Isobaric Vapor-Liquid-Liquid equilibrium data for the binary systems ethyl acetate + water, toluene + water and the ternary system toluene + ethyl acetate + water were determined by a modified equilibrium still, the still consisted of a boiling and a condensation sections supplied with mixers that helped to correct the composition of the recycled condensed liquid and the boiling temperature readings in the condensation and boiling sections respectively. The VLLE data where predicted and correlated using the Peng-Robinson Equation of State in the vapor phase and one of the activity coefficient models Wilson, NRTL, UNIQUAC and the UNIFAC in the liquid phase and also were correlated using the Peng-Robinson Equation of State in both the vapo
... Show MorePracticing physical activity is a very necessary requirement for all segments of society. . Many individuals, regardless of environment, age and gender, are exposed to joint diseases and injuries and pain in the neck for many and varied reasons. Treatment methods and techniques vary according to the severity of the injury, as therapeutic exercises, including stretching exercises, specifically fixed ones, are one of the ways to eliminate cases of muscle and joint dysfunction. Many individuals, regardless of environment, age and gender, are exposed to joint diseases and injuries and pain in the neck for many and varied reasons. Treatment methods and techniques differ according to the severity of the injury, as therapeutic exercises, including
... Show MoreThe research aims to identify the most important variables affecting shooting from jumping high and compare them for the two foot the weak and strong, where the researchers adopted the descriptive method, and the sample was chosen by the intentional method, which consists of (4) players from the Iraqi Sports Army Club, where these variables were studied and their impact on The accuracy of aiming at the two men, and the researchers concluded that most of the players have more accuracy in aiming at the strong leg than at the weak leg, which leads to the loss of many real opportunities during the match because of the players changing the situation or wasting the available opportunity when the position of correction is an opportunity for the w
... Show MoreConservative pipes conveying fluid such as pinned-pinned (p-p), clamped–pinned (c-p) pipes and clamped-clamped (c-c) lose their stability by buckling at certain critical fluid velocities. In order to experimentally evaluate these velocities, high flow-rate pumps that demand complicated fluid circuits must be used.
This paper studies a new experimental approach based on estimating the critical velocities from the measurement of several fundamental natural frequencies .In this approach low flow-rate pumps and simple fluid circuit can be used.
Experiments were carried out on two pipe models at three different boundary conditions. The results showed that the present approach is more accurate for est
... Show MoreIn this study, chemical oxidation was employed for the synthesis of polypyrrole (PPy) nanofiber. Furthermore, PPy has been subjected to treatment using nanoparticles of neodymium oxide (Nd2O3), which were produced and added in a certain ratio. The inquiry centered on the structural characteristics of the blend of polypyrrole and neodymium oxide after their combination. The investigation utilises X-ray diffraction (XRD), FTIR, and Field Emission Scanning Electron Microscopy (FE-SEM) for PPy, 10%, 30%, and 50% by volume of Nd2O3. According to the electrochemical tests, it has been noted that the nanocomposites exhibit a substantial amount of pseudocapacitive activity.
Sol-gel method was use to prepare Ag-SiO2 nanoparticles. Crystal structure of the nanocomposite was investigated by means of X-ray diffraction patterns while the color intensity was evaluated by spectrophotometry. The morphology analysis using atomic force microscopy showed that the average grain sizes were in range (68.96-75.81 nm) for all samples. The characterization of Ag-SiO2 nanoparticles were investigated by using Scanning Electron Microscopy (SEM). Ag-SiO2 NPs are highly stable and have significant effect on both Gram positive and negative bacteria. Antibacterial properties of the nanocomposite were tested with the use of Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) bacteria. The results have shown antibacteri
... Show MoreGraphic design constitutes the human necessity for the design action, so there is no design achievement that is not considered in its founding project and its final realization as a response to a specific necessity. As a result of knowledge, which is the product of experience and is the result of applied science, design is based on observation, study and development, leading to the main goal, which is the utilitarian and aesthetic function that is put into the final consideration of design, and drug packaging design has an important role in all marketing fields, as companies compete with each other to attract the largest number Possible from consumers in a way that guarantees them material profit, and in order to achieve this, it always
... Show MoreThe question about the existence of correlation between the parameters A and m of the Paris function is re-examined theoretically for brittle material such as alumina ceramic (Al2O3) with different grain size. Investigation about existence of the exponential function which fit a good approximation to the majority of experimental data of crack velocity versus stress intensity factor diagram. The rate theory of crack growth was applied for data of alumina ceramics samples in region I and making use of the values of the exponential function parameters the crack growth rate theory parameters were estimated.
This study was carried out to describe the gene expression of the micro RNA 122a gene with the development of diabetes in Iraq. The difference in gene expression between patients and healthy controls was properly considered. In this study, blood was isolated from 121 individuals divided into two groups as follows: 80 samples of diabetic patients and 41 samples from a healthy control. miRNA was isolated and transformed into cDNA, and the expression of mi122a was measured by qRT-PCR. The researchers looked at the relationship between age and gender and the occurrence of diabetes, as well as how they compared to controls. When comparing the mean gene expression level (Ct) of patient groups to the corresponding Ct means in the control group, th
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