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.
In this study, vegetable tanned leather waste of cow (VTLW-C) is used as adsorbent for removing methyl violet 10B dye from aqueous solution. The VTLW-C adsorbent was characterized by FTIR and SEM in order to evaluate its surface properties before using in adsorption experiments. Batch adsorption method was applied to study the effect of different factors such as weight of leather waste, time of shaking, and starting concentration of methyl violet 10B dye. Different isothermal models such as Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (D–R) were used to analyze the experimental data. Kinetic study proceeds using (PFO) kinetic model and (PSO) kinetic model. The results showed better agreement with the Freundlich model; this means
... Show MoreThe current work is focused on the rock typing and flow unit classification for reservoir characterization in carbonate reservoir, a Yamama Reservoir in south of Iraq (Ratawi Field) has been selected, and the study is depending on the logs and cores data from five wells which penetrate Yamama formation. Yamama Reservoir was divided into twenty flow units and rock types, depending on the Microfacies and Electrofacies Character, the well logs pattern, Porosity–Water saturation relationship, flow zone indicator (FZI) method, capillary pressure analysis, and Porosity–Permeability relationship (R35) and cluster analysis method. Four rock types and groups have been identified in the Yamama formation de
Corncob is an agricultural biomass waste that was widely investigated as an adsorbent of contaminants after transforming it into activated carbon. In this research carbonization and chemical activation processes were achieved to synthesize corncob-activated carbon (CAC). Many pretreatment steps including crushing, grinding, and drying to obtain corncob powder were performed before the carbonization step. The carbonization of corncob powder has occurred in the absence of air at a temperature of 500 °C. The chemical activation was accomplished by using HCl as an acidic activation agent. Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), X-ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) facilitate
... Show MoreCover crops (CC) improve soil quality, including soil microbial enzymatic activities and soil chemical parameters. Scientific studies conducted in research centers have shown positive effects of CC on soil enzymatic activities; however, studies conducted in farmer fields are lacking in the literature. The objective of this study was to quantify CC effects on soil microbial enzymatic activities (β-glucosidase, β-glucosaminidase, fluorescein diacetate hydrolase, and dehydrogenase) under a corn (Zea mays L.)–soybean (Glycine max (L.) Merr.) rotation. The study was conducted in 2016 and 2018 in Chariton County, Missouri, where CC were first established in 2012. All tested soil enzyme levels were significantly different between 2016 and 2018
... Show MoreThe aim of the research is to identify an appropriate training method that raises the levels of immune globulins (IgA, IgM, IgG) and white blood cells and the effect of training by (HIT) method using resistance (weights) as a training curriculum that increases immunity and ensures the continuation of the pills after the return of activity from the stone The response to the Covid-19 epidemic among amateur weightlifters, the researchers relied on the method of trace analysis in an experimental way by conducting a pre-, medial and post-test with the same experimental one agroup on a sample of amateur weightlifters in the Fury private hall for weightlifting and body building in Adhamiya, the number of sample members reached (15 players) who int
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The current research aims to examine the effectiveness of a training program for children with autism and their mothers based on the Picture Exchange Communication System to confront some basic disorders in a sample of children with autism. The study sample was (16) children with autism and their mothers in the different centers in Taif city and Tabuk city. The researcher used the quasi-experimental approach, in which two groups were employed: an experimental group and a control group. Children aged ranged from (6-9) years old. In addition, it was used the following tools: a list of estimation of basic disorders for a child with autism between (6-9) years, and a training program for children with autism
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