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.
The main objective of this paper is to designed algorithms and implemented in the construction of the main program designated for the determination the tenser product of representation for the special linear group.
Hypothesis CO2 geological storage (CGS) involves different mechanisms which can store millions of tonnes of CO2 per year in depleted hydrocarbon reservoirs and deep saline aquifers. But their storage capacity is influenced by the presence of different carboxylic compounds in the reservoir. These molecules strongly affect the water wetness of the rock, which has a dramatic impact on storage capacities and containment security. However, precise understanding of how these carboxylic acids influence the rock’s CO2-wettability is lacking. Experiments We thus systematically analysed these relationships as a function of pressure, temperature, storage depth and organic acid concentrations. A particular focus was on identifying organic acid conce
... Show MoreMaximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.
The present work establishes and validates HILIC strategies simple, accurate, exact and precise in pure form and inpharmaceutical dosage for separating and determining theophylline. These methods are developed on HILIC theophyllineseparation in columns ZIC2 and ZIC3. The eluent was prepared by mixing buffer (20% sodium acetate-40 mM, pH 5.5), 80%acetonitrile. The flow rate is 0.8 mL/min, with gradient elution and UV detection at 270 nm. In the ZIC2 and ZIC3 columns oftheophylline determining, the concentration range was 0.01-4μg.ml-1. The lower limit of detection and quantification fortheophylline were determined as 0.130, 0.190 μg.ml-1 and accuracy were 99.70%, 99.58% on ZIC2 and ZIC3, respectively. TheHILIC methods developed and validat
... Show Moreتعد الملابس وسيلة هامة لكل مايقوم به الانسان في حياته العامة ، فهي الانطباع والكلمة الخارجية عن ذاته الداخلية فهي تعكس فكرة الفرد عن ذاته وعن شخصيته , كما تعد وسيلة تعبير جمالية وفنية , فهي تساعد على اخفاء عيوب الجسد وابراز محاسنه . ويتوقف اختيار الفرد لملابسه على مجموعة عوامل منها احتياجه , قدراته المالية , سنه , مركزه الاجتماعي , طبيعة عمله ,الظروف الجوية التي يعيش فيها وعلى مايُؤمن به من قيم و
... Show MoreGas sensors are essential for detecting noxious gases that have a detrimental effect on people's health and welfare. Carbon quantum dots (CQDs) are the fundamental component of gas detectors. CQDs and graphene (Gr) were prepared using the electrochemical method. The gas sensitivity of these materials was evaluated at different temperatures (150, 200, 250 °C) to assess their effectiveness. Subsequently, experiments were conducted at different temperatures to ascertain that the combination of CQDs and Gr, with various percentages of Gr and CQDs, exhibited superior gas sensitization properties compared to CQDs alone. This was evaluated based on criteria such as sensitivity, recovery time, and reaction time. Interestingly, the combination was
... Show MoreThe skin temperature of the earth’s surface is referred to as the Land Surface Temperature (LST). the availability of long-term and high-quality temperature records is important for various uses that affect people’s lives and livelihoods. Much valid information was provided to this research from remote sensing technology by using Landsat 8 (L8) imagery to estimate LST for Al-Ahdab oil field in Wasit city in Iraq. The aim of this research is to analyze LST variations based on Landsat 8 data for 2022 (January, April, July, and October). ArcMap 10.8 was used to estimate LST results. The results values ranged from (about 10 C in January to about 46 C in July). The results show that LS
Tight reservoirs have attracted the interest of the oil industry in recent years according to its significant impact on the global oil product. Several challenges are present when producing from these reservoirs due to its low to extra low permeability and very narrow pore throat radius. Development strategy selection for these reservoirs such as horizontal well placement, hydraulic fracture design, well completion, and smart production program, wellbore stability all need accurate characterizations of geomechanical parameters for these reservoirs. Geomechanical properties, including uniaxial compressive strength (UCS), static Young’s modulus (Es), and Poisson’s ratio (υs), were measured experimentally using both static and dynamic met
... Show MorePlatinum (Pt) supported on sulfated zirconia (SZ) and HY-zeolite as a solid acid catalyst was synthesized successfully for isomerization reaction using precipitation and impregnation method. The physicochemical properties of the catalyst were characterized using various techniques including X-ray diffraction (XRD), Fourier transformation infra-red spectroscopy (FTIR), BET Surface area and pore volume, and Field Emission Scanning Electron Microscopy (FESEM). The prepared composite catalyst Pt/SZ-HY consisted of high Bronsted acidic sites and Lewis acidic sites. The addition of multi-walled carbon nanotubes (MWCNTs) to SZ increased the surface area and pore volume, resulting in smaller crystal sizes and a narrower particle size dist
... Show MoreBackground: The aim of this study was for estimation and comparism of masticatory efficiency in patient wearing heat cured acrylic and flexible base partial denture, finding out the role of peanuts and carrots on the measurement of chewing efficiency, and to find out whether the types of P.D. (being single or two opposing each other) has any effect on the masticatory performance. Materials and methods: Twenty partially edentulous patients were selected. Five of these patients were selected having Kennedy class I with no modification against natural dentition, other 5patients having Cl.I against Cl.I . The other 5 patients having Cl.III against natural dentition and the last 5 patients were with Cl.III against Cl.III. several ways were used
... Show More