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 recent years, there has been a rise in interest in the study of antibiotic occurrence in the aquatic environment due to the negative consequences of prolonged exposure and the potential for bacterial antibiotic resistance. Most antibiotic residues from treated wastewater end up in the aquatic environment as they are not eliminated in facilities that treat wastewater. Antibiotics must be identified in influent and effluent wastewater using reliable analytical techniques for several reasons. Firstly, monitoring antibiotic presence in aquatic environments. Secondly, assessing environmental risks, computing wastewater treatment plant removal efficiencies, and estimating antibiotic consumption. Therefore, this work aims to provide an overview
... Show MoreCopper Zinc Sulphide (Cu0.5Zn0.5S) alloy and thin films were fabricated in a vacuum. Nano crystallized (CZS) film with thick 450±20 nm was deposit at substrates glasses using thermal evaporation technique below ~ 2 × 10− 5 mbar vacuum to investigated the films structural, morphological and optical properties depended on annealing temperatures ( as-deposited, 423, 523 and 623) K for one hour. The influences annealed temperature on structurally besides morphologically characteristics on these films were investigated using XRD and AFM respectively. XRD confirms the formation a mixed hexagonal phase of CuS-ZnS in (102) direction with polycrystalline in nature having very fine crystallites size varying from (5.5-13.09) nm. AFM analys
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Measurement of radon concentration level was carried out in 40 houses in Al – Najaf city during summer season of 2012. Long term measurement of indoor of old building radon concentrations have been taken, using a previously calibrated passive diffusion dosimeters containing CR – 39 solid state nuclear track detectors which are very sensitive for alpha particles. The measurement of the indoor radon concentration obtained in summer in these regions ranged from 11.654±4.216 Bq.m-3 to 53.610±8.777 Bq.m-3. The results were within universally permitted levels. |
<p>Mobility management protocols are very essential in the new research area of Internet of Things (IoT) as the static attributes of nodes are no longer dominant in the current environment. Proxy MIPv6 (PMIPv6) protocol is a network-based mobility management protocol, where the mobility process is relied on the network entities, named, Mobile Access Gateways (MAGs) and Local Mobility Anchor (LMA). PMIPv6 is considered as the most suitable mobility protocol for WSN as it relieves the sensor nodes from participating in the mobility signaling. However, in PMIPv6, a separate signaling is required for each mobile node (MN) registration, which may increase the network signaling overhead and lead to increase the total handoff latency
... Show MoreIn the last few years, the Internet of Things (IoT) is gaining remarkable attention in both academic and industrial worlds. The main goal of the IoT is laying on describing everyday objects with different capabilities in an interconnected fashion to the Internet to share resources and to carry out the assigned tasks. Most of the IoT objects are heterogeneous in terms of the amount of energy, processing ability, memory storage, etc. However, one of the most important challenges facing the IoT networks is the energy-efficient task allocation. An efficient task allocation protocol in the IoT network should ensure the fair and efficient distribution of resources for all objects to collaborate dynamically with limited energy. The canonic
... Show MoreThe liver (hepatic) is one of the largest glands or organs of the digestive system in the body of living organisms, including rodents, take the squirrel in this study for example. The study and the collection of sources emerged to be put into the hands of those, especially those interested in histological studies, including junior or professionals and veterinarians, knowledge of the stains used in the research and their final results.
The purpose of this paper to discriminate between the poetic poems of each poet depending on the characteristics and attribute of the Arabic letters. Four categories used for the Arabic letters, letters frequency have been included in a multidimensional contingency table and each dimension has two or more levels, then contingency coefficient calculated.
The paper sample consists of six poets from different historical ages, and each poet has five poems. The method was programmed using the MATLAB program, the efficiency of the proposed method is 53% for the whole sample, and between 90% and 95% for each poet's poems.
PMMA/TiO2 homogeneous thin films were deposited by using plasma jet system under normal atmospheric pressure and room temperature. PMMA/TiO2 nanocomposite thin film synthesized by plasma polymerization. Titanium oxide was mixed with Methyl Methacrylate Monomer (MMA) with specific weight ratios (1, 3 and 5 grams of TiO2 per 100 ml of MMA). Optical properties of PMMA/TiO2 nanocomposite thin films were characterized by UV-Visible absorption spectra using a double beam UV-Vis-NIR Spectrophotometer. The thin films surface morphological analysis is carried out by employing SEM. The structure analysis are achieved by X-ray diffraction. UV-Visible absorption spectra shows that the increasing the concentration of titanium oxide added to the polym
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XML is being incorporated into the foundation of E-business data applications. This paper addresses the problem of the freeform information that stored in any organization and how XML with using this new approach will make the operation of the search very efficient and time consuming. This paper introduces new solution and methodology that has been developed to capture and manage such unstructured freeform information (multi information) depending on the use of XML schema technologies, neural network idea and object oriented relational database, in order to provide a practical solution for efficiently management multi freeform information system.