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.
A single step extraction-cleanup procedure using porous membrane-protected micro-solid phase extraction (μ-SPE) in conjunction with liquid chromatography–tandem mass spectrometry for the extraction and determination of aflatoxins (AFs) B1, B2, G1 and G2 from food was successfully developed. After the extraction, AFs were desorbed from the μ-SPE device by ultrasonication using acetonitrile. The optimum extraction conditions were: sorbent material, C8; sorbent mass, 20 mg; extraction time, 90 min; stirring speed, 1000 rpm; sample volume, 10 mL; desorption solvent, acetonitrile; solvent volume, 350 μL and ultrasonication period, 25 min without salt addition. Under the optimum conditions, enrichment factor of 11, 9, 9 and 10 for AFG2, AFG1
... Show MoreThe osseodensification (OD) drilling technique was suggested as an alveolar ridge expansion technique, so the aim of this prospective clinical study was to evaluate the amount of bone expansion obtained by the OD drilling technique and its effect on implant stability in patients with narrow alveolar ridges. The width of the alveolar ridge was measured at the crest before and after implant site preparation, whereas the implant stability was measured using Osstell Beacon implant stability quotient (ISQ). The ISQ values were recorded immediately postoperatively and after 16 weeks. Twenty-three patients were included; they received 40 implants. The mean (± standard deviation [SD]) amount of expansion was 1.29 (± 0.41) mm, and the difference b
... Show MoreFlexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec
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تعد الانتخابات بمثابة الطريق المؤدي إلى الديمقراطية كونها النمط الأكثر شيوعاً لمشاركة المواطنين في الحياة السياسية للبلدان واختيار ممثليهم في المجالس التشريعية، حيث أن مطلب إجراء انتخابات حرة ونزيهة لم يعد مطلباً داخلياً فحسب بل مطلباً دولياً يصرّ المجتمع الدولي على الوفاء به وهذا يلقي على عاتق كل دولة أن تضع من الضمانات ما يكفل ممارسة هذه الانتخابات ب
... Show MoreDespite the importance of sustainable development and its dimensions in developing performance and supporting competitive advantage in economic units, there is a gap and lack of coordination between Combined Assurance providers (management, internal audit, external audit) to report on sustainable development, and the research aims to propose a model for the Combined Assurance report to achieve development sustainable development in the Iraqi economic units, especially the Baghdad Municipality, enables assurance providers to coordinate efforts that lead to the achievement of Combined Assurance, The research found the proposed model for the Combined Assurance report in achieving sustainable development in the Iraqi economic units, es
... Show MoreRepresent a topic occupational safety and health management is one of the priorities of the loading organization in the business environment ,and one of the requirement for the success and its impact on the productivity of workers and their performance in an appropriate working environment .The international responses to the problems that accompany the technological and industrial development of the business environment are the issuance of ISO 45001:2018 aimed at providing an appropriate framework for controlling risks , reducing injuries and work accidents and improving work performance ,after realizing the environmental relationship between safe and sound work with competition .The search’s issue is represented with the exist
... Show MoreGroundwater is an important resource that can be used for various purposes. Various factors can change the chemistry of the GW, such as the chemical composition of an aquifer as well as the leaching of human waste into groundwater. The study area is a barren land covered by some sabkhas, in addition to some agricultural fields. The study aims to assess groundwater quality for drinking purposes using the Water Quality Index. The groundwater is chemically heterogeneous and has a wide quality range from very poor to excellent. Evaporation appears to be the controlling factor among the other shallow waters, while relatively deep water is related to rock-soil dominance. Rocks, land use and land cover have helped control the groundwater q
... Show MoreThe rubber ropes exercises affected muscle groups, which in turn affects the corners of the conditions of the body before and over the barrier where affected the time passed. To change the angle of the approaching and payment impact on passing each times the barrier 1-5. That passed over the barrier 1and gate 5 impacts on the nature of the achievement, where time has become less. Find the values of cruise missiles and other phases and stages of pitch angle other categories which it enshrines stood as compelling rejection men's 110m hurdles. Find the value of the instant messaging distances between different barriers and stages. Studies by adding rubber sling barriers race categories, measurement of kinematic variables. Emphasis on the devel
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