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 paper deals with the language of Russian folklore. Folklore is a unique sphere of existence of the language, the most vivid expression of the national mentality. The folklore word embodied the perception and evaluation of the surrounding world. “What did the word in general mean for the life of the people? The word was equated ... with life itself. The word generated and explained life, it was ... the keeper of memory and the guarantee of the infinity of the future. The folklore text is studied by literary critics, ethnographers, historians, culturologists, and art historians. In the twentieth century, a new science emerged - linguo-folkloristics, the goals and objectives of which were formulated by A.T. Khrolenko only in the seven
... Show MoreThe current study was conducted with an aim to know the effect of adding different concentrations of pomegranate peels alcoholic extract (PPAE) on the traits of Awassi ram semen stored at 5°C. Eight ejaculations from three Awassi rams were collected, mixed and diluted with TRIS extender. The semen samples were divided into four equal parts, and then the alcoholic extract of pomegranate peels was added at concentrations of 0, 100, 200 and 300 mg/ 1 ml of extender, which represented each of the treatments C, T1, T2 and T3, respectively. The samples were stored at 5 ° C and semen examinations were performed during periods 0, 24, 48, 72 and 96 hours after collection. Semen traits included calculation percentage of individual motility, viabili
... Show MoreIrinotecan (CPT-11) is a semisynthetic derivative of the antineoplastic agent camptothecin used in a wide range as an anti-cancer agent in many solid tumors because of its cytotoxic effect through the interaction with the topoisomerase I enzyme. The major limiting factors for irinotecan treatment are its association with potentially life-threatening toxicities including neutropenia and acute or delayed-type diarrhea, results from distinct interindividual and interethnic variability due to gene polymorphism.
This is a cross sectional pharmacogentics study was conducted on 25 cancer patients to estimate the prevalence of UGT1A1*93 and ABCC5 allele single nucleotide polymorphism (SNP) in Iraqi cancer patients treated with irinotecan
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The aim of the research is to identify the effect of using the self-questioning strategy on the achievement of fourth-grade students in science and the development of their reflective thinking in physics in the city of Baghdad. The research sample was divided into two groups: an experimental group of (20) students and a control group of (20) students. The researchers developed two tools: a test of (40) multiple-choice questions. The second tool is a test to measure the reflective thinking skills of fourth-grade students. It consists of (25) multiple-choice questions distributed on skills as follow: reflection and observation, detection of inaccuracies, reaching conclusions, giving clear explanations, an
... Show MoreAbstract: The aim of this study was to evaluate the effect of bone density value in Hounsfield unit derived from cone beam computed tomography (CBCT), and implant dimensions in relation to implant stability parameters namely the resonance frequency analysis and the insertion torque (IT) value. It included 24 patients who received 42 dental implants (DI). The bone density of the planned implant site was preoperatively measured using cone beam computed tomography. The implant stability was measured using Osstell implant stability quotient (ISQ). The ISQ values were recorded immediately postoperatively and after 16 weeks. The IT value was categorized as 35 N/cm or > 35 N/cm. The mean (standard deviation) primary stability was 79.58 (5.27) ISQ,
... Show MoreElectronic banking services appeared as a result of laying the foundations for the application of electronic automation in the banking field, and despite the clear expansion in its adoption and implementation as an inevitable necessity imposed by international and national developments, its application was not ideal according to the level that was expected to occur after the abandonment of traditional banking services, which produced some risks Which is evident in the absence of a legal system, whether at the level of proving and authoritative electronic banking services such as electronic signature, Or at the level of protecting the confidentiality of these services and ensuring that they are not exp
... Show MoreThe ring modulator described in part I of this paper is designed here for two operating wavelengths 1550nm and 1310nm. For each wavelength, three structures are designed corresponding to three values of polymer slot widths (40, 50 and 60nm). The performance of these modulators are simulated using COMSOL software (version 4.3b) and the results are discussed and compared with theoretical predictions. The performance of intensity modulation/direct detection short range and long rang optical communication systems incorporating the designed modulators is simulated for 40 and 100Gb/s data rates using Optisystem software (version 12). The results reveal that an average energy per bit as low as 0.05fJ can be obtained when the 1550nm modulator is d
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