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Direct and inverse source problems for degenerate parabolic equations
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Abstract<p>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.</p>
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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Environmental Engineering And Science
Fenton-like degradation of direct blue dye using green synthesised Fe/Cu bimetallic nanoparticles
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This study relates to synthesis of bentonite-supported iron/copper nanoparticles through the biosynthesis method using eucalyptus plant leaf extract, which were then named E-Fe/Cu@B-NPs. The synthesised E-Fe/Cu@B-NPs were examined by a set of experiments involving a heterogeneous Fenton-like process that removed direct blue 15 (DB15) dye from wastewater. The resultant E-Fe/Cu@B-NPs were characterised by scanning electron microscopy, Brunauer–Emmet–Teller analysis, zeta potential analysis, Fourier transform infrared spectroscopy and atomic force microscopy. The operating parameters in batch experiments were optimised using Box–Behnken design. These parameters were pH, hydrogen peroxide (H2O2

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Publication Date
Thu Sep 15 2022
Journal Name
Journal Of Baghdad College Of Dentistry
12- months color stability of direct resin composite veneers in anterior teeth: Clinical trial
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Background: This clinical trial aims to evaluate the color changes of direct resin composite veneer (DCV) restorations based on spectrophotometric analysis of 4 different types of resin composites between the baseline immediately after polishing and after one year of follow-up. Materials and methods: 28 patients were assessed for eligibility for participation, aged between 18 and 38 years old, who indicated for DCV restorations in anterior maxillary teeth were considered for participation in this study. In total, 25 patients who met the inclusion criteria were selected (6 males and 19 females, mean age: 20.9 at the time of restoration placement), and 3 patients were excluded. Partic

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Publication Date
Sun Jun 01 2014
Journal Name
Journal Of Economics And Administrative Sciences
Estimation the reliability function of multi state system by using Direct Partial Logic Derivative
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In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

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Publication Date
Thu Jul 01 2021
The spontaneous emission performance of a quantum emitter coupled to a hybrid plasmonic waveguide with specified output polarization for on-chip plasmonic single-photon source
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Publication Date
Tue May 11 2021
Journal Name
Photonics And Nanostructures - Fundamentals And Applications
The spontaneous emission performance of a quantum emitter coupled to a hybrid plasmonic waveguide with specified output polarization for on-chip plasmonic single-photon source
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Nowadays, most of the on-chip plasmonic single-photon sources emit an unpolarized stream of single photons that demand a subsequent polarizer stage in a practical quantum cryptography system. In this paper, we numerically demonstrated the coupling of the light emitted from a quantum emitter (QE) at 700 nm wavelength to the propagation mode supported by an on-chip hybrid plasmonic waveguide (HPW) polarization rotator. Our results proved that the light emitted is linearly polarized at 0º, 45º/−45º, and 90º with propagation lengths of 5 μm, 3.3 μm, and 3.9 μm, respectively. Moreover, high power-conversion efficiency was obtained from an applied transverse magnetic (TM) mode (0º-polarization) to a transverse electric (TE) (90º-polari

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Publication Date
Wed Mar 30 2022
Journal Name
Journal Of Educational And Psychological Researches
Analyzing the content of the two science books (the two chemistry units) for the intermediate stage according to environmental problems
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    The main goal of the current research is to know -Environmental problems included in the content of the two science books (chemistry units) for intermediate stage

A list of environmental problems had been prepared  and  consisting of (8) main areas which are (air and atmosphere pollution, water pollution, soil pollution, energy, disturbance of biodiversity and environmental balance, waste management, food and medicinal pollution, investment of mineral wealth). Of which (60) sub-problems,  at that time the researcher analyzed the two science books (two chemistry units) for the intermediate stage of the academic year (2020-2021) in light of the list that was prepared, and the validity and consisten

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Publication Date
Thu Jan 01 2015
Journal Name
Journal Of Natural Sciences Research
Isolation and Characterization of Lignin from Iraqi Date Palm Phoenix Dactylifera L. Frond Bases as a Good and Cheap Source of Lignin‏
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Publication Date
Sat Jan 15 2011
Journal Name
International Journal Of Poultry Science
Influence of Source of Oil Added to Diet on Egg Quality Traits of Laying Quail
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This experiment was performed to investigate the influence of different oils in the diets of laying quail on their egg quality characteristics. One hundred and twenty 7-wk old Japanese quails (Coturnix coturnix japonica) were allocated to four groups with three replicates containing 10 quail each (30 quail per each treatment group). They were fed for 13 weeks (including one week of adaptation period) on diets containing 3% oil from different sources, viz. either sunflower (T1), linseed (T2), maize (T3), or fish oil (T4). Inclusion the diet of laying quail with fish oil (T4) and maize oil (T2) resulted in significant increase with respect to egg weight, yolk weight, albumen weight, yolk diameter, yolk height, albumen diameter, albumen height

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Publication Date
Thu Jan 24 2019
Journal Name
Journal Of Education College Wasit University
“They’ve damaged your uniqueness”: Technology as a Source of Dystopia in Caryl Churchill’s A Number
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This study focuses on the impact of technology on creating a dystopian world as presented by the English playwright Caryl Churchill in her play A Number (2002). This dramatic work came as a reaction to the most crucial and valuable turning point in the scientific achievements of human engineering, namely, the cloning of the sheep called Dolly. Therefore, A Number is a play that presents an analytical stage for imagining the biotechnological and scientific future. This dramatic vignette captures the playwright’s fears towards the abnormal progress of technology and science and how far such technological progress affects human relationships and identity. It also portrays how technological progress results in the feeling of a lack of

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Publication Date
Wed Sep 17 2014
Journal Name
African Journal Of Microbiology Research
Xylanase production using fruit waste as cost effective carbon source from thermo-tolerant Bacillus megaterium
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