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.
Carbon nanotubes were prepared by an arc-discharge method,
under different values of pressure of oxygen gas. The structure of
multi-walled carbon nanotubes powders has been characterized by
low-angle X-ray diffraction .The morphology of carbon nanotube
powder was examined by transmission electron microscope. The
capacitance-voltage and current- voltage (dark and illumination
current) characterization were measured under different values of
pressure (10-3, 10-4, 10-5) mbar of oxygen gas
Olanzapine (OLZ) is classified as a typical antipsychotic drug utilized for the treatment of schizophrenia. Its oral bioavailability is 60% due to its low solubility and pre-systemic metabolism. Hence, the present work aims to formulate and evaluate OLZ nanoparticles dissolving microneedles (MNs) for transdermal delivery to overcome the problems associated with drug administration orally. OLZ nanoparticles were prepared by the nanoprecipitation method. The optimized OLZ nanoparticle formula was utilized for the fabrication of dissolving MNs by loading OLZ nanodispersion into polydimethylsiloxane (PDMS) micromould cavities, followed by casting the polymeric solution of polyvinylpyrrolidone(PVP-K30) and polyvinyl alcohol (PVA) to form
... Show MoreIn the current worldwide health crisis produced by coronavirus disease (COVID-19), researchers and medical specialists began looking for new ways to tackle the epidemic. According to recent studies, Machine Learning (ML) has been effectively deployed in the health sector. Medical imaging sources (radiography and computed tomography) have aided in the development of artificial intelligence(AI) strategies to tackle the coronavirus outbreak. As a result, a classical machine learning approach for coronavirus detection from Computerized Tomography (CT) images was developed. In this study, the convolutional neural network (CNN) model for feature extraction and support vector machine (SVM) for the classification of axial
... Show MoreThe necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
... Show MoreMesoporous silica (MPS) nanoparticle was prepared as carriers for drug delivery systems by sol–gel method from sodium silicate as inexpensive precursor of silica and Cocamidopropyl betaine (CABP) as template. The silica particles were characterized by SEM, TEM, AFM, XRD, and N2adsorption–desorption isotherms. The results show that the MPS particle in the nanorange (40-80 nm ) with average diameter equal to 62.15 nm has rods particle morphology, specific surface area is 1096.122 m2/g, pore volume 0.900 cm3/g, with average pore diameter 2.902 nm, which can serve as efficient carriers for drugs. The adsorption kinetic of Ciprofloxacin (CIP) drug was studied and the data were analyzed and found to match well with
... Show MoreIn the present work, Uranium (238U), Thorium (232Th) and Potassium (40K) specific activity concentration in (Bq/kg) was measured in five different types for wheat flours that are available in the Iraqi markets. The gamma spectrometry method with an NaI (Tl) detector has been used for radiometric measurements. Calculations of radium equivalent activity, annual effective dose equivalent, external hazard index (Hex), internal hazard index (Hin), representing gamma index and gamma dose rate in all flour samples were 17.98132 Bq/kg, 0.0100334, 0.04502, 0.04857, 0.06872, 0.125883 and 8.181244 respectively. It is found that the average of specific activity concentration of wheat flour sam
... Show MoreSnS has been widely used in photoelectric devices due to its special band gap of 1.2-1.5 eV. Here, we reported on the fabrication of SnS nanosheets and the effect of synthesis condition together with heat treatment on its physical properties. The obtained band gap of the SnS nanosheets is in the rage of 1.37-1.41 eV. It was found that the photo-current density of a thin film comprised of SnS nanosheets could be enhanced significantly by annealing treatment. The maximum photo-current density of the stack structure of FTO/SnS/CdS/Pt was high as 389.5 mu A cm(-2), rendering its potential application in high efficiency solar hydrogen production.