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.
This research aims to study the methods of reduction of dimensions that overcome the problem curse of dimensionality when traditional methods fail to provide a good estimation of the parameters So this problem must be dealt with directly . Two methods were used to solve the problem of high dimensional data, The first method is the non-classical method Slice inverse regression ( SIR ) method and the proposed weight standard Sir (WSIR) method and principal components (PCA) which is the general method used in reducing dimensions, (SIR ) and (PCA) is based on the work of linear combinations of a subset of the original explanatory variables, which may suffer from the problem of heterogeneity and the problem of linear
... Show MoreThis 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
... Show MoreIn 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
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
... Show MoreNowadays, 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
... Show MoreThe current study was conducted to find out the effect of the sediment source (sedimentary of Iraqi-Iranian borderline and Tigris River) on the content and distribution of feldspar minerals and their effect on the optical properties of these minerals in some soils of Wasit and Maysan province. Eight pedons were chosen to represent the study area, five of them represented sediments coming from the borderline, which included pedons of (Badra, Taj Al-Din, Al-Shihabi, Jassan, and Galat), while two of them represent the sediments of the Tigris River (Essaouira, Al-Dabouni). Finally, the pedon of Ali Al-Gharbi represented the mixing area of sediments of all the torrents coming from borderline and the sediments of the Tigris River. The diagnostic
... Show MoreA program using Mont Carlo techniques has been written to calculate the effective solid angle of the detection system and simulate the response of the HPGe to mono-energetic protons from an extend source. It has been found that the fraction of the protons which leave through the cylindrical surface and deposit only part of their kinetic energy in the crystal increases with proton energy and the consequent increase in their range.
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
... Show MoreThis 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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