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.
ABSTRUCT
This research aims at examining the expected gap between the fact of planning and controlling process of production at the State Company for Electric Industries and implementation of material requirements planning system in fuzzy environment. Developing solutions to bridge the gap is required to provide specific mechanisms subject to the logic of fuzzy rules that will keep pace with demand for increased accuracy and reduced waiting times depending on demand forecast, investment in inventory to reduce costs to a minimum.
The proposed solutions for overcoming the research problem has required some questions reflecting the problem with its multiple dimensions, which ar
... Show MoreMetronidazole-MIPs were prepared by using (MDZ) as the template as well as allylchloride (AYC) or allylbromide (AYB) as monomer, used (TMPTA) tri-methylol propane tri-acrylate or ethylene glycol di-methyl acrylate (EGDMA) as cross-linker and initiator used (BP) benzyl peroxide. By using different plasticizers (di butyl Phthalate (DBPH), Nitrobenzene (NB), oleic acid (OA) and paraffin) for MDZ-MIP1 and (Di-butyl sebecate (DBS), Di-methyl acrylate (DMA), Tributylphosphate(TBP) and Tris(ethylhexyl phosphate (TEHP) ) for MDZ-MIP2. Membranes of MIPs were prepared in PVC matrix. The characterizations of each electrode were determined The Slope range from (55.083 - 43.711) mV/decade, Limit of Detection (8 X 10 -4- 2 X 10-6) and Linearity
... Show MoreFrom 211 urine samples, Gram negative bacteria were isolated from only 61 urine samples with isolation percentage 28.9%. Escherichia coli were isolated percentage 70.49% while Klebsiella pneumoniae and Psendomonas aeruginosa were 8.19% and 6.55%, respectively.Proteus spp. Were isolated from 9 (14.75%), P. mirablis and P. vulgaris were isolates percentage 11.47% and 3.27%, respectively. Uroepithelial Cell Adhesin (UCA) fimbriae expression by P.mirabilis isolates was detected by the high capacity to adhesion to human uroepithetial cells, the isolate p.mirabilis U7 was adhesion to human uroepithelial cells mean no.30.2 bacteria/cell when grown on luria broth at 37C for 24h, but then grown it’s on luria agar at 37C for 24h the adhesion
... Show MoreThe synthesized ligand [4-chloro-5-(N-(5,5-dimethyl-3-oxocyclohex-1-en-1-yl)sulfamoyl)-2-((furan-2-ylmethyl)amino)benzoic acid] (H2L1) was identified utilizing Fourier transform infrared spectroscopy (FT-IR), 1 H, 13 C – NMR, (C.H.N), Mass spectra, UVVis methods based on spectroscopy. To detect mixed ligand complexes, analytical and spectroscopic approaches such as micro-analysis, conductance, UV-Visible, magnetic susceptibility, and FT-IR spectra were utilized. Its mixed ligand complexes [M(L1)(Q)Cl2] [ where M= Co(II), Ni(II) , and Cd(II)] and complexes [Pd(L1)(Q)] and [Pt(L1)(Q)Cl2]; [H2L1] =β-enaminone ligand =L1 and Q= 8-Hydroxyquinoline = L2]. The results showed that the complexes were synthesised utilizing the molar ratio M: L1
... Show MoreEFFECT OF SPRAYING IRON AND ZINC CONCENTRATIONS IN GRAIN AND LEAF CONTENT FOR TWO VARIETIES OF WHEAT CROP
The laboratory experiment was conducted in the laboratories of the Musayyib Bridge Company for Molecular Analyzes in the year 2021-2022 to study the molecular analysis of the inbreed lines and their hybrids F1 to estimate the genetic variation at the level of DNA shown by the selected pure inbreed lines and the resulting hybrids F1 of the flowering gene. Five pure inbreed lines of maize were selected (ZA17WR) Late, ZM74, Late, ZM19, Early ZM49WZ (Zi17WZ, Late, ZM49W3E) and their resulting hybrids, according to the study objective, from fifteen different inbreed lines with flowering time. The five inbreed lines were planted for four seasons (spring and fall 2019) and (spring and fall 2
A simple reverse-phase high performance liquid chromatographic method for the simultaneous analysis (separation and quantification) of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) has been developed and validated. The method was carried out on a NUCLEODUR® 100-5 C18ec column (250 x 4.6 mm, i. d.5μm), with a mobile phase comprising of acetonitrile: deionized water (50: 50 v/v, pH adjusted to 3.6 ±0.05 with acetic acid) at a flow rate 1.5 mL.min-1 and the quantification was achieved at 226 nm. The retention times of FURO, CARB, DIAZ and CARV were found to be 1.90 min, 2.79 min, 5.39 min and 9.56 min respectively. The method was validated in terms of linearity, accuracy, precision, limit of detection and li
... Show MoreCo+2, Ni+2, Cu+2 as well Zn+2 compounds mixed ligand from 8-hydroxyquinoline(8-HQ) also tributylphosphine (PBu3) have been attended at aquatic ethyl alcohol for (1:2:2) (M:8-HQ:PBu3). Produced complexes have been identified by utilizing atomic absorption flame, FT-IR as well UV-Vis spectrum manners also magnetic susceptibility as well as conductivity methods. At addendum antibacterial efficiency from the ligands as well complexes oboist three species about bacteria have been as well examined. Ligands and their complexes show good bacterial efficiencies. Of the gained datum the octahedral geometry was proposed into whole prepared complexes