On the invertibility of differential operators of the second order

We present sufficient conditions for the invertibility of a second-order differential operator with variable coefficients in the space L_p.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 411–413, March, 1995.This paper was partially supported by the International Science Foundation, Grant No. ZA000.     

Assessment of Subgrid-Scale Models for Decaying Compressible MHD Turbulence

Large eddy simulation method is formulated for study of compressible magnetohydrodynamic turbulence and assessment of different subgrid-scale models as applied for decaying case is performed. The filtered equations of compressible magnetopause using the mass-weighted filtering operation are obtained. Mass-weighted filtered equations for large-scale turbulent component comprise subgrid-scale terms and five models for closure of the subgrid-scale terms are suggested. In present paper the obtained results of numerical computations for large eddy simulation are compared with the results of direct numerical simulation of three-dimensional compressible magnetohydrodynamic turbulence. Assessment of five subgrid-scale models of large eddy simulation for MHD flows is fulfilled. The comparisons between large eddy simulation and direct numerical simulation are carried out regarding the temporal evolution of the global quantities kinetic and magnetic energy, cross helicity and the spectra of kinetic and magnetic energy.     

Excitons in heteroepitaxial CdSe/CdS structures

X-ray diffractometry and low-temperature exciton spectroscopy are used to study heteroepitaxial CdSe/CdS layers grown at temperatures of 350–485 °C by MOCVD. The high-temperature samples are found to display the exciton and x-ray diffraction spectra characteristic of hexagonal Wurtzite (W) structures, while the low-temperature samples display the features characteristic of the cubic structure of sphalerite (ZB). A number of the samples have x-ray spectra characteristic of structures with stacking faults (SF), which represent a separate crystalline phase in the structures studied here. It is found that the individual crystalline phases are spatially separated. Fiz. Tverd. Tela (St. Petersburg) 40, 887–889 (May 1998)     

Platinum nanoparticles generated in functionality-enhanced reaction media based on polyoctadecylsiloxane with long-chain functional modifiers

Functionality-enhanced nanostructured matrices generated by intercalating polyoctadecylsiloxane (PODS) with octadecene (ODC) or octadecylamine (ODA) are employed as reaction media in which to grow Pt nanoparticles. Small-angle X-ray scattering (SAXS) signatures confirm that the amphiphilic PODS matrix orders into lamellae with a periodicity (d) of 5.24 nm, which corresponds to the siloxy bilayer and a double layer of alkyl tails. The regular packing of the hydrophobic tails becomes distorted upon introduction of ODC or ODA. Incorporation of K[(C2H4)PtCl3].H2O (a Zeise salt) into the PODS/ODC matrix, followed by reduction of the Pt ions by NaBH4 or H2, results in the localization of Pt compounds and nanoparticles along the siloxy bilayers, which remain dimensionally unchanged. Electron density profiles deduced from PODS/ODA, however, provide evidence for considerable structural reorganization upon metalation with H2PtCl6.6H2O. In this case, the siloxy bilayers broaden due to the presence of PtCl62- ions, and the hydrophobic layers become distorted due to the formation of (PtCl62-)(ODAH+)2 complexes. Subsequent reduction by NaBH4 restores the inherent PODS organization, while H2 reduction partially preserves the distorted matrix, indicating that some Pt nanoparticles form in close proximity to the siloxy bilayer. Transmission electron microscopy reveals that relatively monodisperse Pt nanoparticles measuring approximately 1 nm in diameter are located along the siloxy bilayers, whereas anomalous SAXS further indicates that nanoparticles form aggregates of comparable size to d within the PODS double layers.     

Raman Structural Study of Copolymers of Propylene with Ethylene and High Olefins

Nascent form of random copolymers of propylene with ethylene, 1-butene, 1-hexene, 1-octene, and 4-methyl-1-pentene was studied by Raman spectroscopy. The most significant spectral alterations with a change in propylene content were observed in two lines at 809 and 841 cm⁻¹. The first line corresponds to vibrations of polypropylene helical chains in the crystalline phase, while the second one is associated with vibrations of polypropylene helical chains having isomeric defects. Raman data confirm that conformational composition and phase state of copolymer macromolecules strongly depend on the comonomer content as well as on the size of the comonomer units.     

Homologous series of novel adamantane–colchicine conjugates: synthesis and cytotoxic effect on human cancer cells

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