Asymptotic regularity of solutions to Hartree–Fock equations with Coulomb potential

We study the asymptotic regularity of solutions to Hartree–Fock (HF) equations for Coulomb systems. To deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo‐differential operators on conical manifolds. First, the non‐self‐consistent‐field case is considered, which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator, which guarantee ellipticity for the local part of the Fock operator on the open stretched cone ?₊ × S². This proves the existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed‐point approach based on Cancès and Le Bris analysis of the level‐shifting algorithm, we show via another bootstrap argument that the corresponding self‐consistent‐field solutions to the HF equation have the same type of asymptotic regularity. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis of the selective antimuscarinic agent 4-{[cyclohexylhydroxy(2-methoxyphenyl)silyl]-methyl}-1,1-dimethylpiperazinium methyl sulfate (o-methoxy-sila-hexocyclium methyl sulfate)

The synthesis of the potent and highly selective silicon-containing antimuscarinic agent o-methoxysila-hexocyclium methyl sulfate and its corresponding tertiary amine (isolated as the dihydrochloride) is described. The quarternary compound is an o-methoxy derivative of sila-hexocyclium methyl sulfate, which represents one of the tools currently used in experimental pharmacology for the subclassification of muscarinic receptors. The o-methoxy derivative, the pharmacological profile of which differs substantially from that of the nonmethoxy compound, is also recommended as a tool for the investigation of muscarinic receptor heterogeneity.     

Über ein Problem der Diffusion im Schwerefelde

Zeitschrift für Physik A Hadrons and nuclei - Berechnung der Dichteverteilung als Funktion der Höhe und der Zeit in einer Lösung endlicher Höhe unter der Wirkung von Schwere und...     

Investigation on ignition behaviors of pulverized coal particles in a tubular swirl burner

This paper intensively investigated the ignition of turbulent coal flames in a novel fully-mixed tubular swirl burner. The Nikon D300s digital camera was used to capture the statistical ignition behavior of dispersed coal particle streams in different ambiences. Meanwhile, the combustion dynamics of individual coal particles were also recorded by means of high-speed photography. Two low-rank coal samples, Hulunbel lignite and Zhundong coal, were tested in this study. The ignition delay times of coal particles in the swirl burner were compared with those in a flat-flame burner. In contrast to previous work on a laminar flat-flame burner, the current experimental results show that the turbulent ambience significantly enhances the ignition of all coal samples, which is exceptionally pronounced under high temperature and low oxygen conditions. In addition, the sensitivity analysis suggests that both the enhanced heat and mass transfer contribute to the early ignition in turbulence. The effect of elevated mass transfer coefficient turns prominent in low oxygen fraction ambience, wherein the volatile barrier effect is suppressed by the enhanced mixing process. The combined effect of turbulence favors the shifting of ignition modes to the heterogeneous-dominant region. Last but not least, the ceased volatile flame that visualized in turbulent low oxygen ambience further confirms the important role of heterogeneous ignition.     

Molecular structure and fracture properties of ZrO<Subscript>X</Subscript>/Epoxysilane hybrid films

The mechanical reliability of hybrid films depends critically on their fracture properties which are controlled largely by the film composition and molecular structure. We have investigated the adhesive and cohesive fracture properties of hybrid films processed from 3-glycidoxypropyltrimethoxysilane (GPTMS) and tetra n-propoxyzirconium (TPOZ), for which the roles of molecular structure and composition have not been well established. The influences of film Zr/GPTMS ratio, silane crosslinking, and substrate composition on fracture resistance were quantified in terms of the critical strain energy release rate, G_C Film fracture energy was found to increase, then decrease with increasing Zr/GPTMS ratio. Removal of the epoxy rings of GPTMS from the film was found to drastically decrease the cohesive fracture energy of the film as well as the adhesive fracture energy of the film/epoxy interface. Finally, films deposited on silicon had much higher fracture energies compared to those deposited onto aluminum and titanium from identical sols. FTIR, XPS, and AFM were used to characterize the film structure and fracture surfaces. The molecular-scale mechanisms responsible for the observed trends are discussed. These results provide new insights into the interaction between the substrate chemistry, molecular structure, and mechanical reliability of hybrid sol-gel films.     

Abzählbar erkennbare gruppentheoretische Eigenschaften

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