Chirality due to deuterium substitution: synthesis and circular dichroism of (+)(R) p -2,7-dideuterio-1,6-methano[10]annulene

Summary The title compound was prepared from (–)(S) _p -2,7-dibromo-1,6-methano[10]annulene by treatment withn-Bu-Li and subsequent quenching with D₂O. The optical rotations at four wavelengths and the circular dichroism spectrum are reported.

---

Chiralität durch Deuterium-Substitution: Synthese und Circulardichroismus von (+)(R) _p -2,7-Dideuterio-1,6-methano[10]annulen (Kurze Mitt.)

Zusammenfassung Die Titelverbindung wurde aus (–)(S) _p -2,7-Dibrom-1,6-methano[10]annulen durch Umsetzung mitn-Bu-Li und nachfolgende Reaktion mit D₂O dargestellt. Optische Rotationen bei vier Wellenlängen und das Circulardichroismus-Spektrum wurden bestimmt.

     

Raman spectra and structure of multicomponent oxide planar waveguides prepared by sol-gel

This work was aimed at understanding the structure of SiO₂–MO₂ (M = Ti, Zr, Hf) and SiO₂–HfO₂–MO₂ (M = Ti, Zr) materials, used as mixed oxide glass hosts for Er³⁺ ions in the fabrication of optical planar waveguides by sol-gel processing. This structural study was performed by Waveguide Raman Spectroscopy (WRS), complemented with X-ray diffraction (XRD). The admixture of TiO₂ to HfO₂, SiO₂–HfO₂ and HfO₂–ZrO₂ compositions was found to cause precipitation of nanocrystals of tetragonal HfO₂ or ZrO₂, or the formation of hafnia-titania mixed crystals, depending on the HfO₂/TiO₂ molar ratio.     

Improved square coloring of planar graphs

Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that $\frac{3}{2}\mathrm{\Delta }+1$ colors are sufficient to square color every planar graph of maximum degree Δ. This conjecture has been proven asymptotically for graphs with large maximum degree. We consider here planar graphs with small maximum degree and show that $2\mathrm{\Delta }+7$ colors are sufficient, which improves the best known bounds when $6?\mathrm{\Delta }?31$.     

The sloshing of stratified liquid in a two-dimensional rectangular tank

The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects...     

An anti‐diffusive volume of fluid method for interfacial fluid flows

A volume of fluid (VOF) method is developed combining a first‐order limited downwind scheme with higher order accurate schemes. The method is characterized by retaining a sharp fluid interface and a reduction in numerical diffusion near the interface, but avoids complicated geometrical reconstruction as occurs in most volume tracing algorithms. To demonstrate the accuracy and robustness of the method, a selection of numerical experiments are presented involving a pure advection problem, a water wave impact caused by a dam breaking and liquid sloshing in a partially filled tank. Copyright © 2011 John Wiley & Sons, Ltd.     

Vertex partitions of (C3,C4,C6)-free planar graphs

A graph is $(k_1,k_2)$-colorable if it admits a vertex partition into a graph with maximum degree at most $k_1$ and a graph with maximum degree at most $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is $(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-free planar graph is $(0,3)$-colorable is NP-complete.