Coding and enumeration of trees that can be laid upon a hexagon lattice

A tree that can be superimposed upon a hexagon lattice is called a hexagon lattice tree. A method for mechanically coding, enumerating and drawing these objects is described, and has been tested for trees with up to ten vertices. For storage and information transmission, the code uses an expanded version of theN-tuple code in which edge vector elements having one of four possible values are inserted. For establishing uniqueness, it is used in combination with a hexagon lattice reference grid whose vertices are numbered sequentially in the tightest possible outward spiral. Published rules for the derivation ofN-tuple codes by hand are commented on, and a small error pointed out.     

A note on some coefficients of the Chebyshev polynomial form of the characteristic polynomial

The characteristic polynomial of a graph, which traditionally is written down in descending powers ofX can also be expressed in the mathematically equivalent form of a linear combination of the characteristic polynomials of linear chains, and often this expression is a simpler one. Investigation of the first few coefficients reveals that in this form the even ones are of smaller magnitude because they are more closely related to the cyclomatic number of the graph. On the other hand, the early odd coefficients are the same or are more complicated in composition.     

Vesicles accelerate proton transfer from carbon up to 850-fold

[reaction: see text] We have analyzed the different catalytic effects of surfactant aggregates upon the rate-determining hydroxide ion induced deprotonation reaction of 1. Vesicles are more effective catalysts than micelles, most likely providing a more apolar microenvironment at the substrate binding sites. We suggest that this leads to a catalytic reaction involving less strongly hydrated hydroxide ions. In the case of DODAB and DODAC vesicles, binding of cholesterol to the bilayer further increases the catalytic efficiency.     

Synthesis and acid catalyzed hydrolysis of B2,5 type conformationally constrained glucopyranosides: incorporation into a cellobiose analogue

Isopropyl and p-nitrophenyl α- and β-d-glucopyranosides, restrained in a conformation close to B_2,5 via an oxymethylene bridge have been synthesized. These four glucopyranosides were found to be hydrolyzed at similar rates, close to those observed for the parent unconstrained glucosides. In such derivatives, either α or β, the exocyclic cleaved bond is synperiplanar to an endocyclic oxygen lone pair. This conformationally locked glucopyranosyl moiety was also incorporated into a disaccharide, affording a conformationally restrained cellobiose analogue which was assayed against various glycosidases.     

Neutron diffraction experiments on CsCrI3 at 300, 77, and 1.2°K: H. W. Zandbergen and D. J. W. Ijdo. Gorlaeus Laboratories,University of Leiden,P.O. Box 9502, 2300 RA Leiden,The Netherlands

The orthorhombic α-PbO₂ phase of FeNbO₄ was prepared and its photoelectronic properties measured: Sintered disks were shown to be n type and gave a resistivity of 40 Ω-cm. Measurements of the photoresponse gave a flat-band potential between 0.1 and 0.4 V vs SCE at a pH of 8.5 and an optical band gap of 2.08(2) eV. Several higher-energy band gaps at 2.68(2), 2.94(2), 3.24(2), and 4.38(2) eV were also determined. There appears to be an enhancement of the quantum efficiency due to the presence of [FeO₆] active centers while retaining the fundamental characteristics of the [NbO₆] octahedra.     

Filtering in Legendre spectral methods

We discuss the impact of modal filtering in Legendre spectral methods, both on accuracy and stability. For the former, we derive sufficient conditions on the filter to recover high order accuracy away from points of discontinuity. Computational results confirm that less strict necessary conditions appear to be adequate. We proceed to discuss a instability mechanism in polynomial spectral methods and prove that filtering suffices to ensure stability. The results are illustrated by computational experiments.