Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

A supramolecular hydrogen‐bonded complex between 1,3,5‐tris(diisobutylhydroxysilyl)benzene and trans‐bis(4‐pyridyl)ethylene

The trisilanol 1,3,5‐(HOi‐Bu₂Si)₃C₆H₃ ( 7 ), prepared in three steps from 1,3,5‐tribromobenzene via the intermediates 1,3,5‐(Hi‐Bu₂Si)₃C₆H₃ ( 8 ) and 1,3,5‐(Cli‐Bu₂Si)₃C₆H₃ ( 9 ) forms an equimolar complex with trans‐bis(4‐pyridyl)ethylene (bpe), 7 ·bpe, whose structure was investigated by X‐ray crystallography. The hydrogen‐bonded network features a number of SiO? H(H)Si and SiO? H hydrogen bridges. Evidence was found for cooperative strengthening within the sequential hydrogen bonds. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling of a city canyon problem in a turbulent atmosphere using an equivalent sources approach

The sound propagation into a courtyard shielded from direct exposure is predicted using an equivalent sources approach. The problem is simplified into that of a two-dimensional city canyon. A set of equivalent sources are used to couple the free half-space above the canyon to the cavity inside the canyon. Atmospheric turbulence causes an increase in the expected value of the sound pressure level compared to a homogeneous case. The level increase is estimated using a von Kármán turbulence model and the mutual coherences of all equivalent sources' contributions. For low frequencies the increase is negligible, but at 1.6 kHz it reaches 2-5 dB for the geometries and turbulence parameters used here. A comparison with a ray-based model shows reasonably good agreement.     

Cover Picture

The cover picture shows in the background the whole cell of a methanotrophic bacterium on which are superimposed components of methane monooxygenase (the structure of the hydroxylase component (top), one of the two four-helix bundles that house the catalytic diiron centers (left)) and a schematic diagram of the catalytic cycle by which the enzyme converts dioxygen and methane into methanol and water. More about this unusual enzyme system is reported by Lippard et al. on p. 2782 ff.     

Structural changes by sulfoxidation of phenothiazine drugs

Summary The side-chain conformations of psychoactive phenothiazine drugs in crystals are different from those of biologically inactive ring sulfoxide metabolites. This study examines the potential energies, molecular conformations and electrostatic potentials in chlorpromazine, levomepromazine (methotrimeprazine), their sulfoxide metabolites and methoxypromazine. The purpose of the study was to examine the significance of the different crystal conformations of active and inactive phenothiazine derivatives, and to determine why phenothiazine drugs lose most of their biological activity by sulfoxidation. Quantum mechanics and molecular mechanics calculations demonstrated that conformations with the side chain folded over the ring structure had lowest potential energy in vacuo, both in the drugs and in the sulfoxide metabolites. In the sulfoxides, side chain conformations corresponding to the crystal structure of chlorpromazine sulfoxide were characterized by stronger negative electrostatic potentials around the ring system than in the parent drugs. This may weaken the electrostatic interaction of sulfoxide metabolites with negatively charged domains in dopamine receptors, and cause the sulfoxides to be virtually inactive in dopamine receptor binding and related pharmacological tests.     

Bildung und Kristallstruktur eines dimeren sauerstoffverbrückten Titanaminobisphenoxides

Formation and Crystal Structure of an Oxygen Bridged Titanium Amino Bisphenoxide Di‐(μ‐oxo)‐titan‐bis[aminobisphenoxide] ( 3 ) was obtained by reaction of (i‐Prop)₂TiL* ( 2 ) {L* = O‐4, 6‐(t‐Bu)₂C₆H₂‐2‐CH₂‐[1, 4‐N₂C₅H₁₀]‐2'‐CH₂‐4', 6'‐(t‐Bu)₂C₆H₂O] with water in a molar ratio 1:1 in diethylether. Both i‐Propyl moieties are substituted yielding the dimeric oxygen bridged amino bisphenoxide complex. The six coordinate Ti atoms are a result of Ti—N and Ti—O interactions of the corresponding atoms of the amino bisphenoxide ligand and the bridging O atoms. The central planar Ti₂O₂ ring may be considered as the general structural feature of the title compound: Space group P1¯, Z = 1, lattice dimensions at —60°C: a = 11.6899(4), b = 11.7873(4), c = 12.6462(4) Å, α = 98.070(1), β = 99.660(1), γ = 95.343(1)°, R₁ = 0.0469, wR₂ = 0.1049, GooF = 0.939.