Twists of genus three curves over finite fields

In this article we recall how to describe the twists of a curve over a finite field and we show how to compute the number of rational points on such a twist by methods of linear algebra. We illustrate this in the case of plane quartic curves with at least 16 automorphisms. In particular we treat the twists of the Dyck–Fermat and Klein quartics. Our methods show how in special cases non-Abelian cohomology can be explicitly computed. They also show how questions which appear difficult from a function field perspective can be resolved by using the theory of the Jacobian variety.     

Copper(0) in the Ullmann heterocycle-aryl ether synthesis of 4-phenoxypyridine using multimode microwave heating

The action of nanoparticulate copper catalysts with a mean particle size of 10 nm in the Ullmann ether synthesis is reported using multimode microwave heating and employing stable chloropyridine salts and unactivated phenol, with stabilized copper nanoparticles outperforming other copper catalysts in terms of stability and reusability.     

Stibatriptycene

Stibatriptycene (1c) has been synthesized by cyclization of 9-(o-chlorophenyl)-9,10-dihydro-9-stibaanthracene (2c) with an excess of lithium piperidide. The general applicability of this ring closure reaction, first developed for the synthesis of phosphatriptycene (1a) and presumed to proceed by nucleophilic attack of a carbanionic centre on a (slowly generated) benzyne, has further been demonstrated by a new synthesis of the known arsatriptycene (1b) and by the synthesis of stibatriptycene (1c). The structure of 1c was confirmed by IR, ¹H NMR and, in particular, by ¹³C NMR spectroscopy.     

Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in α2

A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy–Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in α, leading to transformed Hamiltonians with the two-component block accurate through α^2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α^2k. Their relation to other nonsingular methods of relativistic quantum chemistry (the Douglas–Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas–Kroll scheme and amounts to relatively easy modification of the core Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 225–239, 1997     

Multidimensional gas chromatographic separation of selected PCB atropisomers in technical formulations and sediments

A simple dual-column gas chromatographic system with a six-port switching valve has been used to separate the atropisomers of PCB congeners 84, 91, and 95 in technical PCB formulations and in extracts of soil and river sediment. A capillary column coated with a methylphenylsiloxane stationary phase (CP-Sil 8) was used as the first column, for retention window selection, and a permethylated β-cyclodextrin (ChirasilDex) capillary column as the main separation column. Because peak overlap could not be eliminated by optimization of column temperature, the enantiomeric ratios of PCB congeners could not be determined from the original chromatograms. The correct enantiomer ratio was determined from the peak areas obtained by deconvolution of the chromatograms. Whereas the PCB atropisomers considered were present in equal concentrations in the technical PCB formulations, analysis of a river sediment sample confirmed different residual concentrations of the atropisomers of congener 95.     

The influence of the carrier gas on retention in capillary gas-solid chromatography

In capillary gas-solid chromatography where interactions between solute and carrier gas and adsorption of the solute on the surface of the adsorbent are considered to be imperfect, it has been shown that chromatographic retention is determined largely by adsorption processes. It has been established that correlation relationships k(P₂)=A k(P₁) + B, where k is the retention factor, and A and B are equation constants, was valid for use of different carrier gases P₁ and P₂. Column efficiency could be improved by use of carbon dioxide. The advantages of using carbon dioxide as the carrier gas were investigated.     

Conformational comparison of five follicular fluid meiosis-activating sterol-related active and inactive compounds

The crystal structures of five follicular fluid meiosis-activating sterol-related Δ^8,14-sterol compounds are presented. These are 4,4-di­methyl-23-phenyl-24-nor-5α-chola-8,14-dien-3β-ol, C₃₁H₄₄O, 4,4-di­methyl-22-phenyl-23,24-dinor-5α-chola-8,14-dien-3β-ol, C₃₀H₄₂O, (20R)-4,4-di­methyl-22-oxa-5α,20-chol­es­ta-8,14,24-trien-3β-ol, C₂₈H₄₄O₂, 4,4-di­methyl-23-phenyl-22-oxa-24-nor-5α-chola-8,14-dien-3β-ol–water (4/1), 4C₃₀H₄₂O₂·H₂O, and 4,4-di­methyl-5α-cholesta-8,14-dien-3-one, C₂₉H₄₆O. Two of the derivatives are inactive and three are active as agonists. Preliminary structure–activity relationship studies showed that the positions of the double bonds in the skeleton and the structures of the side chains are important determinants for activity. The conformations of the skeletons were compared with double-bond isomers retrieved from the Cambridge Structural Database [Allen & Kennard (1993). Chem. Des. Autom. News, 8 , 1, 31–37]; no significant differences were found. Thus, conformational changes induced by the double bonds are not discriminative with respect to the activity of the compounds. Comparisons of the side-chain conformations of active and inactive structures revealed that the crystal structures were not conclusive as far as correlation of conformation and activity of the side chains were concerned.