On the Construction of a Geometric Invariant Measuring the Deviation from Kerr Data

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation—the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant—however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

Cell Cycle Effects and Concomitant p53 Expression in Hairless Murine Skin after Longwave UVA (365 nm) Irradiation: A Comparison with UVB Irradiation

Abstract— Ultraviolet A (UVA,315–400 nm) radiation is known to be a complete carcinogen, but in contrast to UVB (280-315 nm) radiation, much of the cell damage is oxygen dependent (mediated through reactive oxygen species), and the dominant premutational DNA lesion(s) remains to be identified. To investigate further the basic differences in UVA and UVB carcinogenesis, we compared in vivo cellular responses, viz. cell cycle progression and transient p53 expression in the epidermis, after UVA1 (340-400 nm) exposure with those after broadband UVB exposure of hairless mice. Using flow cytometry we found a temporary suppression of bromodeoxyuridine (BrdU) uptake in S-phase cells both after UVB and UVA1 irradiation, which only in the case of UVB is followed by an increase to well over control levels. With equally erythemogenic doses (1-2 MED), the modulation of BrdU uptake was more profound after UVB than after UVA1 irradiation. Also, a marked transient increase in the percentage of S-phase cells occurred both after UVB and after UVA1 irradiation, but this increase evolved more rapidly after UVA1 irradiation. Further, p53 expression increased both after UVB and UVA1 irradiations, with peak expression already occurring from 12 to 24 h after UVA1 exposure and around 24 h after UVB exposure. Overall, UVA1 radiation appears to have less of an impact on the cell cycle than UVB radiation, as measured by the magnitude and duration of changes in DNA synthesis and cells in S phase. These differences are likely to reflect basic differences between UVB and UVA1 in genotoxicity and carcinogenic action.     

Crystal structure predictions for acetic acid

Possible crystal structures of acetic acid were generated, considering eight space groups and assuming one molecule in the asymmetric unit. Our grid-search method was compared with a Monte Carlo approach as implemented in the Biosym/MSI Polymorph Predictor. This revealed no sampling deficiencies. A large number of possible crystal structures were found (∼100 within only 5 kJ/mol), including the experimental structure. Energy minimizations were done with a united-atoms force field (GROMOS), an all-atoms force field (AMBER), and a potential that describes the electrostatic interactions with distributed multipoles (DMA). In all cases, the experimental structure had a low lattice energy. The number of hypothetical crystal structures was reduced considerably by removing space-group symmetry constraints, or by a primitive molecular dynamics shake-up. Nevertheless, sufficient structures of equal or lower energy compared with the experimental structure remained to suggest that other factors need to be considered for genuine structure prediction. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 459–474, 1998     

MULTIDIMENSIONAL UPWIND RESIDUAL DISTRIBUTION SCHEMES FOR THE CONVECTION–DIFFUSION EQUATION

Multidimensional residual distribution schemes for the convection–diffusion equation are described. Compact upwind cell vertex schemes are used for the discretization of the convective term. For the diffusive term, two approaches are compared: the classical finite element Galerkin formulation, which preserves the compactness of the stencil used for the convective part, and various residual-based approaches in which the diffusive term, evaluated after a reconstruction step, is upwinded along with the convective term.     

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.