Controlling influences in bisspiroketal formation: synthesis of the ABC ring system of azaspiracid

Substitution effects on the stereochemical outcome of bisspiroketalization on the C₁-C₁₇ carbon backbone of azaspiracid is presented. A possible explanation is offered to explain the observed stereochemical outcome.     

GMRES and the minimal polynomial

We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size.Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight.Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.This research was partially supported by National Science Foundation grants DMS-9122745, DMS-9423705, CCR-9102853, CCR-9400921, DMS-9321938, DMS-9020915, and DMS-9403224.     

PHELIX – Status and First Experiments

The high-energy high-power laser system PHELIX (Petawatt High Energy Laser for heavy Ion eXperiments) [1] is currently under construction at the Gesellschaft fuer Schwerionenforschung mbH (GSI) Darmstadt. With PHELIX GSI will offer the unique combination of a high-current, high-energy (GeV/u) heavy-ion beam with an intense laser beam. This will open the door to a variety of fundamental science issues in the field of atomic physics, plasma physics and nuclear physics. The project will gain further interest in the near future by the dramatic increase of the accelerator performance with the starting FAIR project at GSI [2]. This paper reports the current status of the project as well as the laser architecture. The proposed physics program and a first experiment carried out with PHELIX, the realization of a transient collisionally excited x-ray laser [3], will also be reviewed briefly.     

Depolarization in reentrant spin glasses: a comparison between neutron and muon probes

In the amorphous ( Fe_1-x Mn_x)₇₅ P₁₆ B_6 Al_3 alloys, muon and neutron depolarization data, combined with the results of small angle neutron scattering, magnetization and Mössbauer spectroscopy, probe the existence of three distinct magnetic transitions at T_C, T_K and T_F (T_F < _K < _C).     

Visualization of liquid-solid interface morphologies in gallium subject to natural convection

Melting and solidification of pure gallium is studied using real-time radioscopy methods. Sharp contrast between melt and solid phases with a 3% density difference is illustrated. The interfacial shape reflects convective flow in the liquid phase. Comparisons are made between real-time non-intrusive X-ray observations and results gained from probing techniques and numerical simulations reported in the literature. Similar qualitative trends in temperature distribution, yet discrepancies in interfacial location and shape, are exhibited.     

Diacetylenes and mesophases

During the past five years, over 600 papers have been published on research work carried out with diacetylenes. Far fewer papers can be found on diacetylene mesophase studies, and these are reviewed in this paper. Some new findings by the authors are also presented.     

INVARIANT FIELDS AND LOCALIZED INVARIANT RINGS OF p-GROUPS

It is well known that for a p-group, the invariant field ispurely transcendental (T. Miyata, Invariants of certain groupsI, Nagoya Math. J. 41 (1971), 69–73). In this note, weshow that a minimal generating set of this field can be chosenas homogeneous invariants from the invariant ring. As a result,we show that the invariant ring localized at one suitable invariantis the localization of a polynomial subring at this same invariant.This second result is a generalization of a recent result ofthe first author for cyclic groups of order p (H. E. A. Campbell,Rings of invariants of representations of C_p in characteristicp, preprint, 2006). As well, we specialize these results tothis latter case.