On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

The chemical shift tensor for the hydroxyl proton: Ca(OH)2

The proton chemical shift tensor of the hydroxyl proton in calcium hydroxide has been measured using multiple pulse NMR techniques. The tensor is axially symmetric with susceptibility corrected components σ_tT = ?9.3 ± 1 ppm and

ppm relative to TMS. 792 79     

From solution-phase to solid-phase enyne metathesis: crossover in the relative performance of two commonly used ruthenium pre-catalysts

A crossover in the ability of two distinct ruthenium-based metathesis pre-catalysts to effect the synthesis of dialkenylboronic esters in solution and on the solid-phase was observed. Specifically, while the Grubbs 2nd generation pre-catalyst 3 affords a greater degree of conversion to product than the Hoveyda-Grubbs pre-catalyst 2 in a solution-phase enyne-metathesis reaction, this trend is reversed in the solid-phase variant. Systematic investigation showed this trend to be general, regardless of variations in the homoallylic alcohol and alkynylboronic ester components of the reaction, as well as in the type of solid support employed. Experiments to determine a mechanistic hypothesis for this trend highlighted the significance of the ruthenium remaining bound to the substrate after metathetic rearrangement and found the presence of phosphine ligand to be detrimental to the success of the solid-phase reaction. Therefore, these results suggest an expanded role for phosphine-free pre-catalysts, such as 2, in challenging solid-phase metathesis reactions.     

Distribution of reaction products (theory). Investigation of an ab initio energy-surface for F + H2 ⇀ HF + H

Bender, O'Neil, Pearson and Schaefer (BOPS) have computed ab initio energies for 232 collinear configurations of FHH, using extensive configuration interaction. We have fitted these points using an LEPS-type function. Comparison with semi-empirical surfaces for FHH shows that the general form of these surfaces is in good accord with the ab initio findings. Evidence is presented which indicates that the BOPS ab initio surface exhibits too great a drop in energy along the favoured route into the exit valley.     

Solanum-alkaloide—SCVI: Synthese von solafloridin und 25-iso-solafloridin

3β,16α-Diacetoxy-20-(5-methyl-2-pyridyl)-pregna-5,20-diene (2) available from 3β-acetoxy-pregna-5,16-dien-20-one (1) was transformed into solafloridine (11) and 25-iso-solafloridine (13).