Modulation of cross polarization in motionally averaged solids by Variable Angle Spinning NMR

In systems where the dipolar couplings are partially averaged by molecular motion, cross-polarization is modulated by sample spinning. The cross-polariation efficiency in Variable Angle Spinning (VAS) and Switched Angle Spinning (SAS) experiments on mobile samples is therefore strongly dependent on the spinning angle. We describe simulations and experimental measurements of these effects over a range of spinning angles from 0° to 90°.     

Optimisation of linear unbiased intensity estimators for point processes

A general non-stationary point process whose intensity function is given up to unknown numerical factor λ is considered. As an alternative to the conventional estimator of λ based on counting the points, we consider general linear unbiased estimators of λ given by sums of weights associated with individual points. A necessary and sufficient condition for a linear, unbiased estimator for the intensity λ to have the minimum variance is determined. It is shown that there are “nearly” no other processes than Poisson and Cox for which the unweighted estimator of λ, which counts the points only, is optimal. The properties of the optimal estimator are illustrated by simulations for the Matérn cluster and the Matérn hard-core processes. This research was partially supported by Grant Agency of Czech Republic, project No. 201/03/D062.     

Hyperfine structure induced isotopic effects in krypton resonance ionization mass spectrometry

A time-of-flight mass spectrometer combined with a pulsed laser system has been used for determination of krypton isotope ratios of air samples containing 10⁶-10⁷ krypton atoms. A three-color, doubly resonant ionization scheme employing a 116.48 nm transition from the ground into the first 4s²4p⁵(²P°_1/2)5s J = 1 excitation level has been applied. The magnitude of a hyperfine splitting of this level has been estimated for ⁸¹Kr, ⁸³Kr and ⁸⁵Kr isotopes. Hyperfine structure induced isotopic effects have been investigated under different saturation conditions and found to be negligible when the first and the second transitions are strongly saturated.     

Convex geometry of max-stable distributions

It is shown that max-stable random vectors in [0, ∞ ) ^d with unit Fréchet marginals are in one to one correspondence with convex sets K in [0, ∞ ) ^d called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random cross-polytope whose distribution is controlled by the spectral measure of the max-stable random vector. Furthermore, the cumulative distribution function P ξ ≤ x of a max-stable random vector ξ with unit Fréchet marginals is determined by the norm of the inverse to x, where all possible norms are given by the support functions of (normalised) max-zonoids. As an application, geometrical interpretations of a number of well-known concepts from the theory of multivariate extreme values and copulas are provided.      

Unusual methylation reaction of gem-bromofluorospiropentanes with methyllithium

A series of novel gem-bromofluorospiropentanes were synthesized and investigated in the reaction with methyllithium. Either substitution of the fluorine atom for a methyl group or rearrangement into methylated cyclobutene derivatives occurred under these conditions.     

On some versions of the element agglomeration AMGe method

The present paper deals with element‐based algebraic multigrid (AMGe) methods that target linear systems of equations coming from finite element discretizations of elliptic partial differential equations. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate AMGe method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom is based on solving a large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V‐cycle utilizing simple interpolation matrices and nested conjugate gradient (CG)‐based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods. Copyright © 2008 John Wiley & Sons, Ltd.