The combination technique and some generalisations

The combination technique has repeatedly been shown to be an effective tool for the approximation with sparse grid spaces. Little is known about the reasons of this effectiveness and in some cases the combination technique can even break down. It is known, however, that the combination technique produces an exact result in the case of a projection into a sparse grid space if the involved partial projections commute.

The performance of the combination technique is analysed using a projection framework and the C/S decomposition. Error bounds are given in terms of angles between the spanning subspaces or the projections onto these subspaces. Based on this analysis modified combination coefficients are derived which are optimal in a certain sense and which can substantially extend the applicability and performance of the combination technique.     

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

NMRON studies of ferromagnetic hcp and fcc Co

The high resolution hyperfine spectroscopy, modulated adiabatic passage of oriented nuclei (MAPON), has been applied for the first time to high purity, elemental systems. Detailed comparisons between the electric quadrupole hyperfine interactions (EQI’s) and, in particular, their distributions, are obtained for⁶⁰CoCo where the hosts are a single crystal of hcp cobalt and a polycrystalline cobalt foil of predominantly fcc character. For hcp Co, with the electronic magnetization, M, parallel to the c-axis, the mode value P/h=3e²qQ/4I(2I−1)h=−48.5(5) kHz. This fractional distribution implies the sharpest electric field gradient (efg) measured in a metal to date, using MAPON spectroscopy, in excess of two times sharper than that of the most dilute impurity efg in a crystallographically cubic ferromagnetic host. The mode efg is V_zz=−27.3(32)×10¹⁹ Vm⁻². For the polycrystalline, predominantly fcc foil, prepared by quenching, the EQI mode value is P/h=−6.2(4) kHz with a FWHM of 12.0(7) kHz yielding a mode efg of V_zz=−3.5(5)×10¹⁹ Vm⁻².     

Evidence of shear-dependent boundary slip in newtonian liquids

The European Physical Journal E - The flow of Newtonian fluids was studied by directly measuring the hydrodynamic drainage force acting on a sphere approaching a flat surface. Our force...     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

The effect of simultaneous temperature, pressure and stress on the experimental annealing of spontaneous fission tracks in apatite: a brief overview

Tracks made in minerals by the electronic stopping of uranium fission fragments provide a modern geological dating tool, and are believed also to yield specific information on the low-temperature thermal history of rocks. Experimental work showing that the damaged crystal lattice along a fission track recovers primarily as a function of temperature ignored the fact that the basic theory of atomic diffusion requires an exponential decrease in the intrinsic diffusion coefficient with increasing pressure. Here, fission track recovery was experimentally investigated in basic apatite under the simultaneous influences of temperature, pressure and stress. We show that track fading is a complex recovery mechanism responding to several environmental physical parameters simultaneously. In particular a strong decrease in the track recovery rate was observed as a function of increasing pressure. And a nearly temperature-independent recovery was observed in samples under stress.     

Magnetic behaviour and site occupation of YFe12-x V x (x=2,3,4)

The effects of vanadium substitution on the iron magnetism in YFe_12-x V _x compounds (x～2–4) have been studied by⁵⁷Fe Mössbauer spectroscopy. The preference of vanadium atoms for the 8i site of these ThMn₁₂-structure type compounds is confirmed. The rapid collapse of the iron sublattice magnetization with increasing vanadium concentration is analysed in terms of the ‘magnetic valence’ model.     

The power-law tail exponent of income distributions

In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimizing the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data for Australia and Italy.     

New trends in localization theory

In this article we discuss some recent trends in the research of electron and phonon localization, specially in the field of quasiperiodic potentials. Then, a new scheme to detect and classify localization is developed by studying the band scaling of a related supercrystal made from replicas of the system. For one dimension, this leads to the use of dynamical systems theory to obtain the localization length and the scaling exponents of the wave functions.