Sharp estimates in terms of moduli of smoothness for compound cubature rules

Summary In 1980 Dahmen-DeVore-Scherer introduced a modulus of continuity which turns out to reflect invariance properties of compound cubature rules effectively. Accordingly, sharp error bounds are derived, the existence of relevant counterexamples being a consequence of a quantitative resonance principle, established previously.     

Portable and Automatic Mössbauer Analysis

A portable Mössbauer spectrometer, developed for extraterrestrial applications, opens up new industrial applications of MBS. But for industrial applications, an available tool for fast data analysis is also required, and it should be easy to handle. The analysis of Mössbauer spectra and their parameters is a barrier for the popularity of this wide-applicable spectroscopic technique in industry. Based on experience, the analysis of a Mössbauer spectrum is time-consuming and requires the dedication of a specialist. However, the analysis of Mössbauer spectra, from the fitting to the identification of the sample phases, can be faster using by genetic algorithms, fuzzy logic and artificial neural networks. Industrial applications are very specific ones and the data analysis can be performed using these algorithms. In combination with an automatic analysis, the Mössbauer spectrometer can be used as a probe instrument which covers the main industrial needs for an on-line monitoring of its products, processes and case studies. Some of these real industrial applications will be discussed.     

Transport as a consequence of state-dependent diffusion

Overdamped particles subject to a drift in a force field with sinusoidal space dependence and also a sinusoidally modulated space-dependent diffusion, with the same period as the drift, experience a net driving force. The resulting current depends on the amplitude of the modulation of the diffusion and is a periodic function of the phase difference between the sinusoidal drift and the sinusoidal modulation of the diffusion. For small modulation amplitudes a particle subject to state-dependent noise behaves the same way as a particle subject to thermal noise but with a drift which, in addition to the sinusoidal term, contains a net force term [M. Büttiker,Z. Phys. B 68:161 (1987)]. A specific example of this behavior [N. G. van Kampen,IBM J. Res. Dev. 32:107 (1988); R. Landauer,J. Stat. Phys. 53:233 (1988).] is the motion of overdamped particles in a ring subject to a nonuniform temperature field. When the drift and the temperature, which are periodic with a period equal to the ring circumference, are not in phase a noise-induced circulating current results.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Ground-state properties of LiV2O4 and Li1-xZnx(V1-yTiy)2O4

We present susceptibility, microwave resistivity, NMR and heat-capacity results for Li_1-xZn_x(V_1-yTi_y)₂O₄ with 0 ? x ? 0.3 and 0 ? y ? 0.3. For all doping levels the susceptibility curves can be fitted with a Curie-Weiss law. The paramagnetic Curie-Weiss temperatures remain negative with an average value close to that of the pure compound Θ≈ - 36 K. Spin-glass anomalies are observed in the susceptibility, heat-capacity and NMR measurements for both type of dopants. From the temperature dependence of the spin-lattice relaxation rate we found critical-dynamic behavior in the Zn doped compounds at the freezing temperatures. For the Ti-doped samples two successive freezing transitions into disordered low-temperature states can be detected. The temperature dependence of the heat capacity for Zn-doped compounds does not resemble that of canonical spin glasses and only a small fraction of the total vanadium entropy is frozen at the spin-glass transitions. For pure LiV₂O₄ the spin-glass transition is completely suppressed. The temperature dependence of the heat capacity for LiV₂O₄ can be described using a nuclear Schottky contribution and the non-Fermi liquid model, appropriate for a system close to a spin-glass quantum critical point. Finally an ( x / y , T )-phase diagram for the low-doping regime is presented. Received 16 March 2001 and Received in final form 30 October 2001