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.     

Stereocontrolled spirocyclic bislactams derived from pyroglutamic acid

The synthesis of rigid spirocyclic bislactams derived from pyroglutamic acid has been established.     

The frequency scale of speech intonation.

In intonation research, prominence-lending pitch movements have either been described on a linear or on a logarithmic frequency scale. An experiment has been carried out to check whether pitch movements in speech intonation are perceived on one of these two scales or on a psychoacoustic scale representing the frequency selectivity of the auditory system. This last scale is intermediary between the other two scales. Subjects matched the excursion size of prominence-lending pitch movements in utterances resynthesized in different pitch registers. Their task was to adjust the excursion size in a comparison stimulus in such a way that it lent equal prominence to the corresponding syllable in a fixed test stimulus. The comparison stimulus and the test stimulus had pitches running parallel on either the logarithmic frequency scale, the psychoacoustic scale, or the linear frequency scale. In one-half of the experimental sessions, the test stimulus was presented in the low register, while the comparison stimulus was presented in the high register, and, conversely, for the other half of the sessions. The result is that, in all cases, stimuli are matched in such a way that the average excursion sizes in different registers are equal on the psychoacoustic scale.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Luminescent properties of Ce in MSO4 (M: Ca, Sr and Ba) and the effect of Na co-doping

The optical properties of Ce³⁺ in CaSO₄, SrSO₄ and BaSO₄ are reported. The Ce³⁺ ion shows 4f⁰5d¹→²F_5/2,²F_7/2 luminescence in all three sulphates. Co-doping with Na⁺ does not change the local surrounding of the Ce³⁺ ion, but enhances the amount of Ce³⁺ ions built in. Under optical excitation, besides the typical Ce³⁺ doublet emission in the ultraviolet spectral region, band emission around 445 nm was observed. This band emission was not assigned to emission from a Ce³⁺ centre, but to emission from an impurity-trapped exciton. Under X-ray excitation, both Ce³⁺ emission and an emission band around 380 nm was observed. This band was assigned to emission from a self-trapped exciton.     

3D-TOFSIMS characterization of black spots in polymer light emitting diodes

The occurrence and formation of black spots areas in PolyLED devices has been studied by time-of-flight SIMS (TOFSIMS). The composition, shape and position of the black spots is visualised by three-dimensional (3D)-TOFSIMS depth-profiling. It has been established that the formation of non-emissive spots is due to the growth of aluminium oxide clusters at the AlBa/polymer interface. Electron injection in the black spots is lost by the resulting local increase of the resistivity of the cathode.     

Angular self-intersections for closed geodesics on surfaces

In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon's definition of intersection forms for surfaces.

     

Half twists and the cohomology of hypersurfaces

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight , its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondence for certain cubic 4-folds. Received: 25 August 2000; in final form: 8 January 2001 / Published online: 18 January 2002     

Quiver Hopf algebras

In this paper we study subHopfalgebras of graded Hopf algebra structures on a path coalgebra kQ^c. We prove that a Hopf structure on some subHopfquivers can be lifted to a Hopf structure on the whole Hopf quiver. If Q is a Schurian Hopf quiver, then we classified all simple-pointed subHopfalgebras of a graded Hopf structure on kQ^c. We also prove a dual Gabriel theorem for pointed Hopf algebras.