On universal subsets of Banach spaces

We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable . Received July 8, 1997, in final form October 17, 1997     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ − SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×10¹³ cm⁻³) and antimony (Sb: 2×10¹⁸ cm⁻³) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center _μ A1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 61–66 (10 July 1998)     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

A note on a theorem of Raubenheimer and Rode

We prove the converse of Raubenheimer and Rode's Banach algebra version of the Perron-Frobenius Theorem.

     

Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Dynamics in molecular crystals: An application of proton NMR to selectively protonated biphenyl. Do the rings flip together or independently?

The synthesis of a specific isotopomer, C₆D₄H(ortho)-H(ortho)D₄C₆ of biphenyl is reported. The intramolecular dipolar coupling of the protons leads to a well-resolved single-crystal proton nuclear magnetic resonance (NMR) spectrum and allows one to study the dynamics of the phenyl rings in a unique way. At room temperature and above, the most conspicuous dynamical mode consists of 180° ring flips. The present data together with previous measurements of the total flip rate allow us to conclude that the rings flip almost exclusively independently of each other. Between the incommensurate (IC) phase transition of biphenyl at 38 K andT=250 K, the prominent namical mode consists of oscillatory twists ϕ(t) of the two rings. The data allow us to infer the mean square, (φ²), of these twists. (φ²) is found to grow linearly withT for 50<T<200 K. From the slope of (φ²) vs.T the frequency (the wave number[(v)\tilde]\tilde v) is derived. The result is[(v)\tilde] = 20\tilde v = 20 cm⁻¹. ForT<38 K, the spectra give direct evidence of the IC phase transition and its nature (stripelike rather than quiltlike). The temperature dependence of the magnitude of the order parameter of the IC phase is obtained.     

μSR in oxygen deficient YBa2Cu3O x (6.5⩽x⩽7.0)

A systematic μSR study of the local magnetic field distribution in a series of oxygen deficient YBa₂Cu₃O _x samples with 6.5⩽x⩽7.0 is reported. Special attention was given to perform the experiments under the same conditions, so that the oxygen content of the measured samples was the only parameter varied. The behavior of the depolarization rate σ as a function of the oxygen contentx was found to have strong similarities with the behavior of the critical temperatureT _c as a function ofx. In particular, two step-like increases of σ were observed abovex=6.7 and 6.9. The temperature dependence of the normalized depolarization rate σ(T)/σ(0) is well described by the two-fluid model forx⩾6.781(1) and clearly deviates from this behavior forx⩽6.704(1). Our results are compared to those obtained by other groups.     

Multicenter ligand transformations of thioureas on ruthenium clusters

The reaction of trirutheniumdodecacarbonyl with various thioureas was found to give, depending upon the substituents and the reaction conditions, a large variety of tri-, tetra-, penta-, and hexanuclear ruthenium clusters. The ligand systems observed in the products are derived from the thioureas employed; the fragmentation of the thiourea molecules involve N-H, C-S, C-H, and C-N activation processes.