Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group

We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz [6]. Key new features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence of sequences of biholomorphic mappings of domains in Banach spaces.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Injective hulls are not natural

In a category with injective hulls and a cogenerator, the embeddings into injective hulls can never form a natural transformation, unless all objects are injective. In particular, assigning to a field its algebraic closure, to a poset or Boolean algebra its Mac-Neille completion, and to an R-module its injective envelope is not functorial, if one wants the respective embeddings to form a natural transformation. Received January 21, 2000; accepted in final form August 10, 2001. RID="h1" RID="h2" RID="h3" ID="h1"The hospitality of York University is gratefully acknowledged by the first author. ID="h2"Third author partially supported by the Grant Agency of the Czech Republic under Grant no. 201/99/0310, and the hospitality of York University is also acknowledged. ID="h3"Partial financial assistance by the Natural Sciences and Engineering Councel of Canada is acknowledged by the fourth author.     

First identification of excited states in 59Zn

Excited states in ⁵⁹Zn were observed for the first time following the fusion-evaporation reaction ²⁴Mg + ⁴⁰Ca at a beam energy of 60 MeV. The GASP array in conjunction with the ISIS Silicon ball and the NeutronRing allowed for the detection of γ-rays in coincidence with evaporated light particles. The mirror symmetry of ⁵⁹Zn and ⁵⁹Cu is discussed. Received: 28 May 2002 / Accepted: 10 July 2002 / Published online: 3 December 2002 RID="a" ID="a"Present address: Oliver Lodge Laboratory, University of Liverpool, P.O. Box 147, Liverpool, L69 7ZE, United Kingdom; e-mail: ca@ns.ph.liv.ac.uk. RID="b" ID="b"Present address: Physik-Departament, Technische Universit?t München, D-85748 Garching, Germany. Communicated by W. Henning     

Heavy-element chemistry --Status and perspectives

In the past ten years, nuclear chemists have made considerable progress in developing fast on-line separation techniques, which allowed to chemically characterize the first four transactinide elements Rf (rutherfordium, Z = 104), Db (dubnium, Z = 105), Sg (seaborgium, Z = 106), and recently also Bh (bohrium, Z = 107). In all cases the isolated nuclides were unambiguously identified by observing genetically linked decay chains. Nuclides with production cross-sections of less than 100 pb and half-lives as short as a few seconds have been chemically isolated. Thus, chemists have discovered or significantly contributed to the characterization of the nuclear-decay properties of a number of transactinide nuclei. New techniques with greatly improved overall efficiencies should allow chemists to extend their studies to even heavier elements such as Hs (hassium, Z = 108) and to the recently discovered superheavy elements with Z = 112 and 114, which can be produced only with picobarn cross-sections. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: andreas.tuerler@psi.ch     

In-beam spectroscopy of 253, 254No

In-beam conversion electron spectroscopy experiments have been performed on the transfermium nuclei ^{253, 254}No using the conversion electron spectrometer SACRED in nearly collinear geometry in conjunction with the gas-filled separator RITU at the University of Jyv?skyl?. The experimental setup is discussed and the spectra are compared to Monte Carlo simulations. The implications for the ground-state configuration of ²⁵³No are discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: rdh@ns.ph.liv.ac.uk RID="b" ID="b"Present address: GANIL, F-14021 Caen, France. RID="c" ID="c"Permanent address: IReS Strasbourg, IN2P3-CNRS, F-67037-Strasbourg, France. RID="d" ID="d"Present address: CEA/DIF DCRE/SDE/LDN F-91680 Bruyeres-le-Chatel. RID="e" ID="e"Present address: Daresbury Laboratory, Daresbury WA4 4AD, UK. RID="f" ID="f"Permanent address: IPN Lyon, IN2P3-CNRS, F-69037 Lyon, France.     

Stacked lattice boxes

We study the number of solutions of the Diophantine equationn=x ₁ x ₂+x ₂ x ₃+x ₃ x ₄+...+x _k x _k+1 The combinatorial interpretation of this equation provides the name stacked lattices boxes. The study of these objects unites three separate threads in number theory: (1) the Liouville methods, (2) MacMahon's partitions withk different parts, (3) the asymptotics of divisor sums begun by Ingham.Partially supported by National Science Foundation Grant DMS-9206993, USA.     

Théorie de Kasparov équivariante et groupo?des I

Let be a locally compact topological groupoid, A and B two C*-algebras endowed with a continuous action of . We define an operator K-theory group K K (A,B). We describe two basic properties of this theory: the existence of a Kasparov product and functoriality with respect to groupoid cocycles.