Wrinkle-free solutions in the theory of annular elastic membranes

Rotationally symmetric deformations of a flat annular elastic membrane under a gravitational force are studied, with prescribed radial stresses or horizontal displacements at the edges. The small-finitedeflection theory of Föppl-Hencky as well as a simplified version of Reissner's static first approximation theory of thin shells of revolution are applied which lead to consider a single, second-order, ordinary differential equation for the derivation of the principal stresses in the membrane. Using analytical methods, the range of those boundary data is determined for which the solutions of the differential equation are wrinkle free in the sense that both the radial and the circumferential stress components are nonnegative everywhere.     

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

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.     

Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed. Received 20 February 2002 / Received in final form 27 May 2002 Published online 17 September 2002     

Monitoring genomic alterations with a panel of oligonucleotide probes specific for various simple repeat motifs

Germline and somatic instability of the human genome was studied, using synthetic oligonucleotides specific for simple repeat motifs. The following probes were used: (GTG)5, (GACA)4, (GATA)4, (CT)8, (TTAGGG)3, (GT)8, (GAA)6 and (GGAT)4. Each of them is unique with respect to the target regions recognized in the genome. Thus compilation of the various fingerprint data provides a complex map of the genome (and its deviations). While the fingerprints of differentiated somatic tissues never showed any alterations, in tumor tissues (namely gliomas) many changes could be detected. Most of the latter reflect secondary karyological aberrations. In nearly one third of the gliomas, drastically amplified and apparently monomorphic DNA fragments were identified. This marker should make it possible to deal with causal pathogenetic mechanisms as well as novel diagnostic strategies.     

A quasiconformal dynamic property of the disk

It is known that every conformai embedding of the disk into the extended complex plane possesses a r²-quasiconformal extension across eachr-level line (the r²-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther ²-property. Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.