On support points of univalent functions and a disproof of a conjecture of Bombieri

We consider the linear functional for on the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.

     

A uniform boundedness theorem for locally convex cones

We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.

     

Modelling of interfacial damage and delamination of sprayed coatings with cohesive elements

Delamination of thermally sprayed corrosion protection coatings as a consequence of thermo-mechanical fatigue is investigated. This study focusses on the modelling of interfacial damage initiation and evolution under cyclic loading with the help of a cohesive zone model. The presented model features a slight non-linearity at unloading from the exponential “damage locus” as well as cyclic damage accumulation restricted to (re)loading conditions. Additionally, an endurance limit is introduced indicating the maximum sustainable traction for an infinite number of load cycles. The capability of the model is demonstrated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polarized raman spectroscopy on isolated single-wall carbon nanotubes

Polarized micro-Raman spectroscopy has been performed on spatially separated single-wall carbon nanotubes (SWNTs) in the form of individual nanotubes or thin ropes of only a few SWNTs. Different from bulk samples, the Raman spectra are composed of well-resolved peaks which allow a direct comparison of experimental data with theoretical calculations. Orientation-dependent measurements reveal maximum intensity of all Raman modes when the nanotubes are aligned parallel to the polarization of the incident laser light. The angular dependences clearly deviate from the selection rules predicted by theoretical studies. These differences are attributed to depolarization effects caused by the strongly anisotropic geometry of the nanotubes and to electronic resonance effects for excitation at 633 nm.     

Shaping of intense ion beams into hollow cylindrical form

A specifically tailored plasma lens could shape a high-energy, heavy-ion beam into the form of a hollow cylinder without loss of beam intensity. It has been experimentally confirmed that both a positive as well as a negative radial gradient of the current density in the active plasma lens can be the underlying principle. Calculations were performed that yield the ideal current density distribution for both cases. A numerical simulation of an experiment with an intense ion beam highlights that the shaping of the beam increases the achievable compression in a lead sample.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

Low-energy neutron-deuteron reactions with N 3 LO chiral forces

Based on the preformed cluster model (PCM), we have extended our earlier study on cluster decays of heavy parent nuclei to analyze the effects of different nuclear proximity potentials in the ground-state clusterization of superheavy nuclei with Z = 113, 115 and 117. In order to look for the possible role of deformations, calculations are performed for spherical as well as β ₂-deformed choices of fragmentation. The relevance of “hot compact” over “cold elongated” configurations due to orientations is also explored, in addition to the role of Q value and angular momentum ℓ effects. As the PCM is based on collective clusterization picture, the preformation and penetration probabilities get modified considerably, and hence do so the decay constants and half-lives of the clusters, with the use of different nuclear proximity potentials. The comparative importance of nuclear proximity potentials Prox-1977 and Prox-2000 is analyzed and the calculated decay half-lives in the framework of PCM are compared with the recent predictions of the analytical super-asymmetric fission model (ASAFM). The possible role of shell corrections is also investigated for understanding the dynamics of heavy particle radioactivity. Finally, the potential energy surfaces are compared for different proton and neutron magic numbers in superheavy mass region.

     

Spasmodic dysphonia symptoms as initial presentation of amyotrophic lateral sclerosis

A patient initially diagnosed with adductor-type spasmodic dysphonia was referred for botulinum toxin (Botox) injections, but found on subsequent evaluation to have amyotrophic lateral sclerosis, and therefore Botox was not administered. This unique case underscores the need to delay botulinum toxin treatments in any patient with recent onset symptoms, and to obtain thorough motor speech and voice, otolaryngologic, and neurologic evaluation in all patients prior to consideration for injection.