Functions with prescribed singularities

The distributional k-dimensional Jacobian of a map u in the Sobolev space W^1,k-1 which takes values in the the sphere S^k-1 can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M of codimension k can be realized as Jacobian of a Sobolev map valued in S^k-1. In case M is polyhedral, the map we construct is smooth outside M plus an additional polyhedral set of lower dimension, and can be used in the constructive part of the proof of a -convergence result for functionals of Ginzburg-Landau type, as described in [2]. Mathematics Subject Classification (2000) 46E35 (53C65, 49Q15, 26B10, 58A25)     

EPR characterization of new phosphavinyl σ radicals

A number of radicals have been added to 1,3-bis(2,4,6-tri-tert-butylphenyl)diphospha-allene at low temperature in cyclopropane solution. Addition of thiyl and alkoxyl radicals occurs regiospecifically to one of the phosphorus atoms leading to new phosphavinyl radicals, isoelectronic with vinyl radicals, which have been characterised by means of EPR spectroscopy. The results of ab initio calculations are in agreement with the experimentally determined spectral parameters and suggest that these radicals are bent, with a PCP bond angle of ca. 150°. In contrast, silyl and germyl radicals appear to add to the carbon atom of the phosphaallene.     

Steady-state fully noninductive current driven by electron cyclotron waves in a magnetically confined plasma

A steady-state, fully noninductive plasma current has been sustained for the first time in a tokamak using electron cyclotron current drive only. In this discharge, 123 kA of current have been sustained for the entire gyrotron pulse duration of 2 s. Careful distribution across the plasma minor radius of the power deposited from three 0. 5-MW gyrotrons was essential for reaching steady-state conditions. With central current drive, up to 153 kA of current have been fully replaced transiently for 100 ms. The noninductive scenario is confirmed by the ability to recharge the Ohmic transformer. The dependence of the current drive efficiency on the minor radius is also demonstrated.     

ChemInform Abstract: Derivation of Force Field Parameters,and Force Field and Quantum Mechanical Studies of Layered α- and γ-Zirconium Phosphates.

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