Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

Observational evidence of gentle chromospheric evaporation during the impulsive phase of a solar flare

Observational evidence of gentle chromospheric evaporation during the impulsive phase of a C9.1 solar flare is presented using data from the Reuven Ramaty High-Energy Solar Spectroscopic Imager and the Coronal Diagnostic Spectrometer on board the Solar and Heliospheric Observatory. Until now, evidence of gentle evaporation has often been reported during the decay phase of solar flares, where thermal conduction is thought to be the driving mechanism. Here we show that the chromospheric response to a low flux of nonthermal electrons (>= 5 cm(-2) s(-1)) results in plasma upflows of 13 +/- 16, 16 +/- 18, and 110 +/- 58 km s(-1) in the cool He I and O V emission lines and the 8 MK Fe XIX line, respectively. These findings, in conjunction with other recently reported work, now confirm that the dynamic response of the solar atmosphere is sensitively dependent on the flux of incident electrons.

Surface plasmon polariton propagation across a gentle silver step

Surface plasmon polaritons (SPPs) are excited with light of wavelength lambda (1) = 632.8 nm on or near a gentle Ag/Ag step structure using focused beam, prism coupling and detected using a bare, sharpened fibre tip. The tip-sample separation is controlled by means of an evanescent optical field at wavelength lambda (2) = 543.5 nm in a photon scanning tunnelling microscope (PSTM). The SPP propagation properties are first characterised on both the thin and thick sections of the Ag film structure either side of the step, both macroscopically, using attenuated total reflection, and microscopically from the PSTM images; the two techniques yield very good agreement. It is found that the SPP propagation length is similar to 10-11 mum across the step in each direction (thick to thin and vice versa) as observed in the PSTM images. Thus, with reference to the propagation lengths of 14.2 and 11.7 mum for the thick and thin planar parts of the Ag film respectively, it is concluded that the SPPs negotiate the step reasonably successfully. Importantly, also, it is shown that images may be produced, displaying SPPs with either an artificially enhanced (similar to 15-20 mum) or truncated (5-8 mum) propagation length across the step. Consideration of such images leads us to suggest the possibility that the photon tunnelling occurs in a local water environment. (C) 2001 Elsevier Science B.V. All rights reserved.

An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.