The electronic spectrum of a three-dimensional quasicrystal

The electronic spectrum of an icosahedral quasicrystal with a central-atom decoration of the Amman-Mackay network is investigated in the tight-binding approximation. The quasicrystal is described as a structural limit of the optimal cubic approximants with increasing period. The electronic spectra for the first four optimal cubic approximants do not contain the hierarchical gap structure which is typical for the Cantor set of the spectrum of a one-dimensional quasicrystal. At the same time, as the order of the approximant increases, the spectrum becomes singular throughout the entire energy scale. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 557–562 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Investigation of microbial—mineral interactions by Mössbauer spectroscopy

Mössbauer spectroscopy was used to investigate the reactions of microbes with iron minerals in aqueous solutions and as components of rocks in banded iron formations and granite. A microbial biofilm that formed on a wall of an excavated granite vault in a deep underground laboratory initiated this research. At the aerobic face of the biofilm, iron was found in a form of ferrihydrite; in the anaerobic face against the rock, iron was found as very small siderite particles. Laboratory incubations of the biofilm microbial consortium showed different mineral species could be formed. When the microbial consortium from the biofilm was incubated with magnetite grains, up to about 10% of the iron was altered in three weeks to hematite. The ability of the consortium to precipitate iron both as Fe²⁺ and Fe³⁺ in close proximity may have a bearing on the deposition of banded iron formations. These reactions could also be important in microbially induced corrosion.     

On outer automorphism groups of coxeter groups

Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ ₁ andΠ ₂ any two bases of the root system ofW, thenΠ ₂ = ±ωΠ ₁ for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett. This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.