Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

Mössbauer studies on the series La1-xSrxFeO3

Mössbauer spectra have been recorded at 4.2 and 300 K on the series La_1–x Sr _x FeO₃, wherex varies from 0 to 1.0 in steps of 0.1. Neutron diffraction experiments have shown that the crystal structure is orthorhombic for 0x<0.3, rhombohedral for 0.4x0.7, and cubic for 0.8<x1.0. Mössbauer spectra at 4.2 K are composed of magnetic sextet components arising from different charge states of iron ions. In the orthorhombic and rhombohedral phases, the charge states Fe³⁺ and Fe⁵⁺ coexist. In the cubic phase, iron is present as Fe³⁺ and Fe⁴⁺ states. At 300 K, the samples are magnetically ordered in the range 0 x0.3 and the coexistence of Fe³⁺ and Fe⁵⁺ remains. For samples 0.4x1.0, the samples are paramagnetic. Fits to these spectra require two components, one corresponding to an Fe⁴⁺ state, the other being best described as an Fe³⁺ ion forx0.7 but forx>0.7 having a mean charge state which increases to 3.5 forx=1.0.     

Development of a very low energy μ+ beam at PSI

At PSI we are investigating the technique of decelerating an existing very intense secondary beam of surface ⁺ (4 MeV) to an energy of 10 eV using appropriate moderators. These ⁺ can then be used as a source of a tertiary beam of low energy muons with tunable kinetic energy between 10 eV and 10 keV.With a 1000 A layer of solid Argon deposited on an Al substrate we obtain a moderation efficiency (with respect to the number of incoming surface ⁺) of the order of 10^–4.Results of our investigations and the present status of the project are presented together with future plans and possibilities.     

Enlarged scaling ranges for the KS-entropy and the information dimension

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data. (c) 1996 American Institute of Physics.     

Radioactive probe atoms in semiconductors

Progress in semiconductor technology is accompanied by progress in knowledge and control of intrinsic and extrinsic defects in these materials, i.e. of vacancies or self-interstitials and dopant or impurity atoms, respectively. In spite of the large number of different experimental techniques, in particular electrical and optical ones, employed for the characterisation of these defects, there is a shortage of techniques that are able to identify the chemical nature, local structure, and dynamic properties of defects on an atomic scale. The missing sensitivity towards low defect concentrations in the range of 10¹⁶ cm^–3 excludes many techniques which are known to fulfil these requirements. There is a growing number of experimental techniques, however, having in common the application of radioactive isotopes, so-called probe atoms, that deliver the required information also at low defect concentrations. Among the nuclear techniques, which will be discussed in context of their applicability to semiconductors, are the perturbed angular correlation spectroscopy, Mössbauer spectroscopy, and-nuclear magnetic resonance. But also non-nuclear techniques, such as the classical electrical and optical methods, being highly sensitive to low defect concentrations, will be shown to gain the missing sensitivity to the nature of defects if radioactive atoms are employed. For elemental semiconductors as well as for III–V, II–VI, and IV-IV compounds, it will be illustrated to what extent radioactive probe atoms contribute to delivering the needed knowledge and control of defects.     

Oriented local entropies for expansive actions by commuting automorphisms

Given an expansive action α of ?² by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(\alpha ) = \sum\limits_{p \leqslant \infty } {h_p^{(a,b)} } (\alpha )$$ in which the summandh _p ^(a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-adic unit circle, in analogy with the global counterpart. As (a, b) changes, the decomposition (1) changes only when the line through (a, b) passes through one of a finite collection of critical directions, which are explicitly identified.