An integral representation for decomposable measures of measurable functions

Summary We start with a measurem on a measurable space (,A), decomposable with respect to an Archimedeant-conorm on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.The integral naturally leads to a -decomposable measurem on the space of all measurable functions from to [0, 1]. The main result of the present paper is the converse of this, namely that, under natural conditions, any -decomposable measurem on can be represented as an integral of a certain Markov-kernelK. We extend this representation to measures on which have values in a set of distribution functions.These results generalize the work done by the first author in the case of additive measures.     

On the integrated density of states for crystals with randomly distributed impurities

In the present paper, we discuss spectral properties of a periodic Schrödinger operator which is perturbed by randomly distributed impurities; such operators occur as simple models for crystals (or semi-conductors) with impurities. While the spectrum itself is independent of the concentrationp of impurities, for 0<p<1, we focus our attention on the limiting behavior of the integrated density of states _p of the random Schrödinger operator, inside a spectral gap of the periodic operator, asp0. Denoting byU ₀ the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located at the origin, say), we show that the integrated density of states concentrates around the points ofU ₀, in the sense that _p (U ) is of orderp, for any fixed -neighborhoodU ofU ₀, while _p (K)C·p ², for any compact subsetK of the gap which does not intersectU .Research partially supported by Deutsche Forschungsgemeinschaft     

CEMS and DCEMS investigations of Al-implanted iron

-Fe surfaces were implanted with a nominal dose of 5×10¹⁷ Al ions/cm² at 50 keV and a current density of about 3.7 A/cm². Samples of different shapes and thicknesses have been used in order to test the influence of heat flow from specimen to target holder during implantation. Integral and energy differential (depth-selective)⁵⁷Fe conversion electron Mössbauer spectroscopy (CEMS and DCEMS) were employed. The spectra indicated a magnetic phase characterised by a broad hyperfine field distributionP(B _hf), a non-magnetic phase, and -Fe. The relative intensity of the non-magnetic phase was enhanced if the thermal contact during implantation became worse. An energy dependence of DCEM spectra in the L-electron range was observed. Model calculations using L-electron weight functions and experimental concentration profiles obtained by secondary neutral mass spectroscopy (SNMS) yielded fair agreement between calculated and experimental phase signals. The results demonstrate that the non-magnetic Fe-Al alloy phase with high Al concentration is located closer to the surface than the magnetic alloy phase, which extends to much larger depth than expected.     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Threshold conditions for 800 nm pumping of 2 μm Tm : Ho lasers

Pumping requirements of pulsed and continuous wave (CW) 2 m Tm : Ho lasers are investigated experimentally and theoretically for excitation at 800 nm. The influence of the pulse duration on threshold is measured using a chopped Ti : Al₂O₃ laser. Based on the experimental and simulated results the spatial and temporal pump requirements in future quasi-CW high-power diode-pumped 2 m Tm : Ho lasers are determined. The experiments and the model allow the evaluation of different loss mechanisms and indicate significant 540 nm emitting loss mechanisms.