On the Picard principle for Δ?+?μ

Given a (local) Kato measure?μ on ${{\mathbb{R}^d} \setminus \{0\},\,d \ge 2}$ , let ${{\mathcal H}_0^{\Delta+\mu}(U)}$ be the convex cone of all continuous real solutions u?≥ 0 to the equation Δu?+?u μ?=?0 on the punctured unit ball U satisfying ${\lim_{|x|\to 1} u(x)=0}$ . It is shown that ${{\mathcal H}_0^{\Delta+\mu}(U)\ne \{0\}}$ if and only if the operator ${f\mapsto \int_U G(\cdot,y)f(y)\,d\mu(y)}$ , where G denotes the Green function on U, is bounded on ${\mathcal L^2(U,\mu)}$ and has a norm which is at most one. Moreover, extremal rays in ${{\mathcal H}_0^{\Delta+\mu}(U)}$ are characterized and it is proven that Δ?+?μ satisfies the Picard principle on U, that is, that ${{\mathcal H}_0^{\Delta+\mu}(U)}$ consists of one ray, provided there exists a suitable sequence of shells in U such that, on these shells,?μ is either small or not too far from being radial. Further, it is shown that the verification of the Picard principle can be localized. Several results on L ²-(sub)eigenfunctions and 3G-inequalities which are used in the paper, but may be of independent interest, are proved at the end of the paper.     

Recognizing heterogeneous distribution of platinum group elements (PGE) in geological materials by means of the Re-Os isotope system

The identification of uncertainties caused by sample inhomogeneity, as distinct from those caused by sample preparation and measurement, is a challenging task. Use of chemometric methods to separate and estimate these contributions to the combined standard uncertainty of a measurement (uc) of an analytical result requires complex experiments. The difficulty of platinum group element measurement makes this task even more complex. But unless it can be demonstrated that sample inhomogeneity is the major contributor to the high variability of an analytical result one should be careful not to mistakenly attribute this to a nugget effect. In this contribution we are able to demonstrate in two special cases that irreproducible results (up to 90% RSD) for analysis of Os and Re in the pg g(-1) to ng g(-1) range are truly caused by a nugget effect and not by inadequacies of the analytical method.     

Statistical investigations of interferences in graphite furnace atomic absorption spectroscopy

Summary In the first part different methods for studying interferences of the time dependent signal in flameless AAS are presented with emphasis on factorial designs in experimentation as opposed to the one-factor-at-a-time approach.An example of the statistical computations necessary for interpretation of a multifactor experiment is worked out and discussed in detail with special consideration of the explanation of first-order interactions.The influence of instrumentation upon determinations in the graphite furnace is dealt with in the second part: The temperature in the graphite furnace was measured with a pyrometer, a thermocouple and a Hg-thermometer. The results obtained with the pyrometer were in good agreement with the values given by the manufacturer. The stability of the AAS system was checked and found to be sufficient for the investigation of interferences.

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Statistische Untersuchungen über Störungen bei der flammenlosen AtomabsorptionsspektralphotometrieI. Methoden und Apparaturen

Zusammenfassung Im ersten Abschnitt werden die verschiedenen Möglichkeiten zur Untersuchung von Störungen des zeitabhängigen Signals bei der flammenlosen AAS aufgezeigt, wobei besondere Bedeutung den faktoriellen Versuchsplänen im Gegensatz zu einparametrigen Untersuchungen beigemessen wird.Ein Beispiel der statistischen Auswertung zur Interpretation eines Experiments mit mehreren Faktoren wird gebracht, und dabei besonderes Gewicht auf die Erklärung von Wechselwirkungen zwischen zwei Faktoren gelegt.Im zweiten Abschnitt werden die apparativen Einflüsse auf Messungen in der Graphitrohrküvette behandelt. Dazu wurde die Temperatur im Graphitrohr mit einem Pyrometer, einem Thermoelement und einem Quecksilberthermometer gemessen. Die Temperaturen, die mit der pyrometrischen Methode gefunden wurden, stimmen gut mit den vom Hersteller angegebenen Werten überein. Die Stabilität des AAS-Gerätes wurde überprüft: sie reicht für die Durchführung von Interferenzstudien aus.

     

A neural network approach to qualitative analysis in inductively coupled plasma-atomic emission spectroscopy (ICP-AES)

Summary The use of a simple neural network, the Bidirectional Associative Memory (BAM), is described for the qualitative and semiquantitative analysis in ICP-AES. A computer program was developed linking the BAM to the solution of an overdetermined linear equation system by a least squares fit (LSF) using 480 prominent lines of 68 chemical elements. The BAM carries out the qualitative analysis and in the following LSF, the concentrations of the previously found elements are estimated. First, the assessment of the algorithm was performed by analyzing only synthetic spectra without noise, resulting in a recall of 100% for all elements covered. The investigation of spectra affected with noise of various degrees yielded a recall of about 96–97% and an RSD of 3% for spectra of twenty elements at the 10% noise level. A first test of the algorithm with experimental spectra has also given satisfactory results.     

High critical oxygen concentration in microcrystalline silicon solar cells

For microcrystalline silicon based p–i–n solar cells the effect of deposition conditions on the critical oxygen concentration was investigated. All solar cells were prepared by 13.56 MHz plasma‐enhanced chemical vapour deposition. The critical oxygen concentration defines the lowest oxygen concentration in the intrinsic absorber layer causing a deterioration of the solar cell performance. For intentional contamination of ～1.2–1.3 µm thick i‐layers, the oxygen was inserted by a controllable leak at the process gases supply line, i.e. by a gas pipe leak. For µc‐Si:H deposited at a discharge power of 0.53 W/cm² we find a critical oxygen concentration of 1–2 × 10¹⁹ cm^–3 in agreement with values commonly reported in literature. However, changing the deposition conditions, we find that the critical oxygen concentration in µc‐Si:H cells is not fixed. At reduced power of 0.20 W/cm² a much higher value for the critical oxygen concentration of 1 × 10²⁰ cm^–3 is observed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Jensen Measures in Potential Theory

It is shown that, for open sets in classical potential theory and??more generally??for elliptic harmonic spaces Y, the set J _x (Y) of Jensen measures (representing measures with respect to superharmonic functions on?Y) for a?point x????Y is a?simple union of closed faces of the compact convex set $M_x(\mathcal P(Y))$ of representing measures with respect to potentials on?Y, a?set which has been thoroughly studied a?long time ago. In particular, the set of extreme Jensen measures can be immediately identified. The results hold even without ellipticity (thus capturing also many examples for the heat equation) provided a?rather weak approximation property for superharmonic functions holds. Equally sufficient are a?certain transience property and a?weak regularity property. More important, each of these properties turns out to be necessary and sufficient for obtaining (in the classical case) that J _x (Y) coincides with the set of all compactly supported probability measures in $M_x(\mathcal P(Y))$ .     

Thermodynamics of lattice heteropolymers

We calculate thermodynamic quantities of hydrophobic-polar (HP) lattice proteins by means of a multicanonical chain-growth algorithm that connects the new variants of the Pruned-Enriched Rosenbluth Method and flat histogram sampling of the entire energy space. Since our method directly simulates the density of states, we obtain results for thermodynamic quantities of the system for all temperatures. In particular, this algorithm enables us to accurately simulate the usually difficult accessible low-temperature region. Therefore, it becomes possible to perform detailed analyses of the low-temperature transition between ground states and compact globules.     

Conformational transitions of nongrafted polymers near an absorbing substrate

We have performed multi-canonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations binding and nonbinding with the substrate. We discuss the phase diagram in the temperature-solubility plane and highlight the transition path through the free-energy landscape.     

Quantum interference in artificial band structures

Magnetotransport experiments on two-dimensional electron systems with an atomically precise, one-dimensional potential modulation reveal striking quantum interference oscillations. Within a semiclassical framework, they are recognized either as self-interference along closed orbits, many of them rendered possible by magnetic breakdown between Fermi contour segments of the artificial band structure, or as interference-enhanced backscattering. The known commensurability oscillations appear as a special case of the latter mechanism.