Robust Equilibria in Indefinite Linear-Quadratic Differential Games

Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players are looking for robustness and take model uncertainty explicitly into account in their decisions. Specifically, we consider feedback Nash equilibria in indefinite linear-quadratic differential games on an infinite time horizon. Model uncertainty is represented by a malevolent input which is subject to a cost penalty or to a direct bound. We derive conditions for the existence of robust equilibria in terms of solutions of sets of algebraic Riccati equations.     

Two-dimensional asymptotic expansions for large deviations of spherically distributed random vectors if the dominating point degenerates asymptotically

A geometric approach to asymptotic expansions for large-deviation probabilities, developed for the Gaussian law by Breitung and Richter [J. Multivariate Anal.,58, 1–20 (1996)], will be extended in the present paper to the class of spherical measures by utilizing their common geometric properties. This approach consists of rewriting the probabilities under consideration as large parameter values of the Laplace transform of a suitably defined function, expanding this function in a power series, and then applying Watson’s lemma. A geometric representation of the Laplace transform allows one to combine the global and local properties of both the underlying measure and the large-deviation domain. A special new type of difficulty is to be dealt with because the so-called dominating points of the large-deviation domain degenerate asymptotically. As is shown in Richter and Schumacher (in print), the typical statistical applications of large-deviation theory lead to such situations. In the present paper, consideration is restricted to a certain two-dimensional domain of large-deviations having asymptotically degenerating dominating points. The key assumption is a parametrized expansion for the inverse $\bar g^{ - 1} $ of the negative logarithm of the density-generating function of the two-dimensional spherical law under consideration.     

On the Diameter of Plane Curves

Recently, differential geometric properties of embedded projective varieties have gained increasing interest. In this note, we consider plane algebraic curves equipped with the Fubini--Study metric from₂ () and give an estimate for the diameter in terms of the degree, initiated in a paper by F. A. Bogomolov.     

Minimale und maximale Tripelerzeugende und eine Bemerkung zur Tripelbarkeit

Ohne Zusammenfassung     

Bestimmung von Cadmium durch flammenlose Atom-Absorptions-Spektralphotometrie

Zusammenfassung Der Einfluß der Carbidbeschichtung von Graphitrohren auf die Bestimmung von Cd mit der flammenlosen AAS wurde systematisch untersucht. Dazu wurden die Graphitrohröfen mit Zr-, Nb-, Ta-, Mo- und W-Salzlösungen imprägniert, getrocknet und anschließend zur Einleitung der Carbidbildung bei 2600° C geglüht. Es zeigte sich, daß die Oberflächenbehandlung mit Carbidbildnern insgesamt die Lebensdauer des Graphitrohres in Anwesenheit starker Oxidationsmittel erhöht. Außerdem ließen sich höhere Matrix-Zersetzungstemperaturen ohne Cadmium-Verluste erreichen. Die Beschichtung mit Nb-, Ta- und W-Carbid erbrachte auch eine erhöhte Reproduzierbarkeit. Die günstigsten Ergebnisse lieferte die Ta-Beschichtung mit einer Zersetzungstemperatur von 450° C bei Verwendung von N₂-Schutzgas, die bei Anwendung starker Oxidationsmittel auf 600° C gesteigert werden konnte. Damit erlaubt die TaBeschichtung die direkte Cd-Bestimmung selbst in Gegenwart geringer organischer Matrixanteile. Gleichzeitig waren Reproduzierbarkeit und Empfindlichkeit gegenüber dem unbeschichteten Rohr deutlich verbessert.

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Determination of cadmium by flameless atomic-absorption spectroscopy

Summary The influence of coating of graphite furnace tubes with carbide forming metals on the determination of Cd by flameless AAS has been investigated systematically. The graphite furnace tubes have been impregnated with Zr, Nb, Ta, Mo or W salt solutions, dried and subsequently annealed up to 2,600° C to initiate carbide formation. It has been found that the surface treatment with carbide forming metals increased the lifetime of the graphite tube in the presence of strongly oxidizing agents. Furthermore, higher decomposition temperatures could be applied without Cd losses and coating with Nb. Ta and W carbide led to higher reproducibility. Best results have been obtained by coating with Ta allowing a decomposition temperature of about 450° C for N₂ as inert gas, that could even be enhanced to 600° C by application of strongly oxidizing agents. Thereby Ta coating makes possible direct Cd determination even in the presence of small organic admixtures to the matrix. At the same time reproducibility and sensitivity were improved as against the uncoated tube.

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Herrn Prof. Dr. H. Weisz zum 60. Geburtstag gewidmet     

Magnetoresistance anisotropy in Si /SiGe in tilted magnetic fields: experimental evidence for a stripe-phase formation

We observe pronounced transport anisotropies in magnetotransport experiments performed in the two-dimensional electron system of a Si/SiGe heterostructure. They occur when an in-plane field is used to tune two Landau levels with opposite spin to energetic coincidence. The observed anisotropies disappear drastically for temperatures above 1 K. We propose that our experimental findings may be caused by the formation of a unidirectional stripe phase oriented perpendicular to the in-plane field.     

Prospects for the measurement of the structure of the coupling of a Higgs boson to weak gauge bosons in weak boson fusion with the ATLAS detector

The prospects for the measurement of the tensor structure of the vertex between a standard model Higgs boson and two weak gauge bosons using the distribution of the azimuthal angles between the two tagging jets in the weak boson fusion channel are studied in a Monte Carlo analysis using the fast simulation of the ATLAS detector. The decay channels H→τ⁺τ^-→ll+4ν, H→τ⁺τ^-→lh+3ν at m_H=120 GeV and H→W⁺W^-→llνν at m_H=160 GeV are used in the analysis. For a standard model Higgs boson it is found that purely anomalous couplings are expected to be excluded at a confidence level corresponding to 2σ or more at m_H=120 GeV and more than 5σ at m_H=160 GeV from 30 fb^-1 of data. With a value of 1 roughly reproducing the standard model cross section for a purely anomalous coupling, the standard deviation in a measurement of a contribution of a CP even anomalous coupling in addition to the standard model coupling is estimated to be 0.20 at m_H=120 GeV and 0.09 at m_H=160 GeV.