Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

An apparatus for the determination of volatile analytes by stopped-flow injection analysis using an integrated fiber optic detector

A new method for the analysis of volatile analytes using a stopped-flow injection system originating from either a gas or liquid phase has been developed. It uses an integrated fiber optic detector which also serves as a reactor. This system combines the advantages of gas diffusion and stopped-flow, making the overall assay very sensitive. Both gas streams and aqueous solutions containing ammonia were analyzed. The limits of detection are 40 ppb for gas phase analysis and 1.0 ppm for aqueous phase analysis.     

Ergodicity of a Class of Cocycles Over Irrational Rotations

It is proved that if is irrational and L²(S¹) with o(l/n)then for each mZ\{0} the corresponding skew product is ergodic. The rigidity of specialflows over irrational rotations with roof functions whose Fouriercoefficients are in o(l/n) is also shown.     

Sur le comportement asymptotique des potentiels d'une chaîne de Markov sur ℝ d

Résumé Dans cet article j'étudie le comportement à l'infini des potentiels des chaînes de Markov sur ^d (d3) proches du mouvement brownien, tout spécialement le cas des marches aléatoires, ainsi que des critères de transience et de récurrence inspirés de la méthode utilisée.

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We study the asymptotic behaviour of potentials of Markov chains on ^d (d3), closed to Brownian motion, and particularly the case of random walks. Following a similar approach, we give transience and recurrence criteria.

     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

On the interpretation of random forces derived by projection operators

We study the derivation of a Langevin equation from a microscopic basis in order to elucidate the nature of the random force. We arrive at the conclusion that the consistent interpretation of the microscopic Langevin equation in terms of a stochastic differential equation (SDE) is according to I o rules. In addition, the random force is in general not Gaussian, and it is hence not completely characterized by its second moments.     

A new route to trinuclear carbocyanines

Amides or vinylogous amides react with tosyl chloride-pyridine to form activated intermediates which condense with Fischer's base or their vinylogs to give carbocyanine structures. Under the same conditions formylated Fischer's base reacts with vinylogous Fischer's bases to give trinuclear carbocyanines in good yields. Their structure and the limitations of this route are discussed.     

The role of radicals in metal-assisted oxygenation reactions

The oxo-functionalization of organic substrates with the aid of metal oxo moieties is of fundamental importance not only in nature but also in academic and industrial research. Nevertheless the corresponding reaction mechanisms remain among the most enigmatic in chemistry and few of them are understood in detail. Recent research efforts have resulted in significantly improved information: in the cases of many oxygenation reactions evidence has been provided for the occurrence radical intermediates, even though the high selectivity observed suggests to a different mechanism. Examples stem from various areas of chemistry and include processes involving molecular metal oxo complexes, gas-phase and matrix-isolated species, metalloenzymes, and solid-state oxide surfaces. This review treats this seemingly wide variety of systems with the aim of providing an overview of common reactivity patterns and principles, as well as open problems.     

Trennung von V,Cr und Mn aus Stahl und Aktivierungsanalyse der Legierungselemente mit 14 MeV-Neutronen

The elements are separated from iron by solvent-extraction. Cr, V and Mn are separated by ion-exchange chromatography with a strong acidic cation-exchanger. The elements are determined by 14 MeV-neutron activation analysis using γ-spectroscopy. The method is suitable for a concentration range of 0.05 to 5%.