On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Two unusual, competitive mechanisms for (2-ethynylphenyl)triazene cyclization: pseudocoarctate versus pericyclic reactivity

The cyclization of (2-ethynylphenyl)triazenes in ODCB at 200 degrees C gives exclusively cinnolines, whereas addition of CuCl to 1,2-dichloroethane solutions of the triazenes at 50 degrees C results in the sole formation of isoindazoles. DFT calculations and deuterium labeling studies suggest the intermediacy of a 3-dehydrocinnolinium ion, produced through a pericyclic transition state. Calculations and trapping studies strongly implicate a carbene intermediate in isoindazole formation, which proceeds through a pseudocoarctate transition state.     

Gewöhnliche lineare Differentialgleichungen zweiter Ordnung mit Distributionskoeffizient

Zusammenfassung Läßt man in der gew. lin. Dgl. zweiter Ordnung einen Distributionskoeffizient zu, der Ableitung einerL _loc ² -Funktion ist, so existieren eindeutig festlegbare, stetige Lösungen derart, daß die in der Dgl. auftretenden Produkte definiert werden können. Mit einer Regularisierung des Distr.-Koeffizienten können die Lösungen durchC -Funktionen approximiert werden. Es wird der Sturmsche Vergleichssatz verallgemeinert. Hieraus und aus den Eigenschaften der mit zwei Basislösungen gebildeten Lösungskurve folgt die Gültigkeit des Ljapunovschen Satzes über die Eigenwertverteilung der verallgemeinerten Hillschen Dgl. mit positivem Distr.-Koeffizient, falls eine zusätzliche Bedingung erfüllt ist. Die vorliegende Arbeit enthält einige Ergebnisse meiner Dissertation [6] (weitere Resultate und Details finden sich dort).     

Multivalency as a Chemical Organization and Action Principle

Multivalent interactions can be applied universally for a targeted strengthening of an interaction between different interfaces or molecules. The binding partners form cooperative, multiple receptor–ligand interactions that are based on individually weak, noncovalent bonds and are thus generally reversible. Hence, multi‐ and polyvalent interactions play a decisive role in biological systems for recognition, adhesion, and signal processes. The scientific and practical realization of this principle will be demonstrated by the development of simple artificial and theoretical models, from natural systems to functional, application‐oriented systems. In a systematic review of scaffold architectures, the underlying effects and control options will be demonstrated, and suggestions will be given for designing effective multivalent binding systems, as well as for polyvalent therapeutics.     

Structural ordering of ω-ferrocenylalkanethiol monolayers on Au(1 1 1) studied by scanning tunneling microscopy

The self-assembly of ω-ferrocenylalkanethiols (FcCnSH) with different alkyl-spacer lengths on Au(1 1 1) substrates has been studied by scanning tunneling microscopy (STM). Upon deposition at room temperature FcCnSH molecules tend to form multilayers, while by thermal treatment monolayer formation, a rearrangement of the molecules and the formation of ordered domains is achieved. The surface structure of the resulting full coverage self-assembled monolayers is resolved with molecular resolution by STM. The ordered monolayer structure of ω-ferrocenylpropanethiol is discussed in comparison with its bulk crystal structure, derived from single crystal X-ray analysis. Based on these results a monolayer structure of ω-ferrocenylalkanethiols with longer alkyl chains closely related to the bulk crystal structure of the shorter alkyl-spacer derivates is suggested. Our results provide detailed insight into the self-assembly of FcCnSH on gold substrates.     

Imaging delocalized electron clouds: photoionization of C(60) in Fourier reciprocal space

The dynamics of the photoionization of the two outermost orbitals of C(60) has been studied in the oscillatory regime from threshold to the carbon K edge. We show that geometrical properties of the fullerene electronic hull, such as its diameter and thickness, are contained in the partial photoionization cross sections by examining ratios of partial cross sections as a function of the photon wave number in the Fourier conjugated space. Evaluated in this unconventional manner photoemission data reveal directly the desired spatial information.     

Krichever-Novikov-like bases on punctured Riemann surfaces

Bases of holomorphic -differentials on N-punctured Riemann surfaces of arbitrary genus are constructed. The resulting extension of the Virasoro algebra on N-punctured spheres is displayed explicitly.     

Small Solutions of Quadratic Diophantine Equations

We consider quadratic diophantine equations of the shape for a polynomial Q(X₁, ..., X_s) Z[X₁, ..., X_s] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound _s(H) with the following property: if equation (1) hasa solution x Z^s at all, then it has one satisfying For s = 3 and s = 4 no polynomial bounds _s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55.     

A Semigroup Approach to Boundary Feedback Systems

In this paper we convert a (linear abstract) initial boundary value problem into an abstract Cauchy problem on some product space and use semigroup methods to solve it. In particular, we apply spectral theory in order to discuss stability under boundary feedback.     

Republication of: Observations in cosmology

This is a reprinting of a paper by Jerome Kristian and Rainer K. Sachs, first published in 1966, in which they proposed a power-series scheme for reading out various parameters of the Universe directly from observations in a model-independent way. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis and by a brief biography of J. Kristian, compiled by A. Krasiński from internet sources.