Set theory for fuzzy sets of higher level

We extend the usual notion of fuzzy set in such a way that the elements of fuzzy sets again can be fuzzy sets. For such fuzzy sets of higher level the fuzzy set theoretic operations are generalized up to the notion of a fuzzy mapping. In our presentation of the results we use a suitable many valued logic, indicating in this way the close formal connections between fuzzy and classical set theory.     

Predicting equilibrium structures in freezing processes

We propose genetic algorithms as a new tool that is able to predict all possible solid candidate structures into which a simple fluid can freeze. In contrast to the conventional approach where the equilibrium structures of the solid phases are chosen from a preselected set of candidates, genetic algorithms perform a parameter-free, unbiased, and unrestricted search in the entire search space, i.e., among all possible candidate structures. We apply the algorithm to recalculate the zero-temperature phase diagrams of neutral star polymers and of charged microgels over a large density range. The power of genetic algorithms and their advantages over conventional approaches is demonstrated by the fact that new and unexpected equilibrium structures for the solid phases are discovered. Improvements of the algorithm that lead to a more rapid convergence are proposed and the role of various parameters of the method is critically assessed.     

On the existence of solutions of systems of fuzzy equations

A necessary and sufficient condition for the existence of solutions of a fuzzy equation given by E. Sanchez is extended to systems of fuzzy equations.     

Komplexometrische Titrationen

Ohne Zusammenfassung     

Zur Halogenbestimmung in gewissen organischen Verbindungen

Ohne Zusammenfassung     

Efficient iron-mediated approach to pyrano[3,2-a]carbazole alkaloids--first total syntheses of O-methylmurrayamine A and 7-methoxymurrayacine, first asymmetric synthesis and assignment of the absolute configuration of (-)-trans-dihydroxygirinimbine

Iron-mediated oxidative cyclisation provides an efficient approach to pyrano[3,2-a]carbazole alkaloids. Thus, improved routes to girinimbine and murrayacine as well as the first total syntheses of O-methylmurrayamine A and 7-methoxymurrayacine are reported. Asymmetric epoxidation of girinimbine led to (-)-trans-dihydroxygirinimbine and the assignment of its absolute configuration.     

On the Validity of Linear Response Theory in High-Dimensional Deterministic Dynamical Systems

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory’s assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations.     

Microarray‐Based Detection of Dye‐Labeled DNA by SERRS Using Particles Formed by Enzymatic Silver Deposition

The growing interest in DNA diagnostics is addressed today by microarrays with fluoresence detection. In our approach, we utilize spatially defined arrays of short oligonucleotides on a modified glass surface. Surface enhanced resonance Raman scattering (SERRS) is used to obtain molecularly specific spectra of the Raman‐active dye‐labeled DNA. Nanoparticles produced by enzymatic silver deposition are used as SERS‐active substrate. They grow directly on the modified oligonucleotides and only in the spatially defined areas on the chip. Furthermore, they potentially offer several advantages for SERS detection. The nanoparticles are characterized and their ability for use as SERS‐ and SERRS‐active substrate is estimated. Three different Raman‐active dyes are investigated for their potential for involvement in sequence specific DNA analysis.