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.     

Total Synthesis of 7‐ and 8‐Oxygenated Pyrano[3,2‐a]carbazole and Pyrano[2,3‐a]carbazole Alkaloids via Boronic Acid‐Catalyzed Annulation of the Pyran Ring

The boronic acid‐catalyzed annulation of citral opens up a short route to oxygenated cyclized monoterpenoid pyranocarbazole alkaloids. Thus, murrayamine‐D is available in only three steps and 55% overall yield from the corresponding carbazole precursor.     

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.     

First principles analysis of H2O adsorption on the (110) surfaces of SnO2, TiO2 and their solid solutions

Both associative and dissociative H(2)O adsorption on SnO(2)(110), TiO(2)(110), and Ti-enriched Sn(1-x)Ti(x)O(2)(110) surfaces have been investigated at low ((1)/(12) monolayer (ML)) and high coverage (1 ML) by density functional theory calculations using the Gaussian and plane waves formalism. The use of a large supercell allowed the simulation at low symmetry levels. On SnO(2)(110), dissociative adsorption was favored at all coverages and was accompanied by stable associative H(2)O configurations. Increasing the coverage from (1)/(12) to 1 ML stabilized the (associatively or dissociatively) adsorbed H(2)O on SnO(2)(110) because of the formation of intermolecular H bonds. In contrast, on TiO(2)(110), the adsorption of isolated H(2)O groups ((1)/(12) ML) was more stable than at high coverage, and the favored adsorption changed from dissociative to associative with increasing coverage. For dissociative H(2)O adsorption on Ti-enriched Sn(1-x)Ti(x)O(2)(110) surfaces with Ti atoms preferably located on 6-fold-coordinated surface sites, the analysis of the Wannier centers showed a polarization of electrons surrounding bridging O atoms that were bound simultaneously to 6-fold-coordinated Sn and Ti surface atoms. This polarization suggested the formation of an additional bond between the 6-fold-coordinated Ti(6c) and bridging O atoms that had to be broken upon H(2)O adsorption. As a result, the H(2)O adsorption energy initially decreased, with increasing surface Ti content reaching a minimum at 25% Ti for (1)/(12) ML. This behavior was even more accentuated at high H(2)O coverage (1 ML) with the adsorption energy decreasing rapidly from 145.2 to 101.6 kJ/mol with the surface Ti content increasing from 0 to 33%. A global minimum of binding energies at both low and high coverage was found between 25 and 33% surface Ti content, which may explain the minimal cross-sensitivity to humidity previously reported for Sn(1-x)Ti(x)O(2) gas sensors. Above 12.5% surface Ti content, the binding energy decreased with increasing coverage, suggesting that the partial desorption of H(2)O is facilitated at a high fractional coverage.