Time change equations for Lévy-type processes

We consider time change equations for Lévy-type processes. In this context we generalize the results of Böttcher et al. (2013) significantly. Namely, we are able to incorporate measurable instead of continuous multipliers. This opens a gate to find whole classes of symbols for which corresponding processes do exist. In order to establish our results we carefully analyze the connection between time change equations and classical initial value problems. This relationship allows us to transfer well-known results from this classical subject of pure mathematics into the theory of stochastic processes. On the way to prove our main theorem we establish generalizations of results on paths of Lévy-type processes.     

Einfluß der Wolframsäure auf die Gelatinierung der Kieselsäure in stark salzsaurer Lösung.

Ohne Zusammenfassung     

Darstellung von Kleselsäure- und Wolframhydroxydsolen mit Hilfe der Hildebrandzelle

Ohne Zusammenfassung     

The Orthogonal (e,e,e)‐Tris‐Adduct of 9,10‐Dimethylanthracene with C60‐Fullerene: A Hidden Cornerstone of Fullerene Chemistry. Preliminary Communication

Tris(9′,10′‐dimethyl[9,10]ethanoanthracene[11′,12′: 1,9;11″,12″: 16,17;11′′′,12′′′: 30,31])[5,6]fullerene C₆₀, the orthogonal (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene, was obtained from [4+2]‐cycloaddition (Diels–Alder reaction) at room temperature. The thermally unstable orange red (e,e,e)‐tris‐adduct was purified by chromatography and was isolated in the form of red monoclinic crystals. Its C₃‐symmetric addition pattern was established spectroscopically. Its structure could be further investigated by single crystal X‐ray diffraction. The (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene has earlier been suggested as intermediate and reversibly formed critical component in ‘template directed’ addition reactions of C₆₀. This previously elusive compound has now been isolated and structurally characterized.     

Platinum(II) complexes with thiourea derivatives containing oxygen,sulfur or selenium in a heterocyclic ring: computational studies and cytotoxic properties

Platinum(II) complexes with 1-(2-oxolanylmethyl)-2-thiourea, 1-(2-thiolanylmethyl)-2-thiourea and 1-(2-selenolanylmethyl)-2-thiourea were synthesized in order to compare their cytotoxic activities with those of the free thioureas. Their equilibrium geometries and bonding energies in the gas phase and in solution were calculated using density functional theory at the MPW1PW/LanL2DZ level. The IR spectra of the complexes and their free ligands were compared. Stability of the complexes in 0.9% saline aqueous solution was tested by means of HPLC. The cytotoxic activities of the species against five human cell lines were evaluated, as well as the antimicrobial activities against twelve bacterial strains.