First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

Lanthanide nitrate complexes with 2-azacyclononanone

Thermal behavior of rare earth nitrate complexes with 2-azacyclononanone (AZA) with Ln(NO₃)₃·3(AZA) composition (where Ln=Gd, Er and Ho) was analyzed in kinetic point of view. Kinetic parameters were calculated from thermogravimetric data. All obtained results were similar. The first decomposition step was representative to the loss of ligand and the residue was essentially Ln₂O₃. Furthermore, a reaction path was proposed for the thermal decomposition of the Ln(NO₃)₃·3(AZA).     

Über heteroorganische Verbindungen, 39. Mitt.: Neue Darstellungsmethoden für Bis-(dialkylthiophosphinyl)-trisulfide. Reaktionsmechanismus

Zusammenfassung Dialkyl-dithiophosphinsäuren reagieren mit Morpholinoschwefelchlorid zu Bis-(dialkyl-thiophosphinyl)-trisulfiden. In Anwesenheit von Triäthylamin bilden sich die bisher unbekannten S-Morpholino-dialkyl-mercapto-dithiophosphinate, die, dem angenommenen Reaktionsmechanismus entsprechend, mit Chlorwasserstoff und Dithiophosphinsäuren die Bis-(dialkyl-thiophosphinyl)-trisulfide liefern. S-Morpholino-diäthyl-mercapto-dithiophosphinat und Diäthyldithiophosphinsäure setzen sich zu Bis-(diäthyl-thiophosphinyl)-trisulfid um.

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Heteroorganic compounds, XXXIX.: New methods for the preparation of bis-(dialkylthiophosphinyl)-trisulfides, and a reaction mechanism

Dialkyldithiophosphinic acids react with morpholinosulfenyl chloride to give bis-(dialkylthiophosphinyl)-trisulfides. In the presence of triethylamine the hitherto not described S-morpholino-dialkyl-mercapto-dithiophosphinates are formed. According to an assumed reaction mechanism the latter react with HCl and dithiophosphinic acids to give bis-(dialkyl-thiophosphinyl)-trisulfides. S-Morpholino-diethylmercapto-dithiophosphinate and diethyldithiophosphinic acid yield bis-(diethylthiophosphinyl)-trisulfide.

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38. Mitt.:L. Almasi undA. Hantz, Mh. Chem.100, 798 (1969).     

A femtosecond study of the infrared-driven cis-trans isomerization of nitrous acid (HONO)

We investigate the dynamics and mechanism of the IR-driven cis-trans isomerization of nitrous acid (HONO) in a low-temperature krypton matrix applying ultrafast time resolved IR spectroscopy. After excitation of the OH-stretching mode the trans HONO state decays biexponentially on a 8 and 260 ps time scale. The initially excited cis HONO state decays on a 20 ps time scale. Cis HONO isomerizes with 10% quantum yield on a 20 ps time scale to trans HONO. The quantum yield we observe is significantly smaller than the previously reported 100%, which could imply that additional, much slower reaction channels exist. We furthermore developed a four-dimensional model of the system, which includes the three proton intramolecular degrees of freedom of HONO fully quantum mechanically and one intermolecular translational degree of freedom of the molecule in the crystal cage. We find that cis-trans isomerization necessarily is accompanied by a translation of the molecule as a whole in the crystal cage. The translational degree of freedom tunes the intramolecular proton states of HONO with respect to each other. When resonances occur, the proton states might couple and transfer population. We suggest a possible reaction pathway, where the cis OH-stretch excited state first couples to a high cis torsional mode, which then may transfer almost instantaneously to the trans side. The model qualitatively explains all experimental observations.     

A New ent‐Kaurane Diterpene from Stems of Alibertia macrophylla K. Schum. (Rubiaceae)

Phytochemical investigations of the stems of a specimen of Alibertia macrophylla led to the isolation and characterization of the new diterpene ent‐kaurane‐2β,3α,16α‐triol ( 1 ), along with triterpenes 2 – 8 , iridoids 9 – 12 , and phenolic acids 13 – 15 . The structure of 1 was established based on spectroscopic studies (¹H‐ and ¹³C‐NMR, IR, and HR‐ESI‐MS). This is the first report of the isolation of a diterpene from the Alibertia genus in Rubiaceae.