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     

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.     

The adsorption of cationic and amphoteric copolymers on glass surfaces: zeta potential measurements,adsorption isotherm determination,and FT Raman characterization

The adsorption of cationic and amphoteric copolymers onto controlled pore glass (CPG) powders has been studied by measurement of the powder particle zeta (zeta) potential, by determination of the adsorption isotherm, and by FT Raman measurements of the polymer-coated powder. The cationic polymers consisted chiefly of homopolymers of dimethyldiallylammonium chloride (DMDAAC) or copolymers of DMDAAC and acrylamide. The amphoteric polymers studied included copolymers of DMDAAC and acrylic acid. The comonomer ratio was varied to explore the dependence of cationic charge density on the extent and effect of adsorption. Both types of polymers adsorb onto the anionic glass surface via an ion-exchange mechanism. Consequently, a correspondingly higher mass of a low-charge-density copolymer adsorbs than of a cationic homopolymer. The presence of the anionic portion in the amphoteric polymers does not significantly alter this picture. The zeta potential, however, reflects the overall nature of the polymer. Cationic polymers effectively neutralize the glass surface, while amphoteric polymers leave the zeta potential net negative. Adsorption isotherms, determined via the depletion technique using colloidal titration, were used to "calibrate" a FT Raman method. The latter was used to determined the amount of adsorbed polymer under solution conditions in which colloidal titration could not be performed.