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     

Mixtures of lattice polymers with structured monomers

The influence of monomer structure on the thermodynamic properties of lattice model polymer blends is investigated through Monte Carlo computations. The model of lattice polymers with monomer structure has been used extensively in the context of the lattice cluster theory (LCT), a thermodynamic theory for polymer mixtures in the liquid state. The Monte Carlo computations provide the first unequivocal test of the accuracy of the LCT predictions for binary mixtures of polymers with structured monomers. Four types of monomer structures are analyzed, corresponding to to the monomers of polyethylene, polypropylene, polyethylethylene, and polyisobutylene (PIB). Most computations use chains with M=12 and 24 beads and the total volume fraction of the beads is phi=0.6. Both structurally symmetric and asymmetric blends are investigated. For the symmetric case, the predictions of the LCT for the energies of mixing and the liquid-liquid coexistence curves are in qualitative agreement with the Monte Carlo computations, except for the PIB/PIB symmetric blend. For structurally asymmetric blends, the LCT does not capture contributions to the energy of mixing arising solely from structural differences between the components. Computational estimates of the nonideal entropy of mixing indicate that the LCT also underestimates the entropic cost of mixing chains with different structures, thus explaining some discrepancies between the theoretical and the Monte Carlo liquid--liquid coexistence curves.     

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.     

Efficient enantiomeric analysis of primary amines and amino alcohols by high-performance liquid chromatography with precolumn derivatization using novel chiral SH-reagent N-(R)-mandelyl-(S)-cysteine

Novel N-acylated-(S)-cysteine derivative-N-(R)-mandelyl-(S)-cysteine (R-NMC), containing additional chiral center, aromatic and polar alpha-substituents in contrast to the traditionally used enantiomerically pure thiols, has been demonstrated to be an efficient SH-reagent for enantiomeric HPLC analysis of primary nonfunctionalized amines and amino alcohols after precolumn derivatization with o-phthalaldehyde. The R-NMC-derived isoindoles as well as adducts formed using traditional SH-reagents had a characteristic absorption maximum at 340 nm with a molar absorbance 6000 M(-1) cm(-1), were stable during the HPLC-analysis and highly fluorescent allowing to detect 1 fmol of amino compound. Using diastereomeric R-NMC all tested amino alcohols were resolved effectively as well as nonfunctionalized amines, some of which were not resolved by a direct method on a chiral phase. Applying traditional enantiomeric N-acetyl-(S)-cysteine (NAC) only some isoindoles formed by aliphatic amino alcohols have been separated satisfactorily. The enhanced selectivity for R-NMC-derived isomers has been achieved, obviously, due to the involvement of the substituents at an extra chiral center into additional intramolecular interactions.     

Semicontinuous Emulsion Polymerization of Vinyl Acetate. Part I. Homopolymerization with Poly-(Vinyl Alcohol) and Nonionic Coemulsifier

The semicontinuous emulsion polymerization of vinyl acetate has been studied. Poly(vinyl alcohol) as a protective colloid and ethoxylated cetyl alcohol as a coemulsifier were used. The conversion and particle diameter were affected by the stirring speed and the coemulsifier distribution between initial reactor charge and continuously introduced monomer. The amount of unreacted monomer oscillates with time.