Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.     

Integer points on hypersurfaces

Very general hypersurfaces in ⁴ contain r ^2+(4/9) integer points in any ball of radiusr>1. As a consequence, an irreducible algebraic hypersurface in ⁿ (wheren4) which is not a cylinder and is of degreed, contains c(d, n)r ^{n–1–(5/9)} integer points in a ball of radiusr. This improves on the known boundc(d, n)r ^n–(3/2).Meinem verehrten Lehrer Professor E. Hlawka zum siebzigsten Geburtstag gewidmetWritten with partial support from NSF-MCS-8211461.     

Dynamic Fourier transform infrared spectroscopy in polymer research

The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer.     

Competition between van der Waals and hydrogen bonding interactions: structure of the trans-1-naphthol/N(2) cluster

The excitation energy in the multiphoton ionization spectrum of the trans-1-naphthol/N(2) cluster shows only a small red shift with respect to isolated naphthol, indicating a van der Waals pi-bound structure rather than a hydrogen-bonded one. To confirm this interpretation, high-level electronic structure calculations were performed for several pi- and hydrogen-bonded isomers of this cluster. The calculations were carried out at the second order M?ller-Plesset (MP2) level of perturbation theory with the family of correlation consistent basis sets up to quintuple-zeta quality including corrections for the basis set superposition error and extrapolation to the MP2 complete basis set (CBS) limit. We report the optimal geometries, vibrational frequencies, and binding energies (D(e)), also corrected for harmonic zero-point energies (D(0)), for three energetically low-lying isomers. In all calculations the lowest energy structure was found to be an isomer with the N(2) molecule bound to the pi-system of the naphthol ring carrying the OH group. In the CBS limit its dissociation energy was computed to be D(0) = 2.67 kcal/mol (934 cm(-1)) as compared to D(0) = 1.28 kcal/mol (448 cm(-1)) for the H-bound structure. The electronic structure calculations therefore confirm the assignment of the experimental electronic spectrum corresponding to a van der Waals pi-bound structure. The energetic stabilization of the pi-bound isomer with respect to the hydrogen-bonded one is rather unexpected when compared with previous findings in related systems, in particular phenol/N(2).     

A new and versatile Ugi/SNAr synthesis of fused 4,5-dihydrotetrazolo[1,5-a]quinoxalines

A combinatorial synthetic route yielding fused tetrazolo[1,5-a]quinoxalines is described. The use of 2-fluorophenylisocyanide in the Ugi-tetrazole reaction (tetrazole-U-4CR) followed by a nucleophilic aromatic substitution (S_NAr) affords the tricylic tetrazolo[1,5-a]quinoxaline moiety in good yields and with high diversity.     

Analysis of Colubroidea snake venoms by liquid chromatography with mass spectrometry: evolutionary and toxinological implications

The evolution of the venomous function of snakes and the diversification of the toxins has been of tremendous research interest and considerable debate. It has become recently evident that the evolution of the toxins in the advanced snakes (Colubroidea) predated the evolution of the advanced, front-fanged delivery mechanisms. Historically, the venoms of snakes lacking front-fanged venom-delivery systems (conventionally grouped into the paraphyletic family Colubridae) have been largely neglected. In this study we used liquid chromatography with mass spectrometry (LC/MS) to analyze a large number of venoms from a wide array of species representing the major advanced snake clades Atractaspididae, Colubrinae, Elapidae, Homalopsinae, Natricinae, Psammophiinae, Pseudoxyrhophiinae, Xenodontinae, and Viperidae. We also present the first sequences of toxins from Azemiops feae as well as additional toxin sequences from the Colubrinae. The large body of data on molecular masses and retention times thus assembled demonstrates a hitherto unsuspected diversity of toxins in all lineages, having implications ranging from clinical management of envenomings to venom evolution to the use of isolated toxins as leads for drug design and development. Although definitive assignment of a toxin to a protein family can only be done through demonstrated structural studies such as N-terminal sequencing, the molecular mass data complemented by LC retention information, presented here, do permit formulation of reasonable hypotheses concerning snake venom evolution and potential clinical effects to a degree not possible till now, and some hypotheses of this kind are proposed here. The data will also be useful in biodiscovery.     

Highly sensitive semi-quantitative field test for the determination of chromium (VI) in aqueous samples

A method for the semi-quantitative colorimetric determination of chromium(VI) at sub μg/L levels after sorptive preconcentration is presented. The method is based on the retention of the reaction product (preformed in liquid phase) between Cr(VI) and diphenylcarbazide on membrane embedded cation exchange material. The color intensity of the membrane can be correlated to Cr(VI) concentrations in the range 0.05–50 μg/L (i.e. almost three orders of magnitude lower than the conventional spectrophotometric procedure) with a detection limit of about 10 ng/L (using 50 mL of sample volume). Due to the visual inspection mode and comparative color detection the precision is only 30–80% rsd which, however, is regarded as sufficient for screening purposes. Analysis of real samples including different kinds of waters and extracts of soil and filter collected airborne particulate matter demonstrated the applicability of the method for fast and species selective screening. Recovery experiments generally gave reasonably good results, yet also revealed the risk of the conversion of chromium species during sample pretreatment procedures due to redox reactions. Received: 1 December 1997 / Revised: 23 February 1998 / Accepted: 10 March 1998     

Electronic Structure and Photophysical Properties of Isoindole and its Benzo[f]- and Dibenzo[e,g]-Derivatives

The synthesis of N-methyl-benz[f]isoindole ( 2 ) and N-methyl-dibenz[e,g]isoindole ( 3 ) is reported. The NMR. spectra of N-methyl-isoindole ( 1 ) and of 2 have been analysed and the implications concerning the alternation of bond lengths are discussed. The photophysical properties of 1 to 3 have been investigated by the following methods: HeI photoelectron (PE.) spectroscopy, UV./VIS. absorption (polarization measurements by the stretched-foil technique) and emission spectroscopy (fluorescence spectra, lifetimes and quantum yields, phosphorescence spectra), and flash spectroscopy (triplet-triplet absorption spectra). The discussion of the results is based on HMO. and PPP SCF CI. calculations and points to the relationship between the heterocycles 1 to 3 and the corresponding benzenoid hydrocarbons obtained by replacement of the ? NMe? subunit by ? CH?CH? . Some comments concerning the ground state properties of isoindole and related compounds are derived from the analysis of their electronic structure.     

Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach

The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding system yield no trace of the gas-gas and liquid-liquid equilibria, and we conclude that the latter are just artefacts of the PC-SAFT approach. Using PC-SAFT to correlate data for polybutadiene melts, we suggest that discrepancies in modelling the polymer density at ambient temperature and high pressure can be related to the presumably artificial liquid-liquid phase separation at lower temperatures. Thus, particular care is needed in engineering applications of the PC-SAFT theory that aims at predicting properties of macromolecular materials.     

Nucleotides. Part XLVIII. Synthesis of 2′-amino-2′-deoxyarabinonucleoside phosphoramidite building blocks

Chemical syntheses of 2′-amino-2′-deoxyarabinonucleosides of uracil, thymine, cytosine, adenine, and guanine and their conversion into suitably protected 3′-phosphoramidite building blocks 24–28 for oligonucleotide synthesis are described. The 2-(4-nitrophenyl)ethoxycarbonyl (npeoc) group was used for protection of the aglycon and the 2′-amino functions.