Dehn filling in relatively hyperbolic groups

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2π Theorem in the context of relatively hyperbolic groups. The first author was supported in part by NSF Grant DMS-0504251. The second author was supported in part by an NSF Mathematical Sciences Post-doctoral Research Fellowship. Both authors thank the NSF for their support. Most of this work was done while both authors were Taussky-Todd Fellows at Caltech.     

Fast analysis with Zeeman graphite furnace AAS

Stabilized Temperature Platform Furnace (STPF) methods have been adapted and altered to reduce the analytical time to less than 1 min per sample with no loss of analytical precision or accuracy. It is shown that this could be further reduced to about 30 s per sample if certain changes in instrumentation are implemented, especially in the software and firmware that control the autosampler. The sample uptake rate for the autosampler should overlap the cooldown of the tube from the prior determination. Also, the sample should be deposited onto a heated platform. In this work the pyrolysis step and, in most cases, the use of a matrix modifier has been omitted. Since backgrounds were therefore larger, the use of Zeeman correction was usually required, but continuum background correction was not tried. To confirm that these fast analytical methods might be practical, more than 10 standard reference materials were analyzed for several elements including Pb, Cd, Cu, Ni, As and Cr. The paper is not primarily intended to provide routine and reliable methods; it is intended to test the feasibility of these fast methods.     

A counterion condensation theory for the relaxation,rise, and frequency dependence of the parallel polarization of rodlike polyelectrolytes

We calculate the relaxation, rise, and frequency dependence of the parallel polarization of counterions condensed on rodlike polyelectrolytes and charged colloids. Emphasis is placed on an effective counterion mobility along the rod as strongly influenced by electrostatic interactions.     

Synthesis, characterization, and photophysical study of fluorescent N-substituted benzo[ghi]perylene "swallow tail" monoimides

A set of N-substituted benzoperylene monoimide (BPI) fluorophores was synthesized and characterized structurally and photophysically. Condensation of benzo[ghi]perylene-1,2-dicarboxylic anhydride in the presence of "swallow tail" alkyl amines produced fluorophores that are soluble in a range of organic solvents, highly absorbing in the near-UV (ε(334) = 79,000 M(-1) cm(-1)), and fluorescent in the visible range. Photophysical behavior of the compounds was studied with steady-state and time-correlated single photon counting. The synthesized BPIs exhibit positive solvachromatic emission (λ(em) (hexane) = 469 nm; λ(em) (ethanol) = 550 nm) as a function of solvent polarity with little change in their excited-state lifetime (9.6-6.5 ns) and fluorescence quantum yield (0.27-0.44) over the polarity range studied. Solvachromatic shifts were analyzed using the Lippert-Mataga approach. In nonpolar hydrocarbon solvents evidence of dual emission from closely spaced (562 cm(-1)) S(1) and S(2) excited states is observed. Preliminary peak assignments for the anomalous S(2) emission are made.     

Kohlenwasserstoffe

Ohne Zusammenfassung     

Dithiocarbamate complexes of cyclopentadienylcobalt(III), [Co(η-C5H5)(L)(S2CNR2)] (L = ligand)

The reactions of [Co(η-C₅H₅)(L)I₂] with Na[S₂CNR₂] (R = alkyl or phenyl) give [Co(η-C₅H₅)(I)(S₂CNR₂)] (I) when L = CO and [Co(η-C₅H₅)(L)(S₂CNR₂)]I (II) when L is a tertiary phosphine, phosphite or stibine, or organo-isocyanide ligand. In similar reactions [Co(η-C₅H₅)(CO)(C₃F₇)I] gives [Co(η-C₅H₅)(C₃F₇)(S₂CNMe₂)] and [Mn(η-MeC₅H₄)(CO)₂(NO)]PF₆ forms [Mn(η-MeC₅H₄)(NO)(S₂CNR₂)]. The iodide ligands in I may be displaced by L, to give II, or by other ligands such as [CN]^?, [NCS]^?, H₂O or pyridine whilst SnCl₂ converts it to SnCl₂I. The iodide counter-anion in II may be replaced by others to give [BPh₄]^?, [Co(CO)₄]^? or [NO₃]^? salts. However [CN]^? acts differently and displaces (PhO)₃P from [Co(η-C₅H₅){P(OPh)₃}(S₂CNMe)]I to give [Co(η-C₅H₅)(CN)(S₂CNMe₂)] which may be alkylated reversibly by MeI and irreversibly by MeSO₃F to [Co(η-C₅H₅)(CNMe)(S₂CNMe₂)]⁺ salts. Conductivity measurements suggest that solutions of I in donor solvents are partially ionized with the formation of [Co(η-C₅H₅)(solvent)(S₂CNR₂)]⁺ I^? species. The IR and ¹H NMR spectra of the various complexes are reported. They are consistent with pseudo-octahedral “pianostool” molecular structures in which the bidentate dithiocarbamate ligands are coordinated to the metal atoms through both sulphur atoms.