The surgeryL-groups of poly-(finite or cyclic) groups

Both authors were supported in part by the NSF     

The effects of solvation upon the acidities of nitroaromatics

Specific solvation of nitrated phenoxide, anilide and benzyl anions is shown to decrease in that order, with concomitant increases in substituent salvation assisted resonance effects — the nitrobenzyl anions are suggested to be essentially charge-delocalized.     

Towards empirical EPR parameters for characterizing V(IV) complexes

Improved empirical techniques are described for determining the solution structures (coordination numbers and ligand donor groups) of oxoV(IV) complexes from isotropic EPR parameters. These methods will enable more detailed structural information to be obtained than was available previously from such empirical correlations. Assignments of the structures of the V(IV)/oxalate complexes were found to differ from those proposed in the literature and have been important in developing the empirical parameters reported here. In acidic solutions (pH≤1), V(V) oxalate complexes decay slowly to yield three V(IV) complexes, [V(O)(ox)₂]^2?, [V(O)(ox)(OH₂)₃]⁰ andcis-[V(O)(ox)₂(OH₂)]^2? (ox=oxalato(2-)), which have been characterized by EPR spectroscopy. These same three complexes are obtained from the direct reaction of V(IV) with oxalic acid. The structures of these complexes were assigned on the basis of the pH and [oxH₂] dependences of the EPR signals and differ significantly to those reported in the literature. The equilibria among the five- and six-coordinate complexes, and the protonation/deprotonation equilibrium of the six-coordinate species are consistent with the well-studied isoelectronic Cr(V) system.     

A reservoir-type controlled release device using aqueous-organic partitioning and a porous membrane

A reservoir-type controlled release device based on aqueous-organic partitioning is described. The reservoir is bounded by a microporous or porous membrane, either a hollow fiber or a flat film. The agent partitions between phases at the aqueous-organic interface of the reservoir and the pore mouth, and then diffuses through the membrane pore into a surrounding aqueous solution. The partition coefficient significantly influences the rate of release of the agent. The performance of the system is evaluated using model agents. Controlled release from a reservoir containing a pure organic liquid agent is demonstrated using toluene. Zero-order release is achieved for benzoic acid partitioning from an organic reservoir into water-filled pores, and for nicotine partitioning from an aqueous reservoir into organic-filled pores. Studies using benzoic acid demonstrate the effectiveness of a thin, nonporous coating on slowing the rate of release. A fast-dissolving suspension of benzoic acid in decanol extends the duration of zero-order release. Two agents, nicotine and caffeine, are released simultaneously and independently from a divided reservoir. A simplified mathematical model is presented, and experimental results compared well with those predicted by the model.     

Metabolic profiling of valproic acid in patients using negative-ion chemical ionization gas chromatography-mass spectrometry

A negative-ion chemical ionization gas chromatographic-mass spectrometric method for the determination of valproic acid (VPA) and fourteen of its metabolites in a single chromatographic run is reported. The assay features the use of four internal standards and is applicable to the analysis of small serum and urine volumes. A combination of pentafluorobenzyl and trimethylsilyl derivatization resulted in the [M - 181]- ion as the base peak for all the metabolites measured. When these ions were monitored sensitivities in the low picogram levels were achieved. The VPA metabolite profile was determined in pediatric patients on VPA monotherapy and on combined VPA therapy with either carbamazepine or clobazam. The recently characterized diene metabolite, (E,E)-2,3'-diene-VPA, was found to be a major serum metabolite of VPA. In the patient groups taking VPA in combination with carbamazepine, the induction of omega and omega-1 pathways of VPA metabolism was apparent, while the levels of the beta-oxidation products were significantly decreased.     

Foliated control theory, II

The main result is a control theorem for the structure space of E with control near the leaves F in M, where : E M is a fiber bundle over the Riemannian manifold M having a compact closed manifold for fiber and F is a smooth foliation of M, each leaf of which inherits a flat Riemannian geometry from M. A similar result has been proved by the authors under the assumption that each leaf of F is one-dimensional and the fiber of : E M is homotopy stable.Both authors were supported in part by the National Science Foundations.     

Some Non-Homeomorphic Harmonic Homotopy Equivalences

For every dimension 11, we show the existence of non-homeomorphicharmonic homotopy equivalences, where the target manifold hasnegative curvature.     

Critical dynamics of dimers: implications for the glass transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.