Mixed toric residues and tropical degenerations

Building on our earlier work on toric residues and reduction, we give a proof of the mixed toric residue conjecture of Batyrev and Materov. We simplify and streamline our technique of tropical degenerations, which allows one to interpolate between two localization principles: one appearing in the intersection theory of toric quotients and the other in the calculus of toric residues. This quickly leads to the proof of the conjecture, which gives a closed formula for the summation of a generating series whose coefficients represent a certain naive count of the numbers of rational curves on toric complete intersection Calabi-Yau manifolds.     

Volume Computation for Polytopes and Partition Functions for Classical Root Systems

This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we present an efficient computation of the partition function for classical root systems.     

Vector partition functions and index of transversally elliptic operators

This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory are in [4], while in [5] and [6] we shall investigate the cohomological formulas generated by this theory.     

MALDI-TOF/TOF CID study of poly(α-methylstyrene) fragmentation reactions

MALDI-TOF/TOF CID experiments are reported for hydroxylated poly(α-methylstyrene) precursor ions (PAMS: m/z 1,445.9 (n = 10), 2,036.3 (n = 15), 2,626.7 (n = 20), 3,217.1 (n = 25), and 3,807.5 (n = 30), where the number of repeat units n corresponds to the oligomer mass numbers). The influences of structure, molecular weight, and kinetic energy on degradation mechanisms were examined to test the generality of our multi-chain fragmentation model developed for polystyrene. Our results indicate that poly(α-methylstyrene) free radicals are formed initially through multiple chain breaks and subsequently undergo a variety of depolymerization reactions to yield predominantly monomer and dimer species; the intensity of each species depends on the effective kinetic energy selected for the CID process. Each depolymerization mechanism is presented in detail with experimental and computational data to justify/rationalize the process and its kinetic energy dependence. These processes show the complex interrelationships between the various pathways along with preferred production of tertiary radicals, which suppresses the appearance of primary radicals. Additionally, Py-GC/MS experimental data are presented to allow a comparison of the multimolecular free radical reactions in pyrolysis with the unimolecular fragmentation reactions of MS/MS. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Combinations of microphase separation and terminal multiple hydrogen bonding in novel macromolecules

The synthesis and characterization of terminal multiple hydrogen-bonded (MHB) polymers, such as poly(styrene) (PS), poly(isoprene) (PI), and microphase separated PS-b-PI block copolymers, possessing controlled molecular weights and narrow molecular distributions are described. Hydroxyl-terminated polymeric precursors were prepared using living anionic polymerization and subsequent quantitative termination with ethylene oxide. MHB polymers were synthesized in a controlled fashion via end-group modification of these well-defined macromolecular alcohols with excess isophorone diisocyanate and subsequent derivatization of the isocyanate-terminated polymeric intermediate with methyl isocytosine. The glass transition temperatures of the terminal MHB polymers were reproducibly higher than both nonfunctionalized and hydroxyl-terminated polymers at nearly equivalent number average molecular weights. Thin-layer chromatography analysis indicated that the interaction of terminal MHB polymers with silica was stronger as compared to both nonfunctionalized and hydroxyl-terminated polymers. Rheological characterization indicated that the melt viscosity at constant shear rate for various MHB polymers was more than 100 times higher than those for nonfunctionalized and hydroxyl-terminated polymers. Interestingly, the melt viscosity of MHB polymers was higher than those of nonfunctionalized polymers with twice the number average molecular weight. In addition, DSC and rheological characterization also suggested that terminal MHB polymers formed aggregates and not simple dimers in the melt state, and the aggregates were observed to completely dissociate at 80 degrees C.     

Verpacamides A-D, a sequence of C11N5 diketopiperazines relating cyclo(Pro-Pro) to cyclo(Pro-Arg), from the marine sponge Axinella vaceleti: possible biogenetic precursors of pyrrole-2-aminoimidazole alkaloids

[reaction: see text] Four C(11)N(5) diketopiperazine metabolites named verpacamides A (6), B (7), C (8), and D (9) consisting of a proline-arginine dipeptide skeleton have been isolated from the marine sponge Axinella vaceleti. Verpacamides A-D are a sequence of metabolites showing the transformation of proline and arginine into the oxidized guanidinyl-cyclo(Pro-Pro) 8 and 9. Compounds 6-9 are structurally and chemically related to C(11)N(5) pyrrole-2-aminoimidazole metabolites also isolated from the Axinellidae and Agelasidae families of sponges and exemplified by dispacamide A (4) and dibromophakellin (10).