Wave asymptotics for waveguides and manifolds with infinite cylindrical ends

We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the case in certain favorable geometries, then there is an associated asymptotic expansion, up to a $O(t^{-k_0})$ remainder, of solutions of the wave equation on compact sets as $t \to \infty$. In the most general such case we have $k_0=1$, and under an additional assumption on the infinite ends we have $k_0 = \infty$. If we localize the solutions to the wave equation in frequency as well as in space, then our results hold for quite general waveguides and manifolds with infinite cylindrical ends. To treat problems with and without boundary in a unified way, we introduce a black box framework analogous to the Euclidean one of Sj\"ostrand and Zworski. We study the resolvent, generalized eigenfunctions, spectral measure, and spectral thresholds in this framework, providing a new approach to some mostly well-known results in the scattering theory of manifolds with cylindrical ends.Comment: In this revision we work in a more general black box setting than in the first version of the paper. In particular, we allow a boundary extending to infinity. The changes to the proofs of the main theorems are minor, but the presentation of the needed basic material from scattering theory is substantially expanded. New examples are included, both for the main results and for the black box settin

Discovery of TUG-770: a highly potent free fatty acid receptor 1 (FFA1/GPR40) agonist for treatment of type 2 diabetes

Free fatty acid receptor 1 (FFA1 or GPR40) enhances glucose-stimulated insulin secretion from pancreatic β-cells and currently attracts high interest as a new target for the treatment of type 2 diabetes. We here report the discovery of a highly potent FFA1 agonist with favorable physicochemical and pharmacokinetic properties. The compound efficiently normalizes glucose tolerance in diet-induced obese mice, an effect that is fully sustained after 29 days of chronic dosing

A New Nearctic Species of the Genus Tomocerus (Collembola: Entomobryidae).

Tomocerus (Plutomurus) grahami n.sp. is described from Terrero Cave, Terrero, Santa Fe Co., New Mexico. It is the fourth species of the subgenus recorded from North America

Phenotypic and Genotypic Analysis of Amino Acid Metabolism in \u3cem\u3eLactobacillus helveticus\u3c/em\u3e CNRZ 32

This study investigated genetic predictions for amino acid biosynthesis and catabolism by Lactobacillus helveticus CNRZ 32, a commercial cheese flavor adjunct that reduces bitterness and intensifies flavor notes. Conversion of amino acids into volatile and nonvolatile flavor compounds by L. helveticus and other lactic acid bacteria in cheese is thought to represent the rate-limiting step in the development of mature cheese flavor and aroma. One of the primary mechanisms for amino acid breakdown by these microbes involves the reversible action of enzymes involved in biosynthetic pathways, so our group investigated the genetics of amino acid biosynthesis in L. helveticus CNRZ 32. Most lactic acid bacteria are auxotrophic for several amino acids, and phenotypic characterization of L. helveticus CNRZ 32 has shown this bacterium requires 14 amino acids. Reconstruction of amino acid biosynthetic pathways from a draft-quality (incomplete) genome sequence for L. helveticus CNRZ 32 showed generally good agreement between gene content and phenotypic amino acid requirements. One exception involved the requirement ofCNRZ 32 for Asp (or Asn) for growth, where predictions derived from the genome sequence suggested this strain may be able to synthesize Asp from citrate. This prediction was confirmed as Asp auxotrophy in L. helveticus CNRZ 32 could be alleviated by the addition of citrate to a chemically defined medium that lacked Asp and Asn. Genome analysis also predicted that L. helveticus CNRZ 32 possessed ornithine decarboxylase activity, and would therefore catalyze the conversion of ornithine to putrescine, a volatile biogenic amine. Putrescine production in cheese would be undesirable because this compound may impart a rotting flesh flavor and can also have adverse effects on human health. Experiments to confirm ornithine decarboxylase activity in L. helveticus CNRZ 32 using a special growth medium, thin layer chromatography, high performance liquid chromatograph, or 13C nuclear magnetic resonance were unsuccessful, however, which indicated this bacterium does not contribute to putrescine production in cheese