Improved Resolution of (±)-cis-2′-Hydroxy-5,9-dimethyl-6, 7-benzomorphan and Preparation of Racemic, (+)-, and (-)-cis-2-Methylcyclopropyl-2′-hydroxy-5,9-dimethyl-6,7-benzomorphan (Cyclazocine)

We report novel procedures for the efficient resolution of (±)-cis-2 -hydroxy-5, 9-dimethyl-6, 7-benzomorphan via the (-)-N-acetyl-L-glutamate and (+)-α-bromocamphor-φ-sulfonate salts, the direct N-substitution of the (+)-α-bromocamphor-φ-sulfonate salts, and the use of these methods for the synthesis of racemic, (+)-, and (-)-cyclazocine.     

A Brylinski filtration for affine Kac–Moody algebras

Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac–Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac–Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra cohomology vanishing result. We also give an example to show that the Poincare series of the principal nilpotent filtration is not always equal to the q-analog of weight multiplicity. Finally, we give some partial results for indefinite Kac–Moody algebras.     

Some Observations on Measuring Sound Speeds in Polymers Using Time-of-Flight

Experimental Techniques - The time-of-flight method has been used to measure the longitudinal and shear wave speeds in six polymers (polyether ether ketone [PEEK], PEEK with 10% carbon fibers,...     

Convex Entire Noncommutative Functions are Polynomials of Degree Two or Less

We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each other in a very explicit way. In particular, the averaging operator appears to be closely related to the solutions of the associated wave equation. The machinery used allows one to study a class of infinite graphs without assumption on the local finiteness.     

MATHEMATICS,LANGUAGE AND DERRIDA

Abstract

Derrida's revolutionary work in the study of language has seriously challenged the way in which we see words being attached to meanings. This paper makes tentative steps towards examining how his work might assist us in understanding the way in which our attempts to describe or capture our mathematical experiences modify the experience itself. In doing this we draw on the work of Jacques Derrida and John Mason in locating possible frameworks through which to conceptualise the relationship between language and mathematical cognition. It concludes that mathematical meaning never stabilises since it is caught between the individual's ongoing experience and society's ongoing renewal of its conventions. That is, mathematics, language and the human performing them are always evolving in relation to each other.     

Mechanochemical Formation,Solution Rearrangements,and Catalytic Behavior of a Polymorphic Ca/K Allyl Complex

Without solvents present, the often far-from-equilibrium environment in a mechanochemically driven synthesis can generate high-energy, non-stoichiometric products not observed from the same ratio of reagents used in solution. Ball milling 2 equiv. K[A’] (A’=[1,3-(SiMe₃)₂C₃H₃]⁻) with CaI₂ yields a non-stoichiometric calciate, K[CaA’₃], which initially forms a structure ( 1 ) likely containing a mixture of pi- and sigma-bound allyl ligands. Dissolved in arenes, the compound rearranges over the course of several days to a structure ( 2 ) with only η³-bound allyl ligands, and that can be crystallized as a coordination polymer. If dissolved in alkanes, however, the rearrangement of 1 to 2 occurs within minutes. The structures of 1 and 2 have been modeled with DFT calculations, and 2 initiates the anionic polymerization of methyl methacrylate and isoprene; for the latter, under the mildest conditions yet reported for a heavy Group 2 species (one-atm pressure and room temperature).