Obstructions to trivializing a knot

The recent proof by Bigelow and Krammer that the braid groups are linear opens the possibility of applications to the study of knots and links. It was proved by the first author and Menasco that any closed braid representative of the unknot can be systematically simplified to a round planar circle by a finite sequence of exchange moves and reducing moves. In this paper we establish connections between the faithfulness of the Krammer-Lawrence representation and the problem of recognizing when the conjugacy class of a closed braid admits an exchange move or a reducing move.     

Chronic excitotoxicity in the guinea pig cochlea induces temporary functional deficits without disrupting otoacoustic emissions

Brief cochlear excitotoxicity produces temporary neural swelling and transient deficits in auditory sensitivity; however, the consequences of long-lasting excitotoxic insult have not been tested. Chronic intra-cochlear infusion of the glutamate agonist AMPA (a-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) resulted in functional deficits in the sound-evoked auditory brainstem response, as well as in behavioral measures of hearing. The electrophysiological deficits were similar to those observed following acute infusion of AMPA into the cochlea; however, the concentration-response curve was significantly shifted as a consequence of the slower infusion rate used with chronic cochlear administration. As observed following acute excitotoxic insult, complete functional recovery was evident within 7 days of discontinuing the AMPA infusion. Distortion product otoacoustic emissions were not affected by chronic AMPA infusion, suggesting that trauma to outer hair cells did not contribute to AMPA-induced deficits in acoustic sensitivity. Results from the current experiment address the permanence of deficits induced by chronic (14 day) excitotoxic insult as well as deficits in psychophysical detection of longer duration acoustic signals.     

Determining the solution state orientation of a Ti enolate via stable isotope labeling, NMR spectroscopy, and modeling studies

Our group has used Ti-promoted aldol additions with an oxazolidineselone as the chiral auxiliary with much success. In these reactions, the Se atom in the auxiliary both promotes stereospecific addition as well as reports on, through the use of 77Se NMR spectroscopy, the ratio of diastereomers produced and the geometry of intermediates as the reaction proceeds. Through stable isotope labeling and NMR spectroscopy, we are able to experimentally observe a Ti enolate in solution and gain insight into its structure and reactivity. Results from molecular modeling calculations are also presented for comparison with NMR data.     

Sampling and storage of materials for trace elemental analysis

Accurate analysis depends upon a valid, representative and uncontaminated analytical sample. For many trace metals, contamination overwhelms the sample, leading to inaccurate analytical data. Methods of controlling contamination and their implications for better methods of sampling and storage are discussed here.     

Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy

Oblatum 21-I-1991 & 16-IX-1991     

Dynamical generation of quasicrystals

We present a new general mechanism for a dynamical generation (growth) of quasicrystals (and crystals) in any dimension. The growth process proceeds in elementary steps starting from a chosen seed and the notion of an ideal local configuration. Each step is governed by local information inside of the physical space of the quasicrystal: A point is added to existing quasicrystal points only if its locally defined phase matches at that point a freely chosen continuous phase (gauge) in the quasicrystal space within a given precision. Some 2D examples are shown.Work supported in part by the Natural Science and Engineering Research Council of Canada and by the FCAR of Quebec.     

A new route to 1-oxygenated carbazoles. Synthesis of murrayafoline-a

1-Oxygenated carbazoles are prepared in four steps from indole-2-carboxylates by Claisen condensation with butyrolactones, followed by hydrolysis with concomitant decarboxylation, oxidation, and ring closure (Scheme 2); the route is applied to the synthesis of the carbazole alkaloid, murrayafoline-A.