Geometric indices and the Alexander polynomial of a knot

It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.

     

Synthesis of potent beta-secretase inhibitors containing a hydroxyethylamine dipeptide isostere and their structure-activity relationship studies

Several beta-secretase inhibitors were designed based on hydroxyethylamine dipeptide isostere (HDI) structures and were synthesized by a methodology using the aza-Payne rearragement and O,N-acyl transfer reactions to study their structure-activity relationships. Among these pseudopeptides, effective compounds were developed as the first beta-secretase inhibitors containing the HDI transition state mimic with potent enzyme inhibitory activity (IC50 < 100 nM).     

Formal catalytic asymmetric total synthesis of fostriecin

The common synthetic intermediate of a potent and promising anticancer agent, fostriecin, was synthesized using a unique method that combines four catalytic asymmetric reactions as shown above.     

Simultaneous ultramicrodetermination of heterogeneous halogens in organic compounds

The simultaneous ultramicrodetermination of heterogeneous halogens in organic compounds was carried out by the potentiometric titration with 0.002 M silver nitrate after the sample was decomposed by the flask combustion method. In examination of the titration, it was found that clear potential break at the end point was obtained by controlling the delivery speed of the titrant at 0.2 ml/min or slower and the temperature of the solution to be titrated at ca. 10 °C when chloride ion is present. The error due to coprecipitation during the titration and the effect of the mole ratio of heterogeneous halide ions in the sample solution was examined and discussed. The analysis of organic halogen compounds resulted in an error of within 0.4% and standard deviation of less than 0.25%.