Remote asymmetric induction with vinylketene silyl n,o-acetal

A highly regio- and diastereoselective TiCl4-mediated vinylogous Mukaiyama aldol reaction using the chiral vinylketene silyl N,O-acetal has been developed. The present vinylogous Mukaiyama aldol reaction provides a unique and effective means of controlling remote asymmetric induction. The methyl group at the alpha-position is important in achieving a high level of stereoselectivity. From a synthetic point of view, this methodology can provide a one-step construction of delta-hydroxy-alpha,gamma-dimethyl-alpha,beta-unsaturated carbonyl unit that is seen in many natural polyketide products.     

On a p-Local Geometry Associated with a Complex of Non-Trivial p-Subgroups

Let D be a complex of non-trivial p-subgroups of a finite groupG, closed under G-conjugation. In this paper, a p-local geometry^p(G; D) is introduced for G associated with the complex D. Thehomotopy equivalence between ^p(G; D) and D is also studied.2000 Mathematics Subject Classification 20E15, 51E24.     

Nanosecond Time-Gated Spectroscopy of Laser-Ablation Plume of Human Hair to Detect Calcium for Potential Diagnoses

We demonstrate the nanosecond time-gated spectroscopy of plume luminescence in UV laser ablation of human hair. Clear and sharp peaks of calcium ion (Ca⁺) appear in the spectrum although the Ca content is only 0.1% in human hair. Highly sensitive detection of Ca is thus possible. In the experiment, the peak intensity of Ca⁺ was measured for human hair samples of female subjects over a wide range of age, and compared to the bone mineral density of the lumbar vertebrae of the subjects themselves. Our experimental results suggest that this specific spectroscopy has the potential for novel diagnoses including monitoring of daily Ca intake and a screening diagnosis of osteoporosis. The spectroscopic system and time transition of plume-luminescence spectra are also described.     

Absolutely continuous invariant measures for expanding piecewise linear maps

We prove the existence of absolutely continuous invariant measures for arbitrary expanding piecewise linear maps on bounded polyhedral domains in Euclidean spaces ℝ ^d . Oblatum 6-V-1999 & 8-VI-2000?Published online: 11 October 2000     

Affine geometric crystals and limit of perfect crystals

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect crystals of the Langlands dual affine Lie algebra.