Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Magnetic penetration depth in V3Si and LiTi2O4 measured by μSR

Muon spin relaxation (SR) studies have been performed in the normal spinel LiTi₂O₄ and the A-15 superconductor V₃Si to measure the magnetic penetration depth . The relaxation rate(T) 1/² in field-cooled measurements shows a sharp increase belowT _c followed by saturation at low temperatures in both systems. This feature implies an isotropic energy gap without anomalous zeros, and most likelys-wave pairing. The low temperature penetration depth (T 0) is determined to be 2100Å for LiTi₂O₄ and 1300Å for V₃Si respectively. Assuming a clean limit relation ^–2 n _s /m ^*, we derive the Fermi temperatureT _F n _s/ ^2/3 m ^* from the relaxation rate and the Sommerfeld constant asT _F ^3/4–1/4. Unlike conventional superconductors, both LiTi₂O₄ and V₃Si have a large ratio ofT _c /T _F 0.01, only slightly smaller than those ratios in more exotic superconductors.We thank C. Ballard and K. Hoyle for technical assistance. Work at Columbia University is supported by NSF Grant No. DMR-89-13784 and Packard Foundation (YJU). Ames Laboratory is operated for the U. S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. Work at Ames was supported by the Director for Energy Research, Office of Basic Energy Sciences.     

R-matrices for elliptic Calogero-Moser models

The classicalR-matrix structure for then-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independentR-matrix (without spectral parameter) whenn 4. The assumption of momentum independence is sufficient to reproduce the dynamicalR-matrices of Avan and Talon for the type I, II, III degenerations of the elliptic potential. The inclusion of a spectral parameter enables us to findR-matrices for the general elliptic potential.     

Generation of 6-(Trifluoromethyl)-4,5-dihydro-2(3H)-pyridone and the Application to Synthesis of Some Fused Nitrogen Heterocycles Carrying a Trifluoromethyl Group on the Bridgehead Position via Radical Cyclization of Dihydropyridones

Staudinger/aza-Wittig reaction of 6,6,6-trifluoro-5-oxohexanoyl azide with PPh(3) or PBu(3) was examined. A reactive intermediate acyl imine 1 was trapped by methanol. Without nucleophile, isomerized enamide form 3 was obtained. N-Iodobenzoylation and N-haloalkylation of 3 and following radical cyclization via the 5-exo or 6-exo mode gave benzoindolizidinone, indolizidinone, and quinolizidinone derivatives 10-14, which have a trifluoromethyl group at the bridgehead position adjacent to nitrogen. Although LiAlH(4) reduction of 10 and 11 gave a mixture of saturated benzoindolizidine 15 and amino alcohol 16, reduction with BH(3)/THF selectively gave the desired 15 and indolizidine 17 from 13.     

Isolation and Stereostructures of Dolastatin G and Nordolastatin G, Cytotoxic 35-Membered Cyclodepsipeptides from the Japanese Sea Hare Dolabella auricularia

A bioassay-directed fractionation of the cytotoxic constituents of the Japanese sea hare Dolabella auricularia resulted in the isolation of two 35-membered depsipeptides dolastatin G (1) and nordolastatin G (2), which showed cytotoxicity against HeLa S(3) cells with IC(50) values of 1.0 and 5.3 &mgr;g/mL, respectively. The gross structures of these substances were established by spectroscopic analysis including 2D NMR techniques. The absolute stereostructure of 1 was determined by chiral HPLC analysis of amino acid components obtained from acid hydrolysis of 1 and by the enantioselective syntheses of two degradation products arising from polyketide portions. Nordolastatin G (2) is a congener that has the same absolute stereochemistry as that of 1.