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.     

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.     

Quasi-classical limit of Toda hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W _{1 +} symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow _{1 +} symmetries of the dispersionless hierarchy through their action on the tau function.     

Information theory of miniaturization advantages of column liquid chromatography for quantitative analysis

Summary The influences of decreasing column diameter and length on two analytical goals, the precision and solvent efficiency, in reversed-phase liquid-chromatography are studied. Low solvent consumption is one of analytical advantages of miniaturized columns and is shown to be quantitatively evaluated by the precision and solvent efficiency which are defined to be the total Shannon mutual information obtained from an assay and the information obtained in a unit solvent volume, respectively. Analysis of paraben food additives on a microbore column is taken as an example. In trace analysis, the relative standard deviation (RSD) of measurements theoretically derived from the precision is shown to approach to the observed ones.     

Benzoyl(acetylacetonato)nickel(II) complexes containing tertiary phosphine ligands. Their synthesis,dynamic behavior in solution,and decarbonylation

Carbon monoxide is readily inserted into the phenyl—nickel bond of PhNi(acac)(PR₃)_n to give benzoylnickel complexes, PhCONi(acac)PR₃ (R = Ph, Et, cyclo-C₆H₁₁), which were characterized by elemental analysis, IR and NMR spectroscopy, as well as chemical reactions. The reactions of the benzoylnickel complexes with methyl iodide and alcohols give acetophenone and corresponding benzoates, respectively, accompanied by some decomposition reactions. The solid benzoylnickel complexes when heated at elevated temperatures are decarbonylated and biphenyl, benzophenone and carbon monoxide are liberated. The dynamic behavior of the acac ligand in acetone solution was studied and the activation parameters for the acac exchange reactions were obtained. The decarbonylation reaction of the benzoyl complex PhCONi(acac)PPh₃ in acetone was studied by NMR, and found to be first order in the benzoylnickel complex.     

Parallel synthesis of multi-branched oligosaccharides related to elicitor active pentasaccharide in rice cell based on orthogonal deprotection and glycosylation strategy

We describe a parallel and efficient synthesis of multi-branched oligosaccharides 3a-g based upon the structure of the phytoalexin elicitor active branched pentasaccharide 2. One-pot sequential orthogonal deprotection of tetrasaccharide 5 with three different protecting groups provided each of seven glycosyl acceptors 4a-g. Glycosylation of the acceptors 4a-g, followed by deprotection provided branched oligosaccharides 3a-g. All the reaction processes from scaffold 5 to 3a-g except for final hydrogenolysis were achieved utilizing an automated synthesizer in a parallel fashion.     

Concise synthesis of pyrrolophenanthridine alkaloids using a Pd-mediated biaryl coupling reaction with regioselective C-H activation via the intramolecular coordination of the amine to Pd

The concise synthesis of Amaryllidaceae alkaloids, such as anhydrolycorinone, anhydrolycorin-7-one, assoanine, and oxoassoanine, which have a pyrrolophenanthridine skeleton, was achieved in moderate yield using the Pd-mediated biaryl coupling reaction of 1-(2-halobenzyl)-2,3-dihydroindole, which applied the regioselective C-H activation method with intramolecular coordination of the benzylamino group to Pd.