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.     

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.     

Halide-free dehydrative allylation using allylic alcohols promoted by a palladium-triphenyl phosphite catalyst

The triphenyl phosphite-palladium complex was found to effect catalytic substitution reactions of allylic alcohols via a direct C-O bond cleavage. The dehydrative etherification proceeded efficiently without any cocatalysts and bases to give allylic ethers in good to excellent yields.     

Vibronic interactions in negatively charged polyacetylene

Electron-phonon interactions in the monoanions of polyacetylenes such as C2H4 (2tpa), C4H6 (4tpa), C6H8 (6tpa), and C8H10 (8tpa) are studied and compared with those in the monoanions of polyacenes. The C-C stretching A(g) modes around 1500 cm(-1) the most strongly couple to the lowest unoccupied molecular orbitals (LUMO) in polyacetylenes. The estimated total electron-phonon coupling constants for the monoanions (l(LUMO)) are 0.579, 0.555, 0.463, and 0.401 eV for 2tpa, 4tpa, 6tpa, and 8tpa, respectively. The l(LUMO) values for polyacetylenes are much larger than those for polyacenes. Furthermore, the l(LUMO) value for polyacetylene with C(2h) geometry is estimated to be 0.254 eV, and is larger than that (0.024 eV) for polyacene with D(2h) geometry. The phase patterns difference between the LUMO of polyacenes localized on the edge part of carbon atoms, and the delocalized LUMO of polyacetylenes is the main reason for the calculated results. The single charge transfer through the molecule in polyacetylenes are also discussed. The reorganization energies between the neutral molecule and the corresponding monoanion are estimated to be 0.164, 0.144, 0.125, and 0.113 eV for 2tpa, 4tpa, 6tpa, and 8tpa, respectively. Such reorganization energy decreases with an increase in molecular size. The conditions under which the attractive electron-electron interactions are realized in the monoanions of polyacetylenes and polyacenes are discussed. In terms of the electron-phonon interactions and the reorganization energies, the relationships between the normal and possible superconducting states are briefly discussed. We find that the monoanions with smaller molecular size cannot easily become good conductors, however, the conditions under which the interactions between two electrons are attractive are more easily realized in the monoanions with smaller molecular size than in the monoanions with larger molecular size.     

One electron transfer mechanism in the enzymatic oxygenation of sulfoxide to sulfone promoted by a reconstituted system with purified cytochrome p-450

A kinetic study on enzymatic S-oxygenation of sulfoxides to sulfones was carried out by a reconstited system with purified cytochrome P-450. A linear correlation observed between log(Vmax)'s and the one-electron oxidation potentials of sulfoxides suggests that the oxygenation of sulfoxides proceeds via one electron transfer process to the active “oxenoid” intermediate of the enzyme.     

Penicillin-cephalosporin conversion X. New synthesis of dithioazetidinones from thiazoline-azetidinones

New ring-opening reaction of thiazoline-azetidinones 1 to dithioazetidinones 2 was achieved with 2-benzothiazolyl disulfide in aqueous acidic media and its potentiality for the preparation of a variety of cephalosporins 3 from various thiazoline-azetidinones 1 is demonstrated.     

Pi-face-selective Diels-Alder reactions of 3,4-di-tert-butylthiophene 1-oxide and 1-imide and formation of 1,2-thiazetidines

3,4-Di-tert-butylthiophene 1-oxide (1a) reacted with a series of electron-deficient alkenic dienophiles at its syn-pi-face relating to the S=O bond to give [4+2] adducts in excellent yields. The 1-oxide 1a also reacted even with angle-strained dienophiles acenaphthylene and norbornene at its syn-pi-face to afford [4+2] adducts; in the latter case, norbornene reacted exclusively at its exo-pi-face. The oxide 1a reacted with dimethyl acetylenedicarboxylate to produce dimethyl 4,5-di-tert-butylphthalate in high yield with spontaneous extrusion of SO from the initial adduct even at room temperature. Similarly, 3,4-di-tert-butylthiophene 1-(p-toluenesulfonyl)imide (3a) reacted with alkenic dienophiles at its syn-pi-face relating to the S=N bond to give [4+2] adducts in good yields. The reaction of 3a with 4-phenyl-1,2,4-triazoline-3,5-dione (PTAD) afforded a 1,2-thiazetidine 12a, the first example of S-unoxidized 1,2-thiazetidine, in good yield, through rearrangement of the initial [4+2] adduct. The molecular structure of 12a is discussed on the basis of the X-ray crystallographic analysis. Comparison of the foregoing reactions leads to the conclusion that the 1-oxide 1a is more reactive as a diene than the 1-imide 3a, which is more reactive than 3,4-di-tert-butylthiophene 1,1-dioxide. The origin of the syn-pi-face selectivities of 1a and 3a in Diels-Alder reactions is discussed in terms of the orbital mixing rule and steric effect and also based on B3LYP/6-31G(d) calculations.     

On the inverse Sturm-Liouville problem for spatially symmetric operators,II

Using a third order Picard-Fuchs equation we show that a certain two parameter family of planar vectorfields for parameter values in a certain cone has a unique limit cycle, which is born from a Hopf bifurcation and dies in a saddle connection. This removes a superfluous hypothesis in Theorem 3.2, Chapter 13 of S. N. Chow and J. K. Hale (“Methods of Bifurcation Theory,” Springer-Verlag, New York, 1982).