Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.     

Size-selected copper oxide nanoparticles synthesized by laser ablation

Size-tuned copper oxide nanoparticles with sizes of 9, 12, and 15 nm were fabricated by laser ablation and on-line size selection using a differential mobility analyzer at a gas pressure of 666 Pa. The dependence of the particle properties on the in situ annealing temperatures and selection sizes was investigated. The crystalline phases of the nanoparticles fabricated at temperatures below 973 K were assigned to monoclinic cupric oxide (CuO) which converted into cubic cuprous oxide (Cu₂O) when the annealing temperature was above 1,173 K. This indicates that the crystalline phases can be easily controlled by changing the annealing temperature. TEM images confirmed that well-crystallized and well-dispersed CuO and Cu₂O nanoparticles with narrow size distributions were obtained using this method. This fabrication process is useful and promising for the future investigation of the intrinsic size-dependent properties of CuO and Cu₂O.     

On a conjecture of ōshima

The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H(G), and it is known to be nilpotent. ōshima [H. ōshima, Self homotopy group of the exceptional Lie group G₂, J. Math. Kyoto Univ. 40 (1) (2000) 177-184] conjectured: if G is simple, then H(G) is nilpotent of class ?rankG. We show this is true for PU(p) which is the first high rank example.     

Solvation dynamics of coumarin 153 in alcohols confined in silica nanochannels

Solvation dynamics in alcohols confined in silica nanochannels was examined by time-resolved fluorescence spectroscopy using coumarin 153 (C153) as a fluorescent probe. Surfactant-templated mesoporous silica was fabricated inside the pores of an anodic alumina membrane. The surfactant was removed by calcination to give mesoporous silica (Cal-NAM) containing one-dimensional (1D) silica nanochannels (diameter, 3.1 nm) whose inner surface was covered with silanol groups. By treating Cal-NAM with trimethylchlorosilane, trimethylsilyl (TMS) groups were formed on the inner surface of the silica nanochannels (TMS-NAM). Fluorescence dynamic Stokes shifts of C153 were measured in alcohols (ethanol, butanol, hexanol, and decanol) confined in the silica nanochannels of Cal- and TMS-NAMs, and the time-dependent fluorescence decay profiles could be best fitted by a biexponential function. The estimated solvent relaxation times were much larger than those observed in bulk alcohols for both Cal- and TMS-NAMs when ethanol or butanol was used as a solvent, indicating that the mobility of these alcohol molecules was restricted within the silica nanochannels. However, hexanol or decanol in Cal- and TMS-NAMs did not cause a remarkable increase in the solvent relaxation time in contrast to ethanol or butanol. Therefore, it was concluded that a relatively rigid assembly of alcohols (an alcohol chain) was formed within the silica nanochannels by hydrogen bonding interaction and van der Waals force between the surface functional groups of the silica nanochannels and alcohol molecules and by the successive interaction between alcohol molecules when alcohol with a short alkyl chain (ethanol or butanol) was used as a solvent.     

Synthesis of novel pentafluorosulfanylfurans. Two retro-Diels-Alder approaches

The first examples of furan substituted with an SF5 group are reported. 3-pentafluorosulfanylfurans were prepared from their respective 2-pentafluorosulfanyl-5-cyano-7-oxabicyclo[2.2.1]hept-2-ene precursors via retro-Diels-Alder reactions. Also, a tandem cycloaddition/retrocycloaddition reaction between 4-phenyloxazole and 1-pentafluorosulfanylhex-1-yne was used to prepare 3-pentafluorosulfanyl-4-butylfuran. [reaction: see text].     

Synthesis of chiral oxime ethers based on regio- and enantioselective allylic substitution catalyzed by iridium-pybox complex

The oxygen atom of oximes acts as a reactive nucleophile in the iridium-catalyzed allylic substitution of unsymmetrical substrates to give the branched oxime ethers. Among several chiral ligands evaluated, the iridium complex of pybox ligand having phenyl group catalyzed the allylic substitution of phosphates with high activity to form the branched oxime ethers with good enantioselectivities.     

Studies on the biosynthesis of terrecyclic acid A II confirmation of the cyclization mechanism and hydrogen shifts using [2-2H3]acetate and [213C2H3]acetate

Feeding experiments with [2-³H₃]acetate and [2-¹³C²H₃]acetate in $\text{Aspergillus terreus}$ Thom No. 14 indicated that the hydrogen at C-2 in terrecyclic acid A is incorporated without migration from the precursor acetic acid; the results favour our group's earlier speculation for the cyclization to the tricyclic skeleton in the biosynthetic scheme.     

Total synthesis and biological evaluation of pacidamycin D and its 3'-hydroxy analogue

Full details of the total synthesis of pacidamycin D (4) and its 3'-hydroxy analogue 32 are described. The chemically labile Z-oxyacyl enamide moiety is the most challenging chemical structure found in uridylpeptide natural products. Key elements of our approach to the synthesis of 4 include the efficient and stereocontrolled construction of the Z-oxyvinyl halides 6 and 7 and their copper-catalyzed cross-coupling with the tetrapeptide carboxamide 5, a thermally unstable compound containing a number of potentially reactive functional groups. This synthetic route also allowed us to easily prepare 3'-hydroxy analogue 32. The assemblage by cross-coupling of the Z-oxyvinyl halide 6 and the carboxamide 5 at a late stage of the synthesis provided ready access to a range of uridylpeptide antibiotics and their analogues, despite their inherent labile nature with potential epimerization, simply by altering the tetrapeptide moiety.     

Mode change in the self-motion of a benzoquinone disk coupled with a NADPH system

The self-motion of a benzoquinone (BQ) disk on NADPH was investigated as the coupling of an autonomous motor and an enzyme reaction. In the absence of the enzyme reaction, features of motion changed depending on the concentration of NADPH, that is, continuous motion→ intermittent oscillatory motion→ no motion. When the reverse reaction from NADP(+) to NADPH was introduced into the system with the addition of an enzyme reaction, continuous motion changed to intermittent oscillatory motion with small amplitude. The mechanism of this mode change is discussed in relation to the surface tension as a driving force and the time course of UV spectra as a window to the progress of the reaction. Characteristic features of the mode change were qualitatively reproduced by a numerical calculation.