On the class numbers of certain Hilbert class fields

LetL/k be a finite Galois extension with Galois groupG, and a group extension. We study the existence of the Galois extensionM/L/k such that the canonical projection Gal(M/k)→Gal(L/k) coincides with the given homomorphismj:E→G and thatM/L is unramified.     

On-line preconcentration strategies for trace analysis of metabolites by capillary electrophoresis

Analysis of low concentrations of metabolites is required for new fields of biological research, such as metabolomics. In this review, recent work in our laboratory aimed at developing improved strategies for on-line sample preconcentration of metabolites by capillary electrophoresis (CE) is presented. Dynamic pH junction, sweeping and dynamic pH junction-sweeping represent three complementary methods for electrokinetic focusing of large volumes of sample directly on-capillary. Focusing selectivity and focusing efficiency are two factors that can be used to assess the suitability of each method for different classes of metabolites. Buffer properties can be selected to enhance the focusing of specific types of metabolites based on knowledge of the analyte physicochemical properties. The application of on-line preconcentration CE for trace analysis of metabolites in real samples of interest, such as biological fluids and cellular extracts, is also demonstrated. Under optimum conditions, up to three orders of magnitude increase in concentration sensitivity can be realized for several classes of metabolites, including catecholamines, purines, nucleosides, nucleotides, amino acids, steroids and coenzymes. Recent work on hyphenating on-line preconcentration with multiplexed CE is highlighted as a promising platform for sensitive and high-throughput analyses of metabolites.     

Intramolecular oxyselenenylation and deselenenylation reactions in water, conducted by employing polymer-supported arylselenenyl bromide

After immobilizing arylselenenyl bromide on polymer resin, the oxyselenenylation reaction of olefin was carried out in water. An amphiphilic polymer-supported arylselenenyl bromide was employed, and various intramolecular oxyselenenylation and deselenenylation reactions proceeded smoothly in water in fair chemical yields (up to an 83% yield).     

Encapsulations of La@C82 and La2@C80 inside single-walled boron nitride nanotubes

Possibility of encapsulations of metallofullerenes inside single-walled boron nitride nanotubes (BNNTs) is studied by using first-principles calculations. We find that both La@C₈₂ and La₂@C₈₀ can be exothermically encapsulated inside the (17, 0) and (14, 7) BNNTs. The minimum diameters of exothermically encapsulating both La@C₈₂ and La₂@C₈₀ inside BNNTs are predicated to be about 13.4 Å.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

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.     

Isolation, characterization, and theoretical study of La2@C78

A new metallofullerene, La2@C78, has been synthesized by DC arc discharge method, isolated by high-performance liquid chromatography, and characterized by laser desorption time-of-flight mass spectrometry, UV-vis-NIR absorption, differential pulse voltammetry, 13C NMR spectroscopy, and theoretical calculations. The La2@C78/CS2 solution is dark violet and presents several characteristic absorption features at 647, 561, 533, and 386 nm, with an onset around 1000 nm. With respect to empty D3-C78, the capability of La2@C78 as an electron acceptor or donor is stronger. Addition of 1,1,2,2-tetrakis(2,4,6-trimethylphenyl)-1,2-disirane to La2@C78 photochemically, as well as thermally, affords bis- and mono-adducts. Theoretical studies and 13C NMR spectroscopic analysis of La2@C78 indicate that it possesses a D3h-C78 cage (78:5).     

Base-labile tert-butoxycarbonyl (Boc) group on phenols

Phenols are deprotected with weak bases from their tert-butoxycarbonyl (Boc) derivatives. Boc deprotection with bases can avoid side reactions during the deprotection with acids. We note the lability of the Boc to bases and are able to utilize it as a new cleavage condition for synthetic studies.     

Initiation of cationic polymerization of n-butyl vinyl ether by stable cation radicals of substituted phenothiazines

3,7-Diethyl- 10-phenylphenothiazine (DEPPT), a phenothiazine derivative whose 3,7- and 10-positions are blocked, was synthesized. Potentiostatic electrolysis of DEPPT in acetonitrile (ACN) in the presence of 0.1M of LiClO₄ at 0.7 V (vs. Ag/Ag/Cl) yielded the stable cation radical of DEPPT (DEPPT^+·) which was characterized by cyclic voltammetry, UV-visible spectroscopy, and ESR spectrometry. Stable cation radicals of 10-phenylphenothiazine and 3,7-diethyl-10-methylphenothiazine were also prepared. The cationic polymerization of n-butyl vinyl ether was initiated by these cation radicals, including DEPPT^·+. The electron transfer mechanism for the initiation step, which we proposed previously, was supported by the fact that DEPPT^·+ was capable of initiating the polymerization; dimerization of DEPPT^·+ by releasing protons is precluded because 3,7- and 10-positions are all blocked. © 1994 John Wiley & Sons, Inc.