A note on unit and class number of real quadratic fields

Letp be an odd prime withp1 (mod 4) andQ(p) be the real quadratic field. Also let andh denote the fundamental unit and the class number of Q(p), respectively. The main purpose of this paper is to study the explicit expressions of ^h and ^2h , and to discuss the problems related to the conjecture of Ankeny-Artin-Chowla.     

Highly regio- and stereocontrolled SN2′ reactions of gem-difluorinated vinyloxiranes with monoalkylcopper reagents

Reaction of gem-difluorinated vinyloxiranes with RCu(X)Li allowed us to introduce the R group regioselectively at the fluorine-attached terminal carbon atom in an S_N2′ manner to afford (E)-allylic alcohols exclusively, while homoallylic alcohols with anti stereochemical relationship were found to be obtained selectively from higher-ordered cuprates derived from CuCl and RMgBr in a ratio of 1:3.     

Fluorescence spectra,fluorescence quantum yields and fluorescence lifetimes of polymers having trans-1,2-dicarbazolylyclobutane or carbazolyl group

Quantum yields, lifetimes and shapes of fluorescence from polymers containing the trans-1,2-dicarbazolylcyclobutane (DCZB) or carbazolyl structures were studied in N,N-dimethylformamide. No sandwich-type excimer formation was observed for DCZB polymers. The so-called second excimer observed in poly(9-vinylcarbazole) might also be produced in poly(9-ethyl-3-vinylcarbazole).     

Synthesis of 3-substituted 4H-1-benzothiopyran-4-ones

3-Substituted 2-phenyl-4H-1-benzothiopyran-4-ones (thioflavones) were prepared to test antimicrobial activity. It was found that 3-(phenyl)thiochromone derivatives (isothioflavones) were prepared by the Meerwein reaction of thiochromone with p-nitrobenzenediazonium ion. 3-(Formyl)thioflavone exhibits weak antimicrobial activity against Trichophytons and Candida.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Aurilide, a cytotoxic depsipeptide from the sea hare Dolabella auricularia: isolation, structure determination, synthesis, and biological activity

The bioassay-guided fractionation of the cytotoxic constituents of the Japanese sea hare Dollabella auricularia led to the isolation of aurilide (1), a 26-membered cyclodepsipeptide. The gross structure of 1 was established by spectroscopic analysis including 2D NMR techniques. The absolute stereostructure was determined by chiral HPLC analysis of acid hydrolysates of 1 and by the enantioselective synthesis of a degradation product arising from a dihydroxylated fatty acid portion. The enantioselective synthesis of 1 was achieved in 12% overall yield (16 steps) and confirmed the absolute stereostructure of 1. The cytotoxicity of 1 was evaluated using a synthetic sample, which was found to exhibit potent cytotoxicity against HeLa S₃ cells with an IC₅₀ of 0.011 μg/mL. Further biological and pharmacological studies of 1 have been carried out by using synthetic 1.     

Heteroatom-guided torquoselective olefination of alpha-oxy and alpha-amino ketones via ynolates

Ynolates were found to react with alpha-alkoxy-, alpha-siloxy-, and alpha-aryloxyketones at room temperature to afford tetrasubstituted olefins with high Z selectivity. Since the geometrical selectivity was determined in the ring opening of the beta-lactone enolate intermediates, the torquoselectivity was controlled by the ethereal oxygen atoms. From experimental and theoretical studies, the high Z selectivity is induced by orbital and steric interactions rather than by chelation. In a similar manner, alpha-dialkylamino ketones provided olefins with excellent Z selectivity. These products can be easily converted into multisubstituted butenolides and gamma-butyrolactams in good yield.     

Combinatorial synthesis of MUC1 glycopeptides: polymer blotting facilitates chemical and enzymatic synthesis of highly complicated mucin glycopeptides

The chemoselective polymer blotting method allows for rapid and efficient synthesis of glycopeptides based on a "catch and release" strategy between solid-phase and water-soluble polymer supports. We have developed a heterobifunctional linker sensitive to glutamic acid specific protease (BLase). The general procedure consists of five steps, namely (i) the solid-phase synthesis of glycopeptide containing BLase sensitive linker, (ii) subsequent deprotections and the release of the glycopeptide from the resin, (iii) chemoselective blotting of the glycopeptide intermediates in the presence of water-soluble polymers with oxylamino functional groups, (iv) sugar elongations using glycosyltransferases, and (v) the release of target glycopeptides from the polymer platform by selective BLase promoted hydrolysis. The combined use of the solid-phase chemical syntheses of peptides and the enzymatic syntheses of carbohydrates on water-soluble polymers would greatly contribute to the production of complicated glycopeptide libraries, thereby enhancing applicative research. We report here a high-throughput synthetic system for the various types of MUC1 glycopeptides exhibiting a variety of sugar moieties. It is our belief that this concept will become part of the entrenched repertoire for the synthesis of biologically important glycopeptides on the basis of glycosyltransferase reactions in automated and combinatorial syntheses.     

Reduction of acetophenone using supercritical 2-propanol: the substituent effect and the deuterium kinetic isotope effect

The reductions of several substituted acetophenones using supercritical 2-propanol were carried out to estimate the Hammett's reaction constant (ρ=0.33). Also, the reduction of acetophenone using supercritical deuteriated 2-propanol was carried out to determine the rate-determining step. The kinetic isotope effects were observed in the reduction using 2-deuterio-2-propanol (k_H/k_D=1.6) and O-deuterio-2-propanol (k_H/k_D=2.0). These findings suggest that the reaction proceeds via a cyclic transition state between acetophenone and 2-propanol similar to that of the Meerwein-Ponndorf-Verley reduction.     

Asymmetric 1,4-addition of alkenylzirconium reagents to α,β-unsaturated ketones catalyzed by chiral rhodium complexes

Highly enantioselective 1,4-addition of alkenylzirconocene chlorides to α,β-enones was found to be catalyzed by a chiral rhodium complex generated from [Rh(cod)(MeCN)₂]BF₄ and (S)-BINAP. The reaction can be applied to either cyclic or acyclic enones and the optical yield was up to 99% ee. The reaction mechanism would involve the transmetalation between the alkenylzirconocene chloride and the rhodium complex to give the alkenylrhodium species as a key intermediate.