Toroidal Lie algebras and vertex representations

The paper describes the theory of the toroidal Lie algebra, i.e. the Lie algebra of polynomial maps of a complex torus ^××^× into a finite-dimensional simple Lie algebra g. We describe the universal central extension t of this algebra and give an abstract presentation for it in terms of generators and relations involving the extended Cartan matrix of g. Using this presentation and vertex operators we obtain a large class of integrable indecomposable representations of t in the case that g is of type A, D, or E. The submodule structure of these indecomposable modules is described in terms of the ideal structure of a suitable commutative associative algebra.To Professor J. Tits for his sixtieth birthday     

铁电共聚物VDF／TrFE的低温低频介电松弛

在低温低频下用介电松弛方法研究了液氮淬火，熔融慢冷和热处理结晶铁电共聚物ＶＤＦ（７３）／ＴｒＦＥ（２７）的分子运动特征，随结晶度升高，居里点温度降低，铁电－顺电相变区的介电常数增大。室温以下共聚物的频率谱由低频和高频两部分组成。低频部由非晶工区被冻结分子链段的微布朗运动贡献。高频部则由晶区和非晶区分子链段较小尺度的局域运动产生。由两个Ｃｏｌｅ－Ｃｏｌｅ函数对频率谱进行分峰拟合并根据ＷＬＦ方程和Ａｒ     

Reactions of 4-cyano- and 4-methylimidazoles with isocyanates

4-Cyano- and 4-methylimidazoles reacted with methyl and aryl isocyanates to give exclusively 1-(substituted carbamoyl)-4-cyano- and 4-methylimidazoles, respectively. Refluxing of 1-carbamoyl-4-methylimidazoles in nitrobenzene yielded 2-carbamoyl-4-methylimidazoles through a known migration, whereas the 4-cyano analogues could not be caused to migrate. On the other hand, the treatment of 4-cyano-1-(methylcarbamoyl)imidazole with methyl isocyanate under the basic conditions resulted in the formation of 2-methyl-1-(methylcarbamoylimino)-2, 3-dihydro-1H-imidazo[1, 5-c]imidazol-3-one which must be formed via the migration of the carbamoyl group to another nitrogen followed by the intramolecular cyclization of the newly introduced carbamoyl group with its viccyano group.     

Isomerization polymerization of 2-vinyl-1,3-dioxolane by α,α′-azobisisobutyronitrile or by γ-ray irradiation

2-Vinyl-1,3-dioxolane was polymerized by use of α,α′-azobisisobutyronitrile (AIBN) or by γ-ray irradiation. The polymer obtained was white amorphous powder which melted at ca. 70°C. and was soluble in chloroform, acetone, and p-dioxane. The infrared spectrum of the polymer indicated peaks at 1735 cm.^?1 characteristic of the carbonyl group, and at 1200–1000 cm.^?1 characteristic of the acetal group, while no absorption at 990 and 3100 cm.^?1 due to the vinyl group was observed. The spectra of the polymers obtained by AIBN and by γ-ray irradiation were essentially identical. The saponified product of the polymer was white powder and its reduced viscosity was a little larger than that of the original polymer. These results indicate that the polymer has no ester unit in the main chain. The results of gas chromatographic analysis of the saponified product of the polymer, indicate the presence of a small amount of ethyl alcohol. The results of the saponification showed that the ester content in the polymer varied from 7 to 25% depending upon the polymerization temperature. These results indicate that 2-vinyl-1,3-dioxolane polymerized by AIBN or by γ-irradiation with two modes of vinyl and hydrogen migration, yielding a copolymer having the unit structures      

Extraction-spectrophotometric determination of trace iron (II) in sea water with 2-[2-(3,5-dibromopyridyl)azo]-5-diethylaminobenzoic acid

An extraction-spectrophotometric method is described for the determination of traces of iron(II) with 2-[2-(3,5-dibromopyridyl)azo]-5-diethyl-aminobenzoic acid. The reagent forms a stable and blue 12 iron/reagent complex that can be extracted into chloroform. The apparent molar absorptivity of the iron(II) complex is 1.09 × 10⁵ 1 mol^–1 cm^–1 at 624 nm in chloroform. The reagent is relatively selective; interferences from cobalt, copper, nickel and vanadium can be removed by using dimethylglyoxime and EDTA. The method is applied to the determination of iron (II) in sea water and aluminium alloys with good precision and accuracy.     

Interaction of crosslinked polyethylenimine with a homologous series of methyl orange derivatives in aqueous solution

Polyethylenimine (PEI) was crosslinked with dichloroethane, glyoxal, or glutaraldehyde and polymers of various degrees of crosslinkage were made. The insoluble polymers obtained were examined for their ability to bind methyl orange and its homologs, methyl, ethyl, propyl, and butyl orange at 5, 15, 25, and 35°C, respectively, in an aqueous solution. PEI crosslinked with glutaraldehyde showed markedly increased binding affinity toward these cosolutes compared with the polymers crosslinked with dichloroethane or glyoxal. The extent of the binding increased with an increase in the degree of crosslinkage. These results suggest that the enhancement of the binding by the crosslinking is due mainly to a dual effect, introduction of hydrophobic moieties and proximity of neighboring polymer chains. The first binding constants and the thermodynamic parameters that accompanied the binding were calculated. The thermodynamic data show that the binding process is athermal and is stabilized entirely by the entropy term. Water-soluble PEI exhibited stronger cooperative interactions than the crosslinked polymer because the mobilities of the chains of the former are greater than those of the latter.     

N-Allyl-N-tert-butyldimethylsilylamine for chiral ligand-controlled asymmetric conjugate addition to tert-butyl alkenoates

The chiral ligand controlled asymmetric conjugate addition reaction of lithium N-allyl-N-(tert-butyldimethylsilyl)amide to alkenoates proceeded smoothly to give, after protodesilylation, the corresponding 3-allylaminoalkanoates with high enantioselectivities in high yields. The allyl group on the nitrogen atom was easily removable to afford 3-aminoalkanoates.     

INDUCTION OF phr GENE EXPRESSION BY PYRIMIDINE DIMERS IN Escherichia coli

The photoreactivating enzyme (PRE) is concerned with mainly two kinds of light wavelength. The PRE splits UVC (254 nm)-induced pyrimidine dimer by absorbing UVA (320–380 nm) or visible light in its chromophore. The present paper demonstrates that the phr gene expression was efficiently induced in an excision defective strain (uvrA∼) after irradiation by UVC and UVB (290-320 nm), but not by UVA and visible light. In addition, the induced activity was significantly depressed by irradiation with UVA and visible light. Therefore we conclude that the phr gene expression can be induced by pyrimidine dimers.     

Synthesis of 23,23-difluoro-25-hydroxyvitamin D3

23,23-Difluoro-25-hydroxyvitamin D₃ was synthesized from 6β-methoxy-3α,5-cyclo-23,24-dinor-5α-cholan-22-ol.     

Total synthesis of monocyclic β-lactam antibiotics,nocardicin A and D

The total synthesis of monocyclic β-lactam antibiotics, nocardicins A (1a) and D (1d), is described. 3-Aminonocardicinic acid (3-ANA, 2) was synthesized from p-hydroxyphenylglycine via an acid chloride-imine cyloaddition reaction. The side chain amino acid 13 was prepared via a key step of condensation of p-hydroxyacetophenone and α-phthalimidobutyrolactone. Acylation of 3-ANA with 13 gave nocardicin D, from which nocardicin A was obtained by oximation.