Gaudin Model,KZ Equation and an Isomonodromic Problem on the Tours

This Letter presents a construction of isospectral problems on the torus. The construction starts from an SU(n) version of the XYZ Gaudin model recently studied by Kuroki and Takebe within the context of a twisted WZW model. In the classical limit, the quantum Hamiltonians of the generalized Gaudin model turn into classical Hamiltonians with a natural r-matrix structure. These Hamiltonians are used to build a nonautonomous multi-time Hamiltonian system, which is eventually shown to be an isomonodromic problem on the torus. This isomonodromic problem can also be reproduced from an elliptic analogue of the KZ equation for the twisted WZW model. Finally, a geometric interpretation of this isomonodromic problem is discussed in the language of a moduli space of meromorphic connections.     

A sphere as a surface which contains many circles II

A sphereM inE ³ is characterized as a simply connected complete smooth surface which contains a circle through each pointp M contained in a normal plane ofM atp.The author would like to thank Professor K. Ogiue for his valuable suggestions.     

Metal components analysis of metallothionein-III in the brain sections of metallothionein-I and metallothionein-II null mice exposed to mercury vapor with HPLC/ICP-MS

Mercury vapor is effectively absorbed via inhalation and easily passes through the blood–brain barrier; therefore, mercury poisoning with primarily central nervous system symptoms occurs. Metallothionein (MT) is a cysteine-rich metal-binding protein and plays a protective role in heavy-metal poisoning and it is associated with the metabolism of trace elements. Two MT isoforms, MT-I and MT-II, are expressed coordinately in all mammalian tissues, whereas MT-III is a brain-specific member of the MT family. MT-III binds zinc and copper physiologically and is seemed to have important neurophysiological and neuromodulatory functions. The MT functions and metal components of MTs in the brain after mercury vapor exposure are of much interest; however, until now they have not been fully examined. In this study, the influences of the lack of MT-I and MT-II on mercury accumulation in the brain and the changes of zinc and copper concentrations and metal components of MTs were examined after mercury vapor exposure by using MT-I, II null mice and 129/Sv (wild-type) mice as experimental animals. MT-I, II null mice and wild-type mice were exposed to mercury vapor or an air stream for 2 h and were killed 24 h later. The brain was dissected into the cerebral cortex, the cerebellum, and the hippocampus. The concentrations of mercury in each brain section were determined by cold vapor atomic absorption spectrometry. The concentrations of mercury, copper, and zinc in each brain section were determined by inductively coupled plasma mass spectrometry (ICP-MS). The mercury accumulated in brains after mercury vapor exposure for MT-I, II null mice and wild-type mice. The mercury levels of MT-I, II null mice in each brain section were significantly higher than those of wild-type mice after mercury vapor exposure. A significant change of zinc concentrations with the following mercury vapor exposure for MT-I, II null mice was observed only in the cerebellum analyzed by two-way analysis of variance. As for zinc, the copper concentrations only changed significantly in the cerebellum. Metal components of metal-binding proteins of soluble fractions in the brain sections were analyzed by size-exclusion high-performance liquid chromatography (HPLC) connected with ICP-MS. From the results of HPLC/ICP-MS analyses, it was concluded that the mercury components of MT-III and high molecular weight metal-binding proteins in the cerebellum of MT-I, II null mice were much higher than those of wild-type mice. It was suggested that MT-III is associated with the storage of mercury in conditions lacking MT-I, and MT-II. It was also suggested that the physiological role of MT-III and some kind of high molecular weight proteins might be impaired by exposure to mercury vapor and lack of MT-I and MT-II.     

Microdetermination of fluorine in organic compounds by oxygen flask combustion and conductometric titration

For the conductometric titration of fluoride with calcium acetate, solvent system in sample solution and titrant, concentration, and acidity of sample solution were examined to establish the titration conditions. Results of these examinations were transferred to the microdetermination of fluorine in organic compounds using oxygen flask combustion method.Comparative examination between quartz and Pyrex flasks for the combustion of fluorine samples indicated that good results were obtained by the use of the former flask, whereas the use of the latter one gave negative values of 1.0–1.6% due to the formation of boron fluoride during the combustion.     

A study of novel heat-resistant polymers: Preparation of photosensitive fluorinated polybenzoxazole precursors and physical properties of polybenzoxazoles derived from the precursors

A series of novel photosensitive polybenzoxazole precursors were prepared from polycondensation of 2,2-bis(3,3′-amino-4,4′-hydroxyphenyl)hexafluoropropane with photosensitive dicarboxylic acid chlorides such as p-phenylenediacryloyl chloride and benzophenone-4,4′-dicarboxylic chloride. The precursors are soluble in common organic solvents owing to the presence of perfluoromethyl groups in the chain structure, and insolubilized in the solvents on irradiation with the light. Polybenzoxazole patterns with high resolution as well as high aspect ratio were reproduced by baking the precursor patterns at 300°C. The pattern shrinkage on the conversion to polybenzoxazole was slight. The polybenzoxazole films offered good heat-resistance up to 400°C in addition to good electrical properties.     

BINAP/AgOTf/KF/18-crown-6 as new bifunctional catalysts for asymmetric Sakurai-Hosomi allylation and Mukaiyama aldol reaction

A catalytic amount of KF.18-crown-6 complex is effective as a soluble fluoride source to activate an asymmetric Sakurai-Hosomi allylation with BINAP and silver(I) triflate catalyst. The allylation of a variety of aromatic, alpha,beta-unsaturated and aliphatic aldehydes with allylic trimethoxysilane resulted in high yields and remarkable enantioselectivities. In addition, the asymmetric Mukaiyama-type aldol reaction is achieved by using trimethoxysilyl enol ethers in the presence of the same catalysts. High anti selectivity is obtained from E-silyl enol ether, while Z-silyl enol ether gives syn selectivity.     

Cascade Rearrangement of 5-Cyclopentylidenecyclooctanones

Acid-catalyzed rearrangement of 5-cyclopentylidenecyclooctanone derivatives 9a-c was examined to obtain polyspiropolyquinanes 11a-c, considered to have a unique helical structure, through cascade rearrangement pathways consisting of continuous transannular cyclization followed by successive 1,2-alkyl shifts. The substrates were prepared easily by use of the Wittig or McMurry reaction. Reaction of the 5-cyclopentylidenecyclooctanone (9a) with acid gave the expected dispirotriquinane ketone 11a in high yield. The precise mechanism was elucidated by a deuterium-labeling experiment. In the case of the ketone 9b, having another spiroannulated cyclopentane ring attached on 9a, the trispirotetraquiane 11b was not obtained but the bis-propellane-type tetrahydrofuran 25 was produced exclusively. The 5-(5'-cyclopentylidenecyclooctylidene)cyclooctanone (9c) afforded the polycyclic compounds 27-31, depending on the acid used, instead of the desired tetraspiropentaquinane 11c. The structures of the products were determined by NMR spectral data including 2D (13)C INADEQUATE spectra and X-ray crystallographic analyses. The unexpected rearrangement pathways are also discussed.     

Dispersionless Toda hierarchy and two-dimensional string theory

The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of extra states and fields are presented.