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.     

Hierarchy structure in integrable systems of gauge fields and underlying Lie algebras

An improved version of Nakamura's self-dual Yang-Mills hierarchy is presentd and its symmetry contents are studied. The new hierarchy as well as the previous one represents a set of commuting dynamical flows in an infinite dimensional manifolds of loop type, but includes a large set of dependent variables. Because of new degrees of freedom the theory acquires a more symmetric form with richer structures. For example it allows a large symmetry algebra of Riemann-Hilbert type, which is actually a direct sum of two subalgebras (left and right). This phenomenon is basically the same as observed recently by Avan and Bellon on the case of principal chiral models. In addition to these rather familiar symmeties, a new type of symmetries referred to as coordinate transformation type are also introduced. Generators of the above dynamical flows are all included therein. These two types of symmetries altogether form a big Lie algebra, which lead to more satisfactory understanding of symmetry properties of integrable systems of guage fields.     

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.     

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.     

Quasi-classical limit of Toda hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W _{1 +} symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow _{1 +} symmetries of the dispersionless hierarchy through their action on the tau function.     

Circularly polarized luminescence (CPL) characteristics of hydrophobic pyrene derivatives/γ-cyclodextrin (γ-CD) complexes in aqueous solution dissolved by grinding

Circularly polarized luminescence (CPL) organic dyes are currently receiving a great interest, but there are still not many reported observations of CPL spectra of hydrophobic dyes from aqueous solution. We have prepared hydrophobic pyrene derivatives and dissolved them into aqueous solutions with γ-cyclodextrin (γ-CD) by using grinding technique. Among these derivatives, (pyrene-1-carbonyl)serine (PySer) forms a spatially restricted dimer in the hydrophobic chiral cavity of γ-CD and exhibits excimer emission with a high quantum yield of Φ_f?=?0.68. In addition, circular dichroism and CPL signals were induced for the complex. The strong g_CPL value of g_CPL?=?+?2.2?×?10^?3 was obtained, which may be attributed to the interaction between the hydroxyl groups in the side chain of PySer with those of γ-CD and it strengthens the chiral dimeric structure.

Graphic abstract

     

Lead hopping using SVM and 3D pharmacophore fingerprints

The combination of 3D pharmacophore fingerprints and the support vector machine classification algorithm has been used to generate robust models that are able to classify compounds as active or inactive in a number of G-protein-coupled receptor assays. The models have been tested against progressively more challenging validation sets where steps are taken to ensure that compounds in the validation set are chemically and structurally distinct from the training set. In the most challenging example, we simulate a lead-hopping experiment by excluding an entire class of compounds (defined by a core substructure) from the training set. The left-out active compounds comprised approximately 40% of the actives. The model trained on the remaining compounds is able to recall 75% of the actives from the "new" lead series while correctly classifying >99% of the 5000 inactives included in the validation set.     

Selective and sensitive fluorometric determinations of cobalt(II) and hydrogen peroxide with fluorescein-hydrazide

Fluorophotometric determinations of cobalt(II) and hydrogen peroxide were investigated by using the fluorescence reaction between fluorescein-hydrazide (fl-NHNH(2)), and/or hydrogen peroxide, cobalt(II), respectively. The calibration graphs were liner in the range of 0-6.0 ng cobalt(II) and 0-1000 ng hydrogen peroxide per 10 ml at an emission wavelength (E(m)) of 530 nm with an exicitation wavelength (E(x)) of 508 nm, respectively. These proposed methods were selective and simple, and the effect of foreign ions was negligible in comparison with conventional reported methods such as nitroso R,4-(2-pyridylazo)resorcinol(PAR), alizarin, pyridine-2-aldehyde-2-pyridinehydrazone, stilbazo-cobalt(II), etc.