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.     

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.     

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.     

Photoluminescent Ferroelastic Molecular Crystals

Ferroelasticity has been reported for several types of molecular crystals, which show mechanical‐stress‐induced shape change under twinning and/or spontaneous formation of strain. Aiming to create materials that exhibit both ferroelasticity and light‐emission characteristics, we discovered the first examples of ferroelastic luminescent organometallic crystals. Crystals of arylgold(I)(N‐heterocyclic carbene)(NHC) complexes bend upon exposure to anisotropic mechanical stress. X‐ray diffraction analyses and stress‐strain measurements on these ferroelastic crystals confirmed typical ferroelastic behavior, mechanical twinning, and the spontaneous build‐up of strain. A comparison with single‐crystal structures of related gold‐NHC complexes that do not show ferroelasticity shed light on the structural origins of the ferroelastic behavior.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

Optimum contact conditions for miniaturized surface acoustic wave linear motor

This paper reports the successful operation of a 70 MHz driving surface acoustic wave (SAW) linear motor with a miniaturized stator transducer. This paper also deals with an investigation into an optimized slider design for the miniaturized SAW linear motor. The performance of three silicon type sliders, with different projection size, was compared. Output forces of the three sliders were measured with change of pre-load. It was found that the slider with smaller projection tended to produce greater output force.