Anti-self-dual Yang–Mills equations on noncommutative space–time

By replacing the ordinary product with the so-called -product, one can construct an analog of the anti-self-dual Yang–Mills (ASDYM) equations on the noncommutative . Many properties of the ordinary ASDYM equations turn out to be inherited by the -product ASDYM equation. In particular, the twistorial interpretation of the ordinary ASDYM equations can be extended to the noncommutative , from which one can also derive the fundamental structures for integrability such as a zero-curvature representation, an associated linear system, the Riemann–Hilbert problem, etc. These properties are further preserved under dimensional reduction to the principal chiral field model and Hitchin’s Higgs pair equations. However, some structures relying on finite dimensional linear algebra break down in the -product analogs.     

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.     

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.     

GaP:N和GaAs1-xPx:中的束缚激子依赖于激子声子耦合的辐射复合的热猝灭

我们从实验中发现,在N掺杂的GaP和Ga(As,P)中,零声子辐射带与相应的声子伴带的热猝灭过程是不同的。声子伴带的热猝灭强烈地依赖于激子声子的耦合,呈现出一种相干的特性。     

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.     

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.     

Preparation of pH-sensitive liposomes retaining SOD mimic and their anticancer effect

We prepared an anticancer drug based on a pH-sensitive liposome retaining Fe-porphyrin as an SOD mimic. The liposomes contained cationic/anionic lipid combinations and were composed of Fe-porphyrin, 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine, dimethylditetradecylammonium bromide, sodium oleate, and Tween-80. The Fe-porphyrin was released from the liposome at low pH, and the cytotoxicity for cancer cells by the liposome depended on the acidic environments of the endosomes in the cells. Furthermore, although the liposome exhibited an excellent anticancer effect on a gastric cancer cell line, the SOD activity of Fe-porphyrin was shown to have a significant influence on the cytotoxicity toward cancer cells. These findings suggest that the pH-sensitive liposome retaining the Fe-porphyrin as an SOD mimic promises to be a novel anticancer drug for endosomal escape.