REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Gravitação quadrática em (2 + 1)D com e sem termo topológico de Chern-Simons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Amplifier - v. 2, no. 6

In this issue...Butte Civic Center, ROTC program, It Club, Miner's Union Building, Butte, Montana, George Huber, Viola Vestal Coulter Award, Pan American Games

New insights into the pathobiology of Down syndrome--hyaluronan synthase-2 overexpression is regulated by collagen VI α2 chain.

Down syndrome (DS) is a common birth defect characterized by the trisomy of chromosome 21. DS-affected umbilical cords (UCs) of fetuses show altered architecture of the extracellular matrix. Overexpression of the chromosome 21 genes encoding the collagen type VI (COLVI) chains α1(VI) and α2(VI), COL6A1 and COL6A2, respectively, has also reported to occur in the nuchal skin of DS fetuses. The aim of this study was therefore to evaluate the COLVI content in euploid and DS-affected UCs and human skin fibroblasts, and to investigate the relationships between COLVI and hyaluronan (HA) and HA synthase-2 (HAS2). We found that the UCs of DS fetuses showed denser staining of COLVI and increased COL6A2 expression at both early and term gestational ages. In vitro expression studies in DS-derived fibroblasts showed similarly increased amounts of α1(VI) and α2(VI) chains at the protein and transcriptional level, supporting the hypothesis of the gene dosage effect. Furthermore, increased levels of HA and HAS2 were also found in DS-derived skin fibroblast cultures. Notably, silencing of COL6A2 in DS-derived cells resulted in downregulation of HAS2, with a simultaneous decrease in secreted HA. Exogenous addition of COLVI to normal fibroblasts did not have any effect on HAS2 expression. In conclusion, UCs and skin fibroblasts in DS show significant increases in COLVI and HA; the overexpression of COL6A2 in DS tissue and cells is closely related to the increased expression of HAS2. These data may explain the DS phenotypes and their effects in organ tissue maturation.

Sulphur compounds, methane, and phytoplankton during SONNE cruise SO202/2 (Transbrom Sonne)

Here we present results of the first comprehensive study of sulphur compounds and methane in the oligotrophic tropical West Pacific Ocean. The concentrations of dimethylsuphide (DMS), dimethylsulphoniopropionate (DMSP), dimethylsulphoxide (DMSO), and methane (CH4), as well as various phytoplankton marker pigments in the surface ocean were measured along a north-south transit from Japan to Australia in October 2009. DMS (0.9 nmol/l), dissolved DMSP (DMSPd, 1.6 nmol/l) and particulate DMSP (DMSPp, 2 nmol/l) concentrations were generally low, while dissolved DMSO (DMSOd, 4.4 nmol/l) and particulate DMSO (DMSOp, 11.5 nmol/l) concentrations were comparably enhanced. Positive correlations were found between DMSO and DMSP as well as DMSP and DMSO with chlorophyll a, which suggests a similar source for both compounds. Similar phytoplankton groups were identified as being important for the DMSO and DMSP pool, thus, the same algae taxa might produce both DMSP and DMSO. In contrast, phytoplankton seemed to play only a minor role for the DMS distribution in the western Pacific Ocean. The observed DMSPp : DMSOp ratios were very low and seem to be characteristic of oligotrophic tropical waters representing the extreme endpoint of the global DMSPp : DMSOp ratio vs. SST relationship. It is most likely that nutrient limitation and oxidative stress in the tropical West Pacific Ocean triggered enhanced DMSO production leading to an accumulation of DMSO in the sea surface. Positive correlations between DMSPd and CH4, as well as between DMSO (particulate and total) and CH4, were found along the transit. We conclude that both DMSP and DMSO serve as substrates for methanogenic bacteria in the western Pacific Ocean.

Cuarteto 2 [Manuscrito]

Número 296 en el catálogo de Vicente Galbis e Hilari García

Cuarteto 2º [Manuscrito]

Número 296 en el catálogo de Vicente Galbis e Hilari García