Generalized Toda mechanics associated with classical Lie algebras and their reductions

For any classical Lie algebra $g$, we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers $(m,n)$. The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for $\mathfrak{g}=B_{r},C_{r},D_{r}$ with $m,n\leq3$ are also given. For all $m,n$, it is shown that the dynamics of the $(m,n-1)$- and the $(m-1,n)$-Toda chains are natural reductions of that of the $(m,n)$-chain, and for $m=n$, there is also a family of symmetrically reduced Toda systems, the $(m,m)_{\mathrm{Sym}}$-Toda systems, which are also integrable. In the quantum case, all $(m,n)$-Toda systems with $m>1$ or $n>1$ describe the dynamics of standard Toda variables coupled to noncommutative variables. Except for the symmetrically reduced cases, the integrability for all $(m,n)$-Toda systems survive after quantization.Comment: 19 pages, bibte

The Geometric Construction of WZW Effective Action in Non-commutative Manifold

By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge group space we get WZW effective Lagrangian on high dimensional non-commutative space.Especially consistent anomalies derived from this WZW effective action in non-commutative four-dimensional space coincides with those by L.Bonora etc.Comment: 9 pages, latex, no figure

Slowly rotating charged black holes in anti-de Sitter third order Lovelock gravity

In this paper, we study slowly rotating black hole solutions in Lovelock gravity (n=3). These exact slowly rotating black hole solutions are obtained in uncharged and charged cases, respectively. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the uncharged black holes get no corrections from rotation. In charged case, we compute magnetic dipole moment and gyromagnetic ratio of the black holes. It is shown that the gyromagnetic ratio keeps invariant after introducing the Gauss-Bonnet and third order Lovelock interactions.Comment: 14 pages, no figur

Auditor of State Mary Mosiman today released a reaudit report on the Mason City Community School District (District) for the period July 1, 2014 through June 30, 2015. The reaudit also covered items applicable to the years ended June 30, 2016 and June 30, 2017.

Auditor of State Mary Mosiman today released a reaudit report on the Mason City Community School District (District) for the period July 1, 2014 through June 30, 2015. The reaudit also covered items applicable to the years ended June 30, 2016 and June 30, 2017

Natural variation of RGN1a regulates grain number per panicle in japonica rice

The grain number per panicle (GNP) is an important yield component. Identifying naturally favorable variations in GNP will benefit high-yield rice breeding. Here, we performed a genome-wide association study using a mini-core collection of 266 cultivated rice accessions with deep sequencing data and investigated the phenotype for three years. Three genes, i.e., TOTOU1 (TUT1), Grain height date 7 (Ghd7), and Days to heading 7/Grain height date 7.1/Pseudo-Response Regulator37 (DTH7/Ghd7.1/OsPRR37), which regulate GNP, were found in the quantitative trait loci (QTL) identified in this study. A stable QTL, qGNP1.3, which showed a strong correlation with variations in GNP, was repeatedly detected. After functional and transgenic phenotype analysis, we identified a novel gene, regulator of grain number 1a (RGN1a), which codes for protein kinase, controlling GNP in rice. The RGN1a mutation caused 37.2%, 27.8%, 51.2%, and 25.5% decreases in grain number, primary branch number per panicle, secondary branch number per panicle, and panicle length, respectively. Furthermore, breeding utilization analysis revealed that the additive effects of the dominant allelic variants of RGN1a and DTH7 played a significant role in increasing the grain number per panicle in japonica rice. Our findings enrich the gene pool and provide an effective strategy for the genetic improvement of grain numbers

Primer registro de anomalía intersexual gonadal de Trachurus mediterraneus (Steindachner, 1868) desde el Mar de Alborán.

El objetivo principal de este trabajo es dar a conocer el primer registro de una anomalía intersexual gonadal de Trachurus mediterraneus desde el mar de Alborán (Mediterráneo occidental). Este espécimen es el primer registro de intersexualidad para un jurel en el mundo.Postprin

The periodic unfolding method for a class of parabolic problems with imperfect interfaces

In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with ε-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative via a function of order εγ with γ ≤ −1. We give the homogenization results which include those obtained by Jose in [Rev. Roum. Math. Pures Appl. 54 (2009) 189–222]. We also get the corrector results