A q-analogue of gl_3 hierarchy and q-Painleve VI

A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI equation proposed by Jimbo and Sakai.Comment: 14 pages, IOP style, to appear in J. Phys. A Special issue "One hundred years of Painleve VI

Differential-difference system related to toroidal Lie algebra

We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky's (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra \sl_2^{tor}.Comment: 10 pages, 4 figures, pLaTeX2e, uses amsmath, amssymb, amsthm, graphic

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. For this purpose, we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two pseudomomenta have been known. All the eigenstates are systematically produced by starting from the ground state and multiplying these operators to it.Comment: 11 pages, Latex, no figure

OsYSL16 plays a role in the allocation of iron

Graminaceous plants acquire iron by secreting mugineic acid family phytosiderophores into the rhizosphere and taking up complexes of iron and phytosiderophores through YSL (yellow stripe 1-like) transporters. Rice OsYSL15 is a transporter of the iron(III)-2′-deoxymugineic acid complex. OsYSL16 has 85 % similarity to both OsYSL15 and the iron(II)-nicotianamine transporter OsYSL2. In the present study, we show that OsYSL16 functionally complemented a yeast mutant defective in iron uptake when grown on medium containing iron(III)-deoxymugineic acid, but not when grown on medium containing iron(II)-nicotianamine. OsYSL16-knockdown seedlings were smaller than wild-type seedlings when only iron(III)chloride was supplied as an iron source. The iron concentration in shoots of OsYSL16-knockdown plants was similar to that of the wild type; however, they showed more severe chlorosis than wild-type plants under iron-deficient conditions. Furthermore, OsYSL16-knockdown plants accumulated more iron in the vascular bundles of the leaves. Expression of the OsYSL16 promoter fused to the β-glucuronidase gene showed that OsYSL16 is expressed in the root epidermis and vascular bundles of whole plants. The expression was typically observed around the xylem. In the vascular bundles of unelongated nodes, it was detected in the xylem of old leaves and the phloem of new leaves. Graminaceous plants translocate iron from the roots to old leaves mainly via the xylem and to new leaves mainly via the phloem. Our results suggest that OsYSL16 plays a role in the allocation of iron(III)-deoxymugineic acid via the vascular bundles. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11103-012-9930-1) contains supplementary material, which is available to authorized users

The sixth Painleve equation arising from D_4^{(1)} hierarchy

The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 page

Functional representation of the Ablowitz-Ladik hierarchy

The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the inverse scattering approach. After establishing the structure of solutions of the auxiliary linear problems, the ALH, which has been originally introduced as an infinite system of difference-differential equations is presented as a finite system of difference-functional equations. The representation obtained, when rewritten in terms of Hirota's bilinear formalism, is used to demonstrate relations between the ALH and some other integrable systems, the Kadomtsev-Petviashvili hierarchy in particular.Comment: 15 pages, LaTe

Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial

Extending a method developed by Takamura and Takano, we present the Rodrigues formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for the $B_{N}$-type Calogero model with distinguishable particles. Our construction makes it possible for the first time to algebraically generate all the nonsymmetric multivariable Laguerre polynomials with different parities for each variable.Comment: 6 pages, LaTe

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us