Projective reduction of the discrete Painlev\'e system of type (A2+A1)(1)(A_2+A_1)^{(1)}

We consider the q-Painlev\'e III equation arising from the birational representation of the affine Weyl group of type $(A_2 + A_1)^{(1)}$. We study the reduction of the q-Painlev\'e III equation to the q-Painlev\'e II equation from the viewpoint of affine Weyl group symmetry. In particular, the mechanism of apparent inconsistency between the hypergeometric solutions to both equations is clarified by using factorization of difference operators and the $\tau$ functions.Comment: 27 pages, 10 figure

On a q-difference Painlev\'e III equation: II. Rational solutions

Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.Comment: Archive version is already official. Published by JNMP at http://www.sm.luth.se/math/JNMP

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

The Yablonskii-Vorob'ev polynomials $y_{n}(t)$, which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painlev\'{e} equation ($P_{II}$). Here we define two-variable polynomials $Y_{n}(t,h)$ on a lattice with spacing $h$, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when $h=0$. They also provide rational solutions for a particular discretisation of $P_{II}$, namely the so called {\it alternate discrete} $P_{II}$, and this connection leads to an expression in terms of the Umemura polynomials for the third Painlev\'{e} equation ($P_{III}$). It is shown that B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete $P_{II}$, which recovers Jimbo and Miwa's Lax pair for $P_{II}$ in the continuum limit $h\to 0$.Comment: 23 pages, IOP style. Title changed, and connection with Umemura polynomials adde

On a q-difference Painlev\'e III equation: I. Derivation, symmetry and Riccati type solutions

A q-difference analogue of the Painlev\'e III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.Comment: arxiv version is already officia

Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation

We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.Comment: 16 pp; final revised version, will appear in J.Phys. A, minor changes (typos corrected following the Referee's List, aknowledgements and a new reference added

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl

Urine plasmin-like substances as an index of kidney allograft rejections.

Using solid state radioimmunoassays developed by the first author, changes in the urine level of plasmin-like substances (PLS) and fibrin degradation products (FDP) before and after human kidney transplantation were determined in 49 transplant patients. Averages of urine PLS and FDP in a normal population of 51 persons were 0.13+/-0.10 (SD) and 0.14+/-0.07 microng/ml, respectively. In all transplant patients there was an initial rise of both PLS and FDP in urine immediately after transplantation. This elevation peaked on days 4 and 5 and the PLS and FDP levels returned to normal range within 2 weeks in patients without evidence of rejeciton. A secondary rise of urine PLS was detected before or with a rise in serum creatinine in all of the patients experiencing rejections. Of 11 patients who showed a rejection episode within 2 weeks of transplantation, the secondary rise of urine PLS was detectable in 55% of the patients slightly before the serum creatinine level changes; of 6 patients with a rejection episode more than 2 weeks after transplantation, 100% showed a secondary PLS rise 6.7+/-2.3 (SE) days before the serum creatinine increased. The appearance of the secondary rise of urine FDP in the rejecting recipients was slightly later than the rise of PLS. Serial determination of urine PLS levels following human kidney transplantation appears to be an early index of rejections which occurs more than 2 weeks after transplantation, although the clinical usefulness of this measurement is probably limited

Online wide-angle X-ray diffraction/small-angle X-ray scattering measurements for the CO2-laser-heated drawing of poly(ethylene terephthalate) fiber

This is a preprint of an article published in JOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS. Vol 43(9): 1090-1099 (2005).ArticleJOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS. 43(9): 1090-1099 (2005)journal articl

Discrete Painlevé equations from Y-systems

We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction