A Bilinear Approach to Discrete Miura Transformations

We present a systematic approach to the construction of Miura transformations for discrete Painlev\'e equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of $\tau$-functions. Elimination of $\tau$-functions from the resulting system leads to another nonlinear equation, which is a ``modified'' version of the original equation. The procedure therefore yields Miura transformations. In this letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.Comment: 7 pages in TeX, to appear in Phys. Letts.

A Study of the Knowledge and Attitudes of Physicians Toward Victims of Spouse Abuse

The purpose of this study is to measure the knowledge and attitudes of physicians toward victims of spouse abuse. All 150 practitioners in the specialities of emergency medicine, family medicine, obstetrics-gynecology and psychiatry, in a large area general hospital are included in the sampling frame; 76 responded (RR = 51%). Knowledge and attitudes were measured using the Physician Survey on Spouse Abuse. Rosenberg\u27s Tripartite Model of Attitude formed the theoretical basis for this study. Participants were 72% male, 90% white, 88% currently married, with a mean age of 44 years (SD = 7.99). Mean years in practice was 14.61 (SD = 7.71); 63% were in private practice, and 47% practiced in suburban areas. A minority, 21% had no course content on spouse abuse and majority, 81% were not trained in spouse abuse prevention following graduation. Only 27% secured a pass on the knowledge quiz. 68% had positive summary attitude measure. 70% had a positive overall belief, 97% had positive beliefs about physician role, 65% had positive beliefs about victims, and 30% had positive beliefs about resources. 11% had a positive affect score. 84% had positive verbal statements of behavior, 22% had positive behaviors on frequency of suspecting abuse. 50% of the respondents identified 5 or less victims in the past year. Whites had significantly less positive summary attitude measure, beliefs about physician role, and affect scores. Older physicians had significantly less positive overall belief scores, beliefs about victims and identified fewer victims of abuse. Females were significantly more likely to pass the knowledge quiz and they were also more likely to hold positive beliefs about victims of abuse. Married physicians were significantly less likely to pass the knowledge quiz and to have less positive affect scores. Family practitioners were least likely to behave positively toward victims of abuse. Physicians with fewer years in practice were more likely to have positive beliefs about victims. Speciality was the strongest predictor of attitudes. Physicians seem to hold most positive beliefs, are less likely behave positively toward victims of abuse and are even less likely to feel positive about providing services to victims of abuse

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

Studies on Nitrogen and Oxygen Containing Heterocyclic Compounds

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Is my ODE a Painleve equation in disguise?

Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3 a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant under the general point transformation x=Phi(X,Y), y=Psi(X,Y) and it is therefore very difficult to find out whether two equations in this class are related. We describe R. Liouville's theory of invariants that can be used to construct invariant characteristic expressions (syzygies), and in particular present such a characterization for Painleve equations I-IV.Comment: 8 pages. Based on talks presented at NEEDS 2000, Gokova, Turkey, 29 June - 7 July, 2000, and at the AMS-HKMS joint meeting 13-16 December, 2000. Submitted to J. Nonlin. Math. Phy

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