We propose a differential difference equation in R × Z and study it by Hirota’s bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B...

We propose a quantization of the Painlevé system of type A (1) l studied by M. Noumi and Y. Yamada [13]. This quantization has the affine Weyl group symmetry of type A (1) l (l ≥ 2) as well as the Lax representation. For even l, the quantized system of type A (1) l can be obtained as the continuous limit of the discrete system constructed from the affine Weyl group symmetry of type A (1) l+1 .

Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one proceeds in the opposite way, enlarging the nonlinear system to a system of greater dimension. We discuss how this approach is also fruitful in studying non inte...

The tense and lax vowels of German were compared, based on an analysis of the duration, amplitude and velocity characteristics of lip and tongue movement. This study examined firstly whether they show different patterns of compression over changes in speech rate, and secondly whether velocity profiles would reveal evidence of different underlying control mechanisms. CVC movements were segmented...

Security properties are profitably expressed using notions of contextual equivalence, and logical relations are a powerful proof technique to establish contextual equivalence in typed lambda calculi, see e.g. Sumii and Pierce’s logical relation for a cryptographic lambda-calculus. We clarify Sumii and Pierce’s approach, showing that the right tool is prelogical relations, or lax logical relatio...