In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, shadowing and gluing orbit properties, context C 0 incompressible flows generated by Lipschitz vector fields. We prove that a -generic fixed-point free flow satisfies property, it is transitive has dense set points non-wandering set. particular, reparametrized property. als...

After review the quantum Hall effect on the fuzzy two-sphere S2 and Zhang and Hu’s 4-sphere S4, the incompressible quantum Hall fluid on S2, S4 and torus are discussed respectively. Next, the corresponding Laughlin wavefunctions on S2 are also given out. The ADHM construction on S4 is discussed. We also point out that on torus, the incompressible quantum Hall fluid is related to the integrable ...

Article history: Received 1 February 2008 Accepted 6 November 2010

We investigate a new notion of security for “cryptographic functions” that we term seed incompressibility (SI). We argue that this notion captures some of the intuition for the alleged security of constructions in the random-oracle model, and indeed we show that seed incompressibility suffices for some applications of the random oracle methodology. Very roughly, a function family fs(·) with |s|...

The homotopy type of the space of PL homeomorphisms of a Haken 3 manifold was computed in [H1], and with the subsequent proof of the Smale conjecture in [H2], the computation carried over to diffeomorphisms as well. These results were also obtained independently by Ivanov [I1,I2]. The main step in the calculation in [H1], though not explicitly stated in these terms, was to show that the space o...

We present a smoothed particle hydrodynamic model for incompressible fluids. As opposed to solving a pressure Poisson equation in order to get a divergence-free velocity field, here incompressibility is achieved by requiring as a kinematic constraint that the volume of the fluid particles is constant. We use Lagrangian multipliers to enforce this restriction. These Lagrange multipliers play the...

Life is based on two polymers, DNA and protein, whose properties can be described in a simple text file. It is natural to expect that standard text compression techniques would work on biological sequences as they do on English text. But biological sequences have a fundamentally different structure from linguistic ones, and standard compression schemes exhibit disappointing performance on them....