Appearance of quark-hadron duality in the Rein-Sehgal model

Quark-hadron duality in neutrino-nucleon reactions is investigated under the assumption that cross sections in the resonance region are given by the Rein-Sehgal model. The quantitative analysis of the duality is done by means of appropriate integrals of the structure functions in the Nachtmann variable. We conclude that with the definition of the resonance region $W\in (M+m_{\pi}, 2$ GeV) the duality holds for neutrino-proton reaction $F_2$ structure function for $Q^2\in (0.5, 3)$ GeV$^2$ and it is absent for neutrino-neutron reaction.Comment: 4 pages, 7 figures, presented at NuInt05 conference, Okayama, Sept. 26-29, 200

A Phase Transition for Circle Maps and Cherry Flows

We study $C^{2}$ weakly order preserving circle maps with a flat interval. The main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval. We prove that the non-wandering set has zero Hausdorff dimension in the case of degenerate geometry and it has Hausdorff dimension strictly greater than zero in the case of bounded geometry. Our results about circle maps allow to establish a sharp phase transition in the dynamics of Cherry flows

Fine structure of the complex hyperbolic Brownian motion and Rudin’s question

We investigate the fine structure of the complex hyperbolicBrownian motion in the unit ball of Cn. It turns out that the generator of the process is locally very close to the generator of some simple transformation of the classical Brownian motion. This fact helps us to give an intuitive explanation why the invariant Laplace operator in the unit ball of Cn is a difference of two ordinary Laplace operators – the question set by W. Rudin in his monograph Function Theory in the Unit Ball of Cn. In the second part of the paper we find stochastic differential equations for the complex hyperbolic Brownian motion on the ball model of the complex hyperbolic space and furnish in this way an important tool in a further investigation of this process