Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Scientist up to the highest level

Dr. Miroslav Kyrš, DrSc. passed away prematurely and unexpectedly in August 2006 at age of 75. He was a leading person of the Czech radiochemistry during the second half of the 20th century and his results have of world-wide impact. His diligence, intelligence and permanent activity led him to be at first a laboratory chief and subsequently for about 25 years to be a chief of the Radiochemical Department of Czech Nuclear Research Institute (NRI) at Řež near Prague.     

Parton-hadron duality in event generators

The validity of local parton-hadron duality within the framework of HERWIG and JETSET event generators is investigated. We concentrate one ⁺ e ^– annihilations in LEP 2 energy range as these interactions provide theoretically the cleanest condition for the discussion of this concept. We conclude that the concept of local parton-hadron duality is not valid in either of the two generators considered.     

Cartesian currents,weak diffeomorphisms and existence theorems in nonlinear elasticity

Summary In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one orientation-preserving maps that minimize suitable energies associated with hyperelastic materials. The minimizers are also proved to satisfy equilibrium equations. Finally radial deformations are discussed in connection with cavitation.