Vol. 34 No. 2&3 (2002)

The KAM Theory for the persistence of Lagrangean invariant tori in nearly integrable Hamiltonian systems is lobalized to bundles of invariant tori. This leads to globally well-defined conjugations between near-integrable systems and their integrable approximations, defined on nowhere dense sets of positive measure associated to Diophantine frequency vectors. These conjugations are Whitney smooth diffeomorphisms between the corresponding torus bundles. Thus the geometry of the integrable torus bundle is inherited by the near-integrable perturbation. This is of intereet in cases where these…

Compound sums arise frequently in insurance (total claim size in a portfolio) and in accountancy (total error amount in audit populations). As the normal approximation for compound sums usually performs very badly, one may look for better methods for approximating the distribution of a compound sum, e.g. the bootstrap or empirical Edgeworth / saddlepoint approimations. We sketch some recent developments and indicate their relevance in finance. Second, we propos and investigate a simple estimator of the probability of ruin in the Poisson risk model, for the special case where the claim sizes…

Dynamics of a fluxon in a stack of coupled long Josephson junctions is studied numericallv. Based on the numerical simulations, we show that the dependence of the propagation velocity c on the external bias current γ is determined by the ratio of the critical currents of thc two junctions J.

After a brief introduction to the field of Conic Optimization we presentsome interesting applications to the (robust) trus topologr design (TTD)problem, where the goal is to design a truss of a given weight best ableto withstand a set of given loads. We present a linear model for thesingle-load case and semidefinite models for the multi-load and the ro

We give a brief review of some results of our study on one-dimensional shallow nonlinear Bragg grating with nonlinear modulation and deep nonlinear Bragg grating.