We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

Let S = Sg,n be a connected, orientable surface of genus g ≥ 0 with n ≥ 0 punctures. Let Teich(S) denote the corresponding Teichmüller space, and let Mod(S) denote the mapping class group of S. Understanding the analogy of Teich(S) with symmetric spaces is a wellknown theme. Recall that a complete Riemannian manifold X is symmetric if it is symmetric at each point x ∈ X: the map γ(t) 7→ γ(−t) w...

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

© 2007 The Authors. Journal compilation © 2007 International Association of Applied Psychology. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. Blackwell Publishing Ltd Oxford, UK APPS pplied Psychology 0269-994X © Int rnational Association for Applied Psychology, 2007 XXX riginal Arti le GROWTH AND TERRORISM HOBFOLL ET AL....

Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...

Terrorism is an act whose nature and outcome is violence and fear. Regardless of the different forms of the realization of this act in the past, it has taken new forms in the contemporary era due to the advancement of sciences and technologies. To face this phenomenon, then, it is necessary to foresee and apply appropriate and favorable measures. As a victim of internal and external terrorism, ...