According to the Einstein cosmological principle, our universe is homogeneous and isotropic, i.e. its curvature is constant at any point and in any direction. On large scales, when all local irregularities are ignored, this assumption has been confirmed by astronomers. We show that there is no...

Given an Heath-Jarrow-Morton (HJM) interest rate model and a parametrized family of finite dimensional forward rate curves, this paper provides us a way to project this infinite dimensional HJM forward rate curve to the finite dimensional manifold. This projection characterizes banks' behavior...

In this paper we study a capital accumulation model in an optimal control theoretic framework, where the capital stock and the investment rate are modeled as state variables and the change in the investment rate as control. Adjustment costs are introduced for both investment rate and the change...

The method of invariant manifold is developed for a derivation of reduced description in kinetic equations of dilute polymeric solutions. It is demonstrated that this reduced description becomes universal in the limit of small Deborah and Weissenberg numbers, and it is represented by the...

A Poisson coalgebra (Fun(N),Δ) is used to construct integrable Hamiltonian systems. We consider a Poisson structure given by the bivector P=Pab(x)(∂/∂xa)∧(∂/∂xb),x∈R3, which does not form a Lie algebra with respect to the Poisson bracket {xa,xb}P=Pab(x). We prove that this coalgebra...

A generalization of the theorem of V. Bargmann concerning unitary and ray representations is obtained and is applied to the general problem of lifting group actions associated to the extension of structure of a bundle. In particular this is applied to the Poincare group 'P' of a Lorentz manifold...