In this paper, we construct a conformal scattering theory for Dirac fields in the interior of Reissner–Nordström-like black hole, between hole event horizon and Cauchy horizon. The main result is resolution characteristic problem equation on horizons by solving system wave equations re-interpreting its solution as components required solution.

In this paper we address the general problem of approximating, in a certain optimal way, non admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider systems modeled by a subriemanni...

Let V be a vector field distribution on manifold M . We give an efficient algorithm for the construction of local coordinates on M such that V may be locally expressed as some partial prolongation of the contact distribution C (1) q , on the 1 st order jet bundle of maps from R to R, q ≥ 1. It is proven that if V is locally equivalent to a partial prolongation of C (1) q then the explicit const...

The theme of this paper is the generalization of Goursat normal forms for Pfaffian systems with co-dimension greater than two. There are necessary and sufficient conditions for the existence of coordinates that transform a Pfaffian system with co-dimension greater than two into an extended Goursat normal form, which is the dual of the multiple-chain, single-generator chained form mentioned in o...

We show that the category of regular epimorphisms in a Barr exact Goursat category is almost Barr exact in the sense that (it is a regular category and) every regular epimorphism in it is an effective descent morphism.

In this paper, we develop the machinery of exterior diierential forms, more particularly the Goursat normal form for a Pfaaan system, for solving nonholonomic motion planning problems, i.e. planning problems with non-integrable velocity constraints. We apply this technique to solving the problem of steering a mobile robot with n trailers. We present an algorithm for nding a family of transforma...

In this paper, we show how ihe machinery of ederior differential sysiemr can k wed i o help soltie nonholonomic motion planning problems. Since the Gorrsat normal form for ezterior differential systems is dual i o chained form for vectorfields, we solve the problem of steering a mobile robot with n trailers by convcriing ihe system int.0 chained form, doing ihe paih-planning in the chained form...