Sunto. – In this note we survey some recent results on the well-posedness of the ordinary differential equation with non-Lipschitz vector fields. We introduce the notion of regular Lagrangian flow, which is the right concept of solution in this framework. We present two different approaches to the theory of regular Lagrangian flows. The first one is quite general and is based on the connection ...

In this paper Einstein’s field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state space. The system is analyzed qualitatively, using the theory of dynamical systems, and numerically. It is shown that certain special solutions play importa...

Many fundamental problems in the max-plus-algebraic system theory for discrete event systems — among which the minimal state space realization problem — can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (L...

Many fundamental problems in the max-plus-algebraic system theory for discrete event systems — among which the minimal state space realization problem — can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (L...

This paper describes a grammar formalism and a deterministic parser developed for text normalisation in the rVoice text-to-speech (TTS) system. The rules are formulated using regular expressions and converted into a non-deterministic finite-state transducer (FST). At runtime, search is guided by parsing preferences which the user may associate with regular operators; the best solution is determ...

Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over R is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the questio...

The aim of this paper is to continue the research of JMP 46, 042501 (2005) of regular static spherically symmetric spacetimes in EinsteinBorn-Infeld theories from the point of view of the spacetime geometry and the electromagnetic structure. The energy conditions, geodesic completeness and the main features of the horizons of this spacetime are explicitly shown. A new static spherically symmetr...

We present a new algorithm for efficient learning of regular languages from examples and queries. A reliable teacher who knows the unknown regular grammar G (or is able to determine if certain strings are accepted by the grammar) will guide the learner in achieving the goal of inferring an equivalent grammar $\mbox{G}^{*}$. The teacher provides the learner with a structurally complete set of po...