A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Polynomial and linearized normal forms for almost periodic differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

Reconstructing images from their most singular fractal manifold

Real-world images are complex objects, difficult to describe but at the same time possessing a high degree of redundancy. A very recent study [1] on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature. One particular fractal component, related to the most singular (sharpest) transitions in the image, seems to be highly informative about the whole scene. In this paper we will show how to decompose the image into their fractal components.We will see that the most singular component is related to (but not coincident with) the edges of the objects present in the scenes. We will propose a new, simple method to reconstruct the image with information contained in that most informative component.We will see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set.We will discuss the results from the perspective of coding, proposing this method as a starting point for future developments.

Space Manifold dynamics

The term Space Manifold Dynamics (SMD) has been proposed for encompassing the various applications of Dynamical Systems methods to spacecraft mission analysis and design, ranging from the exploitation of libration orbits around the collinear Lagrangian points to the design of optimal station-keeping and eclipse avoidance manoeuvres or the determination of low energy lunar and interplanetary transfers

Space Manifold dynamics

The term Space Manifold Dynamics (SMD) has been proposed for encompassing the various applications of Dynamical Systems methods to spacecraft mission analysis and design, ranging from the exploitation of libration orbits around the collinear Lagrangian points to the design of optimal station-keeping and eclipse avoidance manoeuvres or the determination of low energy lunar and interplanetary transfers