Uncertainty based Multi-Robot Cooperative Triangulation

The paper presents a multi-robot cooperative framework to estimate the 3D position of dynamic targets, based on bearing-only vision measurements. The uncertainty of the observation provided by each robot equipped with a bearing-only vision system is effectively addressed for cooperative triangulation purposes by weighing the contribution of each monocular bearing ray in a probabilistic manner. The envisioned framework is evaluated in an outdoor scenario with a team of heterogeneous robots composed of an Unmanned Ground and Aerial Vehicle.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

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

Una aproximació al pensament algebraic a l'Espanya del segle XVI: estudi del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca

Aquest treball analitza el “Tratado y libro de arte mayor o álgebra” que forma part del manuscrit 2294 de la Biblioteca de la Universitat de Salamanca, datat el 1590. El seu autor és Diego Pérez de Mesa. L’objectiu d’aquest estudi és aportar nous elements que ajudin a entendre quin era l’estatus de l’àlgebra a la Península Ibèrica en un segle que va ser clau en el seu desenvolupament. Primer es descriu el manuscrit i després es reflexiona sobre les seves aportacions a la matemàtica, mostrant algunes característiques originals d’aquesta àlgebra enfront d’altres àlgebres de la Península Ibèrica del segle XVI.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

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.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Exploring triangulation in infancy : Two contrasted cases.

Two contrasted father-mother-infant interactions are observed longitudinally during trilogue play. They illustrate the contribution of recent research to the exploration of triangulation in infancy: namely, the infant's capacity to handle triangular interactions and share her affects with her two parents, and the way that this capacity is recruited in functional versus problematic alliances. It is likely that an infant under stress when interacting with one parent will protest at that parent and also at the other. Such is the case when, for example, the father acts intrusively while playing with his baby. The infant is then driven to avert and turns to the mother. The regulation of this dyadic intrusion-avoidance pattern at family level depends on the family alliance. When coparenting is supportive, the mother validates the infant's bid for help without interfering with the father. Thus, the problematic pattern is contained in the dyad, and the infant's triangular capacities remain in the service of her own developmental goals. But when coparenting is hostile-competitive, the mother ignores the infant's bid or engages with her in a way that interferes with her play with her father. In this case, the infant's triangular capacities are used to relieve the tension between the parents. The importance of tracing family process back to infancy for family therapy is discussed.

Integral inequalities for algebraic and trigonometric polynomials

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

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.