Expansive dynamics and hyperbolic geometry

LetM be a compact Riemannian manifold with no conjugate points such that its geodesic flow is expansive. Then we show that the universal Riemannian covering ofM is a hyperbolic geodesic space according to the definition of M. Gromov. This allows us to extend a series of relevant geometric and topological properties of negatively curved manifolds toM and in particular, geometric group theory applies to the fundamental group ofM.     

Noncommutative Jordan C*-algebras

We introduce noncommutative JB*-algebras which generalize both B*-algebras and JB*-algebras and set up the bases for a representation theory of noncommutative JB*-algebras. To this end we define noncommutative JB*-factors and study the factor representations of a noncommutative JB*-algebra. The particular case of alternative B*-factors is discussed in detail and a Gelfand-Naimark theorem for alternative B*-algebras is given.     

On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

Degree of strata of singular cubic surfaces

We determine the degree of some strata of singular cubic surfaces in the projective space . These strata are subvarieties of the parametrizing all cubic surfaces in . It is known what their dimension is and that they are irreducible. In 1986, D. F. Coray and I. Vainsencher computed the degree of the 4 strata consisting on cubic surfaces with a double line. To work out the case of isolated singularities we relate the problem with (stationary) multiple-point theory.

     

Market Power Issues in Bid-Based Hydrothermal Dispatch

The objective of this work is to investigate market power issues in bid-based hydrothermal scheduling. Initially, market power was simulated with a single stage Cournot–Nash equilibrium model. In this static model the equilibrium was calculated analytically. It was shown that the total production of N strategic agents is smaller than the least-cost solution by a factor of (N/(N+1)). Market power analysis for multiple stages was then carried through a stochastic dynamic programming scheme, where the decision in each stage and state is the Cournot–Nash equilibrium of a multi-agent game. Case studies with data taken from the Brazilian system are presented.     

Quantum Control in Foundational Experiments

We describe a new class of experiments designed to probe the foundations of quantum mechanics. Using quantum controlling devices, we show how to attain a freedom in temporal ordering of the control and detection of various phenomena. We consider wave–particle duality in the context of quantum-controlled and the entanglement-assisted delayed-choice experiments. Then we discuss a quantum-controlled CHSH experiment and measurement of photon’s transversal position and momentum in a single set-up.     

Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].     

Attractor minimal sets for cooperative and strongly convex delay differential systems

We study the skew-product semiflow induced by a family of convex and cooperative delay differential systems. Under some monotonicity assumptions, we obtain an ergodic representation for the upper Lyapunov exponent of a minimal subset. In addition, when eventually strong convexity at one point is assumed and there exist two completely strongly ordered minimal subsets K₁?_CK₂, we show that K₁ is an attractor subset which is a copy of the base. The long-time behaviour of every trajectory strongly ordered with K₂ is then deduced. Some examples of application of the theory are shown.     

Atomic fraction around defects associated with nanoparticles in AlCuMg alloys

A positron annihilation spectroscopy analysis method to obtain a quantitative determination of the chemical composition around defects inside nanoparticles is presented here. This methodology is applied to AlCuMg alloys to study the rapid hardening phenomena associated with solute-vacancy aggregation. Coincidence Doppler Broadening (CDB) and lifetime spectroscopy measurements of reference samples of pure elements with and without defects were analyzed to give quantitative information of the average chemical environment around vacancies, i.e. the atomic fraction of the first neighbors of these defects, in the alloys studied. The accuracy and reproducibility of the methodology is confirmed not only by good fits to the experimental data but, in most cases, by the consistency between the mean lifetime values predicted, using the CDB estimation, and the mean lifetime values independently measured. Discrepancies in the methodology are expected when there is poor CDB contrast between elements, i.e. having similar electronic structure (for example, Al and Mg). The criterion for establishing the statistical accuracy of the separation of elements in these special cases is discussed. The methodology can be applied not only to study homogeneous materials as metallic alloys, but also to study the depth profile in thin films.