Mouvements rigides associés à des masses positives et négatives

The Note deals with rigid solutions of the N-Body Problem, i.e. solutions with constant mutual distances between the bodies. It is shown that for these motions, the configuration is balanced in the sense of Albouy and Chenciner [Invent. Math. 131 (1998) 151–184] even when the masses are of different signs. This fact was proved only for positive masses, using the scalar product they define. A consequence of the result is the constancy of the rotation velocity. It is also shown that any configuration can generate non-planar rigid motions for certain masses. Such motions do not exist with positive masses. All the results can be generalized to systems with N charged particles. To cite this article: M. Celli, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Optimal inspection and perfect repair

Models are developed for decision making about monitoring andmaintenance of systems whose performance through time is describedby a general stochastic process. The system is monitored andpreventive and corrective maintenance actions are carried outin response to the observed system state. The decision processis simplified by using the maximum process as a decision variable.The models developed generalize age replacement models and othersimple maintenance strategies. The approach can deal with failuresthat prevent the system functioning further, and also failuresthat are defined by regulation or economic considerations. Attentionis restricted to perfect repair and inspection, but the structureprovides the framework for further developments.     

CNDO studies of Y-Ba-Cu-O superconductors II. Simple models of YBa2Cu3Ox

The electronic structure of YBa₂Cu₃O_x (x=6 and 7) is investigated using the CNDO molecular orbital method. Electronic structures of model clusters [Cu₃O₁₀]^–15, [Ba₈Cu₃O₁₀]⁺¹, [Y₈Cu₃O₁₀]⁺⁹ of the non-superconducting (x=6) and [Cu₃O₁₂]^–17, [Ba₈Cu₃O₁₂]^–1, [Y₈Cu₃O₁₂]⁺⁷ of the superconducting (x=7) phases are compared. Y and Ba layers cause a considerable electron density transfer from the central Cu(1) region.     

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

A balancing condition for weak limits of families of minimal surfaces

We prove a balancing condition for weak limits of families of embedded minimal surfaces of finite total curvature. We use it to prove compactness theorems for certain families of minimal surfaces.     

The emergence of a giant component in random subgraphs of pseudo‐random graphs

Let G be a d‐regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ which is second largest in absolute value satisfies λ = o(d). Let G_p with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of G_p is O(log n) and if α > 1, then G_p contains a unique giant component of size Ω(n), with all other components of size O(log n). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004