A skew normal dilation on the numerical range of an operator

Simple facts about the Poincaré-Neumann double layer potential are used in the construction of a normal dilation, on the numerical range of an arbitrary Hilbert space operator. Recent and old ideas in the theory of the numerical range are unified by this framework. A couple of mapping results for the numerical range are derived.Revised version: 15 July 2002First author partially supported by the National Science Foundation Grant DMS 0100367, Second author supported by STINT, The Swedish Foundation for International Cooperation in Research and Higher Education.     

Global Euler obstruction and polar invariants

Let be a purely dimensional, complex algebraic singular space. We define a global Euler obstruction Eu(Y) which extends the Euler-Poincaré characteristic in case of a nonsingular Y. Using Lefschetz pencils, we express Eu(Y) as alternating sum of global polar invariants. Partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401.     

Rotational invariance of quadromer correlations on the hexagonal lattice

In 1963 Fisher and Stephenson (Phys. Rev. (2) 132 (1963) 1411) conjectured that the monomer-monomer correlation on the square lattice is rotationally invariant. In this paper we prove a closely related statement on the hexagonal lattice. Namely, we consider correlations of two quadromers (four-vertex subgraphs consisting of a monomer and its three neighbors) and show that they are rotationally invariant.     

Convergence des solutions faibles du système de Vlasov–Maxwell stationnaire vers des solutions faibles du système de Vlasov–Poisson stationnaire quand la vitesse de la lumière tend vers l'infini

We study here the behavior of weak solutions for the relativistic stationary Vlasov–Maxwell system with boundary conditions in a three-dimensional bounded domain with strictly star-shaped boundary, when the light speed becomes infinite. We prove the convergence toward a weak solution for the stationary Vlasov–Poisson system. The time periodic problem and the problem with initial-boundary conditions can be treated by the same method. To cite this article: M. Bostan, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

P ≠ NP for all infinite Boolean algebras

We prove that all infinite Boolean rings (algebras) have the property P ≠ NP according to the digital (binary) nondeterminism.     

Tropophenylene and tropovinylene spiroborates

The reaction of tropolones with 2-alkoxy-1,3,2-dioxaboroles yields crystalline compounds, e.g. III, whose spectra and structure are discussed.     

Rayleigh scattering fromn=2 states of atomic hydrogen

Exact analytic results are presented for the elastic scattering of photons from excited hydrogen atoms in then=2 states. The general form of the matrix elements required is inferred from previous work on the scattering by a completen=2 shell of a model atom, and is expressed in terms of one hypergeometric function of the Gauss type. The low-energy behavior of the matrix elements is discussed and new negative-order sum rules are derived. The cross sections were computed to a high degree of accuracy for values of the photon energy both below and above the photoionization threshold for then=2 states. Detailed results are given for near-resonance scattering (i.e., in the vicinity of Balmer frequencies), due to its relevance for the diagnostics of neutrals in fusion plasmas.     

A fixed-point iteration approach for multibody dynamics with contact and small friction

Acceleration–force setups for multi-rigid-body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients (a Painleve paradox). This difficulty is circumvented by time-stepping methods using impulse-velocity approaches, which solve complementarity problems with possibly nonconvex solution sets. We show that very simple configurations involving two bodies may have a nonconvex solution set for any nonzero value of the friction coefficient. We construct two fixed-point iteration algorithms that solve convex subproblems and that are guaranteed, for sufficiently small friction coefficients, to retrieve, at a linear convergence rate, the unique velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled. In addition, we show that one step of one of the iterative algorithms provides an excellent approximation to the velocity solution of the original, possibly nonconvex, problem if for all contacts we have that either the friction coefficient is small or the slip velocity is small.Subject Index. 70E55, 75M10, 75M15, 90C33A partial version of this work has appeared in the proceedings of the NATO Advanced Studies Institute on Virtual Nonlinear Multibody Systems, Prague, 2002.