Sur les décompositions directes des contractions de l'espace de Hilbert

Soit H un espace de Hilbert séparable, T ∈ $\text{B}$(H) une contraction complètement nonunitaire et H₁ ? H un sous-espace fermé, invariant à T. Le but de cette Note est de trouver une condition nécessaire et suffisante pour qu'il existe un sous-espace fermé H′ ? H, invariant à T et tel que l'espace H se décompose en somme directe $\text{H = H′ ? H}{}_1$ pas nécessairement orthogonale.     

On the shape resonances in NO− and N2−

The method used by Koike and Watanabe to describe negative molecular ion formation is generalized for multiwaves states of the extra electron. The structure of the shape resonances in NO^? and N₂^? is discussed. For the NO^?-captured electron it is found that the dπ-wave component increases with increasing resonance energy.     

On using lens-assisted hologram interferometry to investigate semiconductor device behaviour

The paper analyses some of the causes that limit the performance of the hologram interferometry method when used for the study of the behaviour of semiconductors devices. Then some results are shown obtained by the authors using a method of lens-assisted microscope hologram interferometry for studying such structures. The method allows detection of defects and, besides, it renders quantitatively the structure local non-uniformities during the normal operation of the semiconductor devices.     

Multistep reaction analysis. A numerical approach based on relaxation theory

A general numerical method and program for simulation of the kinetics of multistep reactions is described, with details for collation of data, construction of a mechanistic model, and simulation of reciprocal relaxation times and calculation of individual rate constants. The working scheme of the program includes an initial approximate simulation by adjustment of the rate constants followed by their optimization with a Powell minimization subroutine. The procedure is applied to aromatic nucleophilic addition.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.