Invariant Measures for Cherry Flows

We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.     

A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

Investigation of helium implantation induced blistering in InP

 Four-inch InP wafers were implanted with 100 keV helium ions with a dose of 5×10¹⁶ cm⁻² and subsequently annealed in air in the temperature range of 225-400°C in order to determine the blistering kinetics of these wafers. An Arrhenius plot of the blistering time as a function of reciprocal temperature revealed two different activation energies for the formation of surface blisters in InP. The activation energy was found to be 0.30 eV in the higher temperature regime of 300-400 °C and 0.74 eV in the lower temperature regime of 225-300 °C. The implantation induced damage was analyzed by cross-sectional transmission electron microscopy, which revealed a band of defects extending from 400-700 nm from the surface of InP. The damage band was found to be decorated with a large number of nanovoids having diameters between 2 and 5 nm. These nanovoids served as precursors for the formation of microcracks inside InP upon annealing, which led to the formation of surface blisters.     

On a separation criterion for cohomology groups of (q, n - q)-coronae

We give a separation theorem for (q, n - q)-coronas improving a recent result due to Laurent-Thiébaut and Leiterer.     

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.