On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

Equivalence and conservation rules for the total integral cross section in molecular collisions

The rule of conservation of the total integral cross section o_Tj) is described in a general way using the opacity function. An equivalence rule which states that at the same initial kinetic energy, the total integral cross section from the initial state j is equal to that from the initial state j, i.e., o_Tj) is also presented. Both rules are demonstrated with numerical examples in the He + H₂ collision system and counter-examples are also presented. Possible uses of the rules in the inversion of the intermolecular surface and as an experimental tool are also discussed.     

Spin polarization of semiconductor carriers by reflection off a ferromagnet

We present a theory of generation or alteration of the electron spin coherence and population in an n-doped semiconductor by reflection at the interface with a ferromagnet. The dependence of the spin reflection on the Schottky barrier height and the doping concentration in the semiconductor was computed for a generic model. The theory provides an explanation for the spontaneous electron spin coherence and nuclear polarization in the semiconductor interfaced with a ferromagnet and associated phenomena recently observed by time-resolved Faraday rotation experiments. The study also points to an alternative approach to spintronics different from spin injection.     

On the equivalence of quadratic APN functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to the APN Gold function x^2r+1{x^{2^r+1}} if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2 ⁿ where n ≡ 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.