Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints

Using the theory of exact penalization for mathematical programs with subanalytic constraints, the theory of error bounds for quadratic inequality systems, and the theory of parametric normal equations, we derive various exact penalty functions for mathematical programs subject to equilibrium constraints, and we also characterize stationary points of these programs. The research of this author is based on work supported by the National Sciences and Engineering Research Council of Canada under grant OPG0090391. The research of this author is based on work supported by the National Science Foundation under grants DDM-9104078 and CCR-9213739. Part of this paper was completed while he was visiting The University of Melbourne and The University of New South Wales. The research of this author is based on work supported by the Australian Research Council.     

A positron lifetime study in quenched Pb(Ag) alloys

Positron lifetime measurements have been made in quenched or irradiated pure Pb and in quenched Pb(Ag) alloys. From positron investigation of annealing behaviour, the precipitation of silver atoms in dilute alloys should be understood in terms of (Ag-Pb) interstitially migrating pairs. The presence of di-interstitials (Ag-Ag) or complexes [Ag(S)-V] as mobile defects responsible for the Ag transport process in concentrated alloys is discussed.     

Adding dissipation to the Schrödinger equation from the quantum-potential viewpoint

We discuss methods of adding dissipation to the Schrödinger equation in light of the quantum-potential interpretation of quantum mechanics. This favors nonlinear equations in general and Kostin's Schrödinger-Langevin equation in particular. We give a simple example, the damping of small coherent oscillations.     

Représentation de −1 comme somme de carrés dans un corps cyclotomique quelconque

Let m ≥ 3 be an odd integer, and let K^(m) = Q(e^2πi/m) be the cyclotomic field of the m-th roots of unity. Then s(K^(m)) (the “stufe” of K^(m), that is to say, the smallest number of squares necessary to represent ?1 in K^(m) is equal to 2 or to 4 depending on whether the multiplicative order of 2 modulo m is even or odd.