Addendum to Quantum Wave Function Collapse of a System Having Three anti Commuting Elements.

We indicate a new way in the solution of the problem of the quantum measurement . In past papers we used the well-known formalism of the density matrix using an algebraic approach in a two states quantum spin system S, considering the particular case of three anticommuting elements. We demonstrated that, during the wave collapse, we have a transition from the standard Clifford algebra, structured in its space and metrics, to the new spatial structure of the Clifford dihedral algebra. This structured geometric transition, which occurs during the interaction of the S system with the macroscopic measurement system M, causes the destruction of the interferential factors. In the present paper we construct a detailed model of the (S+M) interaction evidencing the particular role of the Time Ordering in the (S+M) coupling since we have a time asymmetric interaction . We demonstrate that , during the measurement , the physical circumstance that the fermion creation and annihilation operators of the S system must be destroyed during such interaction has a fundamental role

The Painlev\'e methods

This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether ordinary, partial, or discrete.Comment: LaTex 2e, subject index, Nonlinear integrable systems: classical and quantum, ed. A. Kundu, Special issue, Proceedings of Indian Science Academy,

Reductions of Gauss-Codazzi equations

We prove that conformally parametrized surfaces in Euclidean space \Rcubec of curvature $c$ admit a symmetry reduction of their Gauss-Codazzi equations whose general solution is expressed with the sixth Painlev\'e function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko, Eitner and Kitaev 1997) can be recovered by such a reduction.Comment: 25 pages, to appear, Studies in applied mathematic