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In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann a...
The Torelli group, I(Sg), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface.
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by t...
In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between plurih...
In this paper we consider critical points of the following nonlocal energy Ln(u) = Z IRn |(−)n/4u(x)|2dx , (1) where u: Hn/2(IRn) → N N ⊂ IRm is a compact k dimensional smooth manifold w...
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
We define a class of higher-order linear maps that transform quantum operations into quantum operations and satisfy suitable requirements of normality and complete positivity. For this class of maps w...
The goal of this paper is to provide a link between the parameter spaces of two families of one-dimensional dynamical systems, and to shed some light onto some sets of numbers which arise as “exceptio...
We add a last refinement to the results of [BW1] and [BW2] re-lating ideal classes of the Weyl algebra to the Calogero-Moser varieties: we show that the bijection constructed in those papers is unique...
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve...
For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed...

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