9,371 research outputs found
Triviality of the prolongation algebra of the Kuramoto-Sivashinsky equation
The authors apply the well known Wahlquist-Estabrook prolongation technique to the Kuramoto-Sivashinsky equation. The prolongation algebra turns out to be trivial in the sense that it is commutative. This supports nonintegrability of the equation
Unique local determination of convex bodies
Barker and Larman asked the following. Let be a
convex body, whose interior contains a given convex body , and let, for all supporting hyperplanes of , the
-volumes of the intersections be given. Is then
uniquely determined? Yaskin and Zhang asked the analogous question when, for
all supporting hyperplanes of , the -volumes of the "caps" cut off
from by are given. We give local positive answers to both of these
questions, for small -perturbations of , provided the boundary of
is . In both cases, -volumes or -volumes can be replaced by
-dimensional quermassintegrals for or for ,
respectively. Moreover, in the first case we can admit, rather than hyperplane
sections, sections by -dimensional affine planes, where . In fact, here not all -dimensional affine subspaces are needed, but
only a small subset of them (actually, a -manifold), for unique local
determination of .Comment: 16 pdf-page
Quantum tomography of the GHZ state
We present a method of generation of the Greenberger-Horne-Zeilinger state
involving type II and type I parametric downconversion, and triggering
photodetectors. The state generated by the proposed experimental set-up can be
reconstructed through multi-mode quantum homodyne tomography. The feasibility
of the measurement is studied on the basis of Monte-Carlo simulations.Comment: Paper submitted to the proceedings of the III Adriatico Research
Conference on Quantum Interferometry, ICTP, March 1-5,1999. 5 pages, 3 eps
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