1,844 research outputs found
An algebraic formula for the index of a vector field on an isolated complete intersection singularity
Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0,
having an isolated singularity at 0 and X be the germ of a holomorphic vector
field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show
that in this case the homological index and the GSV-index coincide. In the case
when the zero of X is also isolated in the ambient space \CC^{n+k} we give a
formula for the homological index in terms of local linear algebra.Comment: 18 pages; added an example which is not quasi homogeneous. A script
calculating this example can be found at
http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source
file of this articl
Optimization and optimality test for the Max-Cut Problem
We show that the following two problems are polynomially equivalent:\ud
1. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not.\ud
2. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′.\ud
\ud
As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem.\ud
This in turn implies that recognizing optimal cuts in an unweighted graph is NP-hard
Design and Performance of the CMS Pixel Detector Readout Chip
The readout chip for the CMS pixel detector has to deal with an enormous data
rate. On-chip zero suppression is inevitable and hit data must be buffered
locally during the latency of the first level trigger. Dead-time must be kept
at a minimum. It is dominated by contributions coming from the readout. To keep
it low an analog readout scheme has been adopted where pixel addresses are
analog coded. We present the architecture of the final CMS pixel detector
readout chip with special emphasis on the analog readout chain. Measurements of
its performance are discussed.Comment: 8 pages, 11 figures. Contribution to the Proceedings of the Pixel2005
Workshop, Bonn, German
A relaxationless demonstration of the Quantum Zeno Paradox on an individual atom
The driven evolution of the spin of an individual atomic ion on the
ground-state hyperfine resonance is impeded by the observation of the ion in
one of the pertaining eigenstates. Detection of resonantly scattered light
identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state
is free of relaxation and correlated with the detector by a null signal. Null
events represent the straightforward demonstration of the quantum Zeno paradox.
Also, high probability of survival was demonstrated when the ion, driven by a
fractionated pulse, was probed {\em and monitored} during the
intermissions of the drive, such that the ion's evolution is completely
documented.Comment: 7 page
- …