8,932 research outputs found
Ricci flow on compact K\"ahler manifolds of positive bisectional curvature
We announce a new proof of the uniform estimate on the curvature of solutions
to the Ricci flow on a compact K\"ahler manifold with positive
bisectional curvature. In contrast to the recent work of X. Chen and G. Tian,
our proof of the uniform estimate does not rely on the exsitence of
K\"ahler-Einstein metrics on , but instead on the first author's Harnack
inequality for the K\"ahler-Ricc flow, and a very recent local injectivity
radius estimate of Perelman for the Ricci flow.Comment: 4 page
Controlling Chaos in a Neural Network Based on the Phase Space Constraint
The chaotic neural network constructed with chaotic neurons exhibits very rich dynamic
behaviors and has a nonperiodic associative memory. In the chaotic neural network,
however, it is dicult to distinguish the stored patters from others, because the states of
output of the network are in chaos. In order to apply the nonperiodic associative memory
into information search and pattern identication, etc, it is necessary to control chaos in
this chaotic neural network. In this paper, the phase space constraint method focused on
the chaotic neural network is proposed. By analyzing the orbital of the network in phase
space, we chose a part of states to be disturbed. In this way, the evolutional spaces of
the strange attractors are constrained. The computer simulation proves that the chaos
in the chaotic neural network can be controlled with above method and the network can
converge in one of its stored patterns or their reverses which has the smallest Hamming
distance with the initial state of the network. The work claries the application prospect
of the associative dynamics of the chaotic neural network
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