5,204 research outputs found
Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
We construct a four-parameter family of Markov processes on infinite
Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures.
Any process in the family induces a Feller Markov process on the
infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently,
the space of extreme characters of the infinite-dimensional unitary group
U(infinity). The process has a unique invariant distribution which arises as
the decomposing measure in a natural problem of harmonic analysis on
U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194,
this measure can also be described as a determinantal point process with a
correlation kernel expressed through the Gauss hypergeometric function
Reduced Order Controller Design for Robust Output Regulation
We study robust output regulation for parabolic partial differential
equations and other infinite-dimensional linear systems with analytic
semigroups. As our main results we show that robust output tracking and
disturbance rejection for our class of systems can be achieved using a
finite-dimensional controller and present algorithms for construction of two
different internal model based robust controllers. The controller parameters
are chosen based on a Galerkin approximation of the original PDE system and
employ balanced truncation to reduce the orders of the controllers. In the
second part of the paper we design controllers for robust output tracking and
disturbance rejection for a 1D reaction-diffusion equation with boundary
disturbances, a 2D diffusion-convection equation, and a 1D beam equation with
Kelvin-Voigt damping.Comment: Revised version with minor improvements and corrections. 28 pages, 9
figures. Accepted for publication in the IEEE Transactions on Automatic
Contro
Infinite partition monoids
Let and be the partition monoid and symmetric
group on an infinite set . We show that may be generated by
together with two (but no fewer) additional partitions, and we
classify the pairs for which is
generated by . We also show that may be generated by the set of all idempotent partitions
together with two (but no fewer) additional partitions. In fact,
is generated by if and only if it is
generated by . We also
classify the pairs for which is
generated by . Among other results, we show
that any countable subset of is contained in a -generated
subsemigroup of , and that the length function on
is bounded with respect to any generating set
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