19,205 research outputs found
Decompositions and the fixed point property for multifunctions
Relations between the fixed point properties for some classes of multifunctions of a compact Hausdorff space X, of a decomposition space X/D, where D is an upper semi-continuous decomposition of X, and of the members of D are studied. Results are applied to some special decompositions of metric continua
A periodicity criterion and the section problem on the Mapping Class Group
Some years ago, V. Markovic proved that there is no section of the Mapping
Class Group for a closed surface of genus g larger than 5 (in the case of
homeomorphims) and more recently generalized this result with D. Saric to the
case where g is larger than 1. We will state a periodicity criterion and will
use it to simplify some of the arguments given by Markovic and Saric in the
proof of their theorem. The periodicity criterion tells us that a homeomorphism
of a connected surface must be periodic if the set of connected periodic open
sets generates the topology of the surface.Comment: 40 page
Continuous spectral decompositions of Abelian group actions on C*-algebras
Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell
bundles over the Pontrjagin dual of G as continuous spectral decompositions of
G-actions on C*-algebras. We classify such spectral decompositions using
certain dense subspaces related to Marc Rieffel's theory of
square-integrability. There is a unique continuous spectral decomposition if
the group acts properly on the primitive ideal space of the C*-algebra. But
there are also examples of group actions without or with several inequivalent
spectral decompositions.Comment: 34 page
Conditions for Equality between Lyapunov and Morse Decompositions
Let be a continuous principal bundle whose group is
reductive. A flow of automorphisms of endowed with an ergodic
probability measure on the compact base space induces two decompositions of
the flag bundles associated to . A continuous one given by the finest Morse
decomposition and a measurable one furnished by the Multiplicative Ergodic
Theorem. The second is contained in the first. In this paper we find necessary
and sufficient conditions so that they coincide. The equality between the two
decompositions implies continuity of the Lyapunov spectra under pertubations
leaving unchanged the flow on the base space
Bounds for entanglement of formation of two mode squeezed thermal states
The upper and lower bounds of entanglement of formation are given for two
mode squeezed thermal state. The bounds are compared with other entanglement
measure or bounds. The entanglement distillation and the relative entropy of
entanglement of infinitive squeezed state are obtained at the postulation of
hashing inequality.Comment: 3 figure
Non-realizability of the Torelli group as area-preserving homeomorphisms
Nielsen realization problem for the mapping class group
asks whether the natural projection has a section. While all the previous results use torsion
elements in an essential way, in this paper, we focus on the much more
difficult problem of realization of torsion-free subgroups of
. The main result of this paper is that the Torelli group has
no realization inside the area-preserving homeomorphisms.Comment: 22 pages, 5 figure
A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure
A new unified modelling framework based on the superposition of additive submodels, functional components, and
wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented
using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown
analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear
autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional
component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and
multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters
problem, which can be solved using least-squares type methods. An efficient model structure determination
approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization
of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is
employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to
as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to
represent high-order and high dimensional non-linear systems
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