1,615 research outputs found
Property (T) and rigidity for actions on Banach spaces
We study property (T) and the fixed point property for actions on and
other Banach spaces. We show that property (T) holds when is replaced by
(and even a subspace/quotient of ), and that in fact it is
independent of . We show that the fixed point property for
follows from property (T) when 1
. For simple Lie groups and their lattices, we prove that the fixed point property for holds for any if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement
Spin-orbit interaction and spin relaxation in a two-dimensional electron gas
Using time-resolved Faraday rotation, the drift-induced spin-orbit Field of a
two-dimensional electron gas in an InGaAs quantum well is measured. Including
measurements of the electron mobility, the Dresselhaus and Rashba coefficients
are determined as a function of temperature between 10 and 80 K. By comparing
the relative size of these terms with a measured in-plane anisotropy of the
spin dephasing rate, the D'yakonv-Perel' contribution to spin dephasing is
estimated. The measured dephasing rate is significantly larger than this, which
can only partially be explained by an inhomogeneous g-factor.Comment: 6 pages, 5 figure
Linear-time list recovery of high-rate expander codes
We show that expander codes, when properly instantiated, are high-rate list
recoverable codes with linear-time list recovery algorithms. List recoverable
codes have been useful recently in constructing efficiently list-decodable
codes, as well as explicit constructions of matrices for compressive sensing
and group testing. Previous list recoverable codes with linear-time decoding
algorithms have all had rate at most 1/2; in contrast, our codes can have rate
for any . We can plug our high-rate codes into a
construction of Meir (2014) to obtain linear-time list recoverable codes of
arbitrary rates, which approach the optimal trade-off between the number of
non-trivial lists provided and the rate of the code. While list-recovery is
interesting on its own, our primary motivation is applications to
list-decoding. A slight strengthening of our result would implies linear-time
and optimally list-decodable codes for all rates, and our work is a step in the
direction of solving this important problem
Regular graphs of large girth and arbitrary degree
For every integer d > 9, we construct infinite families {G_n}_n of
d+1-regular graphs which have a large girth > log_d |G_n|, and for d large
enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special
set of d+1 generators whose choice is related to the arithmetic of integral
quaternions. These graphs are inspired by the Ramanujan graphs of
Lubotzky-Philips-Sarnak and Margulis, with which they coincide when d is prime.
When d is not equal to the power of an odd prime, this improves the previous
construction of Imrich in 1984 where he obtained infinite families {I_n}_n of
d+1-regular graphs, realized as Cayley graphs on SL_2(q), and which are
displaying a girth > 0,48 log_d |I_n|. And when d is equal to a power of 2,
this improves a construction by Morgenstern in 1994 where certain families
{M_n}_n of 2^k+1-regular graphs were shown to have a girth > 2/3 log_d |M_n|.Comment: (15 pages) Accepted at Combinatorica. Title changed following
referee's suggestion. Revised version after reviewing proces
Sonoluminescing air bubbles rectify argon
The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the
percentage of inert gas within the bubble. We propose a theory for this
dependence, based on a combination of principles from sonochemistry and
hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent
reaction to water soluble gases implies that strongly forced air bubbles
eventually consist of pure argon. Thus it is the partial argon (or any other
inert gas) pressure which is relevant for stability. The theory provides
quantitative explanations for many aspects of SBSL.Comment: 4 page
Differential criterion of a bubble collapse in viscous liquids
The present work is devoted to a model of bubble collapse in a Newtonian
viscous liquid caused by an initial bubble wall motion. The obtained bubble
dynamics described by an analytic solution significantly depends on the liquid
and bubble parameters. The theory gives two types of bubble behavior: collapse
and viscous damping. This results in a general collapse condition proposed as
the sufficient differential criterion. The suggested criterion is discussed and
successfully applied to the analysis of the void and gas bubble collapses.Comment: 5 pages, 3 figure
-Spectral theory of locally symmetric spaces with -rank one
We study the -spectrum of the Laplace-Beltrami operator on certain
complete locally symmetric spaces with finite volume and
arithmetic fundamental group whose universal covering is a
symmetric space of non-compact type. We also show, how the obtained results for
locally symmetric spaces can be generalized to manifolds with cusps of rank
one
Music cognition as mental time travel.
As we experience a temporal flux of events our expectations of future events change. Such expectations seem to be central to our perception of affect in music, but we have little understanding of how expectations change as recent information is integrated. When music establishes a pitch centre (tonality), we rapidly learn to anticipate its continuation. What happens when anticipations are challenged by new events? Here we show that providing a melodic challenge to an established tonality leads to progressive changes in the impact of the features of the stimulus on listeners' expectations. The results demonstrate that retrospective analysis of recent events can establish new patterns of expectation that converge towards probabilistic interpretations of the temporal stream. These studies point to wider applications of understanding the impact of information flow on future prediction and its behavioural utility
Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds
In this paper, we numerically investigate the length spectra and the
low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large
number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero
eigenvalues have been successfully computed using the periodic orbit sum
method, which are compared with various geometric quantities such as volume,
diameter and length of the shortest periodic geodesic of the manifolds. The
deviation of low-lying eigenvalue spectra of manifolds converging to a cusped
hyperbolic manifold from the asymptotic distribution has been measured by
function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of
cusped manifolds in section 2 is correcte
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