32,275 research outputs found
Morphisms, Symbolic sequences, and their Standard Forms
Morphisms are homomorphisms under the concatenation operation of the set of
words over a finite set. Changing the elements of the finite set does not
essentially change the morphism. We propose a way to select a unique
representing member out of all these morphisms. This has applications to the
classification of the shift dynamical systems generated by morphisms. In a
similar way, we propose the selection of a representing sequence out of the
class of symbolic sequences over an alphabet of fixed cardinality. Both methods
are useful for the storing of symbolic sequences in databases, like The On-Line
Encyclopedia of Integer Sequences. We illustrate our proposals with the
-symbol Fibonacci sequences
On the growth behaviour of Hironaka quotients
We consider a finite analytic morphism \phi = (f,g) : (X,p)\to (\C^2,0)
where is a complex analytic normal surface germ and and are
complex analytic function germs. Let be a good
resolution of with exceptional divisor . We denote
the dual graph of the resolution . We study the behaviour of the
Hironaka quotients of associated to the vertices of . We show
that there exists maximal oriented arcs in along which the Hironaka
quotients of strictly increase and they are constant on the connected
components of the closure of the complement of the union of the maximal
oriented arcs
Complements on disconnected reductive groups
We present various results on disconnected reductive groups, in particular
about the characteristic 0 representation theory of such groups over finite
fields.Comment: This version takes into account improvements suggested by G. Mall
Tunnel effect for semiclassical random walk
We study a semiclassical random walk with respect to a probability measure
with a finite number n_0 of wells. We show that the associated operator has
exactly n_0 exponentially close to 1 eigenvalues (in the semiclassical sense),
and that the other are O(h) away from 1. We also give an asymptotic of these
small eigenvalues. The key ingredient in our approach is a general
factorization result of pseudodifferential operators, which allows us to use
recent results on the Witten Laplacian
Comment on "Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models"
Recently Mayer et al. [Phys. Rev. E {\bf 68}, 016116 (2003)] proposed a new
way to compute numerically the fluctuation-dissipation ratios in nonequilibrium
critical systems. Using well-known facts of nonequilibrium critical dynamics I
show that the leading contributions of the quantities they consider are in fact
one-time quantities which are independent of the waiting time. The ratio of
these one-time quantities determines the slope of the straight lines observed
in the fluctuation-dissipation plots of Mayer et al.Comment: 4 pages, 3 figures included, shortened versio
The space of unipotently supported class functions on a finite reductive group
We determine the Lusztig restrictions on the space of class functions with a
unipotent support on a finite reductive group. In particular we give a simple
expression for the Lusztig restrictions of the generalized Green functions and
we describe the Lusztig restrictions of the generalized Gelfand-Graev
representations. We make explicit computations for the Gelfand-Graev
representations associated to the subregular unipotent class. In the case of
SLn we show that the computations can be reduced to the case of GLn' for
various n'.Comment: 21 page
Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications
It is known that ultrasound techniques yield non-intrusive measurements of
hydrodynamic flows. For example, the study of the echoes produced by a large
number of particle insonified by pulsed wavetrains has led to a now standard
velocimetry technique. In this paper, we propose to extend the method to the
continuous tracking of one single particle embedded in a complex flow. This
gives a Lagrangian measurement of the fluid motion, which is of importance in
mixing and turbulence studies. The method relies on the ability to resolve in
time the Doppler shift of the sound scattered by the continuously insonfied
particle.
For this signal processing problem two classes of approaches are used:
time-frequency analysis and parametric high resolution methods. In the first
class we consider the spectrogram and reassigned spectrogram, and we apply it
to detect the motion of a small bead settling in a fluid at rest. In more
non-stationary turbulent flows where methods in the second class are more
robust, we have adapted an Approximated Maximum Likelihood technique coupled
with a generalized Kalman filter.Comment: 16 pages 9 figure
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