924 research outputs found
Connected Lie groups and property RD
For a locally compact group, property RD gives a control on the convolution
norm of any compactly supported measure in terms of the -norm of its
density and the diameter of its support. We give a complete classification of
those Lie groups with property RD.Comment: 29 page
Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect II: Dispersive waves
Previous results on the scattering of surface waves by vertical vorticity on
shallow water are generalized to the case of dispersive water waves. Dispersion
effects are treated perturbatively around the shallow water limit, to first
order in the ratio of depth to wavelength. The dislocation of the incident
wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short
wavelengths the scattering is qualitatively similar to the nondispersive case.
At moderate wavelengths, however, there are two markedly different scattering
regimes according to wether the capillary length is smaller or larger than
times depth. The dislocation is characterized by a parameter that
depends both on phase and group velocity. The validity range of the calculation
is the same as in the shallow water case: wavelengths small compared to vortex
radius, and low Mach number. The implications of these limitations are
carefully considered.Comment: 30 pages, 11 figure
On the divine clockwork: the spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state
The correspondence limit of the atomic elliptic state in three dimensions is
discussed in terms of Nelson's stochastic mechanics. In previous work we have
shown that this approach leads to a limiting Nelson diffusion and here we
discuss in detail the invariant measure for this process and show that it is
concentrated on the Kepler ellipse in the plane z=0. We then show that the
limiting Nelson diffusion generator has a spectral gap; thereby proving that in
the infinite time limit the density for the limiting Nelson diffusion will
converge to its invariant measure. We also include a summary of the Cheeger and
Poincare inequalities both of which are used in our proof of the existence of
the spectral gap.Comment: 30 pages, 5 figures, submitted to J. Math. Phy
Asymptotic singularities of planar parallel 3-RPR manipulators
We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace
Properties making a chaotic system a good Pseudo Random Number Generator
We discuss two properties making a deterministic algorithm suitable to
generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai
entropy and high-dimensionality. We propose the multi dimensional Anosov
symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic
features of this map are useful for generating Pseudo Random Numbers and
investigate numerically which of them survive in the discrete version of the
map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction
Approximation of conformal mappings by circle patterns
A circle pattern is a configuration of circles in the plane whose
combinatorics is given by a planar graph G such that to each vertex of G
corresponds a circle. If two vertices are connected by an edge in G, the
corresponding circles intersect with an intersection angle in .
Two sequences of circle patterns are employed to approximate a given
conformal map and its first derivative. For the domain of we use
embedded circle patterns where all circles have the same radius decreasing to 0
and which have uniformly bounded intersection angles. The image circle patterns
have the same combinatorics and intersection angles and are determined from
boundary conditions (radii or angles) according to the values of (
or ). For quasicrystallic circle patterns the convergence result is
strengthened to -convergence on compact subsets.Comment: 36 pages, 7 figure
Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights
This is the fourth article of our series. Here, we study weighted norm
inequalities for the Riesz transform of the Laplace-Beltrami operator on
Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the
doubling volume property and Gaussian upper bounds.Comment: 12 pages. Fourth of 4 papers. Important revision: improvement of main
result by eliminating use of Poincar\'e inequalities replaced by the weaker
Gaussian keat kernel bound
PHENOTIPICAL STUDY OF CERTAIN MAIZE HYBRIDS AND THEIR PARENTAL FORMS (INBRED LINES) DIFFERENTIATED THROUGH CYTOPLASM
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