4,799 research outputs found
Bimodule structure of the mixed tensor product over and quantum walled Brauer algebra
We study a mixed tensor product of the three-dimensional fundamental
representations of the Hopf algebra , whenever is not a
root of unity. Formulas for the decomposition of tensor products of any simple
and projective -module with the generating modules
and are obtained. The centralizer of
on the chain is calculated. It is shown to be the quotient
of the quantum walled Brauer algebra. The structure of
projective modules over is written down explicitly. It is
known that the walled Brauer algebras form an infinite tower. We have
calculated the corresponding restriction functors on simple and projective
modules over . This result forms a crucial step in
decomposition of the mixed tensor product as a bimodule over
. We give an explicit bimodule
structure for all .Comment: 43 pages, 5 figure
Light scattering by optically anisotropic scatterers II: T--matrix computations for radially and uniformly anisotropic droplets
This is the second paper in a series on light scattering from optically
anisotropic scatterers embedded in an isotropic medium. The apparently complex
T-matrix theory involving mixing of angular momentum components turns out to be
an efficient approach to calculating scattering in these systems. We present
preliminary results of numerical calculations of the scattering by spherical
droplets in some simple cases. The droplets contain optically anisotropic
material with local radial or uniform anisotropy. We concentrate on cases in
which the scattering is due only to the local optical anisotropy within the
scatterer. For radial anisotropy we find non-monotonic dependence of the
scattering cross-section on the degree of anisotropy can occur in a regime for
which both the Rayleigh and semi-classical theories are inapplicable. For
uniform anisotropy the cross-section is strongly dependent on the angle between
the incident light and the optical axis, and for larger droplets this
dependence is non-monotonic.Comment: 14 pages, 6 figures, uses RevTex
Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
We use a nonlocal maximum principle to prove the global existence of smooth
solutions for a slightly supercritical surface quasi-geostrophic equation. By
this we mean that the velocity field is obtained from the active scalar
by a Fourier multiplier with symbol , where
is a smooth increasing function that grows slower than as
.Comment: 11 pages, second version with slightly stronger resul
Waveguide propagation of light in polymer porous films filled with nematic liquid crystals
We theoretically analyze the waveguide regime of light propagation in a
cylindrical pore of a polymer matrix filled with liquid crystals assuming that
the effective radial optical anisotropy is biaxial. From numerical analysis of
the dispersion relations, the waveguide modes are found to be sensitive to the
field-induced changes of the anisotropy. The electro-optic properties of the
polymer porous polyethylene terephthalate (PET) films filled with the nematic
liquid crystal 5CB are studied experimentally and the experimental results are
compared with the results of the theoretical investigation.Comment: 15 pages, 10 figures, revtex4-
Prospects for the Bc Studies at LHCb
We discuss the motivations and perspectives for the studies of the mesons of
the (bc) family at LHCb. The description of production and decays at LHC
energies is given in details. The event yields, detection efficiencies, and
background conditions for several Bc decay modes at LHCb are estimated.Comment: 20 pages, 5 eps-figure
- …