6,375 research outputs found
Differential expansion for link polynomials
The differential expansion is one of the key structures reflecting group
theory properties of colored knot polynomials, which also becomes an important
tool for evaluation of non-trivial Racah matrices. This makes highly desirable
its extension from knots to links, which, however, requires knowledge of the
-symbols, at least, for the simplest triples of non-coincident
representations. Based on the recent achievements in this direction, we
conjecture a shape of the differential expansion for symmetrically-colored
links and provide a set of examples. Within this study, we use a special
framing that is an unusual extension of the topological framing from knots to
links. In the particular cases of Whitehead and Borromean rings links, the
differential expansions are different from the previously discovered.Comment: 11 page
Free-Field Representation of Group Element for Simple Quantum Group
A representation of the group element (also known as ``universal -matrix'') which satisfies , is given in the form where , and and
are the generators of quantum group associated respectively with
Cartan algebra and the {\it simple} roots. The ``free fields'' $\chi,\
\vec\phi,\ \psi\psi^{(s)}\psi^{(s')} =
q^{-\vec\alpha_{i(s)} \vec\alpha_{i(s')}} \psi^{(s')}\psi^{(s)}, &
\chi^{(s)}\chi^{(s')} = q^{-\vec\alpha_{i(s)}\vec\alpha_{i(s')}}
\chi^{(s')}\chi^{(s)}& {\rm for} \ s<s', \\ q^{\vec h\vec\phi}\psi^{(s)} =
q^{\vec h\vec\alpha_{i(s)}} \psi^{(s)}q^{\vec h\vec\phi}, & q^{\vec
h\vec\phi}\chi^{(s)} = q^{\vec h \vec\alpha_{i(s)}}\chi^{(s)}q^{\vec
h\vec\phi}, & \\ &\psi^{(s)} \chi^{(s')} = \chi^{(s')}\psi^{(s)} & {\rm for\
any}\ s,s'.d_Ggg \rightarrow g'\cdot g''{\cal
R}{\cal R} (g\otimes I)(I\otimes g) =
(I\otimes g)(g\otimes I){\cal R}$Comment: 68 page
Bayesian fan charts for U.K. inflation: forecasting and sources of uncertainty in an evolving monetary system
We estimate a Bayesian vector autoregression for the U.K. with drifting coefficients and stochastic volatilities. We use it to characterize posterior densities for several objects that are useful for designing and evaluating monetary policy, including local approximations to the mean, persistence, and volatility of inflation. We present diverse sources of uncertainty that impinge on the posterior predictive density for inflation, including model uncertainty, policy drift, structural shifts and other shocks. We use a recently developed minimum entropy method to bring outside information to bear on inflation forecasts. We compare our predictive densities with the Bank of England's fan charts
Phase behaviour of block copolymer melts with arbitrary architecture
The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for
microphase separation in AB block copolymer melts is generalized for systems
with arbitrary topology of molecules. A diagrammatic technique for calculation
of the monomeric correlation functions is developed. The free energies of
various mesophases are calculated within the second-harmonic approximation.
Model highly-branched tree-like structures are considered as an example and
their phase diagrams are obtained. The topology of molecules is found to
influence the spinodal temperature and asymmetry of the phase diagrams, but not
the types of phases and their order. We suggest that all model AB
block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also
http://rugmd4.chem.rug.nl/~morozov/research.htm
Surface EM waves on 1D Photonic Crystals
We study surface states of 1D photonic crystals using a semiclassical coupled
wave theory. Both TE and TM modes are treated. We derive analytic
approximations that clarify the systematics of the dispersion relations, and
the roles of the various parameters defining the crystal.Comment: 7 pages, 8 figure
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