61,093 research outputs found
Canonical contact structures on some singularity links
We identify the canonical contact structure on the link of a simple elliptic
or cusp singularity by drawing a Legendrian handlebody diagram of one of its
Stein fillings. We also show that the canonical contact structure on the link
of a numerically Gorenstein surface singularity is trivial considered as a real
plane bundle.Comment: The second version is substantially different from the first version.
Bulletin of the London Mathematical Society, 201
Asymmetric simple exclusion process in one-dimensional chains with long-range links
We study the boundary-driven asymmetric simple exclusion process (ASEP) in a
one-dimensional chain with long-range links. Shortcuts are added to a chain by
connecting different pairs of sites selected randomly where and
denote the chain length and the shortcut density, respectively. Particles flow
into a chain at one boundary at rate and out of a chain at the other
boundary at rate , while they hop inside a chain via nearest-neighbor
bonds and long-range shortcuts. Without shortcuts, the model reduces to the
boundary-driven ASEP in a one-dimensional chain which displays the low density,
high density, and maximal current phases. Shortcuts lead to a drastic change.
Numerical simulation studies suggest that there emerge three phases; an empty
phase with , a jammed phase with , and a shock phase
with where is the mean particle density. The shock phase is
characterized with a phase separation between an empty region and a jammed
region with a localized shock between them. The mechanism for the shock
formation and the non-equilibrium phase transition is explained by an analytic
theory based on a mean-field approximation and an annealed approximation.Comment: revised version (16 pages and 6 eps figures
A new realization of rational functions, with applications to linear combination interpolation
We introduce the following linear combination interpolation problem (LCI):
Given distinct numbers and complex numbers
and , find all functions analytic in a simply
connected set (depending on ) containing the points such
that To this end we prove a representation
theorem for such functions in terms of an associated polynomial . We
first introduce the following two operations, substitution of , and
multiplication by monomials . Then let be the
module generated by these two operations, acting on functions analytic near
. We prove that every function , analytic in a neighborhood of the roots
of , is in . In fact, this representation of is unique. To solve the
above interpolation problem, we employ an adapted systems theoretic
realization, as well as an associated representation of the Cuntz relations
(from multi-variable operator theory.) We study these operations in reproducing
kernel Hilbert space): We give necessary and sufficient condition for existence
of realizations of these representation of the Cuntz relations by operators in
certain reproducing kernel Hilbert spaces, and offer infinite product
factorizations of the corresponding kernels
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