595 research outputs found
Regular vs. classical M\"obius transformations of the quaternionic unit ball
The regular fractional transformations of the extended quaternionic space
have been recently introduced as variants of the classical linear fractional
transformations. These variants have the advantage of being included in the
class of slice regular functions, introduced by Gentili and Struppa in 2006, so
that they can be studied with the useful tools available in this theory. We
first consider their general properties, then focus on the regular M\"obius
transformations of the quaternionic unit ball B, comparing the latter with
their classical analogs. In particular we study the relation between the
regular M\"obius transformations and the Poincar\'e metric of B, which is
preserved by the classical M\"obius transformations. Furthermore, we announce a
result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page
Some Applications of the Lee-Yang Theorem
For lattice systems of statistical mechanics satisfying a Lee-Yang property
(i.e., for which the Lee-Yang circle theorem holds), we present a simple proof
of analyticity of (connected) correlations as functions of an external magnetic
field h, for Re h > 0 or Re h < 0. A survey of models known to have the
Lee-Yang property is given. We conclude by describing various applications of
the aforementioned analyticity in h.Comment: 16 page
On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings
We provide a simple lagrangian interpretation of the meaning of the
semi-relative condition in closed string theory. Namely, we show how the
semi-relative condition is equivalent to the requirement that physical
operators be cohomology classes of the BRS operators acting on the space of
local fields {\it covariant} under world-sheet reparametrizations. States
trivial in the absolute BRS cohomology but not in the semi-relative one are
explicitly seen to correspond to BRS variations of operators which are not
globally defined world-sheet tensors. We derive the covariant expressions for
the observables of topological gravity. We use them to prove a formula that
equates the expectation value of the gravitational descendant of ghost number 4
to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199
Aperiodic invariant continua for surface homeomorphisms
We prove that if a homeomorphism of a closed orientable surface S has no
wandering points and leaves invariant a compact, connected set K which contains
no periodic points, then either K=S and S is a torus, or is the
intersection of a decreasing sequence of annuli. A version for non-orientable
surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif
Constraints on the form factors for K --> pi l nu and implications for V_us
Rigorous bounds are established for the expansion coefficients governing the
shape of semileptonic K-->pi form factors. The constraints enforced by
experimental data from tau-->K pi nu eliminate uncertainties associated with
model parameterizations in the determination of |V_us|. The results support the
validity of a powerful expansion that can be applied to other semileptonic
transitions.Comment: 5 pages, 3 figures; references added, version to appear in Phys. Rev.
D alongside hep-ex/060805
Large fluctuations in stochastic population dynamics: momentum space calculations
Momentum-space representation renders an interesting perspective to theory of
large fluctuations in populations undergoing Markovian stochastic gain-loss
processes. This representation is obtained when the master equation for the
probability distribution of the population size is transformed into an
evolution equation for the probability generating function. Spectral
decomposition then brings about an eigenvalue problem for a non-Hermitian
linear differential operator. The ground-state eigenmode encodes the stationary
distribution of the population size. For long-lived metastable populations
which exhibit extinction or escape to another metastable state, the
quasi-stationary distribution and the mean time to extinction or escape are
encoded by the eigenmode and eigenvalue of the lowest excited state. If the
average population size in the stationary or quasi-stationary state is large,
the corresponding eigenvalue problem can be solved via WKB approximation
amended by other asymptotic methods. We illustrate these ideas in several model
examples.Comment: 20 pages, 9 figures, to appear in JSTA
Inversion of perturbation series
We investigate the inversion of perturbation series and its resummation, and
prove that it is related to a recently developed parametric perturbation
theory. Results for some illustrative examples show that in some cases series
reversion may improve the accuracy of the results
Fluctuation force exerted by a planar self-avoiding polymer
Using results from Schramm Loewner evolution (SLE), we give the expression of
the fluctuation-induced force exerted by a polymer on a small impenetrable
disk, in various 2-dimensional domain geometries. We generalize to two polymers
and examine whether the fluctuation force can trap the object into a stable
equilibrium. We compute the force exerted on objects at the domain boundary,
and the force mediated by the polymer between such objects. The results can
straightforwardly be extended to any SLE interface, including Ising,
percolation, and loop-erased random walks. Some are relevant for extremal value
statistics.Comment: 7 pages, 22 figure
On an inverse problem for anisotropic conductivity in the plane
Let be a bounded domain with smooth
boundary and a smooth anisotropic conductivity on .
Starting from the Dirichlet-to-Neumann operator on
, we give an explicit procedure to find a unique domain
, an isotropic conductivity on and the boundary
values of a quasiconformal diffeomorphism which
transforms into .Comment: 9 pages, no figur
Hydrodynamic object recognition using pressure sensing
Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing
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