1,299 research outputs found
Dynamics and Lax-Phillips scattering for generalized Lamb models
This paper treats the dynamics and scattering of a model of coupled
oscillating systems, a finite dimensional one and a wave field on the half
line. The coupling is realized producing the family of selfadjoint extensions
of the suitably restricted self-adjoint operator describing the uncoupled
dynamics. The spectral theory of the family is studied and the associated
quadratic forms constructed. The dynamics turns out to be Hamiltonian and the
Hamiltonian is described, including the case in which the finite dimensional
systems comprises nonlinear oscillators; in this case the dynamics is shown to
exist as well. In the linear case the system is equivalent, on a dense
subspace, to a wave equation on the half line with higher order boundary
conditions, described by a differential polynomial explicitely
related to the model parameters. In terms of such structure the Lax-Phillips
scattering of the system is studied. In particular we determine the incoming
and outgoing translation representations, the scattering operator, which turns
out to be unitarily equivalent to the multiplication operator given by the
rational function , and the Lax-Phillips semigroup,
which describes the evolution of the states which are neither incoming in the
past nor outgoing in the future
Torus fibrations and localization of index II
We give a framework of localization for the index of a Dirac-type operator on
an open manifold. Suppose the open manifold has a compact subset whose
complement is covered by a family of finitely many open subsets, each of which
has a structure of the total space of a torus bundle. Under an acyclic
condition we define the index of the Dirac-type operator by using the
Witten-type deformation, and show that the index has several properties, such
as excision property and a product formula. In particular, we show that the
index is localized on the compact set.Comment: 47 pages, 2 figures. To appear in Communications in Mathematical
Physic
Obstruction Results in Quantization Theory
We define the quantization structures for Poisson algebras necessary to
generalise Groenewold and Van Hove's result that there is no consistent
quantization for the Poisson algebra of Euclidean phase space. Recently a
similar obstruction was obtained for the sphere, though surprising enough there
is no obstruction to the quantization of the torus. In this paper we want to
analyze the circumstances under which such obstructions appear. In this context
we review the known results for the Poisson algebras of Euclidean space, the
sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc
Quantum Probes of Spacetime Singularities
It is shown that there are static spacetimes with timelike curvature
singularities which appear completely nonsingular when probed with quantum test
particles. Examples include extreme dilatonic black holes and the fundamental
string solution. In these spacetimes, the dynamics of quantum particles is well
defined and uniquely determined.Comment: 12 pages, RevTeX, no figures, A few breif comments added and typos
correcte
Mining Uncertain Sequential Patterns in Iterative MapReduce
This paper proposes a sequential pattern mining (SPM) algorithm in large scale uncertain databases. Uncertain sequence databases are widely used to model inaccurate or imprecise timestamped data in many real applications, where traditional SPM algorithms are inapplicable because of data uncertainty and scalability. In this paper, we develop an efficient approach to manage data uncertainty in SPM and design an iterative MapReduce framework to execute the uncertain SPM algorithm in parallel. We conduct extensive experiments in both synthetic and real uncertain datasets. And the experimental results prove that our algorithm is efficient and scalable
An Edgeworth expansion for finite population L-statistics
In this paper, we consider the one-term Edgeworth expansion for finite
population L-statistics. We provide an explicit formula for the Edgeworth
correction term and give sufficient conditions for the validity of the
expansion which are expressed in terms of the weight function that defines the
statistics and moment conditions.Comment: 14 pages. Minor revisions. Some explanatory comments and a numerical
example were added. Lith. Math. J. (to appear
QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS
We present a unified framework for the quantization of a family of discrete
dynamical systems of varying degrees of "chaoticity". The systems to be
quantized are piecewise affine maps on the two-torus, viewed as phase space,
and include the automorphisms, translations and skew translations. We then
treat some discontinuous transformations such as the Baker map and the
sawtooth-like maps. Our approach extends some ideas from geometric quantization
and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE
Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion
We study the numerical solution of the non-relativistic Schr\"{o}dinger
equation for two-electron atoms in ground and excited S-states using
pseudospectral (PS) methods of calculation. The calculation achieves
convergence rates for the energy, Cauchy error in the wavefunction, and
variance in local energy that are exponentially fast for all practical
purposes. The method requires three separate subdomains to handle the
wavefunction's cusp-like behavior near the two-particle coalescences. The use
of three subdomains is essential to maintaining exponential convergence. A
comparison of several different treatments of the cusps and the semi-infinite
domain suggest that the simplest prescription is sufficient. For many purposes
it proves unnecessary to handle the logarithmic behavior near the
three-particle coalescence in a special way. The PS method has many virtues: no
explicit assumptions need be made about the asymptotic behavior of the
wavefunction near cusps or at large distances, the local energy is exactly
equal to the calculated global energy at all collocation points, local errors
go down everywhere with increasing resolution, the effective basis using
Chebyshev polynomials is complete and simple, and the method is easily
extensible to other bound states. This study serves as a proof-of-principle of
the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some
references added, some stylistic changes, added paragraph to matrix methods
section, added last sentence to abstract
Affine equivariant rank-weighted L-estimation of multivariate location
In the multivariate one-sample location model, we propose a class of flexible
robust, affine-equivariant L-estimators of location, for distributions invoking
affine-invariance of Mahalanobis distances of individual observations. An
involved iteration process for their computation is numerically illustrated.Comment: 16 pages, 4 figures, 6 table
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