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An integral equation method for a boundary value problem arising in unsteady water wave problems
In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result
is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem.
Keywords. Boundary integral equation method, Water waves, Laplace’
Study of contamination of liquid oxygen by gaseous nitrogen First quarterly report, 1 Jul. - 30 Sep. 1964
Analytical model development for contamination study of liquid oxygen by gaseous nitroge
Virtual Data in CMS Analysis
The use of virtual data for enhancing the collaboration between large groups
of scientists is explored in several ways:
- by defining ``virtual'' parameter spaces which can be searched and shared
in an organized way by a collaboration of scientists in the course of their
analysis;
- by providing a mechanism to log the provenance of results and the ability
to trace them back to the various stages in the analysis of real or simulated
data;
- by creating ``check points'' in the course of an analysis to permit
collaborators to explore their own analysis branches by refining selections,
improving the signal to background ratio, varying the estimation of parameters,
etc.;
- by facilitating the audit of an analysis and the reproduction of its
results by a different group, or in a peer review context.
We describe a prototype for the analysis of data from the CMS experiment
based on the virtual data system Chimera and the object-oriented data analysis
framework ROOT. The Chimera system is used to chain together several steps in
the analysis process including the Monte Carlo generation of data, the
simulation of detector response, the reconstruction of physics objects and
their subsequent analysis, histogramming and visualization using the ROOT
framework.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics
(CHEP03), La Jolla, Ca, USA, March 2003, 9 pages, LaTeX, 7 eps figures. PSN
TUAT010. V2 - references adde
Protecting Quantum Information with Entanglement and Noisy Optical Modes
We incorporate active and passive quantum error-correcting techniques to
protect a set of optical information modes of a continuous-variable quantum
information system. Our method uses ancilla modes, entangled modes, and gauge
modes (modes in a mixed state) to help correct errors on a set of information
modes. A linear-optical encoding circuit consisting of offline squeezers,
passive optical devices, feedforward control, conditional modulation, and
homodyne measurements performs the encoding. The result is that we extend the
entanglement-assisted operator stabilizer formalism for discrete variables to
continuous-variable quantum information processing.Comment: 7 pages, 1 figur
Interpolation of Hilbert and Sobolev Spaces:\ud Quantitative Estimates and Counterexamples
This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces and , for and an open . We exhibit examples in one and two dimensions of sets for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large
Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples
This paper provides an overview of interpolation of Banach and Hilbert
spaces, with a focus on establishing when equivalence of norms is in fact
equality of norms in the key results of the theory. (In brief, our conclusion
for the Hilbert space case is that, with the right normalisations, all the key
results hold with equality of norms.) In the final section we apply the Hilbert
space results to the Sobolev spaces and
, for and an open . We exhibit examples in one and two dimensions of sets
for which these scales of Sobolev spaces are not interpolation scales. In the
cases when they are interpolation scales (in particular, if is
Lipschitz) we exhibit examples that show that, in general, the interpolation
norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio
of these two norms can be arbitrarily large
Quantum correlations in the temporal CHSH scenario
We consider a temporal version of the CHSH scenario using projective
measurements on a single quantum system. It is known that quantum correlations
in this scenario are fundamentally more general than correlations obtainable
with the assumptions of macroscopic realism and non-invasive measurements. In
this work, we also educe some fundamental limitations of these quantum
correlations. One result is that a set of correlators can appear in the
temporal CHSH scenario if and only if it can appear in the usual spatial CHSH
scenario. In particular, we derive the validity of the Tsirelson bound and the
impossibility of PR-box behavior. The strength of possible signaling also turns
out to be surprisingly limited, giving a maximal communication capacity of
approximately 0.32 bits. We also find a temporal version of Hardy's nonlocality
paradox with a maximal quantum value of 1/4.Comment: corrected versio
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