354 research outputs found
Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
We show the David-Jerison construction of big pieces of Lipschitz graphs
inside a corkscrew domain does not require its surface measure be upper Ahlfors
regular. Thus we can study absolute continuity of harmonic measure and surface
measure on NTA domains of locally finite perimeter using Lipschitz
approximations. A partial analogue of the F. and M. Riesz Theorem for simply
connected planar domains is obtained for NTA domains in space. As a consequence
every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure
Probabilistic analysis of the upwind scheme for transport
We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon
Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I
Classical Schur analysis is intimately connected to the theory of orthogonal
polynomials on the circle [Simon, 2005]. We investigate here the connection
between multipoint Schur analysis and orthogonal rational functions.
Specifically, we study the convergence of the Wall rational functions via the
development of a rational analogue to the Szeg\H o theory, in the case where
the interpolation points may accumulate on the unit circle. This leads us to
generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields
asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction,
Section 5 (Szeg\H o type asymptotics) is extende
The MINERA Data Acquisition System and Infrastructure
MINERA (Main INjector ExpeRiment -A) is a new few-GeV neutrino
cross section experiment that began taking data in the FNAL NuMI (Fermi
National Accelerator Laboratory Neutrinos at the Main Injector) beam-line in
March of 2010. MINERA employs a fine-grained scintillator detector capable
of complete kinematic characterization of neutrino interactions. This paper
describes the MINERA data acquisition system (DAQ) including the read-out
electronics, software, and computing architecture.Comment: 34 pages, 16 figure
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on polarized 3He target
Inclusive 3He(e,e') and exclusive 3He(e,e'n) processes with polarized
electrons and 3He have been theoretically analyzed and values for the magnetic
and electric neutron form factors have been extracted. In both cases the form
factor values agree well with the ones extracted from processes on the
deuteron. Our results are based on Faddeev solutions, modern NN forces and
partially on the incorporation of mesonic exchange currents.Comment: 28 pages, 29 Postscript figure
Hardy's inequality for functions vanishing on a part of the boundary
We develop a geometric framework for Hardy's inequality on a bounded domain
when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8
allowing to relax the assumptions in the main results. Final version
published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-
Diabetes Care in Black and White Veterans in the Southeastern U.S.
Abstract available at publisher's web site
Micrometeoroid Events in LISA Pathfinder
The zodiacal dust complex, a population of dust and small particles that
pervades the Solar System, provides important insight into the formation and
dynamics of planets, comets, asteroids, and other bodies. Here we present a new
set of data obtained using a novel technique: direct measurements of momentum
transfer to a spacecraft from individual particle impacts. This technique is
made possible by the extreme precision of the instruments flown on the LISA
Pathfinder spacecraft, a technology demonstrator for a future space-based
gravitational wave observatory that operated near the first Sun-Earth Lagrange
point from early 2016 through Summer of 2017. Using a simple model of the
impacts and knowledge of the control system, we show that it is possible to
detect impacts and measure properties such as the transferred momentum (related
to the particle's mass and velocity), direction of travel, and location of
impact on the spacecraft. In this paper, we present the results of a systematic
search for impacts during 4348 hours of Pathfinder data. We report a total of
54 candidates with momenta ranging from 0.2 to
230. We furthermore make a comparison of these candidates
with models of micrometeoroid populations in the inner solar system including
those resulting from Jupiter-family comets, Oort-cloud comets, Hailey-type
comets, and Asteroids. We find that our measured population is consistent with
a population dominated by Jupiter-family comets with some evidence for a
smaller contribution from Hailey-type comets. This is in agreement with
consensus models of the zodiacal dust complex in the momentum range sampled by
LISA Pathfinder.Comment: 22 pages, 14 figures, accepted in Ap
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