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 MINERν\nuA Data Acquisition System and Infrastructure

MINER$\nu$A (Main INjector ExpeRiment $\nu$-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. MINER$\nu$A employs a fine-grained scintillator detector capable of complete kinematic characterization of neutrino interactions. This paper describes the MINER$\nu$A 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$\,\mu\textrm{Ns}$ to 230$\,\mu\textrm{Ns}$. 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