Surgery groups of the fundamental groups of hyperplane arrangement complements

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin full braid groups. As a consequence we explicitly compute the surgery groups of the Artin pure braid groups. This is obtained as a corollary to a computation of the surgery groups of a more general class of groups, namely for the fundamental group of the complement of any fiber-type hyperplane arrangement in the complex n-space.Comment: 11 pages, AMSLATEX file, revised following referee's comments and suggestions, to appear in Archiv der Mathemati

Expected Supremum of a Random Linear Combination of Shifted Kernels

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order \log\log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order \sqrt{n\log n} for all reasonable coefficient statistics.Comment: To appear in the Journal of Fourier Analysis and Application

Deflation techniques for finding distinct solutions of nonlinear partial differential equations

Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find starting points that lie in different basins of attraction. In this paper, we present an infinite-dimensional deflation algorithm for systematically modifying the residual of a nonlinear PDE problem to eliminate known solutions from consideration. This enables the Newton-Kantorovitch iteration to converge to several different solutions, even starting from the same initial guess. The deflated Jacobian is dense, but an efficient preconditioning strategy is devised, and the number of Krylov iterations are observed not to grow as solutions are deflated. The power of the approach is demonstrated on several problems from special functions, phase separation, differential geometry and \ud fluid mechanics that permit distinct solutions

Conditions for one-dimensional supersonic flow of quantum gases

One can use transsonic Bose-Einstein condensates of alkali atoms to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determine the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. The transition to supersonic speed occurs at the potential maximum and the Hawking temperature is entirely determined by the curvature of the potential

A Model for Effective Professional Development of Formal Science Educators

The Lunar Workshops for Educators (LWE) series was developed by the Lunar Reconnaissance Orbiter (LRO) education team in 2010 to provide professional development on lunar science and exploration concepts for grades 6-9 science teachers. Over 300 educators have been trained to date. The LWE model incorporates best practices from pedagogical research of science education, thoughtful integration of scientists and engineer subject matter experts for both content presentations and informal networking with educators, access to NASA-unique facilities, hands-on and data-rich activities aligned with education standards, exposure to the practice of science, tools for addressing common misconceptions, follow-up with participants, and extensive evaluation. Evaluation of the LWE model via pre- and post-assessments, daily workshop surveys, and follow-up surveys at 6-month and 1-year intervals indicate that the LWE are extremely effective in increasing educators' content knowledge, confidence in incorporating content into the classroom, understanding of the practice of science, and ability to address common student misconceptions. In order to address the efficacy of the LWE model for other science content areas, the Dynamic Response of Environments at Asteroids, the Moon, and moons of Mars (DREAM2) education team, funded by NASA's Solar System Exploration Research Virtual Institute, developed and ran a pilot workshop called Dream2Explore at NASA's Goddard Space Flight Center in June, 2015. Dream2Explore utilized the LWE model, but incorporated content related to the science and exploration of asteroids and the moons of Mars. Evaluation results indicate that the LWE model was effectively used for educator professional development on non-lunar content. We will present more detail on the LWE model, evaluation results from the Dream2Explore pilot workshop, and suggestions for the application of the model with other science content for robust educator professional development

Ion Trap Mass Spectrometers for Identity, Abundance and Behavior of Volatiles on the Moon

NASA GSFC and The Open University (UK) are collaborating to deploy an Ion Trap Mass Spectrometer on the Moon to investigate the lunar water cycle. The ITMS is flight-proven throughthe Rosetta Philae comet lander mission. It is also being developed under ESA funding to analyse samples drilled from beneath the lunar surface on the Roscosmos Luna-27 lander (2025).Now, GSFC and OU will now develop a compact ITMS instrument to study the near-surface lunar exosphere on board a CLPS Astrobotic lander at Lacus Mortis in 2021

Radio Observations of HD 80606 Near Planetary Periastron

This paper reports Very Large Array observations at 325 and 1425 MHz (90cm and 20cm) during and near the periastron passage of HD 80606b on 2007 November 20. We obtain flux density limits (3-sigma) of 1.7 mJy and 48 microJy at 325 and 1425 MHz, respectively, equivalent to planetary luminosity limits of 2.3 x 10^{24} erg/s and 2.7 x 10^{23} erg/s. These are well above the Jovian value (at 40 MHz) of 2 x 10^{18} erg/s. The motivation for these observations was that the planetary magnetospheric emission is driven by a stellar wind-planetary magnetosphere interaction so that the planetary luminosity would be elevated. Near periastron, HD 80606b might be as much as 3000 times more luminous than Jupiter. Recent transit observations of HD 80606b provide stringent constraints on the planetary mass and radius, and, because of the planet's highly eccentric orbit, its rotation period is likely to be "pseudo-synchronized" to its orbital period, allowing a robust estimate of the former. We are able to make robust estimates of the emission frequency of the planetary magnetospheric emission and find it to be around 60--90 MHz. We compare HD 80606b to other high-eccentricity systems and assess the detection possibilities for both near-term and more distant future systems. Of the known high eccentricity planets, only HD 80606b is likely to be detectable, as HD 20782B b and HD 4113b are both likely to have weaker magnetic field strengths. Both the forthcoming "EVLA low band" system and the Low Frequency Array may be able to improve upon our limits for HD 80606b, and do so at a more optimum frequency. If the low-frequency component of the Square Kilometre Array (SKA-lo) and a future lunar radio array are able to approach their thermal noise limits, they should be able to detect an HD 80606b-like planet, unless the planet's luminosity increases by substantially less than a factor of 3000.Comment: 9 pages; accepted for publication in A