Direct measurement of the size of 2003 UB313 from the Hubble Space Telescope

We have used the Hubble Space Telescope to directly measure the angular size of the large Kuiper belt object 2003 UB313. By carefully calibrating the point spread function of a nearby field star, we measure the size of 2003 UB313 to be 34.3$\pm$1.4 milliarcseconds, corresponding to a diameter of 2400$\pm$100 km or a size $\sim5$% larger than Pluto. The V band geometric albedo of 2003 UB313 is $86\pm7$%. The extremely high albedo is consistent with the frosty methane spectrum, the lack of red coloring, and the lack of observed photometric variation on the surface of 2003 UB313. Methane photolysis should quickly darken the surface of 2003 UB313, but continuous evaporation and redeposition of surface ices appears capable of maintaining the extreme alebdo of this body

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem

A wide variety of articles, starting with the famous paper (Gidas, Ni and Nirenberg in Commun. Math. Phys. 68, 209-243 (1979)) is devoted to the uniqueness question for the semilinear elliptic boundary value problem -{\Delta}u={\lambda}u+u^p in {\Omega}, u>0 in {\Omega}, u=0 on the boundary of {\Omega}, where {\lambda} ranges between 0 and the first Dirichlet Laplacian eigenvalue. So far, this question was settled in the case of {\Omega} being a ball and, for more general domains, in the case {\lambda}=0. In (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)), we proposed a computer-assisted approach to this uniqueness question, which indeed provided a proof in the case {\Omega}=(0,1)x(0,1), and p=2. Due to the high numerical complexity, we were not able in (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)) to treat higher values of p. Here, by a significant reduction of the complexity, we will prove uniqueness for the case p=3

A Precise Measurement of the Weak Mixing Angle in Neutrino-Nucleon Scattering

We report a precise measurement of the weak mixing angle from the ratio of neutral current to charged current inclusive cross-sections in deep-inelastic neutrino-nucleon scattering. The data were gathered at the CCFR neutrino detector in the Fermilab quadrupole-triplet neutrino beam, with neutrino energies up to 600 GeV. Using the on-shell definition, ${\rm sin ^2\theta_W} \equiv 1 - \frac{{\rm M_W} ^2}{{\rm M_Z} ^2}$, we obtain ${\rm sin ^2\theta_W} = 0.2218 \pm 0.0025 ({\rm stat.}) \pm 0.0036 ({\rm exp.\: syst.}) \pm 0.0040 ({\rm model})$.Comment: 10 pages, Nevis Preprint #1498 (Submitted to Phys. Rev. Lett.

Specific Control of Pseudomonas aeruginosa Surface-Associated Behaviors by Two c-di-GMP Diguanylate Cyclases

The signaling nucleotide cyclic diguanylate (c-di-GMP) regulates the transition between motile and sessile growth in a wide range of bacteria. Understanding how microbes control c-di-GMP metabolism to activate specific pathways is complicated by the apparent multifold redundancy of enzymes that synthesize and degrade this dinucleotide, and several models have been proposed to explain how bacteria coordinate the actions of these many enzymes. Here we report the identification of a diguanylate cyclase (DGC), RoeA, of Pseudomonas aeruginosa that promotes the production of extracellular polysaccharide (EPS) and contributes to biofilm formation, that is, the transition from planktonic to surface-dwelling cells. Our studies reveal that RoeA and the previously described DGC SadC make distinct contributions to biofilm formation, controlling polysaccharide production and flagellar motility, respectively. Measurement of total cellular levels of c-di-GMP in ∆roeA and ∆sadC mutants in two different genetic backgrounds revealed no correlation between levels of c-di-GMP and the observed phenotypic output with regard to swarming motility and EPS production. Our data strongly argue against a model wherein changes in total levels of c-di-GMP can account for the specific surface-related phenotypes of P. aeruginosa

Protocol for an observational study on the effects of adolescent sports participation on health in early adulthood

We will study the impact of adolescent sports participation on early-adulthood health using longitudinal data from the National Survey of Youth and Religion. We focus on two primary outcomes measured at ages 23--28 -- self-rated health and total score on the PHQ9 Patient Depression Questionnaire -- and control for several potential confounders related to demographics and family socioeconomic status. Comparing outcomes between sports participants and matched non-sports participants with similar confounders is straightforward. Unfortunately, an analysis based on such a broad exposure cannot probe the possibility that participation in certain types of sports (e.g. collision sports like football or soccer) may have larger effects on health than others. In this study, we introduce a hierarchy of exposure definitions, ranging from broad (participation in any after-school organized activity) to narrow (e.g. participation in limited-contact sports). We will perform separate matched observational studies, one for each definition, to estimate the health effects of several levels of sports participation. In order to conduct these studies while maintaining a fixed family-wise error rate, we developed an ordered testing approach that exploits the logical relationships between exposure definitions. Our study will also consider several secondary outcomes including body mass index, life satisfaction, and problematic drinking behavior

Satellites of the largest Kuiper Belt objects

We have searched the four brightest objects in the Kuiper Belt for the presence of satellites using the newly commissioned Keck Observatory Laser Guide Star Adaptive Optics system. Satellites are seen around three of the four objects: Pluto (whose satellite Charon is well-known and whose recently discovered smaller satellites are too faint to be detected), 2003 EL61 (where a second satellite is seen in addition to the previously known satellite), and 2003 UB313 (where a satellite is seen for the first time). The object 2005 FY9, the brightest Kuiper Belt object (KBO) after Pluto, does not have a satellite detectable within 0".4 with a brightness of more than 1% of the primary. The presence of satellites around three of the four brightest KBOs is inconsistent with the fraction of satellites in the Kuiper Belt at large at the 99.2% confidence level, suggesting a different formation mechanism for these largest KBO satellites. The two satellites of 2003 EL61, and the one satellite of 2003 UB313, with fractional brightnesses of 5% and 1.5%, and 2%, of their primaries, respectively, are significantly fainter relative to their primaries than other known KBO satellites, again pointing to possible differences in their origin

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure