New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.Comment: 29 pages; final version; to appear in Constructive Approximatio

Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft

More than 635 000 positional observations (mostly radiotechnical) of planets and spacecraft (1961-2010), have been used for estimating possible changes of the gravitation constant, the solar mass, and semi-major axes of planets, as well as the value of the astronomical unit, related to them. The analysis of the observations has been performed on the basis of the EPM2010 ephemerides of IAA RAS in post-newtonian approximation. The obtained results indicate on decrease in the heliocentric gravitation constant per year at the level $\dot {GM_{Sun}}/GM_{Sun} = (-5.0 \pm 4.1) 10^{-14} (3\sigma).$ The positive secular changes of semi-major axes $\dot a_i/a_i$ have been obtained simultaneously for the planets Mercury, Venus, Mars, Jupiter, Saturn, as expected if the geliocentric gravitation constant is decreasing in century wise. The change of the mass of the Sun $M_{Sun}$ due to the solar radiation and the solar wind and the matter dropping on the Sun (comets, meteors, asteroids and dust) was estimated. Taking into account the maximal limits of the possible $M_{Sun}$ change, the value $\dot G/G$ falls within the interval $-4.2\cdot10^{-14} < \dot G/G < +7.5\cdot10^{-14}$ in year with the 95% probability. The astronomical unit (au) is only connected with the geliocentric gravitation constant by its definition. In the future, the connection between $GM_{Sun}$ and au should be fixed at the certain time moment, as it is inconvenient highly to have the changing value of the astronomical unit.Comment: 20 pages, 4 tables, accepted for publication in Solar System Research, 2011 (Astronomicheskii vestnik

Sarcopenia in COPD: a systematic review and meta-analysis

COPD is associated with a progressive loss of muscle mass and function. However, there is an unmet need to define and standardise methods to estimate the prevalence of sarcopenia in COPD patients.We performed a systematic review and meta-analysis of the prevalence of this extrapulmonary manifestation in COPD patients. We searched Embase, Medline (Ovid), CINAHL (EBSCO), Web of Science, Scopus and Google Scholar for studies published up to January 17, 2019, assessing sarcopenia in COPD patients based on low muscle mass and decreased muscle function. Interventional studies, in vitro experiments, protocols or reviews and meta-analyses were excluded. We estimated heterogeneity (I2) and assessed significance (Q) using a Chi-squared test for estimates obtained from random-effects models.4465 articles were initially identified. After removing the duplicates and applying the selection criteria, we reviewed 62 full-text articles. Finally, 10 articles (n=2565 COPD patients) were included in this systematic review and meta-analyses. Overall, the prevalence of sarcopenia in patients with COPD was 21.6% (95% CI 14.6-30.9%, I2=94%), ranging from 8% in population-based to 21% in clinic-based studies, and 63% in COPD patients residing in nursing homes.Sarcopenia is frequently observed in COPD patients, with varying prevalence across population settings. Sarcopenia in COPD should be assessed using standardised tests and cut-off points from sarcopenia consensus criteria for clinical practice and international comparisons

PTF11iqb: cool supergiant mass-loss that bridges the gap between Type IIn and normal supernovae

The supernova (SN) PTF11iqb was initially classified as a Type IIn event caught very early after explosion. It showed narrow Wolf–Rayet (WR) spectral features on day 2 (as in SN 1998S and SN 2013cu), but the narrow emission weakened quickly and the spectrum morphed to resemble Types II-L and II-P. At late times, H? exhibited a complex, multipeaked profile reminiscent of SN 1998S. In terms of spectroscopic evolution, we find that PTF11iqb was a near twin of SN 1998S, although with somewhat weaker interaction with circumstellar material (CSM) at early times, and stronger interaction at late times. We interpret the spectral changes as caused by early interaction with asymmetric CSM that is quickly (by day 20) enveloped by the expanding SN ejecta photosphere, but then revealed again after the end of the plateau when the photosphere recedes. The light curve can be matched with a simple model for CSM interaction (with a mass-loss rate of roughly 10?4 M? yr?1) added to the light curve of a normal SN II-P. The underlying plateau requires a progenitor with an extended hydrogen envelope like a red supergiant at the moment of explosion, consistent with the slow wind speed (&lt;80?km?s?1) inferred from narrow H? emission. The cool supergiant progenitor is significant because PTF11iqb showed WR features in its early spectrum – meaning that the presence of such WR features does not necessarily indicate a WR-like progenitor. Overall, PTF11iqb bridges SNe IIn with weaker pre-SN mass-loss seen in SNe II-L and II-P, implying a continuum between these types

PTF11iqb: cool supergiant mass-loss that bridges the gap between Type IIn and normal supernovae

The supernova (SN) PTF11iqb was initially classified as a Type IIn event caught very early after explosion. It showed narrow Wolf–Rayet (WR) spectral features on day 2 (as in SN 1998S and SN 2013cu), but the narrow emission weakened quickly and the spectrum morphed to resemble Types II-L and II-P. At late times, H? exhibited a complex, multipeaked profile reminiscent of SN 1998S. In terms of spectroscopic evolution, we find that PTF11iqb was a near twin of SN 1998S, although with somewhat weaker interaction with circumstellar material (CSM) at early times, and stronger interaction at late times. We interpret the spectral changes as caused by early interaction with asymmetric CSM that is quickly (by day 20) enveloped by the expanding SN ejecta photosphere, but then revealed again after the end of the plateau when the photosphere recedes. The light curve can be matched with a simple model for CSM interaction (with a mass-loss rate of roughly 10?4 M? yr?1) added to the light curve of a normal SN II-P. The underlying plateau requires a progenitor with an extended hydrogen envelope like a red supergiant at the moment of explosion, consistent with the slow wind speed (&lt;80?km?s?1) inferred from narrow H? emission. The cool supergiant progenitor is significant because PTF11iqb showed WR features in its early spectrum – meaning that the presence of such WR features does not necessarily indicate a WR-like progenitor. Overall, PTF11iqb bridges SNe IIn with weaker pre-SN mass-loss seen in SNe II-L and II-P, implying a continuum between these types

Pulsar-wind nebulae and magnetar outflows: observations at radio, X-ray, and gamma-ray wavelengths

We review observations of several classes of neutron-star-powered outflows: pulsar-wind nebulae (PWNe) inside shell supernova remnants (SNRs), PWNe interacting directly with interstellar medium (ISM), and magnetar-powered outflows. We describe radio, X-ray, and gamma-ray observations of PWNe, focusing first on integrated spectral-energy distributions (SEDs) and global spectral properties. High-resolution X-ray imaging of PWNe shows a bewildering array of morphologies, with jets, trails, and other structures. Several of the 23 so far identified magnetars show evidence for continuous or sporadic emission of material, sometimes associated with giant flares, and a few possible "magnetar-wind nebulae" have been recently identified.Comment: 61 pages, 44 figures (reduced in quality for size reasons). Published in Space Science Reviews, "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release

Pion photoproduction on the nucleon in the quark model

We present a detailed quark-model study of pion photoproduction within the effective Lagrangian approach. Cross sections and single-polarization observables are investigated for the four charge channels, $\gamma p\to \pi^+ n$, $\gamma n\to \pi^- p$, $\gamma p\to \pi^0 p$, and $\gamma n\to \pi^0 n$. Leaving the $\pi N\Delta$ coupling strength to be a free parameter, we obtain a reasonably consistent description of these four channels from threshold to the first resonance region. Within this effective Lagrangian approach, strongly constrainted by the quark model, we consider the issue of double-counting which may occur if additional {\it t}-channel contributions are included.Comment: Revtex, 35 pages, 16 eps figures; version to appear on PR

Field Measurements of Terrestrial and Martian Dust Devils

Surface-based measurements of terrestrial and martian dust devils/convective vortices provided from mobile and stationary platforms are discussed. Imaging of terrestrial dust devils has quantified their rotational and vertical wind speeds, translation speeds, dimensions, dust load, and frequency of occurrence. Imaging of martian dust devils has provided translation speeds and constraints on dimensions, but only limited constraints on vertical motion within a vortex. The longer mission durations on Mars afforded by long operating robotic landers and rovers have provided statistical quantification of vortex occurrence (time-of-sol, and recently seasonal) that has until recently not been a primary outcome of more temporally limited terrestrial dust devil measurement campaigns. Terrestrial measurement campaigns have included a more extensive range of measured vortex parameters (pressure, wind, morphology, etc.) than have martian opportunities, with electric field and direct measure of dust abundance not yet obtained on Mars. No martian robotic mission has yet provided contemporaneous high frequency wind and pressure measurements. Comparison of measured terrestrial and martian dust devil characteristics suggests that martian dust devils are larger and possess faster maximum rotational wind speeds, that the absolute magnitude of the pressure deficit within a terrestrial dust devil is an order of magnitude greater than a martian dust devil, and that the time-of-day variation in vortex frequency is similar. Recent terrestrial investigations have demonstrated the presence of diagnostic dust devil signals within seismic and infrasound measurements; an upcoming Mars robotic mission will obtain similar measurement types

Anomalous accelerations in spacecraft flybys of the Earth

[EN] The flyby anomaly is a persistent riddle in astrodynamics. Orbital analysis in several flybys of the Earth since the Galileo spacecraft flyby of the Earth in 1990 have shown that the asymptotic post-encounter velocity exhibits a difference with the initial velocity that cannot be attributed to conventional effects. To elucidate its origin, we have developed an orbital program for analyzing the trajectory of the spacecraft in the vicinity of the perigee, including both the Sun and the Moon¿s tidal perturbations and the geopotential zonal, tesseral and sectorial harmonics provided by the EGM96 model. The magnitude and direction of the anomalous acceleration acting upon the spacecraft can be estimated from the orbital determination program by comparing with the trajectories fitted to telemetry data as provided by the mission teams. This acceleration amounts to a fraction of a mm/s2 and decays very fast with altitude. 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