Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Eine Fehlerquelle bei der Bestimmung des Acetons nach der Jodoformmethode

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Stellar Crowding and the Science Case for Extremely Large Telescopes

We present a study of the effect of crowding on stellar photometry. We develop an analytical model through which we are able to predict the error in magnitude and color for a given star for any combination of telescope resolution, stellar luminosity function, background surface brightness, and distance. We test our predictions with Monte Carlo simulations of the LMC globular cluster NGC 1835, for resolutions corresponding to a seeing-limited telescope, the $HST$, and an AO-corrected 30-m (near diffraction limited) telescope. Our analytically predicted magnitude errors agree with the simulation results to within $\sim$20%. The analytical model also predicts that errors in color are strongly affected by the correlation of crowding--induced photometric errors between bands as is seen in the simulations. Using additional Monte Carlo simulations and our analytical crowding model, we investigate the photometric accuracy which 30-m and 100-m Extremely Large Telescopes (ELTs) will be able to achieve at distances extending to the Virgo cluster. We argue that for stellar populations work, ELTs quickly become crowding-limited, suggesting that low--Strehl AO systems may be sufficient for this type of science.Comment: 25 pages, 19 figures in 35 separate files, Astronomical Journal, accepte

Evaluation of whole-wheat flour blends with fat replacer.

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Alignment Timescale of the Microquasar GRO J1655-40

The microquasar GRO J1655-40 has a black hole with spin angular momentum apparently misaligned to the orbital plane of its companion star. We analytically model the system with a steady state disc warped by Lense-Thirring precession and find the timescale for the alignment of the black hole with the binary orbit. We make detailed stellar evolution models so as to estimate the accretion rate and the lifetime of the system in this state. The secondary can be evolving at the end of the main sequence or across the Hertzsprung gap. The mass-transfer rate is typically fifty times higher in the latter case but we find that, in both cases, the lifetime of the mass transfer state is at most a few times the alignment timescale. The fact that the black hole has not yet aligned with the orbital plane is therefore consistent with either model. We conclude that the system may or may not have been counter-aligned after its supernova kick but that it is most likely to be close to alignment rather than counteralignment now.Comment: Accepted for publication in MNRA

Reactive nitrogen budget during the NASA SONEX Mission

The SASS Ozone and Nitrogen Oxides Experiment (SONEX) over the North Atlantic during October/November 1997 offered an excellent opportunity to examine the budget of reactive nitrogen in the upper troposphere (8–12 km altitude). The median measured total reactive nitrogen (NOy) mixing ratio was 425 parts per trillion by volume (pptv). A data set merged to the HNO3 measurement time resolution was used to calculate NOy (NOy sum) by summing the reactive nitrogen species (a combination of measured plus modeled results) and comparing it to measured NOy (NOy meas.). Comparisons were done for tropospheric air (O3 \u3c100 parts per billion by volume (ppbv)) and stratospherically influenced air (O3 \u3e 100 ppbv) with both showing good agreement between NOy sum and NOy meas. (slope \u3e0.9 and r² ≈ 0.9). The total reactive nitrogen budget in the upper troposphere over the North Atlantic appears to be dominated by a mixture of NOx (NO + NO2), HNO3, and PAN. In tropospheric air median values of NOx/NOywere ≈ 0.25, HNO3/NOy ≈ 0.35 and PAN/NOy ≈ 0.17. Particulate NO3− and alkyl nitrates together composed \u3c10% of NOy, while model estimated HNO4 averaged 12%. For the air parcels sampled during SONEX, there does not appear to be a large reservoir of unidentified NOy compounds

Observations of heterogeneous reactions between Asian pollution and mineral dust over the Eastern North Pacific during INTEX-B

In-situ airborne measurements of trace gases, aerosol size distributions, chemistry and optical properties were conducted over Mexico and the Eastern North Pacific during MILAGRO and INTEX-B. Heterogeneous reactions between secondary aerosol precursor gases and mineral dust lead to sequestration of sulfur, nitrogen and chlorine in the supermicrometer particulate size range. Simultaneous measurements of aerosol size distributions and weak-acid soluble calcium result in an estimate of 11 wt% of CaCO_3 for Asian dust. During transport across the North Pacific, ~5–30% of the CaCO_3 is converted to CaSO_4 or Ca(NO_3)_2 with an additional ~4% consumed through reactions with HCl. The 1996 to 2008 record from the Mauna Loa Observatory confirm these findings, indicating that, on average, 19% of the CaCO_3 has reacted to form CaSO_4 and 7% has reacted to form Ca(NO_3)_2 and ~2% has reacted with HCl. In the nitrogen-oxide rich boundary layer near Mexico City up to 30% of the CaCO_3 has reacted to form Ca(NO_3)_2 while an additional 8% has reacted with HCl. These heterogeneous reactions can result in a ~3% increase in dust solubility which has an insignificant effect on their optical properties compared to their variability in-situ. However, competition between supermicrometer dust and submicrometer primary aerosol for condensing secondary aerosol species led to a 25% smaller number median diameter for the accumulation mode aerosol. A 10–25% reduction of accumulation mode number median diameter results in a 30–70% reduction in submicrometer light scattering at relative humidities in the 80–95% range. At 80% RH submicrometer light scattering is only reduced ~3% due to a higher mass fraction of hydrophobic refractory components in the dust-affected accumulation mode aerosol. Thus reducing the geometric mean diameter of the submicrometer aerosol has a much larger effect on aerosol optical properties than changes to the hygroscopic:hydrophobic mass fractions of the accumulation mode aerosol. In the presence of dust, nitric acid concentrations are reduced to 85% to 60–80% in the presence of dust. These observations support previous model studies which predict irreversible sequestration of reactive nitrogen species through heterogeneous reactions with mineral dust during long-range transport