text:
\section{Introduction}
\label{sec:intro}

Asteroid physical properties provide important constraints on the
formation and evolution of our Solar System, including clues to the
different phases of orbital instability and migration of the giant
planets \citep[see, e.g.,][]{Morbidelli2015}.  Collisions within the
asteroid belt can play a major role altering the asteroid population.
These clues are recorded in the shapes of individual asteroids, so
that a global understanding of the shape distribution --- as informed
by a large catalog --- provides insight into our Solar System's
evolution.

Shape information can be determined for individual asteroids from
photometric data over a long period of time, with Doppler-delay radar
imaging, with ground-based adaptive optics techniques, or {\it in
  situ} via spacecraft data. These last three techniques are limited
in the number of targets that can be reasonably observed. As a result,
only a small percentage of km-scale main belt asteroids have known
shapes and spin-pole orientations. For instance, the DAMIT
database\footnote{Database of Asteroid Models from Inversion
  Techniques:
  \url{http://astro.troja.mff.cuni.cz/projects/asteroids3D/web.php}}
\citep{Durech2010} holds information for less than 1,000 asteroids as
of writing this. Currently, the predominant method for determination
of asteroid shape and spin properties is the inversion of dense
photometric lightcurves, as initially developed by
\citet{Kaasalainen2001a} and \citet{Kaasalainen2001b}. Without dense
photometric data it is difficult to derive detailed shape and spin
pole orientations for individual asteroids. With a sufficiently large
dataset, however, it is possible to determine a statistical shape
distribution, even if only a small number of data points are present
for each individual asteroid. The advantage of a large untargeted
dataset is that it provides an estimate for a population's shape
distribution without being subject to observational biases in favor of
elongated objects (i.e.,~higher lightcurve amplitudes) that are
commonly present in targeted observations. Previous work on the shape
distribution for main belt asteroids (MBAs) has been carried out by
\citet{McNeill2016}, \citet{Cibulkova2016}, \citet{Nortunen2017}, and
\citet{Cibulkova2018}.

European Space Agency's Gaia astrometric space observatory
\citep{Gaia2016} measures the positions, distances, proper motions,
and other physical properties of more than one billion stars in our
galaxy with unprecedented accuracy. In addition to its main mission,
Gaia will also observe a significant fraction of the currently known
asteroid population (${\sim}$350,000 Solar System small bodies) and
discover previously unknown asteroids \citep{Spoto2018}.  The sample
of Gaia-observed asteroids provides a large uniform and
magnitude-limited set of observations perfectly suited to
independently investigate the distribution of asteroid shapes.

\section{Gaia Data Release 2}
\label{sec:gaia}

Gaia Data Release~2 \citep[DR2,][]{Spoto2018} includes 1,977,702
astrometric observations
of 14,099 pre-selected asteroids, observed between 5 August 2014 and
23 May 2016.  Solar System moving objects are identified through
association with known asteroids with well-defined orbits.
The majority of DR2 asteroids are main belt asteroids, but the sample
also includes a small number of Near-Earth Asteroids, Jupiter
Trojans, and trans-Neptunian objects. Each ``transit'' of a target
across the detector array leads to 9 individual detections across a
typical time span on the order of 40~s. Target positions and epochs
are provided for individual detections, whereas
photometric information is averaged per transit.
Photometric information on asteroids in DR2 is limited to Gaia $G$ band (0.33--1.0~$\mu$m)
magnitudes, fluxes, and flux uncertainties.

\section{Data Analysis}
\label{sec:analysis}

\subsection{Data Preparation}
\label{sec:preparation}

All DR2 asteroid observations were downloaded from CDS Vizier\footnote{\url{http://vizier.u-strasbg.fr/viz-bin/VizieR}}. Since the photometry
per object is the average of all individual observations within a
single transit, we extract only the midtime epoch from each transit.
The maximum number of transits for any individual object is 53 and the
median number of transits per target is 9. We require a minimum of 5
transits per object to be considered in this analysis. While this
  criterion is somewhat arbitrary, it allows for a meaningful
  statistical analysis of the data set, which is not guaranteed
  for a smaller number of observations. For each transit, we derive
approximate $G$ band magnitude uncertainties from the provided fluxes
and flux uncertainties.
We obtain ephemerides for the respective epochs and relative to Gaia
using the {\tt astroquery.jplhorizons}
module,
which queries ephemerides from the JPL Horizons system
\citep{Giorgini1996}. For each $G$ band observation, we derive the
reduced $G$ band magnitude, $G_{11}(\alpha)$, which corrects for
geometric effects as a result of the heliocentric distance of the
target, $r$, and the distance from the observer, $\Delta$, but
preserves the solar phase angle ($\alpha$) dependence of the
brightness: $G_{11}(\alpha) = G - 5 \log_{10} r \Delta$. We remove all
objects that are not considered main belt asteroids from our sample
since the population sizes of near-Earth asteroids, Jupiter Trojans,
and trans-Neptunian objects in DR2 are insufficient for this
analysis. Our final sample consists of 121,819 $G$ band photometric
observations of 12,059 different main belt asteroids.

\subsection{Phase Correction and Amplitude Measurement}
\label{sec:phasecurve}

Variations in the $G_{11}(\alpha)$ magnitudes are the result of
lightcurve variations due to the irregular shapes of asteroids and
their rotation, as well as solar phase angle effects \cite[see,
e.g.,][]{Bowell1989}. In order to extract shape information from the
data, the phase angle effect has to be corrected for. On average, DR2
observations span a phase angle range of 6\degr\ around an average
phase angle of 19\degr, which is insufficient to perform a reliable
phase curve fit. In order to correct for solar phase angle effects on
the Gaia photometry, we instead use existing phase curve information
on our targets from
\citet{Veres2015} and \citet{Oszkiewicz2011}. While \citet{Veres2015}
only used photometric observations obtained by Pan-STARRS1
\citep{Kaiser2010}, \citet{Oszkiewicz2011} compiled low-precision
photometric data from the Minor Planet
Center\footnote{\url{https://minorplanetcenter.net/}} (MPC). Both
sources make use of the $H$-$G_{12}$ two-parameter phase function
\citep{Muinonen2010} and provide measured absolute magnitudes ($H$)
and slope parameters ($G_{12}$) with corresponding
uncertainties. Preference is given to slope parameters reported by
\citet{Veres2015} if their measurement is based on at least 5
observations; this selection is based on the improved reliability
  and existence of photometric uncertainties in the Pan-STARRS1 data
  in contrast to the MPC data. If no measurement from
\citet{Veres2015} is available, we adopt the slope parameter reported
by \citet{Oszkiewicz2011}.
In our final sample, 56\% of the $G_{12}$ slope parameters were taken
from \citet{Veres2015} and 44\% were taken from
\citet{Oszkiewicz2011}. Only 24 targets in our sample had no
measurement of the slope parameter $G_{12}$ from neither
\citet{Veres2015} nor \citet{Oszkiewicz2011}; these targets were
rejected from our further analysis.

Based on the solar phase angles during the Gaia observations
and the slope parameter $G_{12}$ from the literature, we correct the
$G_{11}(\alpha)$ magnitudes for phase angle effects, resulting in
normalized $H_G$ absolute magnitudes that reveal the targets'
lightcurve variations. In order to account for uncertainties in the
derivation of the slope parameter $G_{12}$, we adopt a Monte Carlo
approach in which we vary $G_{12}$ using a Gaussian model based on the
$G_{12}$ uncertainties reported by  \citet{Veres2015} or
  \citet{Oszkiewicz2011}; the latter source utilizes asymmetric
uncertainties, which we adopt throughout this work.
We
vary $G_{12}$ using two different Gaussian distributions corresponding to the upper and lower 1$\sigma$ uncertainties, re-derive the magnitude offsets and $H_G$
values, and calculate the weighted standard deviation (we use the
inverse square uncertainties of the Gaia photometry as weights) of the
resulting $H_G$ magnitudes. We adopt the average of the weighted $H_G$
standard deviations from 1,000 Monte Carlo runs as the target's
lightcurve amplitude. This method tends to underestimate large lightcurve
amplitude, especially in the case of sparse data; our derived
amplitudes $A$ hence represent lower limits of the real lightcurve
amplitudes (see Section \ref{sec:validation} for a discussion). Figure
\ref{fig:analysis_example} shows an example of the method that we use
to derive lightcurve amplitudes. Finally,
we use a linear regression model ({\tt scipy.stats.linregress})
  to identify objects with strong linear slopes in their $H_G$
  magnitudes as a function of solar phase angle, which are most likely
  caused by incorrect phase slope parameters $G_{12}$. Objects with
  coefficient of determination parameters $r^2 > 0.5$ or $p$-values
  less than 0.05 are rejected as they unanomously point to severe
  sloping. These criteria are somewhat arbitrary and result from the
  visual inspection of a few hundred objects. However, they provide a
  conservative rejection scheme.

\begin{figure}
\epsscale{0.8}
\plotone{fig1.pdf}
\caption{Example lightcurve amplitude derivation for asteroid (79)
  Eurynome. The diagram shows differential absolute magnitudes in $G$
  band ($H_G$) derived using the method defined in Section
  \ref{sec:phasecurve} and plotted against solar phase angle. These
  differential magnitudes are obtained by subtracting the weighted
  average $H_G$ from the individual measurements to better visualize
  the scatter around the target's normalized average absolute
  magnitude (red line). We drive the lower limit lightcurve amplitude
  (peak-to-peak) as two times the standard deviation (dashed lines) of
  this scatter. In the case of Eurynome, we derive a lower limit
  amplitude of 0.10~mag from 36 DR2 observations. The Asteroid
  Lightcurve Database \citep{Warner2009} lists a maximum lightcurve
  amplitude of 0.25~mag, which is consistent with our lower limit. The
  sloping of the $H_G$ magnitudes as a function of solar phase angles
  suggests that the adopted $G_{12}$ photometric slope parameter does
  not describe the target's phase curve well in this particular
  case. The linear regression analysis for this data set yields a
    coefficient of determination parameter $r^2 = 0.003$ and a
    $p$-value of 0.75, which does not lead to a rejection of this object
    from our sample (see Section
  \ref{sec:phasecurve}).  \label{fig:analysis_example}}
\end{figure}

\section{Results}
\label{sec:results}

For each DR2 target, we derive the lower limit lightcurve amplitude
using the method introduced in Section \ref{sec:analysis}. The results
for all 11,665 main belt asteroids for which this method
succeeded (84.3\% of the complete DR2 sample; 98.6\% of the main
  belt asteroids in the sample with sufficient data as defined in
  Section \ref{sec:preparation}) are listed in
Table~\ref{tab:results}.

\begin{deluxetable*}{lcccccccccccc}
\tablecaption{DR2 Main Belt Asteroid Lightcurve Amplitudes and Auxiliary Data \label{tab:results}}
\tablecolumns{9}
\tablewidth{0pt}
\tablehead{
\colhead{MPC} &
\colhead{Amp.\tablenotemark{a}} &
\colhead{$N_{\mathrm{obs}}$\tablenotemark{b}} &
\multicolumn2c{Phase Angle\tablenotemark{c}} &
\multicolumn4c{Slope Parameter\tablenotemark{d}} &
\colhead{SDSS Color\tablenotemark{e}} &
\colhead{$a$\tablenotemark{f}} &
\colhead{Diameter\tablenotemark{g}} &
\colhead{Albedo\tablenotemark{h}}\\[-5pt]
\colhead{Number} &
\colhead{(mag)} &
\colhead{} &
\colhead{Min (\degr)} &
\colhead{Max (\degr)} &
\colhead{$G_{12}$} &
\colhead{$\sigma_+$} &
\colhead{$\sigma_-$} &
\colhead{Source} &
\colhead{$a^{\text{*}}$} &
\colhead{(au)} &
\colhead{(km)} &
\colhead{$p_V$}
}
\startdata
8 & 0.15 & 8 & 17.2 & 28.2 & 0.33 & 0.08 & -0.08 & o & ... & 2.201 & 158.4 & 0.21 \\
33 & 0.11 & 26 & 12.5 & 26.3 & 0.15 & 0.53 & -0.53 & v & ... & 2.876 & 50.9 & 0.24 \\
280 & 0.11 & 27 & 14.3 & 22.3 & 0.38 & 0.31 & -0.31  & v & -0.04 & 2.942 & 55.8 & 0.03 \\
460 & 0.10 &  8 & 17.2 & 20.7 & 0.32 & 0.11 & -0.11 & o & 0.09 & 2.717 & 19.7 & 0.26 \\
11644 & 0.13 &  7 & 12.2 & 17.4 & -0.41 & 0.31 & -0.31  & v  & 0.01 & 3.118 & 13.4 & 0.09 \\
... & ... & ... & ... & ... & ... & ... & ...& ... & ... & ...\\
\enddata
\tablenotetext{a}{Lightcurve amplitude lower limit as derived with the method defined in Section \ref{sec:analysis}. We provide the nominal peak-to-peak value.}

\tablenotetext{b}{Number of observations in DR2 with photometric measurements used in this analysis; all objects with $N_{\mathrm{obs}} < 5$ have been removed from this sample.}

\tablenotetext{c}{Solar phase angle range over which this object has been observed in degrees. We provide the minimum ({\em Min}) and maximum ({\em Max}) solar phase angle as provided in DR2.}

\tablenotetext{d}{Adopted photometric slope parameter $G_{12}$ as defined by \citep{Muinonen2010}. We provide the adopted value ($G_{12}$) with corresponding upper ($\sigma_+$) and lower ($\sigma_-$) $1\sigma$ uncertainties, and the source of these values ({\em Source}): ``{\em o}'' refers to \citet{Oszkiewicz2011} and ``{\em v}'' refers to \citet{Veres2015}.}

\tablenotetext{e}{Color parameter $a^{\text{*}}$ as defined by \citet{Ivezic2001} and obtained from the Sloan Digitized Sky Survey Moving Object Catalog \citep{Ivezic2005}.}

\tablenotemark{f}{Semi-major axis of the target as obtained from the Minor Planet Center database in astronomical units.}

\tablenotemark{g}{Asteroid diameter as derived by \citet{Mainzer2016} in kilometers.}

\tablenotemark{h}{Asteroid geometric albedo ($V$ band) as derived by \citet{Mainzer2016}.}

\tablecomments{This table is only a representative excerpt and is published
in its entirety in the machine readable format.  A portion is
shown here for guidance regarding its form and content.}
\end{deluxetable*}

\subsection{Asteroid Shape Distribution}
\label{sec:results_shapes}

In order to derive the average shape distribution of main belt
asteroids, we implement the model used by \citet{McNeill2016}. This
model generates a synthetic population of asteroids with random shapes
and spin pole orientations and compares them to the observed data
using a $\chi^2$ goodness of fit test. Shapes are generated assuming a
triaxial ellipsoidal shape with axis ratios $b/a$ and $b/c$; we
generate random ratios $0.2 \leq b/a < 1.0$ and presume $b=c$. We
assume the spin pole latitudes and longitudes of the observed objects
based on the distribution for small (diameter ${\leq}30$~km)
  asteroids obtained by \citet{Hanus2011}; spin frequencies are
derived from a uniform distribution covering 1--10.9~day$^{-1}$,
corresponding to rotational periods ranging from the spin barrier at
2.2~h to a period of 24~hr. This assumption is consistent with the
flat distribution of measured rotational frequencies at small sizes
\citep{Pravec2002}.  We account for phase angle variations in each
target by assigning monotonically increasing or decreasing phase angle
values based on the ensemble properties of DR2 targets (see Section
\ref{sec:phasecurve} and Table \ref{tab:results}). We furthermore
account for the fact that lightcurve amplitudes measured as part of
this work represent lower limits by increasing each measured amplitude
by 51\% and adding a noise contribution following a normal
distribution with a relative standard deviation of 20\% in each Monte
Carlo run. This approach is justified in Section \ref{sec:validation}.

Based on 10,000 Monte Carlo runs using 11,665 synthetic objects each,
we find an average aspect ratio for main belt asteroids
$b/a=0.80\pm 0.04$. The nominal value is defined as the
global minimum $\chi^2$ of all model runs; the uncertainty is derived
within a reasonable range ($\chi^2 \leq 2$) around the global minimum of the
distribution. We discuss this result in Sections \ref{sec:previouswork} and \ref{sec:limitations}.

\subsection{Trends and Correlations}
\label{sec:results_trends}

We investigate potential correlations between our derived lightcurve
amplitudes and intrinsic target properties: semi-major axis, color,
albedo, and diameter.
For this analysis, we match our sample target list with
previously derived asteroid color parameters $a^{\text{*}}$
\citep{Ivezic2001} from the Sloan Digital Sky Survey (SDSS) Moving
Object Catalog \citep[Data Release 3,][]{Ivezic2005}, diameters and
albedos of WISE-observed small bodies \citep{Mainzer2016}, as well as
semi-major axes as provided by the Minor Planet Center database.
  We use {\tt sbpy.data.Names.parse\_asteroid} to parse the respective
  asteroid identifiers in the different archives to perform the object
  matching. The SDSS color parameter $a^{\text{*}}$ is derived as the
average over all available measurements; in order to reject outliers,
we restrict ourselves to the range $-0.3 < a^{\text{*}} <
0.3$.
Similarly, WISE diameters and albedos are derived as averages if
multiple observations are available.

Matching objects and measured properties are listed in Table
\ref{tab:results} and plotted in Figure \ref{fig:correlations}. Aspect
ratios ($b/a$) have been derived from the
lower limit amplitudes $A$ using the relation
$b/a = 10^{-0.4\cdot A}$. We furthermore repeat the analysis performed
in Section \ref{sec:results_shapes} for sub-samples that are defined
based on the respective parameter distributions. The sub-sample
definitions and average aspect ratio results are listed in Table
\ref{tab:subsamples}. In order to derive the latter, we use the exact same model as described in Section \ref{sec:results_shapes} but applied to the individual sub-samples.

\begin{deluxetable*}{lccrc}
\tablecaption{Sub-Sample Definitions and Average Aspect Ratios\label{tab:subsamples}}
\tablecolumns{5}
\tablewidth{0pt}
\tablehead{
\colhead{Parameter} &
\colhead{Range} &
\colhead{Description} &
\colhead{$N_{\mathrm{obj}}$\tablenotemark{a}} &
\colhead{Average Aspect Ratio ($b/a$)}}
\startdata
Semi-major axis ($a$) & $a < 2.5$~au & inner main belt & 4,054 & $0.79\pm0.03$ \\
& $2.5 \leq a < 2.82$~au & middle main belt & 3,880 & $0.79\pm0.03$ \\
& $a \geq 2.82$~au & outer main belt & 3,731 & $0.79\pm0.03$ \\
\hline
Intrinsic Color ($a^{\text{*}}$) & $a^{\text{*}} < 0$ & blueish asteroids & 1,008 & $0.79\pm0.03$ \\
& $a^{\text{*}} \geq 0$ & reddish asteroids & 2,547 & $0.79\pm0.03$ \\
\hline
Diameter ($d$) & $d < 10$~km & small asteroids & 5,821 & $0.79\pm0.03$ \\
& $10 \leq d < 50$~km & medium-sized asteroids & 3,673 & $0.80\pm0.03$ \\
& $d \geq 50$~km & large asteroids & 468 & $0.86\pm0.05$ \\
\hline
Geometric Albedo ($p_V$) & $p_V \leq 0.1$ & primitive asteroids & 2,827 & $0.80\pm0.03$ \\
& $p_V > 0.1$ & non-primitive asteroids & 7,135 & $0.79\pm0.03$ \\
\hline
--- & --- & all main belt asteroids & 11,665 & $0.80\pm0.04$\\
\enddata
\tablenotetext{a}{Number of objects in this subsample.}
\end{deluxetable*}

We find no significant differences in the average aspect ratios
derived from our model (see Section \ref{sec:results_shapes}) in
sub-samples based on intrinsic color, semi-major axis, and geometric albedo.
However, we find a difference in the average aspect ratio
  between medium-sized asteroids and large asteroids (see Table
  \ref{tab:subsamples} for definitions) at the $1\sigma$ level: our
  model suggests that main belt asteroids with diameters
${\geq} 50$~km are rounder than smaller asteroids, which
  agrees with trends from previous studies \citep{Cibulkova2016,
    Nortunen2017, Cibulkova2018}.

  We also use a $k$-sample Anderson-Darling test ({\tt
    scipy.stats.anderson\_ksamp}) to investigate differences in the
  amplitude distributions in the individual sub-samples. We find the
  null-hypothesis that the different subsamples in semi-major, object
  diameter, intrinsic color, and object albedo come from the same
  distribution can be rejected at the 1\% level. This indicates clear
  differences in the amplitude distributions as a function of these
  parameters, which do not affect the average aspect ratios derived
  from our model (see Figure \ref{fig:correlations}).
More detailed studies
will be possible with the availability of a better coverage of the asteroid population with Gaia Data Release 3.

\begin{figure}
\epsscale{1}
\plotone{fig2.pdf}
\caption{Correlations of the $b/a$ aspect ratios measured in this work
  with other target properties from the literature: semi-major axis
  (top left), target diameter (top right), intrinsic color (bottom
  left), and geometric albedo (bottom right). Semi-transparent dots
  represent individual objects. The colored error symbols
  represent the average $b/a$ aspect ratio per sub-population as
  indicated by the vertical dashed lines (compare to Table \ref{tab:subsamples}). \label{fig:correlations}}
\end{figure}

\section{Discussion}
\label{sec:discussion}

\subsection{Comparison to previous work}
\label{sec:previouswork}

We compare our derived mean aspect ratio for main belt
  asteroids ($b/a=0.80\pm0.04$) with previous results.
  \citet{McNeill2016} derived the average triaxial shape parameters of
  main belt asteroids with diameters ${\leq}20$~km from Pan-STARRS1
  observations as ($1:0.85\pm 0.13:0.71\pm 0.12$; this value has been
  updated to $1:0.83\pm 0.07: 0.70\pm 0.06$ with the updated form of
  the model which now more accurately accounts for phase angle
  amplitude correction), which agrees within the uncertainties with
  our findings for the same size regime. \citet{Cibulkova2016} find
  aspect ratios $b/a={\sim}0.63$ for main belt asteroids with
  diameters smaller than 25~km and $b/a={\sim}0.77$ for main belt
  asteroids greater than 50~km from the Lowell photometric database
  \citep{Bowell2014}. Both results are lower than our estimates --
  implying a higher average elongation of the targets -- although the
  general trend of larger objects being rounder is consistent with our
  results. This effect might be caused by the large individual
  photometric uncertainties (0.1--0.2~mag) of the data sample used in
  that work, which might overestimate lightcurve amplitudes
  \citep{Cibulkova2018}. \citet{Nortunen2017} use dense photometric
  observations \citep[e.g., from WISE,][]{Wright2010}, finding
  probability density functions for the triaxial shape parameters that
  agree with our result for asteroids with diameters greater than
  50~km, but they also find asteroids smaller than 50~km to be more
  elongated ($b/a{\sim}0.55$) than in this work. This discrepancy
  might point to an albedo-based selection bias in our sample of
  optically observed asteroids that is not existent in the WISE sample
  that affects this measurement. Detailed modeling of this bias and
  the underlying elongation distributions will be necessary to confirm
  this hypothesis, which we defer to the future when we can make use
  of a larger number of Gaia-observed main belt asteroids.  Finally,
  based on a prolate spheroidal shape model ($a \geq b = c$) and
  Pan-STARRS1 photometric data, \citet{Cibulkova2018} find
  $b/a\sim0.8$ for main belt asteroids with diameters greater than
  12~km, which also agrees with our result.

\subsection{Validation of our approach}
\label{sec:validation}

We compare our lower-limit amplitudes against previously measured
amplitudes cataloged in the Asteroid Lightcurve Database
\citep[LCDB,][]{Warner2009}, restricting ourselves to the most reliable
information from that source (uncertainty parameter $U$=3).  The
amplitude comparison is plotted in the top panel of Figure
\ref{fig:lcdb}.  We find a significant fraction of small-amplitude
($A_{\mathrm{LCDB}}\leq$0.25~mag) targets to have overestimated amplitudes. This
effect is at least in part caused by incorrect phase slope parameters
$G_{12}$, which can lead to an artificial sloping of the derived $H_G$
magnitudes as a function of solar phase angle and hence lead to an
overestimation of the lightcurve amplitude.
Additional effects may include amplitude modulations as a function of
a target's observer-centric ecliptic longitude \citep[see][and Section
\ref{sec:limitations} for a discussion]{Bowell2014}. For larger
amplitudes ($A_{\mathrm{LCDB}}>0.25$~mag) the comparison shows a clear
underestimation of large amplitudes on our side. This effect is caused
by the incomplete sampling of the target's lightcurve. We quantify
this underestimation by fitting a linear slope to the data shown in
Figure \ref{fig:lcdb} (top). Based on this fit, we find that we
underestimate the lightcurve amplitudes by 51\%; the scatter of the
data points with respect to this slope is 20\%, providing a measure of
uncertainty for an individual object after applying the average 51\%
correction. We use these findings in Section \ref{sec:results_shapes}
to correct our derived lower-limit lightcurve amplitudes. The bottom
panel of Figure \ref{fig:lcdb} shows that this offset is independent
of the number of observations per target. However, we find amplitudes
derived from many observations to be more reliable.

\begin{figure}
\epsscale{0.7}
\plotone{fig3.pdf}
\caption{{\bf Top}: Comparison of derived lower-limit lightcurve
  amplitudes and previously derived lightcurve amplitudes from the
  Asteroid Lightcurve Database \citep[LCDB,][]{Warner2009}. The red
  line indicates unity; the blue dashed line represents a linear fit
  to the scatter cloud. The colors of the points corresponds to the
  color scheme used in the bottom panel. {\bf Bottom}: Amplitude
  residuals (this work minus LCDB) as a function of the number of
  observations per target. The black line indicates a running average
  over 100 adjacent data points. \label{fig:lcdb}}
\end{figure}

\subsection{Limitations of this Analysis}
\label{sec:limitations}

This analysis is limited by a number of simplifications.
In our derivation of the lightcurve
amplitudes of our targets (Section \ref{sec:phasecurve}) we ignore the
effect of the solar phase angle on the lightcurve amplitude. From the
limited amount of DR2 observations, we are unable to account for this
effect on a per-object basis. Instead, we investigate the magnitude of
this effect on the ensemble of measured lightcurve amplitudes using
the relation derived by \cite{Zappala1990} and an assumed average
phase slope parameter of 0.02~mag/degree together with the average
solar phase angle in our sample (19\degr). Based on these assumptions,
we expect our lightcurve amplitudes to be overestimated by
40\%. However, in Section \ref{sec:validation}, our comparison of the
lightcurve amplitudes derived in this work with previously measured
lightcurve amplitudes from the literature shows that we are on average
underestimating lightcurve amplitudes. We interpret this discrepancy
as a sign that the effect of the solar phase angle on the lightcurve
amplitude is insignificant for our ensemble analysis.

Furthermore, the spin pole orientations of the majority of our sample
targets are unknown. For individual objects, this lack of information
can be critical in two ways: (1) the relative orientation of the spin
pole axis to the observer directly modulates the observed lightcurve
amplitude in a geometrical effect, and (2) the orientation of the spin
poles axis introduces additional variability that can exceed the
target's lightcurve amplitude as a function of the observer-centric
ecliptic longitude \citep[see, e.g.,][]{Bowell2014}.

We justify the use of the spin pole distribution derived for asteroids
smaller than 30~km \citep{Hanus2011} in our model (Section
\ref{sec:results_shapes}) with the fact that the majority of our
sample objects with measured diameters fall into this size regime
(${\sim}$90\%). Nevertheless, we investigate the impact of this choice
on the results and redo the analysis in Section
\ref{sec:results_shapes} based on a uniform distribution of spin poles
in both ecliptic latitude and longitude. This distribution agrees with
the distribution for larger asteroids \citep{Hanus2011} and represents
the extreme opposite to our original choice, allowing us to probe any
differences in the results. The resulting average aspect ratios for
all samples agree with our nominal results within their 1$\sigma$
uncertainties. This observation is supported by the results of a
Kolmogorov-Smirnov test \citep[e.g.,][]{Press1992} in which we compare
the de-biased amplitude distributions generated in our model based on
the different spin pole distributions and find no significant
differences between those distributions.

Finally, we assume in our derivation of the average aspect ratios that
the $b$ and $c$ axis ratios of our asteroids will be equal. Shape
models from dense light curve inversion are the only existing data
sets which can detail the relationship between these axes. These data,
however, are incomplete and likely to be biased toward higher $b/c$
values. Allowing $b/c$ to vary will slightly inflate the value
obtained for the $b/a$ axis ratio but not to an extent greater than
the uncertainties produced by the model.

\section{Conclusions}
\label{sec:conclusions}

We measure lower limit lightcurve amplitudes for 11,665
main belt asteroids in the Gaia Data Release 2 catalog. We
  derive the mean aspect ratio for main belt asteroids as
$b/a=0.80\pm0.04$, which is in agreement with previous studies. We
investigate trends in the shape distribution as a function of
semi-major axis, intrinsic color, diameter, and geometric albedo,
using data from the literature. Based on our model simulations,
  we find that main belt asteroids greater than 50~km in diameter
have on average higher $b/a$ aspect ratios (are rounder) than smaller
asteroids. We furthermore find significant differences in the
  derived lower limit amplitude distributions with respect to
  semi-major axis, intrinsic color ($a^*$), and geometric albedo.  We
predict that more detailed population and shape distribution studies
will be possible with the availability of Gaia Data Release 3.

\acknowledgments

The authors would like to thank an anonymous referee for a
  thorough review that improved the quality of this work
  significantly.  This work is supported in part by NSF award
1229776.  This work has made use of data from the European Space
Agency (ESA) mission {\it Gaia}
(\url{https://www.cosmos.esa.int/gaia}), processed by the {\it Gaia}
Data Processing and Analysis Consortium (DPAC,
\url{https://www.cosmos.esa.int/web/gaia/dpac/consortium}). Funding
for the DPAC has been provided by national institutions, in particular
the institutions participating in the {\it Gaia} Multilateral
Agreement.  This research has made use of the VizieR catalogue access
tool, CDS, Strasbourg, France. The original description of the VizieR
service was published in A\&AS 143, 23

\vspace{5mm}
\facility{Gaia}

\software{astropy \citep{astropy}, astroquery
  (\url{https://github.com/astropy/astroquery}), matplotlib
  (\url{https://matplotlib.org/}), numpy
  (\url{http://www.numpy.org/}), scipy (\url{https://scipy.org}),
    sbpy (\url{https://sbpy.org}), topcat
  (\url{http://www.star.bris.ac.uk/~mbt/topcat/}) }

redpajama_set_name: RedPajamaArXiv


text:
Bandar-e Shenas (, also Romanized as Bandar-e Shenās; also known as Bandar-e Shīās, Shenās, and Shīās) is a village in Moghuyeh Rural District, in the Central District of Bandar Lengeh County, Hormozgan Province, Iran. At the 2006 census, its population was 1,631, in 274 families.

References

Populated places in Bandar Lengeh County

redpajama_set_name: RedPajamaWikipedia


With the latest technology Remote Deposit allows you to make deposits from the convenience of your office, day or night.
Scan deposits safely and accurately from the convenience of your office, day or night. Funds are electronically sent to the bank allowing you the ability to view web based images and reports while saving you time and money.


text:
Q: How to give permission to non-sudo users to download software in their own directory? I am a sudo user to a remote node (ubuntu 20.04). My role is to facilitate multiple users of the node by generating their credentials. I downloaded RDP and remote desktop for them.
However, none of them is able to download any software or package whatsoever (E.g., IntelliJ). neither from the Software Centre nor through the command line.
They require the root password for the same; which I cannot give to them.
Also, downloading software as a sudo every time someone needs a new software is not feasible.
What to do?

redpajama_set_name: RedPajamaStackExchange


ASKO's washing machines provide the best possible washing and drying results, handling your clothes with care, thanks to the Active Drum™ solution which optimizes the washing result but minimize the wear on your clothes. ASKO's washing machines are the only ones on the market not to have any rubber seal. This means less cleaning, no residual detergents and maybe more importantly, no more leaking.
Vibrations in a washing machine contribute to wear and reduce the life span. We have made our machines extra sturdy by building on four powerful shock absorbers rather than two shock-absorber legs. Many manufacturers stabilize their washing machines with concrete. We've chosen cast iron, which lasts longer. Because this also reduces vibrations, there is less wear on the machine. It is also easier to recycle iron, another benefit for the environment. Cast iron also provides for higher spin speeds (1800 rpm), making the spin cycle more efficient.
If you want to be sure your washing machine will stay fresh for many years, an outer drum in stainless steel is far preferable to plastic. You can spin at higher speeds (up to 1800 rpm), and you can also disinfect thanks to a high water temperature. The drawback of a plastic outer drum is that it attracts dirt and ages quicker at high temperatures. The stainless steel outer drum lasts longer than plastic.


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text:
Q: sweet.js cannot return #`else` main.js
import {另} from './chinese-macros';
另 {
}

chinese-macros.js
export syntax 另 = function(ctx) {
    return #`else`;
}

main.js should compile to else {} but I get this error message instead:
throw this.createError(start, "not a valid expression");

Any help would be greatly appreciated.

A: else {} by itself is an invalid expression, that's why you're receiving that error message. What (I believe) you're doing is trying to replace if and else into Chinese. So assuming you've made a macro for an if statement, the compiler will end up evaluating the macro for if, then separately evaluating for the else macro.
What you should do instead is build up a macro for the if/else-if/else statement in one macro, much like how the tutorial builds one for a cond expression: http://sweetjs.org/doc/1.0/tutorial.html#_sweet_cond. Notice how they iterate through keywords starting with case then default, and throwing an error if none of those two appear (invalid syntax). It's the same idea for what you want to achieve except doing if, else if, and else in that order... while adding more error handling and accounting for the different syntax.


This show is performing in performing in the Anatomy Lecture Theatre from 24th-29th. Buy tickets here.
In 1885 Sarah Henley throws herself off a bridge. She lives. In 2015 Sarah talks about this and other things that push us over the edge. It is not about suicide, well, only a bit, it's about love and what it makes us do. Inspired by real heart-breaking stories; some given, some found, some stolen.
An act of public self-help, absurd melodrama and poetic meanderings around our perpetual preoccupation with this pumping organ.
Winner of the 100˚ Jury Prize Berlin, making its UK debut.


text:
Q: With Django, what is the best practice way to add up a specific field on each object in a queryset? This is how I'm currently getting a total of each object.balance in my queryset. It feels wrong. Is there a better way? (I'm struggling to explain/write the question so just see the code below :) )
# models.py

...

class Foo(models.Model):

    ...

    balance = models.DecimalField(
        max_digits=10,
        decimal_places=2,
    )

    ...
...

# utils.py

...

def get_the_total():
    objects = Foo.objects.all()

    total_balance = 0

    for object in objects:
        total_balance += object.balance

    return total_balance

...

A: There is Sum() built-in to Django:
Foo.objects.aggregate(Sum('balance'))


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I am a brand new customer. The customer service is excellent, the repair was excellent, I looked at the completed repair myself, and I appreciate the integrity, humanity, respect, and the way that my vehicle and I were treated. Their word is good and they have heart. Thank you.


text:
Christian Meinig
Christian.Meinig@noaa.gov
Staff Affiliation:
NOAA/PMEL
PMEL Division:
Engineering Development
Meinig CV
Chris Meinig is the Director of the Engineering Development Division at PMEL. He leads a diversified team of engineers and technicians specializing in the research, development and deployment of ocean and atmospheric instruments and observing platforms. His work is global in scope and include moorings, ships, ROVs, underwater gliders and unmanned surface and aerial vehicles and has logged over 550 days at sea.
Chris received his Master's in Mechanical Engineering from the University of Washington and has been with PMEL since 1994. He has been granted two U.S. patents and has four times been honored with Department of Commerce Gold Medals and Silver Medals for his engineering contributions to ocean observing systems. He has received two NOAA Technology Transfer Awards for transitioning government research to industry
Back to People

redpajama_set_name: RedPajamaCommonCrawl


If you have to undertake maintenance tasks for your Audi A6 3.2 FSI Quattro Automatic then it is usually a good idea to have a Workshop Manual for a reference in the event you need to know easy methods to take out a particular component including Wheel and install it again accordingly.
Audi A6 3.2 FSI Quattro Automatic Workshop Manuals offer you identifiable diagnostic guidelines with regards to your car therefore if something is not working it can help you figure out what the issue is and ways to repair it. After that you can analyse if you can do this by yourself or if the job is simply too big you can make a reservation for your A6 3.2 FSI Quattro Automatic right into a suitable repair garage.


Honestly, who was stupid enough to do this? Somebody at Microsoft nicked code from a Canadian company called Plurk, which not only has an awful name but also makes a (yuck) microblogging application.
Seriously, though, we feel for Plurk, and Microsoft has admitted to being in the wrong here. But who on Planet Redmond did this? We doubt it was on executive orders or anything like that. Still, somebody somewhere should have caught the stolen code (the theft wasn't subtle), and, more importantly, somebody else shouldn't have stolen it in the first place. Unemployment office, get ready for another application or two (or more).


Wire is a very versatile element that can be added to any page.
Most craft stores carry a variety of coloured wires of all thicknesses, but ordinary wire you find laying around the house works as well (just make sure it's not hooked up to something).
Whatever wire you use, be aware of sharp, jagged edges. They can damage photos or puncture holes in your page protectors, if they're not filed down properly.
Wire is so easy to manipulate you'll literally find hundreds of uses.
• Run a piece of wire through a paper crimper for a new, wavy look (place the wire between two pieces of paper to protect your crimper).
• Fold it into any number of designs: flowers, leaves, curly-cues, any simple shape that would add to your layout is at your fingertips when you have wire on hand.
• Use wire to make a page title. It's remarkably easy to turn wire into beautiful cursive.
• 'Hang' elements using wire.
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Remember, any time an article interests you, click on the title (in this case, wired) to be sent to a page with further information, related articles, or great free stuff!
How do you make curves in wires, without bending the wire and getting kinks??
A great tool to keep curves smooth is to wrap the wire around a pencil or anything round. The curves look polished, not bumpy.


Qorygore's video reportedly received nearly 600,000 views before YouTube removed it.
He later said that he "respected" the dead body even though he filmed it.
A YouTube celebrity is being widely criticized for filming a dead body in Japan's Aokigahara forest, less than a year after Logan Paul got in trouble for the same stunt.
The video, posted by Qorygore, a YouTube star with about 800,000 followers who's popular in Indonesia for his videos about gaming and rap. It showed him vlogging from the "suicide forest" Aokigahara, famous for being the site of a disproportionate number of suicides. Qorygore found what he said was a dead body covered by a raincoat and included it in his video.
"I went all the way to Japan. This is Logan Paul 2.0," he said in the video according to The Daily Dot.
Read more: YouTube released a movie with Logan Paul less than a year after his infamous 'suicide forest' video.
Qoygore's video also received severe backlash in the YouTube comments and on Twitter.
After YouTube removed Qorygore's video, the vlogger justified his actions in an interview with fellow YouTuber Eno Bening. He said he had a permit that allowed him to film dead bodies in the forest, and suggested the body may have been fake anyway.
"It was a pile covered by a raincoat like [a ghost]. Because I respected the dead body, I didn't get really close to him," he said, according to a translation from Coconuts Jakarta.
In another video published hours later, Qorygore clarified that he wasn't trying to be disrespectful. He said he only showed the raincoat instead of the body underneath it.
"Because I respected the dead body, I didn't get close to it." he said.
For more stories, head to INSIDER's homepage.


text:
The 2021 Leinster Senior Football Championship Final was played at Croke Park in Dublin on 1 August 2021. It was contested by Dublin and Kildare. Dublin won an 11th consecutive title.

Match details

Notes

References

2L Final
Leinster Senior Football Championship Finals
Dublin county football team matches
Kildare county football team matches


I'm not casting a spell over their children.
Imogen of the Internet has created a seminal classification of thirty distinct varieties of chatspeak, some now facing linguistic extinction.
The cat took advantage of the high grass to creep on the bird.
Knut appears to be in pain.
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Why did you decide to not go to Boston with Hughes?
Why aren't you already on board the ship?
Presley asked Julianto to give a speech at his school.
Jeff said he would do his homework right after dinner.
Thank you for the introduction.
Do you have a needle to sew on these buttons?
I cannot mention Taninna's name in presence of her father!
Are you questioning my judgment on this matter?
When she kissed me, I felt she was honest with me.
I know how much money you have in the bank.
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Patty is an old boyfriend of Hartmann's.
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The community will benefit from the new industry.
Patrice's parents don't like me.
Huey called Amigo up and asked her what her schedule was.
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Any neutrinos traveling faster than light would radiate energy away, leaving a wake of slower particles analogous to the sonic boom of a supersonic fighter jet.
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Bruce went up to her room and didn't come down, even for supper.
Billie was reloading his gun.
Marcel hardly ever listens to the radio.
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You must be prepared for the fact that he could drop by at any moment.
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She was full of joy.
The airline makes sure to send your luggage all the way to the final destination as soon as possible, or at a later date at the passenger's choice.
There is a movement against Japanese goods in that country.
Kyle loves talking about politics.
Do you think Kelvin will go swimming with us tomorrow?
Tanaka has been refusing to take his medicine.
Alberto said that he doesn't want a promotion.
Kusum appears to be a bit nervous.
Squirrels like to eat nuts.
In Europe the schools start up in September.
I thought Billie would be in Boston by now.
It is a great honor to be invited.
They brought solid fuel with them.
Stefan saw his reflection in the mirror.
No other creatures can fly as far as fast or as long as birds.
I can't find my red hat anywhere.
Whom the gods would destroy, they first make mad.
We saw the Venus of Willendorf in Vienna.
Imagine that you have a time machine.
Dan discussed with his friends how to have his articles published.
Revised said he'd help me find what I need.
Dannie pulled back the curtain.
I don't think I can get there in time.
I was half asleep when I went home.
The hill commands a fine view.
Can I play some music?
There was a curtain which was covering the door.
The teacher ran up the stairs.
I assume you'll be going to the dance with Kayvan.
The situation there was critical.
You can give Nikolai all of it, if you want to.
I don't see Grace doing that.
Kosh is a Vorlon ambassador in the Babylon 5 space station.
It's up to you to decide whether we'll go there or not.
Can you see the big white building over there?
Spass eats only raw vegetables.
Switching on a fleshlight won't help you see in the dark.
I have to go back to work now.
They're all grinning at her.
He is admittedly an able leader.
Kyu took some time off to travel.
You're not doing anything wrong.
Angela wrote a letter to his brother in Boston.
That was the first time I was ever alone with Nancy.
The situation is better, if anything.
Fashions grow old and die.
Can you play the organ?
Kusum is always complaining about something.
Would you sing us a song in French?
Rudolph didn't have to listen to Murray.
Just shut up and get on with your work!


A significant priority for Health Select is to attract and retain a skilled workforce and to provide them with outstanding career development opportunities.
Our recruitment process includes an Interview, an Observation Day, Driving Assessment and an Induction Day.
Expressions of interest are invited for casual Registered Nurses, and Patient Transport Officers in both Metro and regional areas.
National Police Certificate issued by Victoria Police dated within 6 months - reason for check: PTO or ATA or RN1 (Ambulance).
For further information, please call on 03 9874 4868.


To honor two people for their service to the Neonatal Intensive Care Unit at Abington Hospital-Jefferson Health, neonatologists there are starting college scholarship funds in their names - and awarding the initial scholarships to the two babies who have most touched their hearts by overcoming adversity.
About 650 newborns a year spend an average of 14 days in the unit. The first two NICU Scholars were there a lot longer and had very difficult experiences, from cardiac issues to infections, said Gerard Cleary, neonatology chief.
Daniel Krupp weighed 21/2 pounds when he was born on July 6, 2014, at week 27. He went home to Mount Laurel a little over two months later; his father died six months after that.
Daniel will be the Ara S. Moomjian Scholar, honoring a physician who recently retired from Newborn Special Care Associates, the neonatology practice at Abington.
Cyamir Hooks weighed one pound when he was born on Oct. 19, 2014, at 22 weeks and six days into the pregnancy, a time when most babies don't survive. "He beat incredible odds just to be here," Cleary said, recalling how his young parents from Philadelphia would do their college homework by the isolette incubator during his 154 days in the NICU.
Cyamir will be the H.F. "Gerry" Lenfest Scholar, honoring the philanthropist and former owner of the Inquirer, the Daily News, and Philly.com for his guidance on pediatric models of care, especially involving the NICU.
Cleary said the neonatology practice would contribute $5,000 to each scholarship fund. New contributions for additional babies will be added each year.
An awards ceremony is scheduled for Tuesday morning at Abington.


2. Dongwon Tech adopted an advanced management system and have strived to become a pioneer in the industry. The company is committed to transforming itself into a global management system that creates new values by strengthening its competitiveness and core capabilities such as an anemometer, an electric rudder angle indicator and an engine telegraph.
We are looking forward to make great partnerships with business partners who are not only interested in our products but also able to understand our industry.
Just as we pioneered the marine path with our challenging and creative spirit, we will continue to open up a new chapter in the business with our accumulated know-how and faithful services.
The 21st century requires us to respond to the changes, and to innovate ourselves in the wake of the acceleration of digital information and borderless competition.


Discussion in 'General Discussion' started by Devil Inside, Mar 22, 2004.
A few days ago awstats stopped being added to users directory.
The option is still enabled in WHM however.
I am able to manually add the directory then run logs to add them. But why would it suddenly stop doing it automatically?
Anyone know how to fix this or experience this before?
I just did some more looking and seeing that the tmp directory as a whole is not being added.


text:
Home » News » IPL 7: We showed character to win, says Virat Kohli
IPL 7: We showed character to win, says Virat Kohli
Royal Challengers Bangalore captain Virat Kohli praised his players for showing character in their five-wicket win over formidable Chennai Super Kings in an IPL match in Ranchi on Sunday.
"Great win for us, especially after the wicket played in the second innings. Today (Sunday) was a great example of the character in the side. You have (Chris) Gayle hitting out there, then AB (de Villiers) and Yuvi in such for, you back your team," Kohli said after his side's victory which kept them in the hunt for a play-off berth.
"It was about rotating strike as much as possible and hitting with the turn and not trying something fancy. Because with the old ball, it was not turning as much so you can stay on the backfoot and work it away," he said.
Asked about the last few balls of his side's run chase, Kohli said, "I did not send any message. Yuvi told me he wanted Abu Nechim to get a single, but he just stepped out and slammed the ball for six. That's the belief players have now."
Man of the Match AB de Villiers
Quality Proof else theyungdrungbon.com cipro online no prescription for one – keep this star http://theyungdrungbon.com/cul/buy-viagra-belgium-155/ who I'll rub.
for his cameo of 14-ball 28 said the wicket was a difficult one to play shots. "Probably one of the most difficult wickets that I played on. I got some of the balls away. I looked foolish a couple of times and took it to the end. I was disappointed to get out at the time, but Yuvi did it for us in the end," he said.
Chennai captain Mahendra Singh Dhoni said his side were 10 runs short while batting first. "They (Bangalore) bowled very well, especially in the last four overs. We lost five to 10 runs and if not more," he said.
Dhoni, however, praised his slow bowlers for making a match out of it after Chennai scored a modest 138 for four after electing to bat.
"Knew the pitch would slow down further, the spinners did maintain the pressure and that's one of the reasons why the game went close," said Dhoni.
Asked if a pattern was developing, with such close losses so close to the playoffs, Dhoni said, "Not really, the best thing about statistics is we can have a pattern and it changes.
"It's something the commentators can talk about and they have to talk about something," he said.
Asked about the advantage of playing at the 'home venue', Dhoni said, "Not really, it maybe your home venue but the team that wins plays better cricket."
Source : The Indian Express
Chennai Super Kings IPL 7: We showed character to win Royal Challengers Bangalore captain says Virat Kohli Virat Kohli 2014-05-19
Tagged with: Chennai Super Kings IPL 7: We showed character to win Royal Challengers Bangalore captain says Virat Kohli Virat Kohli
4 CMC medicos torture, kill monkey, suspended
Agusta Westland row: Chair has not authenticated any paper tabled by Subramanian Swamy
Star studded music launch of Avan Ivan
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Parrot arrested for helping drug dealers in Columbia


In Local Government Week, we like to invite people to become more familiar with Council's facilities and services and to come along to some of the free activities offered during the week.
There are the essential services that everyone expects from Local Government such as town planning, waste disposal, road maintenance, parks and gardens, sporting facilities and public amenities.
Councils are also responsible for maintaining libraries, swimming pools, cemeteries, animal control, weed control, community events, tourism and visitor information.
In Gunnedah we also operate services for youth, frail aged and disabled people and community transport and we run the Saleyards and The Civic Centre with its cinema, live theatre and art gallery.
Some fun filled activities on offer for Local Government Week are history walks, competitions, movies and lucky door prizes.


Have you have ever wondered why people at wine tastings ritualistically tilt their glass, swirl the wine around the bowl, sniff the wine and then gargle the wine before spitting it out?
No, they are not wasting their wine. Besides insuring you will be able to drive home, this method will help you assess, the quality of a wine.
Step 1- Testing the color and clarity of a wine.
For red wines, tilt the glass against a white background. Examine the edge, or lip, of the wine against the glass. If you see a dark color that runs clear to the edge this indicates a young wine. A slightly lighter color that holds to the center of the glass with a wide clear lip is indicative of an older wine.
For white wines, clarity is assessed by searching straight down into the wine. The higher the clarity, the wine will appear to sparkle, rather like diamonds.


text:
Astrostephane is een geslacht van zeesterren uit de familie Brisingidae. De wetenschappelijke naam van het geslacht werd in 1917 voor het eerst voorgesteld door Walter Kenrick Fisher. Hij stelde geen formele diagnose en beschrijving op maar gaf de kenmerken in een tabel voor alle op dat moment onderscheiden geslachten in de Brisingidae. Als typesoort wees hij de een jaar eerder door hem benoemde Brisinga moluccana aan.

Soorten
 Astrostephane acanthogenys (Fisher, 1916)
 Astrostephane moluccana (Fisher, 1916)

Brisingida


Get into the habit of telling your dog off for doing this, and you may simply be confusing them and damaging your relationship with your furry friend. It's against their natural inclinations and may actually cause them to do more of the things you're trying to get them to stop.
So many adjectives, but you can add that Munchkin kitties are also curious and cuddly!
From behavioral studies to research on tumors, dogs make up the subjects of far more research studies compared to cats. Experts weigh in on why this bias exists and whether putting more time and effort into feline research could further the human-feline bond.


text:
>Music
>Count Basie
Count Basie Autographs, Memorabilia & Collectibles
About this Signer
Born: August 21, 1904 in Red Bank, New Jersey
Died: April 26, 1984 in Hollywood, Florida
Biography | show moreshow less
William "Count" Basie (1904-1984) is credited with introducing blues to mainstream audiences through his polished versions of blues rhythms. Basie and his Big Band had over 30 recordings in the Top 40 from 1937 to 1968. Taught piano by his mother, Basie began his career on the vaudeville circuit in the early 1920s. In 1927, the young musician was stranded in Kansas City, changing his life and career. Within two years, he joined Benny Moten's Kansas City Orchestra and became an important part of its rhythm section. Moten's sudden death in 1935 gave Basie his "big break." Along with Moten's nephew, the Count took over the group, which soon evolved into the Count Basie Orchestra. By the peak of the Big Band Era, he was a major factor in both that movement and in jazz circles. Basie also composed the band's signature tune, "One O'Clock Jump", now a jazz standard. His astute recognition of talent added to the band's perfection with musicians such as Lester Young and vocalists such as Billie Holiday. Basie also appeared in films, beginning in 1938. His last was a memorable scene with his orchestra in Mel Brooks' Blazing Saddles (1974). The Count Basie Orchestra still tours today, playing the famous arrangements that Basie pioneered.
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COUNT BASIE - AUTOGRAPH SENTIMENT SIGNED CO-SIGNED BY: DICK HAYNES, MARILYN HARE, CHILI WILLIAMS - HFSID 27140
Guestbook page signed by band leader Count Basie, radio host Dick Haynes, actress Marilyn Hare and pin-up girl Chili Williams, better known as "the Polka Dot Girl". With small b/w photos in unknown hand.
COUNT BASIE - AUTOGRAPHED SIGNED PHOTOGRAPH - HFSID 101534
COUNT BASIE. Photograph signed: "Best Wishes/Count Basie". B/w, 9¾x7¾ overall, image 9¼x6½ (one surface). Publicity photograph by James J. Kriegsmann, New York. Captioned at lower margin: "Count Basie and His Orchestra".
COUNT BASIE - DOCUMENT SIGNED 01/24/1949 - HFSID 257335
COUNT BASIE Count Basie signed this contract in 1949 to release the William Morris Agency as his agent for $1,015.72. Document signed "Count Basie". Also signed by representative of the William Morris Agency. 8¼x10¾, 2 pages, single-sided sheets, on William Morris Agency letterhead with two file holed at top edge. Jan.
COUNT BASIE. Document signed: "Count Basie", 1p, 8½x11 carbon. New York, N.Y., 1944 March 18. Basie agrees to furnish a vocalist during his engagements at the Roxy Theatre and also that the contract prices of such engagements include the cost of such vocalist.
COUNT BASIE - INSCRIBED PICTURE POSTCARD SIGNED - HFSID 49132
COUNT BASIE Signed b/w Mutoscope picture postcard of Count Basie sitting at a piano in a tux Inscribed picture postcard signed "to Gil/Count Basie". B/w, 3¼x5¼ card, one surface. Captioned: "Count Basie/Courtesy of Music Corporation of America/A Mutoscope Card/Made in USA". Postcard by Mutoscope.
COUNT BASIE - PICTURE POST CARD SIGNED - HFSID 53744
COUNT BASIE Signed b/w Mutoscope picture postcard of Count Basie sitting at a piano in a tux Picture postcard signed "Count/Basie". B/w, 3¼x5¼ card, one surface. Captioned: "Count Basie/Courtesy of Music Corporation of America/A Mutoscope Card/Made in USA". Postcard by Mutoscope. Blank on message side.
COUNT BASIE Signed b/w picture postcard of a smiling Count Basie from the shoulders up in a coat, white shirt and tie Picture postcard signed "Count/Basie" in blue ink. B/w, 3½x5½ overall, 3x5 image, one surface. Captioned: "Count Basie". Blank on message side.
COUNT BASIE - RECORD ALBUM COVER SIGNED CO-SIGNED BY: FREDDIE GREEN - HFSID 168919
COUNT BASIE, CO-SIGNED: FREDDIE GREEN Copy of Verve's The Best of Count Basie, signed by Basie and Freddie Green, rhythm guitarist with Count Basie and his Orchestra Record album cover signed "CBasie" and "Freddie/Green" in green ink on back cover. Color, 12¼x12¼. Copy of The Best of Count Basie by Basie.
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text:
The Loneliest Planet by Randy Ross
Self-promotion and publishing tips for writers, international travel stories for those who hate travel, NC-17 erotica and erotic humor, and lots of useless relationship advice.
Self Promotion for Writers
For Bitter Singles
Trip Around the World
Professional update -- plea for help!
Apologies in advance to anyone who has already seen this on Facebook or elsewhere. But d-day is approaching and I'm getting nervous!
I) Executive summary
- I've been working on a novel for the last five years and will be circulating to agents in early 2014. The working title for the novel: "The Loneliest Planet."
- I reworked excerpts from the novel into a one-man show called "The Chronic Single's Handbook." I'll be performing the show at two fringe theater festivals next week (two shows in Portland, ME.) and in late July (five shows in D.C.)
- Can you help me get the word out about the show?
*Mention to people you know who might go, post on Twitter, Facebook, etc. (Sample Tweets and links below.)
*Any help appreciated! My big fear: I've spent four months rehearsing and $1,200 on acting lessons to prepare for these festivals -- and no one shows up to the shows.
Sample Tweet:
A friend will perform his show, The Chronic Single's Handbook, in Maine (6/29-30) & D.C. (7/19-28) Please go or RT http://ow.ly/meo8v
Sample Facebook Post:
A friend will perform his one-man comedy play, The Chronic Single's Handbook, in Maine (6/29-30) & D.C. (7/19-28). The play is about a never-married guy who takes a trip around the world looking for the woman of his dreams. Please go or share. http://ow.ly/meo8v
II) More Detail than you want
1) Here are some links to youtubes of me performing two scenes from the show around Boston. For the theater festivals, I'll have props and no mic, which means I'll be able to move around the stage.
- Opening scene:
"Chronically single? You've got lots of company"
Content warning for adults situations, black tongues, sadistic medical professionals.
http://www.chronicsingle.com/2013/04/chronically-single-youve-got-plenty-of.html
- "The Day I Was Almost Gay"
Content warning for prescription drug abuse, gooey sunburns, and men kissing on the lips.
http://www.theloneliestplanet.com/2012/05/new-video-of-day-i-almost-became-gay.html
2) Here's an online flyer for the show (Twitter and Facebook links go to this page: http://www.chronicsingle.com/2013/05/the-chronic-singles-handbook-shows-for.html
The Chronic Single's Handbook
One man's global search for love
A solo performance inspired by actual events featuring Randy Ross
A body-spa named The Curious Finger.
Early praise for The Chronic Single's Handbook:
"Hysterical, side-splitting, profound, a tour-de-force of droll insight. One of the year's best."
-- Randy Ross, writer/performer, The Chronic Single's Handbook
"The balance on your credit card is overdue. Please remit immediately."
-- Bank of West Boston
6/29, 6/30: Portland, ME, PortFringe, fringe theater festival
- Location: Portland Stage Company (PSC) Storefront theater space. Directions
- Times: Saturday 6/29 at 6:00PM, Sunday 6/30 matinee at 1:00PM
- Tickets, more information.
(tickets cost $10)
*Note: "The Chronic Single's Handbook" may also be listed at "The Handbook for the Chronically Single."
- Show program
7/19 - 7/27: Washington, D.C., Capital Fringe, fringe theater festival
- Location: Gearbox, 1021 7th St NW, 3rd floor, D.C. 20001
- Times (five shows) FR 7/19 6:45PM | SU 7/21 9:30PM | TU 7/23 9:30PM | TH 7/25 10:00PM
SA 7/27 2:PM
- Tickets, more information
(ticket available in early June. Cost $17, plus $5 or so for festival pass)
--rr
Posted by Randy Ross at 3:56 PM
The Loneliest Planet
"Vicodin, Klonopin, or Heineken"
"Why I'm over 40 and Still Single"
"The Day I Was Almost Gay"
- Margarita Island, Venezuela
- Karpathos, Greece
- Garden Route, South Africa
- Bangkok and Vietnam
- Melbourne, Australia
Self-Promotion for Writers: Dump Social Media, Emb...
Top Secret Work Habits of the Successful Novelist
about writing humor (17)
airplane sex (1)
Asian massage (5)
bad dates (9)
be an author humor (17)
book marketing tips (82)
dating middle age (14)
erotic humor (10)
funny sex (9)
how not to find love (9)
how to get a man (3)
international sex (6)
living alone (5)
marriage material (2)
never married (5)
revelstoke skiing (2)
sexy massage (3)
single life (8)
skiing drinking (2)
weird travel (3)
Novel Now on Sale
Links to an Amazon page
Like My Stuff? Send Me $2 for a Cup of Coffee?
Sign-Up by E-Mail (receive a free humor ebook)
My Travel Tips Web Site
RossTravels.com
Brother, can you spare a Like?
The Dream Catchers (experiences and tours in Costa Rica)
@ Merlene Fawdry
Chronic Single
free Fiction, Screenplays, Plays
James A. Martin
Paul Gillis
Poet, playwright, and performer Michael Mack - Official Site
Susan Tejada, author of In Search of Sacco and Vanzetti
SUSTAINABLY blogs
The Dreamcatchers
The Erotic Literary Salon: Online
The Writer's Drawer - The Writer's Drawer - homepage
Writing Contemplative life Essays
Randy Ross is a writer, performer, and Web consultant. His fiction and humor have appeared in The Drum, Black Heart Magazine, Side B Magazine, and Calliope, among others. His comedic novel, God Bless Cambodia, was sold to The Permanent Press, a publisher of literary fiction. Publication date: April 2017.
His one-man show, The Chronic Single's Handbook, based on the novel, has been featured at fringe theater festivals in the U.S., Canada, and Edinburgh, Scotland.
He writes a popular blog and lectures about self-promotion and marketing for writers. For seven years, Ross was the executive editor for an award-winning Web site (PCWorld.com). He holds a masters in journalism from Northwestern University.
For more information visit www.randyrossmedia.com or e-mail him at randy@randyrossmedia.com
Copyright © 2015 by Randy Ross
All rights reserved. Material on this site may not be reproduced or used in any manner without the express written permission of the author. Linking to the site is appreciated. Please contact: Randy Ross at randy@randyrossmedia.com with any questions.
This Web site expresses the ideas of the author. The content is not intended to be advice. I explicitly deny any liability for advice taken by any party reading the content contained on this site.
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View full sizeAP File PhotoWayne State wide receiver Troy Burrell (1) is stopped after a fist down by Pittsburg State defender Elijah Olabode (3) in the first half of their NCAA Div II National Championship college football game in Florence, Ala. , Saturday, Dec. 17, 2011.
ALLEN PARK -- Detroit Lions rookie quarterback Kellen Moore is the most notable undrafted free agent signed after this year's NFL Draft, but several other college players are now under contract.
In addition to the 13 undrafted players previously reported on MLive.com, there are seven other players who have been signed since the draft, according to sources.
The Lions will also invite several undrafted players to tryout during next week's rookie mini-camp. Detroit's camp will be held May 11-13 at its Allen Park facility.


DESCRIPTION The Internet Systems Consortium DHCP Relay Agent, dhcrelay, provides a means for relaying DHCP and BOOTP requests from a subnet to which no DHCP server is directly connected to one or more DHCP servers on other subnets. It supports both DHCPv4/BOOTP and DHCPv6 protocols.
OPERATION The DHCP Relay Agent listens for DHCPv4 or DHCPv6 queries from clients or other relay agents on one or more interfaces, passing them along to upstream servers or relay agents as specified on the command line. When a reply is received from upstream, it is multicast or unicast back downstream to the source of the original request.
-6 Run dhcrelay as a DHCPv6 relay agent. Incompatible with the -4 option.
-4 Run dhcrelay as a DHCPv4/BOOTP relay agent. This is the default mode of operation, so the argument is not necessary, but may be specified for clarity. Incompatible with -6.
In DHCPv4 mode, a list of one or more server addresses must be speci- fied on the command line, to which DHCP/BOOTP queries should be relayed.
-c COUNT Maximum hop count. When forwarding packets, dhcrelay discards packets which have reached a hop count of COUNT. Default is 10. Maximum is 255.
-d Force dhcrelay to run as a foreground process. Useful when run- ning dhcrelay under a debugger, or running out of inittab on System V systems.
-p PORT Listen and transmit on port PORT. This is mostly useful for debugging purposes. Default is port 67 for DHCPv4/BOOTP, or port 547 for DHCPv6.
-q Quiet mode. Prevents dhcrelay6 from printing its network con- figuration on startup.
-a Append an agent option field to each request before forwarding it to the server. Agent option fields in responses sent from servers to clients will be stripped before forwarding such responses back to the client. The agent option field will con- tain two agent options: the Circuit ID suboption and the Remote ID suboption. Currently, the Circuit ID will be the printable name of the interface on which the client request was received. The client supports inclusion of a Remote ID suboption as well, but this is not used by default.
-A LENGTH Specify the maximum packet size to send to a DHCPv4/BOOTP server. This might be done to allow sufficient space for addi- tion of relay agent options while still fitting into the Ether- net MTU size.
-D Drop packets from upstream servers if they contain Relay Agent Information options that indicate they were generated in response to a query that came via a different relay agent. If this option is not specified, such packets will be relayed any- way.
-i ifname Listen for DHCPv4/BOOTP queries on interface ifname. Multiple interfaces may be specified by using more than one -i option. If no interfaces are specified on the command line, dhcrelay will identify all network interfaces, eliminating non-broadcast interfaces if possible, and attempt to listen on all of them.
-m append|replace|forward|discard Control the handling of incoming DHCPv4 packets which already contain relay agent options. If such a packet does not have giaddr set in its header, the DHCP standard requires that the packet be discarded. However, if giaddr is set, the relay agent may handle the situation in four ways: It may append its own set of relay options to the packet, leaving the supplied option field intact; it may replace the existing agent option field; it may forward the packet unchanged; or, it may discard it.
-I Force use of the DHCPv6 Interface-ID option. This option is automatically sent when there are two or more downstream inter- faces in use, to disambiguate between them. The -I option causes dhcrelay to send the option even if there is only one downstream interface.
-l [address%]ifname[#index] Specifies the lower network interface for DHCPv6 relay mode: the interface on which queries will be received from clients or from other relay agents. At least one -l option must be included in the command line when running in DHCPv6 mode. The interface name ifname is a mandatory parameter. The link address can be specified by address%; if it isnt, dhcrelay will use the first non-link-local address configured on the inter- face. The optional #index parameter specifies the interface index.
-u [address%]ifname Specifies the upper network interface for DHCPv6 relay mode: the interface to which queries from clients and other relay agents should be forwarded. At least one -u option must be included in the command line when running in DHCPv6 mode. The interface name ifname is a mandatory parameter. The destination unicast or multicast address can be specified by address%; if not specified, the relay agent will forward to the DHCPv6 All_DHCP_Relay_Agents_and_Servers multicast address.
It is possible to specify the same interface with different addresses more than once, and even, when the system supports it, to use the same interface as both upper and lower interfaces.
SEE ALSO dhclient(8), dhcpd(8), RFC3315, RFC2132, RFC2131.
BUGS Using the same interface on both upper and lower sides may cause loops, so when running this way, the maximum hop count should be set to a low value.


text:
This Many Boyfriends
Label: Angular Records Release Date: 08/10/2012
by Kat Waplington October 5th, 2012
With a squeal of feed-back, a riff of purest indie-disco and Richard Brooke's crisp first line, "You love pop songs about love more than being in love in the first place", This Many Boyfriends and their self-titled debut album burst out of the speakers in a blast of nostalgia, the sound of a beleaguered genre returning to the modern day, a return to the indie of old.
This Many Boyfriends may be short, but it's nothing less than a mission statement. Lyrically and sonically, the album is an audio compilation of the band's record collections, managing to jam in namedrops as diverse as Talking Heads, Kylie and Jason, and Bruce Springsteen. Fronted by lead vocals that combine Morrisey's best deadpan delivery with Ryan Jarman's Yorkshire drawl (and, let's face it, it's not only the accent that invites Cribs comparisons), This Many Boyfriends have thrown out a first album that all but forces the listener to visualise their evident delight in making it.
Whilst the oh-so-jangly guitar and dry witticisms do certainly bring to mind Johnny Marr's other, big brother band, there's no sign of the Smiths' literary obsessions nor of their famed misery. Indeed, the band lost rhythm guitarist Peter Sykes to a brain haemorrhage in 2011, but maintain that drawing on his death for inspiration would have belittled it, instead choosing to play on his memory and to keep their music as light-hearted as possible. On the whole, the songs are short, sharp and sweet, often accompanied by a lyrical cousin of indie rom-coms like Juno or (500) Days of Summer.
Opener, 'Tina Weymouth' sets the bar for the record, including indie-punk, many a janglin' guitar and nostalgic, sweet lyrics centred on the Eighties, sounding like a slightly beefed up Los Campesinos! Next up, 'Young Lovers Go Pop!', which - pleasing pun notwithstanding - is a step-up, with murky, churning guitars and acapella Futureheads-style backing vocals.
In line with their refusal to write music about anything except music, 'Communist' is hardly a political spiel but instead reflects "I should be a communist, I tried, I failed. I'm far too decadent.", then kicks into a soaring bubblegum pop chorus. Current single 'Number 1' is a slight departure in style, rather like the quieter songs on the Vaccines' debut. It's quite nice, but the band are evidently having more fun on the breakneck, sunny songs than this slightly more reflective offering.
"I didn't leave when you said you didn't like Springsteen. I didn't even flinch when you said you hated the Go-Betweens. But what you said about Baby Honey was truly unforgivable, so I had to cry. I don't like you cos you don't like the Pastels" – and a million future indie-discos kick off, pints spill and old cliques bearhug each other. Much like 'Hey Scensters!', 'Caught By The Fuzz' and most Larrikin Love singles, this is pure indie disco gold. Punky, poppy and lyrics that you can pull absurd faces to. It also sounds, for all This Many Boyfriends' referencing of street-cred worthy indie giants, an awful lot like Avril Lavigne's "Hey hey, you you, I don't like your girlfriend" song... so there's that.
With 'That's What Diaries Are For' comes the album's most Cribs-esque track, but closer to their more recent releases than their early noughties albums, as referenced elsewhere on This Many Boyfriends. But with references to Kylie and fanzines, it's still firmly stuck in the 1980s.
Closer 'Everything' is certainly the album's darkest song, with detuned guitar bends and less saccharine lyrics – possibly a sign of things to come, now they've proved how much they love fun, indie pop and more fun. And with a skwark of feedback, the album zips out as quickly as it had begun. Short, sharp and sweet; coming in at less than 45 minutes.
It might be shameless navel-gazing 'indie about indie' (about indie?) – but the name dropping is second to the musical quality of the homages the band render to their pin-ups. Though it's nothing revolutionary, in an age where decent straight up indie seems rather rare and unfashionable, it's certainly worth a listen.
Kat Waplington's Score
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The Bloom and the Blight
The Telescopes, 93 Million Miles From The Sun, Rosco, Black Light White Light at The Leopard, Doncas


Whether faced with difficult decisions in the care of a loved one, planning for the future, or handling matters after the passing of family member or friend, John B. Henry, III, can offer legal counsel and guidance in the areas of Guardianship, Probate and Estate Administration, Estate Planning, and other civil matters.
Guardianship is a court created and administered process designed to protect the physical, mental, and financial well-being of an adult who is in need of care due to developmental disability, injury, or disease, or a minor that is in need of care or that stands to receive or inherit money. Mr. Henry is aware of the often difficult and emotional decision to pursue guardianship for a disabled or incapacitated loved one who is in need of care and assistance. To learn more about guardianships and the options available in assisting someone in need of care and assistance, visit Texas Guardianship Law: Understanding and Navigating the Process or follow John B. Henry, III, Attorney at Law's Blog for news and updates on Texas guardianship, probate, estate planning, and elder law.
Probate is the legal process by which the estate of a deceased individual is administered and settled, establishing rights to property for the beneficiaries named in a will or heirs that may exist at law, subject to the just debts and costs of administration of an estate. Frequently, probate is referred to as a time intensive and cost extensive process. In practice, however, probate can be a very time efficient and cost effective process--especially in the state of Texas that continues to create and revise simplified probate procedures to enhance Texans' access to administrating the estate of deceased loved ones. To understand more about the alternatives that exist in administering and settling an estate after a loved one's passing, visit Texas Probate Law: Procedures, Alternatives, and Settling an Estate.
Special needs planning focuses on how best to meet the needs of a loved one who is disabled and in need or will become in need of assistance. In this area, Mr. Henry counsels his clients through the care planning process, public benefits program eligibility with programs like SSI and Medicaid, resource referrals, and special needs trusts formation, modification, and trust advising. Special needs trusts can be used to maintain public benefits eligibility for a loved one in need of the services offered by public benefits programs while supplementing the needs of your loved one that public benefits programs do not cover. To understand more about special needs planning, visit Special Needs Planning: Creating and Enhancing Systems of Support.
Mr. Henry has experience in creating estate plans for his clients, including wills, trusts, statutory durable powers of attorney dealing with financial matters, medical powers of attorney, and directives to physicians commonly known as "living wills." Estate planning is about effectively planning for seen and unforeseen contingencies in life up to and including death or incapacity. A good and periodically reviewed estate plan creates comfort in providing assurance that you have taken the steps necessary for you and those you care about. To see more about estate planning options, visit Estate Planning: Creating a Plan for the Future.
Aside from Mr. Henry's primary areas of practice, he advises and represents clients in other civil matters, including elder law, family law, ad valorem property tax, consumer law, and personal injury.


text:
MEPs Debate Non-Enforcement of Rules
Poultry welfare Transportation Equipment & innovation Government and regulatory
EU - Rules to protect animals are not enforced properly according to two British MEPs who will raise the issue in a debate in Parliament today.
The chair of Parliament's Agriculture Committee Neil Parish said that reports he received from organisations contain "significant evidence that the existing legislation is not being enforced in several member states".
Mr Parish said he had "pressed the European Commission many times on this, yet still nothing seems to be done", while Ms Lynne said "it is vital that EU Governments and the EU Commission act quickly to ensure that existing rules are properly enforced, with punishments to match."
Liz Lynne, the Liberal Democrat MEP, said "I hope Thursday's debate will raise awareness of the issue, both among my fellow MEPs and among the public in general, and will be a step towards alleviating the avoidable trauma these animals are subjected to."


text:
Q: Why can "a mod n and a mod m" be simplified to "a mod n*m"? In the classic FizzBuzz programming problem the programmer is tasked with either printing out "Fizz", "Buzz", "FizzBuzz", or $n$, for $0 \le n \le k$  for some $k$, depending on whether $n$ is divisible by 3, 5, both 3 and 5, or neither. Here an example output for $0 \le n \le 10$:
FizzBuzz           0 mod 15 = 0
1
2
Fizz               3 % 3 = 0
4
Buzz               5 % 5 = 0
Fizz               6 % 3 = 0
7
8
Fizz               9 % 3 = 0
Buzz               10 % 5 = 0

One common solution is to just check if each condition satisfies one of the following equations and to react accordingly:
 - $ n\mod5 = 0$ and $n\mod 3 = 0$
 - $ n\mod5 = 0$
 - $ n\mod3 = 0$
But sometimes people replace the first condition with $n \mod 15 = 0$.
So I guess my real question is, why are these two conditions interchangeable? Obviously this solution just multiplies $3$ and $5$, but why are we allowed to do that?

A: n mod 3 = 0 $\implies n = 3k$ for some $k \in{\mathbb{Z}}$ and similarily, n mod 5 = 0 $\implies n = 5z$ for some $z \in{\mathbb{Z}}$, so $n = 3\cdot 5 \cdot x$ for some $x \in{\mathbb{Z}}$ which is equivalent to n mod 15 = 0

A: We're allowed to do this only if the moduli in question are coprime numbers. This has been proved by the Chinese Remainder Theorem.
If you're interested on why it doesn't work for numbers which aren't coprime, you can make use of the Fundamental Theorem of Finite Abelian Group, which tells us that $\mathbb{Z}_{pq} \cong  \mathbb{Z}_p \oplus \mathbb{Z}_q$, iff $(p,q) = 1$


text:
Latest in Royal Enfield
Royal Enfield Rumbler 350 launched in Australia
Royal Enfield exports the Interceptor 650 and the Continental GT 650 to Australia
Royal Enfield Thunderbird X launched at Rs.1.56 lakh
2018 Royal Enfield Thunderbird 500X, 350X launch on Feb 28
Royal Enfield Thunderbird 500X and 350X launching on February 22
Royal Enfield Classic 500 Stealth Black limited edition launched at Rs. 1.90 lakh
A company backed by Nest co-founder Tony Fadell is taking Andy Rubin's startup to court.
Arun Chandrasekharan
13 Dec, 2017 in Royal Enfield
Royal Enfield has launched the limited edition Stealth Black Classic 500 at a sticker price of Rs.1.90 Lakhs (Ex. Showroom) in the country. They will be limited to just 15 units while being sold via a unique online sale. These motorcycles were a part of National Security Guards' Motorcycle Expedition 'Fight against Terror' ride in September 2017. The sale will go online on December 13th 2017 on www.royalenfield.com/bravehearts, wherein interested buyers can register themselves and express their interest starting December 8th 2017.
Covering over 8000-kms crossways the breadth and length of India on these motorcycles, 15 Brave heart Black Cat NSG Commandos spread the message of collective duty towards fighting terror among citizens. This NSG motorcycle expedition also commemorated the NSG's 33 years of service to the nation. Flagged off on 07th September 2017 by Mr. Kiren Rijiju, Union Minister of State for Home Affairs of India, 15 Black Cat commandos of NSG rode through NSGs Mumbai, Kolkata, Hyderabad, Chennai and Gandhinagar bases and culminated their expedition on 16th October 2017 at the NSG headquarters in Manesar, Haryana, wherein they were felicitated by the Vice President of India – Shri Venkaiah Naidu.
Royal Enfield limited edition Stealth Black Classic 500 motorcycles would come decorated with a unique NSG insignia, which is commemorative of the ride and the journey undertaken by the commandos across India. The Classic Stealth black 500-cc is the latest color variant of the best-selling Classic franchise which is equipped with both rear and front disc brakes. For those asking, on the sale day, users need to login to the website and proceed to make a payment of Rs.15, 000 to book their motorcycle of choice. The whole proceeds from the sale of these 15 motorcycles will go to Prerna, a not-for-profit initiative held by NSG for differently abled kids. The Classic 500 is one of the most successful products from Royal Enfield's fleet in the mid-size motorcycle segment in India.
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New Records Available To Search This Findmypast Friday, 24 May 2019
I received this information from Findmypast today:
New Records Available To Search This Findmypast Friday
There a more than 58 million new records and newspaper articles available to search this Findmypast Friday, including:
Britain, Physicians and Surgeons, 1830-1923
Search for your English ancestry in thousands of pages from the Calendar of The Royal College of Surgeons in England and Members of The Royal College of Physicians. Containing over 31,000 names, these publications will provide you with your ancestor's residence and years of appointment.
The Royal College of Physicians (RCP) is a professional body founded in 1518, which promotes the best health and healthcare for all and has played a pivotal role in raising standards. It is the oldest medical college in England. For the first four centuries, women were excluded from the RCP. A bylaw was passed in 1909 allowing women to take examinations. Within the records, you can find the name Helen MacKay, the first female fellow.
Prisoners of War 1715-1945
Over 876,000 additional records created by the International Committee of the Red Cross during the First World War have been added to our collection of Prisoner of War records. Between 1914 and 1918, all belligerent countries involved provided lists of prisoners to the ICRC, which created an index card for each prisoner and detainee.
The records in this collection are diverse and varied and comprise original source material provided by The National Archives, as well as transcript only records from other sources. These records not only include military personnel but also civilians, diplomats, missionaries and merchant seamen.
British Armed Forces, First World War Soldiers' Medical Records
Over 85,000 additional records have also been added to our collection of First World War Soldiers' Medical Records. Including both transcripts and images of original documents, these records will enable you to discover when and where your ancestor was wounded, the nature of their disease or wound, the medical facility they were sent to and the dates of their treatment as well as details pertaining to their military career.
This collection comprises The National Archives' series, MH106, War Office: First World War Representative Medical Records of Servicemen. The records include admissions and discharge records from hospitals, field ambulances, and casualty clearing stations. You will also find records from Queen Alexandra's Military Hospital before the First World War, dating from 1910.
British Armed Forces and Overseas Browse
Browse through more than 85,000 additional records from The National Archives related to births, marriages, and deaths of British civilians and members of the armed forces. The records include individuals who were working or travelling abroad or who were serving their countries overseas. The details found in each record will depend on the original source.
Canada, Ontario, Oddfellows Life Insurance Applications images
Images have now been added to the index of Ontario, Oddfellows Life Insurance Applications we published last week. These two page documents will reveal a range of additional information including marital status, membership details, medial history, the ages, state of health (if living) or cause of death of parents and siblings, the names of next of kin and physical descriptions.
International Records Update – Germany
Over 57 million German births, baptisms, marriages and burials are now available to search and explore on Findmypast. Consisting of three new indexes covering the years 1558 to 1958, these new additions will generate hints against your Findmypast family tree.
British & Irish Newspaper Update
This week we have added 57,277 new pages to our collection of historical British & Irish newspapers. We are excited to welcome specialist sporting title – the Football Post (Nottingham) – to our collection, with 1069 issues added so far. We have also updated five of our existing titles, including three of our London titles – the Harrow Leader, the Ealing Leader and the Hayes & Harlington Gazette – as well as the Reading Evening Post and the Buckinghamshire Examiner.
Disclosure: I have a complimentary subscription to Findmypast, and have accepted meals and services from Findmypast, as a Findmypast Ambassador. This has not affected my objectivity relative to Findmypast and its products.
The URL for this post is: https://www.geneamusings.com/2019/05/new-records-available-to-search-this_24.html
Please comment on this post on the website by clicking the URL above and then the "Comments" link at the bottom of each post. Share it on Twitter, Facebook, or Pinterest using the icons below. Or contact me by email at randy.seaver@gmail.com.
Labels: FindMyPast, Online resources, UK/Ireland Resources
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