text:
\section{Introduction}\label{Intro}

Due to its proximity and high central surface brightness, the elliptical galaxy
M32 has often served as a unique testing ground for evaluating the modelling of
the integrated light of galaxies and thereby disentangling key aspects of the
star formation and chemical enrichment histories of galaxies.  In fact, M32 is
still the only elliptical galaxy for which it is possible to obtain both
integrated light spectroscopy and an extensive CMD of the giant branch (using {\it HST}) at
the same location in the galaxy.  Thus it presents a powerful testing ground of
the reality of integrated light analyses of galaxies.  Unfortunately, M32
represents a rather special case elliptical, given its status as a low-mass
satellite galaxy to M31, its probable tidal truncation as a result of close
proximity to M31 (e.g., Bekki et~al.\  2001; Choi, Guhathakurta, \& Johnston 2002),
and its rare (cE) morphology.  Hence it is encouraging
that resolved star studies of the upper giant branch of
the more normal and massive elliptical galaxy NGC 3379 have been pursued
recently by Gregg et~al.\  (2004).  Given its proximity, however, M32 remains the
ideal galaxy for testing inferences from integrated light spectroscopy and
broadband colors against resolved star observations.

In the context of constraining galaxy formation scenarios, determining radial
population gradients in elliptical galaxies can play a key role.  Specifically,
the predicted gradient in metallicity is substantially flatter in the case
of a hierarchical structure formation picture than it is for a monolithic
collapse scenario (e.g., Kobayashi \& Arimoto 1999).  Due to the high
surface brightness of M32, one can readily study the integrated spectrum
out to a radial distance of 30\char'175 , or 1 effective radius, R$_e$.  However,
previous studies of radial color and line strength gradients in M32 have led
to strikingly discordant results.  On the one hand,
Peletier (1993) finds that all colors, as well as the CO index, remain constant
with radius, and concludes that no age gradient exists in M32.  Moreover,
in {\it HST}
images of the central regions of M32, Lauer et~al.\  (1998),
find no gradient in V$-$I color, and only a very small blueing in U$-$V
with increasing radius.  In addition, {\it some} individual spectral features
exhibit no signs of a radial gradient in line strength.  Specifically,
both the Mg$_2$ index (Davidge 1991) and Mg~$b$ index (Gonz\'alez 1993; Fisher, Franx, \& Illingworth 1995)
appear to be constant with radius, as is Fe5015 (Fisher, Franx, \& Illingworth 1995).
There is, however, considerable uncertainty concerning the flatness of the
Mg$_2$ radial profile, since Hardy et~al.\  (1994) report a decline in this
index with radius out to a distance of 60\char'175 , or approximately 2 effective
radii, $R_e$.

On the other hand,
Cohen (1979), Davidge, de Robertis, \& Yee (1990), and Davidge (1991) have
found radial line strength gradients
in a number of spectral features, as have Fisher, Franx, \& Illingworth (1995) for the
$\lambda$4668 feature.  The long-slit data of Gonz\'alez (1993), as reported in
Fisher, Franx, \& Illingworth (1995; cf., their Fig. 9), indicates a decrease in H$\beta$
strength with increasing radius. However,
Hardy et~al.\  (1994) find a flat profile in H$\beta$ out to 60\char'175\  in radius.
In addition, neither Fisher, Franx, \& Illingworth (1995) nor del Burgo et~al.\
(2001) find a radial trend in H$\beta$, although the latter two studies reach
only to 20\char'175\  and 15\char'175\  respectively.  In addition, Ohl et~al.\  (1998) have
found a strong far-UV (FUV) (1500\AA) color gradient in M32, such that the
FUV$-$B color becomes  bluer at increasing radial distance, which is the reverse
of the other early-type galaxies that they studied. Ohl et~al.\  speculate that the
FUV gradient in M32 could be due to increasing age with radius, but also mention
the possibility of a varying helium abundance.  Such a UV color gradient,
however, has {\it not} been found in recent GALEX observations (Gil de Paz et~al.\
2003).
As summarized by Davidge (1991), although there is considerable disagreement
between investigators about the reality of line strength gradients in many (if not
most) features, a consistent interpretation of both line strength and color
behavior can be found if there is a radial gradient in M32 in both age and
chemical composition, in the sense that the age increases with radial distance
while the metallicity decreases.

The most comprehensive study to date of the resolved stellar population of M32
has been carried out by Grillmair et~al.\  (1996), who
resolved individual stars down to slightly below the level of the horizontal
branch (HB) with {\it HST} WFPC2. The
observations cover an area at a radius of $\sim$1$-$2\char'023  ($\sim$2$-$4 $R_e$), with the PC chip field
centered at 58\char'175\  from the nucleus.  Grillmair et~al.\  (1996) find a large
spread in metallicity among the giant branch stars, although the
spread is less than that predicted in the simple closed box model of Searle \&
Sargent (1972).  The peak in the metallicity distribution appears to be near
solar, with a metal-weak tail extending to below [Fe/H]=$-$1.
A mean iron abundance of [Fe/H]=$-$0.25 is derived for an assumed
mean age of 8.5 Gyr, which is consistent with the results
inferred from modeling of the integrated
light indices of Gonz\'alez (1993), extrapolated out to the radius of the PC
chip.  In contrast, integrated light studies of the nucleus of M32 typically
indicate a mean age of $\sim$3$-$7 Gyr and [Fe/H]$\sim$0.0 (e.g., Jones \&
Worthey 1995; Vazdekis \& Arimoto 1999; Trager et~al.\  2000; Worthey 2004;
Caldwell, Rose , \& Concannon 2003; Schiavon, Caldwell, \& Rose 2004).
A number of studies have been made in the past of the AGB-tip stars in M32,
first from ground-based optical and IR imaging in good seeing (Freedman 1989,
1992; Davidge \& Nieto 1992; Elston \& Silva 1992), and recently from adaptive
optics IR imaging from CFHT and Gemini-North by Davidge (2000) and Davidge et~al.\
(2000).  The earlier work found AGB-tip stars luminous enough to indicate the
presence of a substantial ($\sim$10$-$15\%) intermediate age population in M32,
while the adaptive optics studies have now pushed the same conclusion to a
radial distance of only 2\char'175 .  As reported by Davidge et~al.\  (2000), the
implication of this recent work is that an intermediate age population is
uniformly spread over at least the central 2\char'023\  of M32, with no evidence
for a radial age gradient.  On the other hand, {\it HST} near-UV imaging of M32
by Brown et~al.\  (1998) reveals that the resolved UV-bright stars are more
centrally concentrated than the underlying unresolved UV sources, which
indicates some type of radial population gradient.

It is clearly important to resolve the apparent discrepancy that exists between
color-based measurements and those based on individual absorption features
(as well as the implications of the resolved star imaging),
since many conclusions about the behavior of early-type galaxies are based on
colors alone (given that high S/N ratio long-slit spectroscopy is difficult to
obtain for distant galaxies).  If radial population gradients in
age and metallicity exist in M32, in approximate proportions so as to cancel
out the primary color effects that each alone causes, as the line strength
measurements suggest, then the interpretation of color gradients in more distant
galaxies could be problematic.  With that issue in mind,
we present integrated light spectroscopy for M32
out to a radial distance of $\sim$30\char'175\  ($\sim$1 $R_e$). While not far enough to overlap with
the {\it HST} CMD study of Grillmair et~al.\  (1996), a sufficient radial distance
from the nucleus is achieved to establish the existence of a significant radial
population gradient
in M32, and thereby to link the CMD study with the numerous integrated
light analyses of the nucleus.
The emphasis of our study is on decoupling age and metallicity
effects using measurements of several Balmer lines.

Here we combine long-slit spectroscopy from three telescope, spectrograph,
and detector combinations to evaluate the radial behavior of stellar populations
in M32.  The plan of the paper is as follows.  In \S 2 we describe the three
spectroscopic datasets, while the spectral indicators and populations
synthesis models employed are presented in \S 3.  In \S 4 we first establish
from two of the datasets that there is a small but significant radial change in
the light-weighted mean age and metallicity of M32 from the nucleus out to a
radial distance of 30\char'175 .  Then we demonstrate how scattered light from the
bright nucleus of M32 leads to an artificially strong apparent population
gradient in the third dataset.  Some implications of the observed age/metallicity
gradient are briefly considered in \S5.

\section{Observational Data}\label{data}

\subsection{Subaru + FOCAS}\label{Subaru}

Long-slit spectra have been obtained of the elliptical galaxy M32 with the
8-m Subaru telescope at Mauna Kea with the FOCAS imaging spectrograph
(Kashikawa et~al.\  2000).  All spectra were obtained on the night of January 27,
2003.  The
spectra are imaged onto a 2K X 4K MIT CCD with 15 $\mu$ pixels, and binned
by a factor of two in the spatial direction, to achieve 0.2\char'175 /pixel.  A
slit width of 0.6\char'175\  was used, and the spectra cover the wavelength region
3960 $-$ 5560~\AA \ at a dispersion of 0.655 \AA/pixel, and a spectral
resolution of 93 ~km~s$^{-1}$\ , or $\sim$3.1~\AA \ FWHM at 4200~\AA..  The slit was oriented
at a position angle of 80$^{\circ}$ E of N for all observations, which is only
10$^{\circ}$ from the minor axis, at $\sim$70$^{\circ}$ E of N (Tonry
1984; Kent 1987 both report the PA of the major axis of M32 to be
$\sim$$-$20$^{\circ}$ E of N).

The following exposures have been acquired.  First, two 300 second exposures were
made with the slit centered on the nucleus of M32.  Then, a series of three 900 second
exposures were made with the slit offset by 10\char'175\  from the nucleus, to moderate
scattered light from the nucleus for analysis of the fainter outer region of M32.
In addition, a
900 second sky exposure was taken at a position offset by 6\char'023\  East from
the nucleus of M32.  Note that the precise locations and PA of
the slit for both the M32 and sky exposures is critical here, since we found
from both these, and earlier, observations that the slit can intersect one or
more planetary nebulae (PN) in M32 and/or a faint HII region in the outer disk
of M31.  We indeed find that our slit position centered on the nucleus of M32
intersects two PN that are $\sim$8 and 9.5\char'175\  along the slit to the NE,
specifically, PN \#24 and \#25 in Table 6 of Ciardullo et~al.\  (1989).

Data reduction was carried out mainly with IRAF packages in the standard way for
long slit data; i.e. overscan correction, bias subtraction, flat fielding,
$\lambda$ calibration, sky subtraction and flux calibration.
Cosmic rays were removed and interpolated by using the ``cleanest'' task
in the REDUCEME package (Cardiel et al. 1998). We initially ran automatic
finding with the following parameters: SIGTHRESHOLD=6.0 in Searching Square=15.
We took care to avoid mis-identification of CRs around the peak of flux in the
spatial direction. Then we checked by eye in three-dimensional surface plots of
flux versus position on the CCD frame and edited out CRs found that way.
Since CRs can strongly affect the narrowly defined
H$\gamma_{\sigma<130}$ measurement, we checked whether
CRs exist around  the H$\gamma$ feature. Fortunately we found no CR within
the passbands of the H$\gamma_\sigma$ index.

\subsection{Mt. Hopkins 1.5-m + FAST Spectrograph}\label{FAST}

Long-slit spectra of M32 have also been obtained with the FAST spectrograph
(Fabricant et~al.\  1998) on the 1.5m Tillinghast telescope of the Whipple Observatory, during the
night of 27 December 2002.  A 600 gpm
grating was used with a 3\char'175\  slit, which gave a spectral coverage of from 3600 to
5500 \AA, at a resolution of 3.1 \AA \ FWHM, and a dispersion of 0.75 \AA/pixel on
the Loral 3K X 1K CCD.  The pixel scale along the slit is 0.57\char'175\  per
15$\micron$m pixel; however, the data were binned by 4 pixels along the slit,
to reduce the effective read noise in the outer low surface brightness regions
of M32. The detector has a read noise of 8.6 e$^-$ and a gain of
1.2 e$^-$/ADU.  A 300 second exposure was taken with the slit centered on the
nucleus of M32, at a PA of $-$20 E of N, i.e., with the slit aligned on the major
axis of the galaxy.  Then the telescope was moved sufficiently in Right
Ascension (RA) so as to move the slit 5\char'175\  off the center of M32, and
a 900 second exposure was taken.
Next, two 900 second exposures were taken with the
slit offset by 15\char'175\  from the center of M32, again with the repositioning
done in RA only.  These were sandwiched around a 900 second sky
exposure, with the slit offset by 10\char'023\  due South of the center of M32.
Finally, a series of seven 900 second exposures were taken with the slit offset
by 30\char'175\  from the center of M32.  Again the offset was made in RA,
specifically, 2.9 seconds, which results in the slit being displaced by 30\char'175\
from the center of M32.
Three more sky exposures and four arc lamp exposures were interspersed with
these exposures, to provide reliable background subtraction and wavelength
calibration.  Two of the sky exposures were offset by 15\char'023\  due South, while
the third was offset by only 10\char'023 .  Given the major axis orientation of the
Tillinghast/FAST slit and the near-minor axis orientation of the Subaru slit, we have
sampled both principal axes of M32.

In additon to the above observations, we make use of a series of eight 4-minute
exposures on the nucleus of M32 taken on 28 December 2000 with the same instrument
configuration as above.  The sole difference is that binning along the slit
direction was 3 pixels instead of 4 pixels per bin.  The total 32 minutes
integration provides superior S/N compared to the 5-minute nuclear exposure
on 27 December 2002, and the splitting of the integration into eight separate
exposures provides added information on errors in the spectral indices.

The Tillinghast/FAST spectra were processed as follows.  After bias-removal and flat-fielding, the
next step was cosmic ray (CR) removal.  For the 15\char'175\  and 30\char'175\  offset spectra,
the procedure is as follows.  A difference frame was created between two
individual exposures, a and b, with the difference frame given by a$-$b.
In this difference frame, all pixels with counts below $-$100 were
flagged, and replaced with a 0, while all other pixels were set equal to 1.  Thus we
produce a mask frame with CRs flagged as zeros.  Then we ran a program that extends each
of the masked pixels by 1 pixel in each direction, to fully mask the wings of CRs.  Using
this revised mask file, the IRAF {\em fixpix} routine was run on frame b, to interpolate
over the pixels contaminated by CRs.  This produced a CR-cleaned version of frame b.
To clean frame a, a b$-$a difference frame was created, and then the same procedure employed.
Using this technique, all frames were cleaned of CRs, except for the single short exposure
centered on the nucleus of M32, and the 5\char'175\  offset exposure.  The same procedure was
followed to clean the sky frames of CRs.

The next step was to carry out sky subtraction.  We found that the arc lamp exposures did
not show zero point shifts greater than 0.3 pixels over the course of the M32 observations.
Consequently, we felt safe in directly subtracting the nearest sky exposure in UT to a
given M32 exposure, which simplifies matters.  We then extracted one-dimensional
spectra from the two-dimensional sky-subtracted, CR-cleaned data frames using
the IRAF {\em apall} task.  An aperture is defined, a trace is made of the
variation in the slit position of the aperture as a function of the
dispersion direction, and then the one-dimensional extraction is made based
on the trace.  Wavelength calibration was supplied by the nearest (in time) arc
exposures.

\subsection{KPNO 4-m + R-C Spectrograph}\label{Mayall}

Long-slit spectra of M32 were acquired with the Kitt Peak National Observatory
(KPNO) 4-m Mayall telescope by Dr. Lewis Jones, as part of his PhD
thesis (cf., Jones 1999), on the nights of June 18-20, 1996.  The standard
R-C spectrograph was used along with a 632 grooves/mm grating KPC-22B, in
second order, producing a dispersion of 0.7 \AA/pixel and a resolution of
1.8 \AA \ FWHM on the TK2B 2048$^2$ CCD detector.  The wavelength range covered
is 3300 \AA \ $-$ 4770 \AA.  The detector read noise and gain are 4 e$^-$ and
2 e$^-$/ADU respectively.  The full 5\char'023\  slit is covered at a scale of
0.69\char'175 /pixel; the slit width was 300 $\mu$m, or 2\char'175 .  Due to the late
rising of M32, and the desire to observe it at a minimum air mass, the
following strategy was used.  On each of the
three nights of observation, two 1800 second
exposures were taken of M32 at the end of the night, preceded by an 1800 second
sky exposure.  The sky exposure was taken at a Right Ascension that matched
the mean airmass of the
M32 observations.  However, on the first two nights the last M32 exposure
extended far enough into the dawn twilight that the background level was
substantially elevated; the M32 exposures were taken earlier on the third night,
and did not suffer from this problem.  We consequently have not used the last
M32 exposures on the first and second nights.
Thus a total of 2 useful hours of integration on M32 was obtained
through 4 individual exposures, and 1.5 hours of sky observation in three
exposures.  On each night the slit was rotated to the parallactic angle
corresponding to the middle of the M32 observations.  The positon angle was
at 102\arcdeg, 100\arcdeg, and 155\arcdeg, respectively, for the first,
second, and third nights.  The position angle for the third night is,
coincidentally, within a few degrees of the major axis of M32.

Analysis of the above spectra was carried out in the NOAO IRAF software
package.  After initial trimming, bias-removal, and flat-fielding,
the next step was to clean the numerous CRs from the individual
sky exposures.  This was done in a two-step process.  First, the IRAF routine
'cosmicrays' was run, with the following parameters:
Threshold= 10.0, fluxratio=  5.00, window=7, npasses=5.  This approach removed
a majority of the CRs, but still left an unacceptable number in the
images.  Further lowering of the threshold for CR removal led to
removal of high points which are not CRs.  Instead, as a second step,
the 'median' routine was run, using a 1 x 10 median filter, with the large
binning factor oriented parallel to the slit.  This step is successful
at removing the remaining CRs, except for a few pathological cases which are
extended right along the slit direction.  The CR-cleaned sky exposures were
then directly subtracted from the two M32 exposures from the particular night.

The next step involved removing the remaining CRs from the four individual
sky-subtracted M32 exposures.  In addition, the data
frames needed to be transformed into a coordinate system in which the
slit axis and dispersion axis are orthogonal and oriented along columns and
rows.  The CRs were cleaned from the sky-subtracted M32 frames using the
same technique as described earlier for the FAST spectrograph data.  That is,
CRs were identified and eliminated from difference images between two
exposures.
A problem with this procedure is that the counts in the few
central rows of the M32 spectra are very high, and do not reproduce well from
one exposure to another.  Thus many pixels in the central few rows are flagged.
To avoid losing all information in the cenral few rows, all of the flagged
pixels were subsequently reset to avoid interpolation.  As a result, there
is the possibility of badly positioned CRs to produce contamination in the
inner spectral indices.  We did, in fact, detect an instance of such a
contaminated spectral index, and recalculated it without the frame
which contains the CR hit.
Note that we could use the second M32 exposures on the first and second nights
for the CR-cleaning purpose, since their backgrounds were only mildly elevated.

Following CR-removal, the four sky-subtracted M32 frames were
transformed into a coordinate system in which the slit axis and dispersion axis
are orthogonal and oriented directly along columns and rows.
The transformation was carried out using the 'fitcoords' routine in
IRAF.  Then all four frames were averaged into a sky-subtracted
wavelength-calibrated frame.  Note that this composite M32 long-slit
spectrum consists of two exposures at PA=101\arcdeg and two at PA=155\arcdeg.
Hence the final long-slit spectrum represents a crude azimuthal average of
the spectral behavior of M32.  From this final averaged M32 frame
spectra were extracted at various slit positions, and flux-calibrated using the
flux-calibrated spectrum of the nuclear region of M32 from L. Jones's (1999)
PhD thesis.

\subsection{Extraction of Spectra}\label{extract}

One-dimensional spectra were extracted from the two-dimensional data frames
using the IRAF `aptrace' routine to trace the deviation of the M32 spectra
from an idealized spectrum oriented strictly along the CCD rows.   In
performing the extraction (in the 'apall' routine) we used unweighted
extraction (as opposed to variance-weighted), since all CRs had been
identified and removed by this point.  To determine the light-weighted mean
radius of each extracted spectrum, we numerically integrated a radius-weighted
de Vaucouleurs r$^{1/4}$ surface brightness profile (de Vaucouleurs 1948)
over the extracted length
and width of the slit.  Following Kent (1987) we assumed a mean
ellipticity of 0.17 for M32, and effective radii along the major and minor axes
of 35\char'175\  and 29\char'175\  respectively.  Given that the Tillinghast/FAST data were taken with
the slit aligned parallel to the major axis of M32, the extractions out to a
light-weighted radius of $\sim$39\char'175\  correspond to $\sim$1.3 R$_e$ along the
minor axis. The Subaru slit was positioned very close to the minor axis, and
the data samples out to 30\char'175 , or 0.9 R$_e$, along the major axis.  A journal
of observations, specifying the PAs and locations of the various extractions,
is given in Table \ref{tab:journal}.

\subsection{Spectral Resolution}\label{resolution}

To make a consistent set of measurements of the spectral
indicators described in \S\ref{resolution}, it is necessary to carefully match the
spectral resolution at all positions along the M32 slit, and to determine
the radial velocity at each extracted slit position.  Resolution
variations along the slit can be due either to variation in the internal
velocity dispersion from the center outwards in the galaxy or to variations
in the spectrograph image quality. While velocity broadening produces an
effective resolution change that is contant in $\delta\lambda$/$\lambda$,
spectrograph image quality may vary in a complex manner both along
the slit and along the dispersion axis.  In what follows, we have
assumed that velocity broadening provides the dominant contribution to
variations in spectral resolution along the slit.

The degree of velocity broadening for the M32 spectra extracted at various
slit positions was determined by cross-correlation with a
template spectrum, using the IRAF 'fxcor' task in the 'rv' package.
The template is a model spectrum for a 3.55 Gyr solar abundance population from
Vazdekis (1999 and available at the URL
http://www.iac.es/galeria/vazdekis/vazdekis\_models.html).  This model spectrum
is created from a composite of
various stellar spectra in the Jones Coud\'e Feed Spectral Library, which is
available in the NOAO ftp archive (see below in \S\ref{otherdata}).  The
resolution of the stellar spectra, and thus of our model template,
is 1.8 \AA \ FWHM.  This is different from the 3.1 \AA \ resolution typical
of our M32 observations.  The fxcor task
returns a measure of the FWHM of the cross-correlation peak.  To calibrate
this parameter, the template spectrum was Gaussian-smoothed by varying
$\sigma$'s and cross-correlated against the original unsmoothed spectrum.
The restricted wavelength region of $\lambda$$\lambda$4000 $-$ 4400 \AA \ was
used, thereby avoiding the Ca II H and K lines.  A fit
was made to the width parameter versus smoothing $\sigma$, in all cases by
making a 9-point Gaussian fit to the cross-correlation peak.  From a cubic
fit to peak width versus $\sigma$, a correspondence
between the two quantities was established.  Using
this calibration procedure, all of the extracted spectra of M32 at different
locations along the slit were smoothed to the same final spectral resolution.
Specifically, all extracted spectra were smoothed to a final Gaussian $\sigma$
of 130 ~km~s$^{-1}$\ , which is in quadrature with the original 1.8 \AA \ FWHM of the
template spectrum.  Thus the final spectral resolution is equivalent to
4.75 \AA \ at $\sim$4300 \AA.

\subsection{Other Observational Data}\label{otherdata}

In addition to the M32 long-slit spectra described above, we use two other
sources of data.  First, we use an integrated spectrum of the metal-rich
Galactic globular cluster 47 Tuc obtained by A. Leonardi and J. Rose with
the CTIO 1.5-m telescope in November 1995.  An integrated spectrum of the
nucleus of M32 was also acquired with the same equipment on the same night, as
M32 transited the meridian, with the slit rotated to the parallactic N-S
position angle.  The characteristics of these spectra, which have a
resolution of 3.1 \AA \ FWHM, are described in Leonardi \& Rose (2003).
Hence a direct comparison is made between M32 and 47 Tuc with
the identical instrument setup, and can thus be tied in to the long-slit M32
data.

Second, we make use of two extensive libraries of stellar spectra
obtained with the coud\'e feed telescope at KPNO.  The first library, of 684 stellar
spectra, is publicly available at an NOAO FTP site
(ftp://ftp.noao.edu/catalogs/coudelib/).  The characteristics of
the spectra are decribed in Jones (1999) and in the readme file at the
website.  In brief, the spectra were acquired at 1.8 \AA \ resolution (FWHM),
and cover two wavelength intervals, 3820 $-$ 4500 \AA \ and 4780 $-$ 5460 \AA.
We hereafter refer to this spectral database as the Jones Coud\'e Feed
Spectral Library (JCFSL).

The JCFSL spectra, as well as the M32 spectra and the 47 Tuc
integrated spectrum, have been smoothed to the lowest spectral resolution of
3.1 \AA \ FWHM set by the CTIO 1.5-m 47 Tuc data.  In the case of the JCFSL,
for which resolution differences are due to spectrograph resolution rather than
velocity broadening, a gaussian smoothing by a $\sigma$ of 1.75 pixels in linear
wavelength is necesary to attain the resolution of the 47 Tuc integrated
spectrum.

The second spectral library, which became available while work for this paper
was in progress, is the more extensive Indo-US Library of Coud\'e Feed Stellar
Spectra (hereafter, IUCFSL), which includes 1273, covered at a spectral
resolution of $\sim$1.2 \AA  \ FWHM. For most stars the entire region 3460 $-$
9464 \AA \ is covered.  The characteristics of this library, which is also
publicly available at an NOAO website (http://www.noao.edu/cflib/), are
discussed in Valdes et~al.\  (2004).  For these spectra, a correspondingly higher
level of smoothing is required to attain the overall resolution of our M32 data.

Finally, to obtain a well-defined zero-point velocity determination, the radial
velocity for each of the extracted M32 spectra, and the 47 Tuc spectrum, was
determined using as template a population model spectrum based on a weighted composite of
JCFSL stars.  The method of producing the model spectrum, which has an age of
4 Gyr and solar chemical composition, is discussed in \S\ref{models}.

\section{Spectral Indices and Population Models}\label{indmod}

\subsection{Spectral Indices}\label{sect:indices}

In this section we characterize the different types of spectral indices used
in our study.  Since these spectral indicators are all discussed extensively
elsewhere in the literature, we simply give brief summaries of their principal
characteristics and refer the reader to other sources for a more extensive
description.

There are a number of possible ways to isolate and measure an individual
spectral feature.  Here we rely on three different methods, which each have
particular advantages depending on the degree of line crowding, spectral
resolution used, and importance of spectral resolution effects.  The first
type of measurement, which we refer to here as narrow-band equivalent width
indices, are the most familiar and have been widely used in the Lick system
of spectral indicators (e.g., Burstein et~al.\  1984; Worthey et~al.\  1994).  These
Lick equivalent width indices place a bandpass of typically 30$-$40 \AA \
(although some of the bluer indices have narrower bandpasses)
centered on a particular spectral feature, and then use bandpasses of similar
width on either side of the feature to provide a pseudo-continuum reference.
Due to their relatively broad width, the pseudo-continuum bandpasses often
contain fairly strong absorption lines.  The
second system of measurements, which have been primarily developed in
Rose (1984; 1994), measure the relative depth of two neighboring features
without reference to the continuum.  This is accomplished by measuring the
residual central intensities in the two neighboring absorption lines, and
forming their ratio.  Alternatively, a similar type of ratio can be measured
by using two neighboring pseudo-continuum peaks in the spectrum.  The term
``pseudo-continuum'' is employed here to emphasize that for integrated spectra
of galaxies, the true continuum is rarely measured; instead a local peak is
measured that comes closest to the true continuum value.  We refer to these
measurements as line ratio indices.  A third set of measurements involve
isolating the pseudo-continuum peaks on either side of the absorption feature of
interest, and then directly measuring a pseudo-equivalent width.  These
pseudo-continuum peaks, which are apparently free of absorption lines, at the
spectral resolutions typical of galaxy integrated spectroscopy, are defined
either by using the pixel with the highest counts as the local pseudo-continuum
peak or with an extremely narrow bandpass.  In this paper we make particular use
of this approach to isolate the H$\gamma$ absorption feature.  Variants of this
approach have been defined by Rose (1994), Jones \& Worthey (1995),
Vazdekis \& Arimoto (1999), and Vazdekis et~al.\  (2001b).  In the latter two
references, great care has been taken to minimize the effect of spectral
resolution on the index, which is a major problem for this kind of index
(i.e., a pseudo-equivalent width is highly sensitive to slight changes in spectral
resolution).  In Vazdekis et~al.\  (2001b), the metallicity sensitivity of the
index is reduced as well, by partially covering the neighboring metallic line
centered on $\lambda$ 4352 \AA.  This newest refinement on measuring the
strength of H$\gamma$ is referred to as the  H$\gamma_{\sigma<130}$ index.

\subsubsection{Errors in Spectral Indices}\label{errors}

Errors in the observed spectral indices can arise from limitations in
photon statistics, read noise, and flat field accuracy as well as from
systematics of subtracting the sky background.  The optimal means of assessing
the random errors in spectral indices is from the scatter in values in repeat
observations.  For the nucleus of M32 we have eight 4-minute exposures, and
thus can establish a robust determination of the standard error in the mean
index from the rms scatter.  Outside the nucleus, for each extraction at a
different radial distance we have divided the long-slit
observations into two non-overlapping regions on either side of the peak in the
light profile.
We have then computed
the rms scatter in each spectral index from the pairs of observations on
opposite sides of the nucleus of M32 at the various radial positions.  Thus for
each index we have an assessment of the random errors at each slit position
outside the nucleus from the scatter in only two independent measurements.
Hence, the error for a particular index at a
particular radial position has a considerable uncertainty from the above
approach.  Alternatively, we have computed the errors in spectral indices on the
basis of pure photon statistics and read noise in the CCD.  While this
approach is far more reliable statistically, it provides a less
comprehensive assessment of total uncertainties in the measurements.
Fortunately, we find that on average the photon statistical errors are
generally consistent with the observed scatter from the paired observations.
As a result, the $\pm$1$\sigma$ errors on spectral indices cited
in Tables~\ref{tab:Subaru} and \ref{tab:FAST} are
the more statistically secure errors derived from photon statistics.

We also calculated the potential effect of errors produced by uncertainties in
the background subtraction.
All data reduction procedures as described above were repeated with the sky
exposures both enhanced and reduced by 10\%.  The spectral indices were
recalculated with the modified sky background subtraction, and the rms scatter
between the results obtained with enhanced and reduced sky values was
calculated for each index.  The result is that even for the largest off-nuclear
radial position,
the average error introduced by mis-subtraction of sky is significantly less
than the errors from photon statistics.
Thus, even at the furthest radial position, and with a
generous evaluation of the sky background uncertainty, the errors from uncertain
sky removal are considerably less than the random errors.  At smaller radial
distances, the sky errors will clearly be of even less significance.  The one
serious problem involved with background subtraction occurs if the slit for
the ``sky'' exposure or for the M32 exposure intersects a faint HII region in
the disk of M31 an/or
a planetary nebula in M32 or M31.  The result is contamination of the Balmer
lines with emission.  We have in fact mentioned such problems, both on the
central Subaru slit (two PNe on the slit) and on a
Tillinghast/FAST background exposure.

Data on the spectral indices and their errors for the different radial slit
positions in M32 are listed in Table \ref{tab:Subaru} for the Subaru/FOCAS
data and in Table \ref{tab:FAST} for the Tillinghast/FAST data.

\subsection{Population Synthesis Methods}\label{models}

A comparison of the observed index strengths to those predicted by
stellar population synthesis models allow us to make a quantitative
statement on the radial age/metallicity changes in M32. The most popular
approach followed by these models is to predict the strengths of
the strongest absorption features in galaxy spectra (Worthey 1994;
Vazdekis et al. 1996). These models make use of polynomial fitting
functions which relate the strengths of these features to stellar
atmospheric parameters (i.e., T$_{eff}$, log~g, and [Fe/H]) on the
basis of the Lick/IDS stellar spectral library (Gorgas et al. 1993;
Worthey et al. 1994).
A number of shortcomings of this approach prevent us from fully exploiting the
information present in the high quality spectra of M32.
Among these problems is the fact that the spectral resolution of these models
(FWHM$>$8.5~\AA) is much lower than that intrinsic to M32. Moreover, the bluer
the wavelength the lower the resolution (e.g., FWHM$\sim$11.5~\AA\ for
$\lambda\sim$4000~\AA) (see Worthey \& Ottaviani 1997). Also, the fact that
the Lick/IDS stellar library was not flux-calibrated forces us to transform
our data to the Lick/IDS instrumental response curve to be able to compare
the model predictions with the measured line-strengths. In addition,
since these models only predict a specified number of spectral indices
rather than the full spectra, we would be throwing away much of the
information present in the M32 spectra, which is contained in the weaker
spectral lines.

A further step in the modelling has been recently achieved by synthesizing
full spectral energy distributions (SEDs) for old-age single burst stellar
populations (SSPs) at a spectral resolution with FWHM=1.8\AA~(Vazdekis 1999;
Schiavon, Barbuy, \& Bruzual 2000;
Schiavon 2004) and flux-calibrated response. These newly developed models
are based on the JCFSL, i.e., the extensive empirical stellar spectral library of
Jones (1999) that we have described above.
This new approach (see also Bruzual \& Charlot 2003) allows us to analyze a
galaxy spectrum at a spectral
resolution limited only by its dynamics (i.e., its velocity dispersion,
to which the model spectra should be smoothed). Thus, all the indices
described in \S\ref{sect:indices} can be measured directly on the model SEDs.
It is worth recalling that, thereafter, when we refer to the Lick indices
we are not meaning those indices predicted by the previous models
(with the specific instrumental response curve and resolutions of the
Lick/IDS system), but we use the Lick index definitions for measuring
these indices on the smoothed model SEDs (i.e., with flux-calibrated
response and the resolution of M32).

In this paper we make use of two sets of models that differ in their
essential ingredients. Whereas those of Vazdekis (1999) (as recently
updated in Vazdekis et~al.\  2003) make use of the latest version of the
Padua isochrones (Girardi et al. 2000), that of Schiavon (2004) uses
the same isochrones and a new set of fitting functions to Lick/IDS
indices.  Furthermore, Vazdekis (1999) transforms the theoretical
parameters of these isochrones to the observational plane following
empirical stellar libraries such as those of Alonso, Arribas, \&
Martinez-Roger (1996,1999) whereas Schiavon (2004) adopts the same
calibrations for F, G and K stars, and calibrations by Westera
et al. (2002) for cooler and hotter stars.  All of these models make
use of scaled solar isochrones, thus do not directly model the non-solar
abundance ratios found below.

\section{Radial Population Trends in M32}

\subsection{Evidence for an Age and Metal-Abundance Gradient}

The central question of this paper is whether a population
gradient is present within the inner 30\char'175\  ($\sim$100 pc of M32.  We address this issue
in Figs.~\ref{fig:M32Sub} and \ref{fig:M32FAST}, where spectral index
data from the Subaru and Tillinghast/FAST observations, respectively, are plotted as a
function of radial distance from the nucleus of M32.  To best disentangle
age from metallicity effects,
we have plotted spectral indices that measure the primarily age
sensitive Balmer lines versus an index that primarily responds to
mean metallicity.  Specifically, in Figs.~\ref{fig:M32Sub} and
\ref{fig:M32FAST} the right hand panel is a plot of the Lick
H$\beta$ index versus the [MgFe] index, while the left panel is a plot of the
Vazdekis et~al.\  (2001b) H$\gamma_{\sigma<130}$ index versus the same metallicity
sensitive [MgFe] index.  The [MgFe] index is a composite of both Fe-dominated
absorption lines and the 5175 \AA \ feature of the $\alpha$-element Mg, as
defined in Gonz\'alez (1993; ${\rm[MgFe]} = \sqrt{Mg~b\times (Fe5270 + Fe5335)/2}$), thus providing an assessment of the overall heavy
element abundance.  In fact, Thomas, Maraston, \& Bender (2003) find it to
be such a good tracer of overall metallicity that it is essentially independent
of [$\alpha$/Fe] (see also Bruzual \& Charlot 2003; Vazdekis et~al.\  2001a).
In both plots we have included a grid of indices
based on the previously described single stellar population models of
Vazdekis (1999, and updated in Vazdekis et~al.\  2003) that cover
a range in age and [Fe/H].  The primarily horizontal lines connect models with
the same age while the primarily vertical lines connect models with the same
[Fe/H].

The main result of Figs.~\ref{fig:M32Sub} and \ref{fig:M32FAST} is that a small age
and metallicity trend does indeed exist within the central $\sim$30\char'175\  (1 $R_{e}$)
of M32, in
the sense that the age increases from the center outward while the metallicity
slightly decreases.  Specifically, from the Subaru data plotted in
Fig.~\ref{fig:M32Sub} it is evident that the light-weighted mean age
increases from $\sim$3$-$4 Gyr in the nucleus to $\sim$6$-$7 Gyr at $\sim$30\char'175\  radius,
while the light-weighted mean metallicity (as measured by [MgFe])
decreases from almost exactly solar in the nucleus to $\sim$$-$0.3 at
30\char'175 .  There is good agreement between the results obtained from the
H$\beta$ index and those from the H$\gamma_{\sigma<130}$ index.  The FAST
data, plotted in Fig.~\ref{fig:M32FAST}, provides similar results, particularly
with regard to the H$\beta$ versus [MgFe] plot.  The trend in
H$\gamma_{\sigma<130}$ versus [MgFe] is less convincing, likely due to the
lower S/N ratio of the Tillinghast/FAST data.

The overall trend in mean metallicity, as defined by [MgFe], can be further
refined to individual elements.  In Figs.~\ref{fig:M32Sub2}, \ref{fig:M32Sub3},
\ref{fig:M32Sub6}, and \ref{fig:M32Sub5} we plot the H$\beta$ and
H$\gamma_{\sigma<130}$ indices versus the Lick Fe3
(where Fe3 = (Fe4383+Fe5270+Fe5335)/3) , Mg~$b$, CN2, and G4300
indices, respectively, for the Subaru data.  Overall, the basic trend
of decreasing
metal abundance with increasing radius is apparent.  However, as has been
discussed in Schiavon et~al.\  (2004) and Worthey (2004), there are zero point
differences from one metal indicator to another with respect to the models
that indicate slight departures from a solar abundance ratio pattern in M32.
Specifically, the central values in M32 indicate that [Fe/H]$\sim$=+0.1 (as
seen in the Fe3 index in Fig.~\ref{fig:M32Sub2}), while [Mg/H]$\sim$=$-$0.1
(Fig.~\ref{fig:M32Sub3}), and the data for the CN2 index
(Fig.~\ref{fig:M32Sub6}) indicates that [C+N/H]$\sim$+0.1.  In
Fig.~\ref{fig:M32Sub5} the central value of the G-band, as characterized by the
G4300 index, implies that [C/H]$\sim$$-$0.2.  In addition, the size of the radial
gradient is different in some features, indicating that there is a radial
trend in abundance patterns as well.  We illustrate this fact in the case of
[Mg/Fe] by plotting the Mg~b index versus Fe3 in Fig.~\ref{fig:M32S6}.
The M32 nucleus is
clearly shifted from the grid of solar abundance ratio models in the plot,
in the sense that Mg~b is too weak for the given Fe line strength.  However, at
larger radial distances there is a systematic shift of the M32 data towards the
model grid, indicating that [Mg/Fe] outside the nucleus shifts closer to the
solar abundance ratio.  We quantify the shift in [Mg/Fe] using the following
procedure.  Since the Mg~$b$ index is dominated by Mg and the Fe3 index by Fe
(Tripicco \& Bell 1995), we can extract approximate abundances for [Mg/H]
and [Fe/H] from the respective indices.  Specifically, plots of Mg~$b$ versus
both H$\beta$ and H$\gamma_{\sigma<130}$ provide nearly orthogonal age versus
metallicity model grids, allowing for a convenient approximation of [Mg/H]
(cf., Fig.~\ref{fig:M32Sub3}).  Similarly, plots of Fe3 versus both
H$\beta$ and H$\gamma_{\sigma<130}$ provide an approximation of [Fe/H]
(cf., Fig.~\ref{fig:M32Sub2}).  From the two individual abundances we
then infer [Mg/Fe].  Taken at face value, we find an
increase in [Mg/Fe] from $-$0.25 in the center of M32 to $-$0.08 at 30\char'175\
radius.  Note that an alternative approach for obtaining the [Mg/Fe] ratios can
be followed using models specifically computed for different
$\alpha$-enhancements (e.g. Trager et al. 2000; Thomas et al. 2003), on the
basis of the sensitivities of these lines to the abundance changes of the
different species as tabulated in Tripicco \& Bell (1995).

The lower S/N ratio FAST data,
not plotted, shows essentially the same abundance patterns and trends as for
the Subaru data.  The slight
enhancement of Fe above solar, along with the underabundance of Mg
and overabundance of CN with respect to solar, have also been reported in
Schiavon et~al.\  (2004), based upon the same FAST data as used here, but
incorporating Schiavon's (2004) population synthesis models.

To further illustrate the changing absorption line strengths with radius, in
Fig.~\ref{fig:ratiospec} we have plotted the ratio between the spectrum at
$\sim$30\char'175\  and that in the nucleus.  As can be seen in the ratio spectrum,
all major spectral features, including Ca II H and K and the Balmer lines
H$\delta$, H$\gamma$, and H$\beta$, appear in emission, indicating that these
features are deeper in the nuclear spectrum, as is expected if the central
population of M32 is both older and more metal-rich than at 30\char'175 .  That is,
the smaller (in equivalent width) Balmer lines at larger radial distance
reflect an older age.

\subsection{Effect of Scattered Light on Observed Line Strength Gradients}

While the Subaru and Tillinghast/FAST data indicate only a very modest trend in age and
metal-abundance in the central 30\char'175\  of M32, the KPNO 4-m data present a
very different story.  In Fig.~\ref{fig:M32_4m} the KPNO data are plotted
for a variety of spectral indicators versus the H$\gamma_{\sigma<130}$ age
indicator.  The Vazdekis model grids are again plotted, as in the previous
Figs.  Also plotted, as a representative population with age $\sim$12 Gyr and
[Fe/H]$\sim$$-$0.7, is the integrated spectrum of the Galactic globular cluster
47 Tucanae.  The KPNO data indicate a strong radial age and metallicity
gradient in M32, with the central age and metallicity in agreement with that
found in the Subaru and FAST data, but with the data at 30\char'175\  radius
apparently having about the same age and metallicity as 47 Tuc.  Thus the
KPNO 4-m results are in striking disagreement with those found from the
Subaru and Tillinghast/FAST data, in that the gradient seen in the KPNO data is much more
pronounced than that found in the Subaru and FAST data.

A clue to understanding the large apparent line strength gradients in the
KPNO data is present in the behavior of the deepest lines in the spectrum, i.e.,
the Ca II H and K lines.  Since the integrated spectrum of M32 is overwhelmingly
dominated by cool stars, as is demonstrated below in \S\ref{hotstars}, the
depths of the Ca II H and K lines should not vary appreciably with distance
from the nucleus.  Instead, these lines have substantially lower depths in the
nucleus as opposed to in the outer regions, as is illustrated in
Fig.~\ref{fig:depths}, where the spectrum at 30\char'175\  outside the nucleus is
normalized to and overplotted on the nuclear spectrum.  We quantify the
difference in Ca II H and K line depths seen in Fig.~\ref{fig:depths} by
using the pseudocontinuum peaks just shortward of Ca II K and longward of
Ca II H as references.  Specifically, the mean ratio between the line depth and
neighboring pseudocontinuum peak is 67\% smaller in the nucleus of M32 than it
is at 30\char'175\  outside the nucleus.

The elevated appearence of the Ca II line bottoms in the outer region spectrum
indciates that the Ca II lines (as well as all other spectral features) are
diluted by scattered light in the spectrograph.  Specifically, we speculate
that scattered light from the semi-stellar nucelus of M32, which reaches a
peak flux $\sim$100 times higher than at 30\char'175\  radius, contaminates the
spectrum at larger radii.  To further assess this conjecture we have generated a
featureless continuum with the same spectral response as for the raw observed
spectrum of the M32 nucleus.  We chose the scattered light component in this
manner because analysis of the scattered light spectrum of a star, HD187691,
taken on the same night as the M32 data shows the spectrum of the scattered
light ot be a highly diluted version of the star's spectrum, with a raw flux
distribution roughly similar to that of the star.  We added the above
featureless continuum in varying amounts to the M32
nuclear spectrum, up to a level that reproduces the line depths in Ca II H and
K at 30\char'175\  radius.  We have measured spectral indices in these artificially
diluted spectra of M32, and find that the entire radial population gradient in
the KPNO 4-m data can be accounted for by scattered light contamination.  The
results of the scattered light simulation are plotted in Fig.~\ref{fig:scatter},
where the actual observed and simulated data are seen to overlap fully.
Basically, dilution by scattered light weakens all spectral features, including
both Balmer lines and metal lines.  Hence, one would expect scattered light to
produce an artificially older and more metal-poor spectrum, as is measured in
the KPNO 4-m data.

Given the evident problem of scattered light in the KPNO 4-m data, can we be
sure that the more modest detected trend towards older and more metal-poor
mean population in M32 with increasing radius in the Tillinghast/FAST and Subaru data is
not also a spurious result?  We argue that the FAST and Subaru data are free
from scattered light problems becasue we have offset the slit from the nucleus
in the long exposure spectra which are used to extract information at larger
radii.  This is especially true for the FAST data, where we have obtained
spectra with the slit offset by 5\char'175 , 15\char'175 , and 30\char'175\  from the
nucleus, so that our results always refer to spectra that are extracted from
regions where the flux is at the highest levels.  Clearly, the greatest
scattered light problem arises when the nucleus, which is 100 times brighter
than at 30\char'175\  radius, is positioned on the slit.  Given the excellent
agreement between the Subaru and FAST data, we expect that by removing the
nucleus from the slit in both datasets, we have basically alleviated the
scattered light problem entirely.

To summarize, we have found a modest, but significant, radial population trend
in the central region of M32, such that the light-weighted mean age and
metallicity of M32 goes from $\sim$3$-$4 Gyr and [MgFe]=0.0 in the nucleus to
$\sim$6$-$7 Gyr and [MgFe]=$-$0.3 at 30\char'175\  radius.  A much stronger radial
population trend seen in the 4-m data is found to be an artifact of scattered
light in the spectra, produced by the location of the bright semi-stellar
nucleus of M32 on the spectrograph slit.

\subsection{Comparison with the Results of Worthey (2004)}

In a recent preprint, Worthey (2004) also has obtained long-slit spectra for
M32, out to $\sim$45\char'175\  radius.  He finds the mean age and metallicity
for the nucleus of M32 to be 4 Gyr and +0.05, which is consistent with our
nuclear results.  He also finds that the mean age increases by a factor of
2.5 from the nucleus to 1 R$_e$, while the abundance drops by 0.3 dex.  Again,
our results are in good agreement with Worthey's, since we find the age
to increase by a factor 2, and abundance to decrease by 0.25 dex.  In addition,
Worthey (2004) finds that [Mg/Fe] is underabundant by $\sim$$-$0.1, which is
very close to our mean value of $\sim$$-$0.15.  However, he does not report a
radial gradient in [Mg/Fe] (we find that [Mg/Fe] inceases from $-$0.25 at the
nucleus to $-$0.08 at 1 R$_e$).  Finally, Worthey (2004) reports that CN indices
actually increase from the nucleus out to a maximum at 4\char'175\  radius before
dropping at larger radii.  We instead see a monotonic decrease in CN from the
nucleus outward.  On the whole, the two studies are in excellent accord.

\subsection{Limits on the Role of Hot Stars}\label{hotstars}

The above results, taken at face value, indicate a $\sim$3 Gyr age gradient
within the central 30\char'175\  of M32.  However, it has been pointed out
previously (e.g., Maraston \& Thomas 2000; de Propris 2000; Brown et~al.\  2000)
that a relatively
small population of hot stars (i.e., from a young hot star population, a
metal-poor population, or a blue straggler population), if present in
early-type galaxies, could ``contaminate'' the integrated spectrum, thereby
producing articially young light-weighted mean ages from models which
lack that component.  Thus we now consider whether the apparent age gradient
in M32, from $\sim$4 Gyr in the center to $\sim$7 Gyr at 30\char'175\  radius, could
instead result from the changing influence of a relatively small hot population.
To explain our case, there must exist a hot component in the center of M32 that
is less prevalent as one goes radially outward from the nucleus.

The hot star hypothesis can be tested by examining the behavior of the Ca II
index that was originally utilized by Rose (1985; 1994) and more extensively
modelled in Caldwell, Rose, \& Concannon (2003) and Leonardi \& Rose (2003).
The Ca II index, which is basically constant in
cool stars, declines very steeply towards early F and A stars as Ca II H and K
disappear and H$\epsilon$ (which is coincident in wavelength with Ca II H)
increases in strength towards the higher temperature
stars.  Specifically, the decline in the Ca II index sets in at T$_{eff}$ above
$\sim$8000 K for solar abundance stars.  As is summarized in Rose (1985; 1994)
and Caldwell, Rose, \& Concannon
(2003), a small deficit in the Ca II index, compared with the ``expected''
value of 1.20 for a strictly old population, is observed in the nucleus
of M32.  The deficit of $\sim$0.05 from the ``expected''
value indicates that $\sim$3\% of the light at
4000 \AA \ in M32 is provided by hot (i.e., A-type) stars.  This population
fails by a factor of 5 to account for the overall strong Balmer lines
observed in M32, i.e., an intermediate-age ($\sim$4 Gyr old) population is
required to explain the integrated spectrum of M32.  Here we consider whether
a gradient in the hot population might provide an explanation for the
$\sim$3 Gyr age gradient observed in the central 30\char'175\  of M32.

Unfortunately, the Subaru spectra do not extend blueward enough to provide
coverage of Ca II K, and the KPNO 4-m  spectra are compromised by scattered
light, hence we rely exclusively on the FAST data.   The Ca II index at various
radii in M32 is plotted in Fig~\ref{fig:caII}.  Within the observational errors
the Ca II index is seen to be roughly constant, indicating that the $\sim$0.05
deficit in the index due to a hot star population is present in essentially
constant proportion from the nucleus through a radius of 30\char'175 .  To
realize the implication of the small, constant Ca II deficit in M32, we have
done the following exercise.  We have both added and subtracted in varying
amounts the spectrum of the A4V star HD136729 to the central Tillinghast/FAST spectrum of
M32.  Here we have used the spectrum of HD136729 available in the IUCFSL,
and have rebinned it and smoothed it to match that of the M32 data.  We have
also normalized the HD136729 to that of M32 at 4000 \AA.  Specifically, we
added and subtracted the spectrum of HD136729 at 5\%, 10\%, and 20\% of the
level of M32 (at 4000 \AA).  The effect on the Ca II index of M32 can be seen
in Fig~\ref{fig:caII}.  Subtracting or adding only a 5\% contribution from
HD136729 at 4000 \AA \ changes the Ca II index of M32 by $\pm$0.09, which is
substantially higher than the observed deficit of $\sim$0.05 of M32 from the
``standard'' value of 1.2 for an entirely cool star population.  Thus only
$\sim$3\% of the light at 4000 \AA \ in M32 comes from hot stars.  Furthermore,
this contribution is constant to within $\sim$$\pm$0.02 in the Ca II index over
the central 30\char'175\  of M32.  If we now consider the impact of a 3\% contribution
of A4V light at 4000 \AA \ on the H$\beta$ index, we find that the H$\beta$ index
changes by only $\pm$0.09 as the 3\% A4 star contribution is added and
subtracted.  As can be seen in Fig.~\ref{fig:M32Sub}, a change in H$\beta$ of
0.09 produces only a tiny effect on the derived age.  Given that we find the
Ca II index to vary radially by less then 0.02, we thus infer that a gradient
in H$\beta$ due to a gradient in hot star contribution can be present at no more
than the 0.04 level in that index, which is far below the observed H$\beta$
radial gradient of $\sim$0.4.

Finally, we have repeated the above analysis using the solar abundance 0.32
Gyr model population from Vazdekis (1999), and obtain very similar results as
were obtained with the A4V star, since the 0.32 Gyr model spectrum is
similar to that of the A4V star HD136729 in the blue.  Thus we also conclude
that at most only $\sim$3\% of the light at 4000 \AA \ in M32 comes from a
$\sim$0.3 Gyr population.

\subsection{Limits on Contamination from Emission Lines}\label{emission}

Another important issue to consider is the possibility that contamination from
emission lines could be systematically affecting the results derived from the
absorption line indices.  The most obvious concern is emission fill-in for
the Balmer lines.  Here we are primarily interested in the potential effect
of a radial {\it gradient} in emission producing spurious population effects.
Since the data indicate that
age systematically increases with increasing radial distance from the
center of M32, we must assume then that emission contamination also increases
with radial distance, if it is producing a spurious age increase due to emission
fill-in of the Balmer lines.  Such a scenario is perhaps somewhat contrived, in
that one might expect such emission to be centrally concentrated, but we will
consider that possibility nonetheless.

There are three potential sources of emission contamination.  The first occurs
if the spectrograph slit intersects a planetary nebula either, in M32 or M31,
and can contaminate either the slit position through M32 or the offset ``sky''
slit position.  The second possibility is that the slit can be positioned on
an HII region in M31.  Again, this could be either the slit positioned on M32
or at the offset sky position.  Finally, there can in principle be a weak AGN
emission spectrum in the nucleus of M32.

All three sources of emission are plausible problems.  Ciardullo et~al.\  (1989)
report positions for seven planetary nebulae (PNe) within the central 30\char'175\  of
M32.  As mentioned earlier, the Subaru spectrum through the nucleus of M32, at
a PA of 80\arcdeg E of N in fact intersect two of these PNe's, \#24 and 25
in the Ciardullo et~al.\  (1989) Table 6.  Inclusion of these two PNe lead to a
very significant fill-in of the Balmer lines at 10\char'175\  radius.  We have
also found that a sky position for spectra taken of M32 with the FLWO 1.5-m
and the FAST spectrograph that are not used in this paper is contaminated with
a faint HII region from the M31 disk on part of the slit.  In that case we
observed an unexpected enhancement in the H$\beta$ absoprtion strength in M32,
since H$\beta$ absorption in our sky position was artificially lowered due to
fill-in from the HII region emission.  Finally, M32 is known to harbor a
central mass concentration (Tonry 1984; Dressler \& Richstone 1988; van der
Marel et~al.\  1994, 1998; Verolme et~al.\  2002).  Thus an AGN spectrum is not
unexpected.

The possibility that emission fill-in is an important effect in the nucleus of
M32 (and for other low-luminosity early-type galaxies) has been discussed
in Jones (1999).  Here we briefly summarize the conclusions.  Gonz\'alez (1993)
detected a slight amount (0.11 \AA \ in equivalent width) of [OIII]$\lambda$5007
emission in the nuclear spectrum of M32.  Jones's (1999) spectra do not cover
[OIII]$\lambda$5007, but provide tight upper limits on
[OII]$\lambda$3727, from which strong constraints can be set on the type of
emission spectrum that is contributing to M32.  In particular, a LINER spectrum
is decisively ruled out, since, based on the observed [OIII]$\lambda$5007
emission of 0.11 \AA \ in equivalent width found by Gonz\'alez (1993), one
predicts an equivalent width of [OII]$\lambda$3727 in excess of the observed
upper limit.
Instead, the two possibilities that remain are either
planetary nebula emission or emission from an HII region.  In both cases, the
amount of emission predicted at H$\gamma$ from the small [OIII]$\lambda$5007
detection by Gonz\'alez (1993), is only 0.008 \AA \ in the planetary nebula
case and 0.005 \AA \ in the HII region case, which leads to an age
adjustment of $<$1 Gyr.  Note that the adjustment is such that emission tends
to make the galaxy look {\it older} than it actually is.

We have reinvestigated the nuclear spectrum of M32 using the eight 4-minute
exposures acquired with the FAST spectrograph.  These spectra cover both
[OIII]$\lambda$5007 and [OII]$\lambda$3727.  A key issue in emission line
detection is to find an appropriate template spectrum, which matches the
absorption features of M32 but is certified to be without emission
contamination itself.  For a template we have used the synthesized integrated
spectrum of the Galactic cluster M67 from Schiavon et~al.\  (2004).  In the
Schiavon et~al.\  (2004) paper M67 was found to have a very similar age and
chemical composition to the luminosity-weighted mean age and metallicity of
M32.  Since the M67 integrated spectrum is built up from coadding spectra of
individual stars in M67, the resultant integrated spectrum is certainly free
from emission.  In addition, the M67 spectra were acquired with the same FAST
spectrograph and grating combination as for M32.  We have registered
the M67 spectrum to that of M32 and formed the ratio spectrum between the two.
The ratio spectrum is plotted in the region of [OII]$\lambda$5007 and
[OIII]$\lambda$3727 in Figs.~\ref{fig:emis5007} and \ref{fig:emis3727}
respectively.
We do not see any conclusive signs of either [OIII]$\lambda$5007 or
[OII]$\lambda$3727.  Rather, we establish an upper limit to the
equivalent width of [OIII]$\lambda$5007 of 0.05 \AA, and a limit to
[OII]$\lambda$3727 of 0.15 \AA.  The fact that our upper limit on
[OIII]$\lambda$5007 conflicts with the detection by Gonz\'alez (1993) can be due
to the different apertures used for the ``nucleus'' of M32.  In any case,
emission contamination of the Balmer lines in the center of M32 is small.

Given that we have established the nuclear spectrum of M32 to contain little
or no emission contamination, we now use the nuclear spectrum of M32 as a
template and divide it into the other spectra extracted at different radii.
We then look for [OII]$\lambda$3727 and [OIII]$\lambda$5007 emission in these
template-normalized spectra.  Due to the radial gradient in the absorption
spectrum of M32,
using the nuclear spectrum of M32 as a template is not completely
successful at cleanly removing the underlying absorption spectrum in the
neighborhood of [OII]$\lambda$3727 and [OIII]$\lambda$5007 at extra-nuclear
positions in M32.  This problem is particularly apparent at the blue end of
the spectrum, where all of the key spectral features (such as Ca II H and K)
appear in emission, since they are deeper in the M32 nucleus, as well as in
the Balmer lines.  However,
applying a conservative upper limit defined from the spurious peaks in the
neighborhood of [OII]$\lambda$3727 we conclude that the equivalent width of
[OII]$\lambda$3727 emission is below 0.2 \AA \ FWHM at all locations along
the slit out to $\sim$30\char'175 , and the limit on [OIII]$\lambda$5007 is
$\sim$0.05 \AA.  For high-excitation emission spectra, such as from PNe and
metal-poor HII regions, the limit on [OIII]$\lambda$5007 emission produces
a stringent limit on H$\beta$ emission.  On the other hand, for low-excitation
HII regions, the [OII]$\lambda$3727 emission
exceeds H$\beta$ emission, thus the limit on [OII]$\lambda$3727 emission
produces a strict limit on H$\beta$ emission.  In short, we find that emission
line fill-in in the outer region of M32 cannot account for the observed age
and metallicity trend with radius.  As well, if the gradient were due to
discrete PNe and/or HII regions on the slit, we would readily detect them on
the original two-dimensional spectra, as we have done in a couple of cases.

\section{Discussion}\label{discuss}

The results from the previous section suggest that there is a radial gradient
in the mean age and metallicity in the central regions of M32, such that the
mean age rises from $\sim$3$-$4 Gyr in the nucleus to $\sim$6$-$7 Gyr at 30\char'175\
radius, while the metallicity drops from [Fe/H]$\sim$0.0 to $\sim$$-$0.3.
In addition, we infer a slight gradient in [Mg/Fe] such that [Mg/Fe] increases
from $-$0.25 in the nucleus to $-$0.08 at 30\char'175\  radius.  These age and
chemical enrichment trends all point towards a more extended history of star
formation and chemical enrichment in the nucleus of M32 than at 1 R$_e$.
Of particular note is that the higher mean overall metallicity in the center
of M32, coupled with the lower ratio of the
$\alpha$-element Mg relative to Fe, imply both a greater chemical
enrichment in the nucleus as well as a longer time period for that
enrichment, since [$\alpha$/Fe] may be a reflection of relative timescales of
Type II versus Type Ia supernovae.  In short, a consistent picture of the
radial line strength trends in M32 emerges from this study.

As was mentioned in the Introduction, no gradient in broad passband colors has
been found for the central regions of M32 in either the optical or IR
(Peletier 1993), which appears to contradict the distinct age/metallicity
gradient found in our spectra.  However, the trend is towards older age and
lower metal-abundance as one proceeds radially outward.  An increase in age
produces a reddening of colors while the decrease in metallicity has the
opposite effect.  Thus we have the interesting situation in which the
competing effects of age and metallicity lead to no variation in optical/IR
colors.  To investigate the plausibility of this assertion, we have assessed
the B$-$V and U$-$B colors predicted from our stellar population models.
The model B$-$V color for a 4 Gyr solar abundance population is 0.89, as opposed
to 0.86 for a 7 Gyr, [Fe/H]=$-$0.3 population.  Thus the radial change in
color is very small and difficult to detect.  For U$-$B the model color shifts
from 0.44 to 0.37 from the younger to the older population, which is again a
small shift, but perhaps should be detectable.  We note, however, that our
models are based on the clear oversimplification of a single population  at
each radius that is entirely at the luminosity-weighted mean value, while in
reality there must  be a spread in both age and metallicity.  In addition, our
models are basically limited to solar abundance ratios, while our data for M32
indicates departures from that pattern.  In fact, while the model B$-$V color
for the center of M32 is consistent with the observed color, to within the
uncertainties of Galactic reddening in that direction, the model U$-$B colors
are systematically bluer than the observed colors reported in Peletier (1993)
by $\sim$0.1$-$0.15.
We also note that some spectral features, e.g.,
Mg~$b$, also show no significant line strength gradient, again because an
older population tends to have stronger Mg~$b$, while a more metal-poor
population tends to have weaker Mg~$b$, as can be seen in
Fig.~\ref{fig:M32Sub3}.  Hence the most striking line strength
gradients that we observe are in the Balmer lines.

It is important to bear in mind that the above inferences about radial
population trends are for the
light-weighted mean population.  An alternative scenario to the possibility
of an overall shift of the bulk of the population to a younger age, as one
proceeds to smaller radii, is to invoke a shifting balance between two
populations.  Specifically, one can speculate that there was an initial star
formation episode $\sim$11 Gyr ago, as suggested by the presence of blue
horizontal branch stars in color-magnitude diagrams derived from HST images
(Ikuta 2001; Alonso-Garcia et~al.\  2003), as well as a more recent, higher
metallicity, star formation episode perhaps 2$-$3 Gyr ago.  The observed population
trend can then be seen as a higher concentration of the younger population in
the center of M32.  Such a population structure would in fact be a natural
result of the scenario proposed by Bekki et~al.\  (2001), in which centralized
star formation in M32 is triggered by the tidal field of M31.
To discriminate between a mean trend and a changing balance between two
populations is beyond the scope of this paper.  It should be kept in mind
that the more complex modelling involved with a two-population scenario could
as well impact the details of conclusions about the small gradient in
non-solar abundance ratios (viz., in [Mg/Fe]) found earlier.
Note that in any case
the younger population cannot be any younger than $\sim$2 Gyr, or it
would produce a strong signature in the Ca II index discussed in
\S\ref{hotstars}.

Finally, we return to the issue of scattered light in M32.  In the Introduction
we mentioned the conflicting results of several previous long-slit spectroscopic
studies of M32.  Most, if not all, of these studies involve spectra taken with
the slit passing through the nucleus of M32, hence they are particularly
vulnerable to effects of scattered light.  Perhaps the major discrepancies
between studies are due to varying degrees of scattered light.
In addition, while M32 represents an especially pathological case of
a bright nucleus as a source of scattered light, it is not inconceivable that
studies of radial population gradients in other early-type galaxies can have
been compromised by scattered light as well.

\acknowledgements

We wish to thank S. M. Faber for the crucial suggestion of scattered
light as a source of spurious age/metallicity gradients in M32.  Thanks are
also due to Dr. R. Peletier and Drs. C. Ikuta for their efforts in securing
the Subaru/FOCAS observations.
This research has been partially supported by NSF grant AST-9900720 to the
University of North Carolina.  It has also been supported in part by a
Grant-in-Aid for Scientific Research by the Japanese Ministry of Education,
Culture, Sports, Science and Technology (No. 13640230).

redpajama_set_name: RedPajamaArXiv


text:
#include "adian_lists.h"

#define CURRENT_TIME Scheduler::instance().clock()

//---------------------------Failed Path List Implementation------------------------//

Adian_Failed_Path_list::Adian_Failed_Path_list() {}

void Adian_Failed_Path_list::add_new_packet(int uid, failed_path fp, double expire) {
	// It is already confirmed that entry for uid do not exit in the map

	// fp is not in list form
	pl_t newlist;
	newlist.push_back(fp);

	// insert path
	fl_[uid] = newlist;

	// insert expiry time
	el_[uid] = expire;
}

void Adian_Failed_Path_list::add_failed_path(int uid, nsaddr_t next_hop, nsaddr_t daddr) {

	// convert path to structure
	failed_path newpath;
	newpath.next_hop = next_hop;
	newpath.daddr = daddr;

	// First check if entry exists for uid
	fpl_t::iterator it = fl_.find(uid);

	if(it == fl_.end()) {
		// Entry does not exists
		add_new_packet(uid, newpath, CURRENT_TIME+FAILED_PATH_EXPIRE_TIME);
	}
	else {
		// Entry corrosponding to uid exists
		// push the path to the list of failed paths
		fl_[uid].push_back(newpath);
		// recently accessed, so add expiry time
		add_expire_time(uid, FAILED_PATH_EXPIRE_TIME);
	}
}

void Adian_Failed_Path_list::rm_entry(int uid) {
	// add check for entry exists or not
	fl_.erase(uid);
	el_.erase(uid);
}

int Adian_Failed_Path_list::check_failed_path(int uid, nsaddr_t next_hop, nsaddr_t daddr) {

	// first check if entry exists
	fpl_t::iterator it = fl_.find(uid);

	if(it == fl_.end()) {
		// entry does not exists
		return 0;	// false - entry do not exist
	}
	else {
		// entry for uid exists
		// now check if next_hop and daddr exists in the list
		pl_t::iterator list_it;
		for(list_it = fl_[uid].begin(); list_it != fl_[uid].end(); list_it++ ) {
			// iterate over whole list and check values
			if ((*list_it).next_hop == next_hop && (*list_it).daddr == daddr) {
				// path found
				return 1;
			}
		}
		return 0;
	}
}

void Adian_Failed_Path_list::add_expire_time(int uid, double extra_time) {
	//find the entry
	uid_expire_t::iterator it = el_.find(uid);
	if(it == el_.end()) {
		// uid not in list
		return;
	}
	else {
		(*it).second += extra_time;
	}
}

/*
double Adian_Failed_Path_list::expire_time(int uid) {
	// check if exists
	uid_expire_t::iterator it = el_.find(uid);

	if(it == el_.end()) {
		// uid not in list
		return 0.0;
	}
	else {
		return (*it).second;
	}
}
*/

void Adian_Failed_Path_list::purge() {
// remove the expired entries

	//loop through the map and check for expired entries
	fpl_t::iterator it;
	uid_expire_t::iterator it_expire;

	for(it = fl_.begin(); it != fl_.end();) {

		it_expire = el_.find(it->first);
		if(it_expire == el_.end()) {
		// if the entry in expire list for this uid do not exist, invalid entry, so remove

			// This may cause error because of version of c++ being used
			// Following code works for c++11
			// http://stackoverflow.com/questions/263945/what-happens-if-you-call-erase-on-a-map-element-while-iterating-from-begin-to

			//it = fl_.erase(it);		// to make iterator consistent `it =`
			fl_.erase(it++);		// for c++03

		}
		else if(it_expire->second <= CURRENT_TIME) {
		// or if entry exists and it has expired, then also remove
			//it = fl_.erase(it);
			fl_.erase(it++);
			//it_expire = el_.erase(it_expire);
			el_.erase(it_expire++);
		}
		else {
			it++;
		}
	}

}

//-------------------------------Reply route list implementation ------------------------

//constructor
Adian_Reply_Route_list::Adian_Reply_Route_list(){ }

//to add a new reply route to the list
void Adian_Reply_Route_list::add_reply_route(u_int32_t seq_no, nsaddr_t reply_to, double expire_time){
	rl_[seq_no] = reply_to; //adds reply_to in route list corresponding to the seq_no
	el_[seq_no] = expire_time; //adds expire_time in expire list corresponding to the seq_no
}

void Adian_Reply_Route_list::rm_reply_route(u_int32_t seq_no){
	seq_expire_t::iterator el_it;
	route_list_t::iterator rl_it;

//find the expiry time and reply to nodde corresponding to that seq_no and remove it
	el_it = el_.find(seq_no);
	rl_it = rl_.find(seq_no);

	el_.erase(el_it);
	rl_.erase(rl_it);
}

//return return to node with this seq_no
nsaddr_t Adian_Reply_Route_list::lookup(u_int32_t seq_no){
	route_list_t::iterator rl_it;

	rl_it = rl_.find(seq_no);
	if(rl_it != rl_.end())
		return rl_it->second;
	else
		return 0; // not found
}

//remove already expired enteries
void Adian_Reply_Route_list::purge(){
	seq_expire_t::iterator el_it;
	route_list_t::iterator rl_it;

	for (rl_it = rl_.begin(); rl_it !=rl_.end();)
	{
		el_it = el_.find(rl_it->first); //if entry is not in expire list it will delete it from router list also.
		if(el_it == el_.end()){
			//rl_it = rl_.erase(rl_it);
			rl_.erase(rl_it++);
		}
		else if(el_it->second <= CURRENT_TIME){ //if expire time is les than current time it will delete that entry from both
			//rl_it = rl_.erase(rl_it);
			rl_.erase(rl_it++);
			//el_it = el_.erase(el_it);
			rl_.erase(rl_it++);
		}
		else{
			rl_it++;
		}
	}
}

//----------------------------------------Data source list----------------------------------

//constructor
Adian_Data_Source_list::Adian_Data_Source_list(){ }

//to add a new source to the list
void Adian_Data_Source_list::add_data_source(int uid, nsaddr_t source_addr, double expire_time){
	sl_[uid] = source_addr;
	el_[uid] = expire_time;
}

//to remove a data source from the list
void Adian_Data_Source_list::rm_data_source(int uid){
	uid_expire_t::iterator uel_it;
	src_list_t::iterator srcl_it;

//find the expiry time and reply to nodde corresponding to that seq_no and remove it
	uel_it = el_.find(uid);
	srcl_it = sl_.find(uid);

	el_.erase(uel_it);
	sl_.erase(srcl_it);
}

//to return source node which generated this packet(uid)
nsaddr_t Adian_Data_Source_list::lookup(int uid){
	src_list_t::iterator srcl_it;

	srcl_it = sl_.find(uid);
	return srcl_it->second;
}

//to remove the expired entries from both lists
void Adian_Data_Source_list::purge(){
	uid_expire_t::iterator uel_it;
	src_list_t::iterator srcl_it;

	for (srcl_it = sl_.begin(); srcl_it != sl_.end();)
	{
		uel_it = el_.find(srcl_it->first); //if entry is not in expire list it will delete it from source list also.
		if(uel_it == el_.end()){
			//srcl_it = sl_.erase(srcl_it);
			sl_.erase(srcl_it++);
		}

		else if(uel_it->second <= CURRENT_TIME){ //if expire time is les than current time it will delete that entry from both
			//srcl_it = sl_.erase(srcl_it);
			sl_.erase(srcl_it++);
			//uel_it = el_.erase(uel_it);
			el_.erase(uel_it++);
		}
		else{
			srcl_it++;
		}
	}
}

//---------------------------------Attempt list-------------------------------------------

//constructor
Adian_Attempt_list::Adian_Attempt_list(){ }

//add a new entry to the attempt list
void Adian_Attempt_list::add_entry(int uid, int max_attempts, double expire_time){
	al_[uid] = max_attempts;
	el_[uid] = expire_time;
}

//to remove an entry from attempt list
void Adian_Attempt_list::rm_entry(int uid){
	attempt_list_t::iterator al_it;
	uid_expire_t::iterator	el_it;

	al_it = al_.find(uid);
	el_it = el_.find(uid);

	al_.erase(al_it);
	el_.erase(el_it);
}

//to reduce the number of attemts upon failure
int Adian_Attempt_list::decrease_attempts(int uid){
	attempt_list_t::iterator al_it;
	al_it = al_.find(uid);
	al_it->second -=1;//decreases no of attempts by one

	return al_it->second;
}

//purge() function to remove duplicate and already expired enteries
void Adian_Attempt_list::purge(){
	uid_expire_t::iterator el_it;
	attempt_list_t::iterator al_it;

	for (al_it = al_.begin(); al_it != al_.end();)
	{
		el_it = el_.find(al_it->first); //if entry is not in expire list it will delete it from attempt list also.
		if(el_it == el_.end()){
			//al_it = al_.erase(al_it);
			al_.erase(al_it++);
		}

		else if(el_it->second <= CURRENT_TIME){ //if expire time is les than current time it will delete that entry from both
			//al_it = al_.erase(al_it);
			al_.erase(al_it++);
			//el_it = el_.erase(el_it);
			el_.erase(el_it++);
		}
		else{
			al_it++;
		}
	}
}

redpajama_set_name: RedPajamaGithub


All domestic flights and chartered flights (office and electorate) claimed by Nick McKim are ranked from highest to lowest based on the value claimed. The top 10 flights are shown here.
The 10 most visited locations counts the number of times Nick McKim claimed a domestic or chartered flight to or from a particular location.


Since 1999, on the base of the Institute the programme of extended professional training and retraining of the bacteriologists and assistant bacteriologists has been present. Annually, there are from 4 to 6 cycles of thematic advanced training ("The selected issues of general and specific sanitary bacteriology", "Bacteriology", "Microbiological diagnostic of the acute enteric infections", "Laboratory science in bacteriology", "Sanitary microbiological research of the natural, fresh and waste waters", "Sanitary microbiological research of food and drink"), where up to 30-40 bacteriologists and 20-25 assistant bacteriologists are trained.
Specialized department of microbiology has been established by the ICIS and Orenburg Agrarian University to integrate higher education with the academic sciences, to provide the scientific researches with the personnel as well as to develop and perfect the system of innovative education.
Thirteen workers of the ICIS are also involved in teaching on subjects like microbiology and biology in the Orenburg State Medical University, Orenburg Agrarian University and Orenburg State University. The researchers of the ICIS in cooperation with the professors from the Orenburg State Medical University, has elaborated a range of study guides of federal level for the students and the attendees of extended education courses.
The staff of the ICIS fulfills awareness-building with the citizens of Orenburg. Academician O.V. Bukharin regularly gives public lectures in the Orenburg Regional Public Library after N.K. Krupskaya. The workers of the ICIS share the results of their researches on the radio, as well as in the local and the state press, they take active part in exhibitions. With the help of young scientists the scholarly knowledge is being popularized in many forms among school children and students. They organize scientific lectures and practical workshops in schools and in the Orenburg Regional Ecological and Biological Centre for Children, practical lessons, field trips and lectures as parts of "Doors Open" days in the Institute and the Academies of School Sciences for the Gifted High-school Students, individual lessons with the interested school children, guiding in competitions participation.


Success of biologic drugs, owing to their capability to treat chronic diseases, has taken the pharmaceutical industry to a new level. Biologics, offering enhanced curing abilities without side effects are being widely used to treat chronic ailments such as cancer and other autoimmune diseases. With FDA approval, several companies have been introducing novel biologic drugs for various therapeutic areas. This has made delivery of biologics an important aspect.
11.3.9. West Pharmaceutical Services Inc.


Prevention, diagnosis, and treatment of adult diseases, especially for those patients with chronic diseases.
Prevention and treatment of a wide range of mild to moderate illnesses and injuries for all ages.
Screening, diagnostic services and follow up treatment for reproductive conditions and sexually transmitted infections. Family planning and pregnancy prevention services.
Counseling and psychiatric services are integrated with your primary care provider and supports caring for you as a "whole person".
Medication and disease management that helps to control and prevent the complications of chronic illnesses such as diabetes, hypertension, and asthma.
Assistance with Medi-Cal, Covered California and Cal Fresh (food stamps) applications and other community resources.


text:
Q: Really slow For loop How can I set my loop faster?
I have 4 columns and more than 250 rows and it takes like 5 minutes to loop this:
Application.Calculation = xlCalculationManual
Call CPU0

Dim TableA As Range:    Set TableA = Range("L_PriceA")

With TableA
LongA = TableA.Rows.Count
    For s = 1 To LongA
       .Cells(s, 3).Value = "dynamic"
       .Cells(s, 4).Value = "dynamic"
       .Cells(s, 5).Value = "dynamic"
       .Cells(s, 6).Value = "dynamic"
    Next
End With

"dynamic" will be data from xml because nobody helped me with THIS and I don't know :/. Also looked at some loop problems here in stackO, but no main boost.

A: Looping over a range is slow.  Avoid it by moving your data to Variant Array, something like this:
Dim dat As Variant
Dim s As Long

With TableA
    LongA = .Rows.Count
    dat = .Value  ' TableA must be at least 6 columns wide
    For s = 1 To LongA
       dat(s, 3) = "dynamic"
       dat(s, 4) = "dynamic"
       dat(s, 5) = "dynamic"
       dat(s, 6) = "dynamic"
    Next
    TableA.Value = dat
End With

redpajama_set_name: RedPajamaStackExchange


Naughty Fox is on the prowl, and the animals of Potter's Barn Farm must come up with a plan to get rid of him once and for all. It's time to create a Barnyard Hullabaloo! Bestselling author Francesca Simon spins a truly irresistible yarn in this lovely book from the new Orion Early Reader series. With simple text, appealing colour pictures and lots of comical characters, it's just the job for little farmyard fans!


text:
Долон-Нур, Долонно́р, иначе Долу́нь () — уезд аймака Шилин-Гол автономного района Внутренняя Монголия (КНР). Название уезда происходит от монгольского «Долоо нур» («Семь озёр» — когда-то здесь было семь водоёмов, которые к настоящему времени пересохли).

История
Уезд был образован в 1913 году и вошёл в состав Специального административного района Чахар (察哈尔特别区), впоследствии преобразованного в провинцию Чахар. В 1930-х годах эти места стали ареной противоборства китайских и японских войск. 22 сентября 1950 года уезд был передан из провинции Чахар в состав аймака Шилин-Гол.

Административное деление
Уезд делится на 2 посёлка и 3 волости.

Примечания

Ссылки

Уезды Шилин-Гола

redpajama_set_name: RedPajamaWikipedia


text:
BTS Make History at the 2021 American Music Awards
Continuing to prove they are the ones to watch, BTS made history once again at…
Olivia Rodrigo, The Weeknd, Bad Bunny, and More Earn 2021 American Music Awards Nominations
The nominees for the 2021 American Music Awards (AMAs) are out now and Olivia Rodrigo leads…
Justin Bieber and Shawn Mendes Drop Joint Single 'Monster': 'Love You First'
Treading on the common impression of ego, perfection, and the cusp of fame, the Canadian…
by Lizet Chavez
Bebe Rexha, Doja Cat, Dan + Shay, Lewis Capaldi, Machine Gun Kelly, and the Weeknd Set to Perform at the 2020 American Music Awards
Bebe Rexha featuring Doja Cat, Dan + Shay, Lewis Capaldi, Machine Gun Kelly, and The…
Bad Bunny to Star Opposite Camila Mendes, Pete Davidson and More, and Executive Produce STXfilms Drama 'American Sole'
Latin Grammy Award-winning global superstar Bad Bunny will be making his feature film debut in…
'Empire' Star Taraji P. Henson to Host the 2020 American Music Awards
The multifaceted Golden Globe-winning actor, best-selling author and producer Taraji P. Henson is set to…
BTS to Perform New Single and 'Dynamite' at the 2020 American Music Awards
Following a teaser for their upcoming album BE featuring the text "Life Goes On," it…
The Weeknd and Roddy Ricch Dominate 2020 AMAs Nominations Followed by Taylor Swift, Megan Thee Stallion and Bad Bunny
The Weeknd and Roddy Ricch dominate the 2020 American Music Awards nominations with eight nods…
2020 American Music Awards to Return in the Fall to ABC
Music's hottest night of the year, the 2020 American Music Awards returns to ABC on…

redpajama_set_name: RedPajamaCommonCrawl


text:
District Court (Fla.) Says Text Message Program that Dialed from Uploaded List of Numbers Did Not Use an ATDS
In Ramos v. Hopele of Fort Lauderdale, LLC, 2018 WL 4568428, at *1–2 (S.D.Fla., 2018), Judge Moreno adopted the Magistrate's recommendation and granted summary judgment to a TCPA defendant who sent text messages to an uploaded list of numbers.
Defendant's Motion for Summary Judgment is GRANTED. The defining issue in the Report and Recommendation and Plaintiff's principal objection to the Magistrate's Report is whether the EZ-texting program at issue in this case qualifies as an automatic telephone dialing system as defined by the Telephone Consumer Protection Act and the Federal Communications Commission's orders. The Court agrees with the Report and Recommendation that ACA Int'l v. FCC, 885 F.3d 687, 695 (D.C. Cir. 2018) is binding on this Court and that its interpretation of the FCC's orders establishes the standard to determine the issue at hand. Under ACA, the appropriate standard to determine whether the EZ-texting program is an automatic telephone dialing system is whether the program (1) lacks the capacity to randomly or sequentially generate phone numbers, or alternatively, (2) lacks the ability to send messages without human intervention. ACA, 885 F.3d at 702; Swaney v. Regions Bank, No. 13-00544, 2018 WL 2316452 (N.D. Ala. May 22, 2018) (stating that in ACA, the D.C. Circuit invalidated portions of the FCC's 2015 order, but reaffirmed the FCC's 2003 determination that the "defining characteristic of an [automatic telephone dialing system] is the capacity to dial numbers without human intervention") (quoting 2003 FCC Order at 14092). In this case, it is undisputed that the Defendant's Manager, David Pentecost, signed into the Defendant's system and created a list of customer phone numbers, based on various criteria, such as the date of purchase, amount spent, and the customer's address. He then removed any landline phone numbers, incapable of receiving a text message, and uploaded an Excel spreadsheet onto the EZ-texting website. Pentecost then wrote the message, programmed the date and time of delivery, and the cell phones scheduled to receive the message. He then hit send. This Court agrees with the Report and Recommendation that this amount of human intervention is sufficient to negate the EZ-texting program as an automatic telephone dialing system within the applicable standard. Plaintiff's main objection is that even though Pentecost created the list of numbers, drafted the text message, and programmed the timing of delivery, the EZ-texting program had that capacity and therefore, it comes under the purview of the Telephone Consumer Protection Act as an automatic telephone dialing system. Plaintiff asserts that the record evidence establishes the system's capacity, and, at the very least, creates an issue of fact as to whether the program had this capacity to generate numbers and send the messages. The declaration of Jagannathan Thinkaran, the CEO of CallFire, the company that owns the EZ-texting program, confirms that the program can only be used to send messages to specific identified numbers that have been inputted into the system by the customer, which in this case Pentecost inputted. Thinkaran adds that the system does not have the ability to send messages automatically or to generate phone numbers. Plaintiff's objections focus on the testimony of its expert Randall Snyder, who testified that the Rand( ) function in Excel could be used to generate numbers, but Snyder also testified that he did not test out this function. (D.E. 100-1 at 10-12). In any event, the ACA decision states that the FCC could not expand the statutory definition of an automatic telephone dialing system to include "dial[ing] from an externally supplied set of numbers" such as Excel. ACA, 885 F.3d at 702 (declining to adopt the expansive view of an automatic telephone dialing system espoused in the FCC's 2015 order). The Court finds that Snyder's testimony is insufficient to create an issue of material fact and that Thinkaran's testimony, coupled with the undisputed evidence of Pentecost's actions in this case, establish that the EZ-program texting system is not an automatic telephone dialing system under the Telephone Consumer Protection Act.
CEB Prac. Guide § 2B.23: ATDS TCPA


text:
Kings of Orient,
Dresden, D.C.
When I woke up the place was on fire. I didn't know where I was. Smoke and flames everywhere.
I ran around screaming, trying to find a way out. The hallway was burning. My hair caught on fire. Somehow I made it to the cellar. I remember falling down some stairs.
An old drunk was lying in the corner.
I shouted.
"Help! Fire!"
Even down here you could smell the smoke, like when the wind blows round your campfire. Crackling sounds from upstairs nearly drowned out my voice.
"Huh? Wha?"
the drunk mumbled.
"Look! I'm burned! Fire! We have to get out!"
I yelled in his face, started shaking him.
"Let go!"
He twisted around.
"What fire? There isn't any goddam fire."
Orange light from the far wall lit up his face.
"Just listen! Look around! The ceiling! Gonna fall on us! Which way do we go?"
He stared at me.
"Look, sonny,"
gruff, bleary.
"There isn't any fire. You're acting like some kind of radical. Bug off! Lemme alone."
He looked at an empty bottle on the floor, made a face.
Drunk and stupid, I thought. The pain came back, and I grabbed him.
"Just tell me how to get out of here!"
I shrieked.
His arm swung up and bashed me in the head.
"Out! Talk sense if you're going to talk! What do you mean, out?"
He was bigger than me so I ran.
иии
I found another stairway and went up. Couldn't breathe to run any more. Heat made me sweat. Too thirsty.
One of the doors opened. Another guy was standing there.
"Hey!"
"Where are you going?"
"Don't know! Help! On fire!"
"Calm down!"
He was stern.
"I know there's a fire. You're not burning now. Just sit down."
I sat. The floor was hot.
"How do we get out?"
I asked. At least somebody knew what was going on. Something crashed nearby.
"We don't,"
said the guy.
"We wait here for the soldiers. They're busy pouring gasoline. The worst thing we can do is panic. We have to stay put and stay calm."
"But, but,"
I was still breathless.
"We'll...get... burned..."
"Maybe so, but that's a risk we have to take. There's no reason to worry."
I heard more beams crashing. Then it hit me. Gasoline?
"Why are they spreading gas!"
I yelled.
"To put out the fire, you idiot! Why else would they do something like that! They ran out of propane!"
"But we're trapped!"
"Shut up!"
He was feeling the stress.
"You're getting hysterical! I don't know! Just keep quiet!"
I couldn't stand it. I just started to laugh, and cry. My hands hurt where they got burned. I hit him, then I ran off like crazy.
I don't know where I went. The fear got worse. I was alone. A door blew out right after I passed it. The blast burned my back. I was frantic.
Then I got to a hall with an indoor pool. I ran straight for it.
There were soldiers.
"Stop!"
they called out. I kept going. They grabbed me. The lake was crystal clear, still as stone. I screamed and bit them and tried to get loose.
"No, no! Help! Help! Let go!"
They wouldn't. Everything popped. I gave up. Who cares? I started to cry. They dragged me to an office. The captain was there. He was on the phone. Papers all over.
"Well,"
he said after a while.
"How are things?"
He didn't look up from the paperwork.
"I hurt all over,"
I said.
"What about the fire?"
"Oh, that. You must have come from one of the primary infiltration quadrants. We're safe here."
He chuckled.
"The water. Why aren't they putting out the fire?"
He frowned.
"They didn't tell you much, did they. When the soldiers put water on the fire it burns hotter. Besides, we're not supposed to put it out."
I stared at him.
"We have to keep it going, don't you see? That's why we're here. I coordinate the placement of the gunpowder and the hydrogen."
"Did you start the fire?"
"Well, not exactly, no."
He paused to light a cigar.
"The higher-ups did. There was too much phlogiston."
"Oh."
"The scientists over at the planning center found out about it. Sheer chance. It's all too complex for a man like me."
He started chuckling again.
"Funny about the planning center. Computer printouts keep catching on fire. They're having a devil of a time staying on top of the phlogiston calculations."
"Why don't they run?"
"Why should they? Fires aren't dangerous. Studies show it. A million times we'll see a fire that never even bothers us. The chances of any one fire ever doing actual harm are so low that it's absurd. Everyone blows it out of proportion."
He frowned again.
I was tired of all this.
"Can I go in the pool? Just for a while?"
"Oh, no. I couldn't allow that. What good would it do?"
"But I'm burned!"
"But you're just a single person, my boy. So what if you cooled off? You don't even exist outside the context. You might throw the phlogiston calculations way off."
This was deep for him.
"Can't I go to the hospital, or something?"
This made him laugh.
"I'm sorry. They really didn't tell you anything. We had to burn all the hospitals, during the airlift. All the phlogiston flowing around near the patients. It would have started something without warning. We're burning the whole city. If we didn't, it might catch fire."
"The whole city?"
"Yes, yes!"
He was growing impatient with my questions.
"Don't you see! If it caught fire without warning it might spread! Don't you realize what a responsibility this is? We have so much trouble."
Gerry Reith


text:
Hamza Testouri (born 30 August 1987) is a Tunisian football defender.

References

1987 births
Living people
Tunisian footballers
ES Beni-Khalled players
CS Sfaxien players
EGS Gafsa players
ES Métlaoui players
AS Gabès players
JS Kairouan players
EO Sidi Bouzid players
Olympique Béja players
Association football defenders
Tunisian Ligue Professionnelle 1 players