text:
\section{Introduction}
Proper motion measurements of infrared (IR) stars in the central
1\arcsec~of the Galaxy suggest the existence of a supermassive
black hole (SMBH) with a mass of several million solar masses
(M$_\odot$) at the position of the compact radio source Sgr A*
\citep{scho02,ghez03,ghez05}. A recent determination of the mass
(4.2$\times$10$^6$ M$_\odot$) has been reported by \citet{ghez08} and
\citet{gill09}. The radio source size, 37$^{+16}_{-10}$ $\mu$as,
was determined with recent very long baseline interferometry (VLBI)
observations at 1.3 mm, suggesting that the intrinsic shape of Sgr A*
is not symmetric about the SMBH, and that it arises from the surrounding
accretion flow \citep{doel08}.
Accretion onto Sgr A* must also be fed at various times by the
numerous gas streams that have been observed in the surrounding
HII region, Sgr A West, notably the ionized ``Mini-spiral''
arms discovered by  \citet{lo83} and \citet{eker83} with the Very
Large Array (VLA). The VLA and IR observations have revealed
that Sgr A West consists of high velocity bulk flows toward,
or around, Sgr A*. The radial velocity fields of the ionized flows were
imaged based on  IR observations of the [Ne II] 12.8 $\mu$m
fine-structure line \citep{lacy80,sera85,sera88}, the IR recombination
lines Br-$\alpha$ and/or Br-$\gamma$ \citep{geba87,herb93,paum04} and
VLA observations of the H76$\alpha$ line \citep{schw89} and the H92$\alpha$
line \citep{rob93,rob96}. \cite{schw89} found a nearly complete
ionized ring from the H76$\alpha$ line data and the kinematics of
this ionized ring could be modeled with a circular orbit. \citet{lacy91}
interpreted the kinematics combining the Northern Arm and Western Arc as a
one-armed spiral in a Keplerian disk with nearly circular orbits.
Later, Roberts and Goss (1993) used VLA observations of the H92$\alpha$
line to divide the ionized ``ring'' into three separate components:
the Western Arc, which is indeed in circular motion, the Northern Arm,
and the Bar.
The H92$\alpha$ line observations were subsequently
used by \cite{liszt03} to argue that the Bar and the
Eastern Arm together represent a single stream of gas orbiting
about the Galactic center.
Recently, Paumard et al. (2004) used observations of the
Br-$\gamma$ line to suggest that the motions of the ionized stream
in the Northern Arm could be fitted with a family of elliptical, Keplerian
orbits.

Using high-resolution radio observations,  the motions of the HII components
on the sky plane can be elucidated. Large proper motions of the HII
components were inferred from data acquired during the period 1991--1997
\citep{yusef98,zhao98,zhao99}. A noticeable fraction of the HII
components shows large motions that cannot be explained purely in terms
of the bounded orbital motions occurring in reaction to the central
gravitational field. The large peculiar motions might be explained by
stellar winds or stellar wind interactions, possible explosive events,
or debris ejected from a partially disrupted stellar envelope of a star
due to the tidal force near the SMBH. These explanations need to be
assessed with the improved observations presented here.

In this paper, we present new results on the dynamics of the ionized gas in the
central 3 pc of the Galaxy based on  VLA measurements of three-dimensional
velocities, along with numerical modeling. Section 2 describes observations and data
reductions. Section 3 shows the measurements of proper motions and radial velocities.
Section 4 presents the results on the three-dimensional velocities of individual sources
and regions. Section 5 describes the dynamical models for the Mini-spiral arms in Sgr A West.
Section 6 discusses an MHD effect on the detailed structure of the ionized streams.
Section 7 summarizes the results and conclusions.

\section{Observations and data reductions}

\subsection{Data at 1.3 cm}
The new observations of Sgr A* and its vicinity were made at 1.3 cm on
2004 December 23 and 2005 April 26 with the VLA in its A and B configurations,
respectively, in order to better determine the proper motions of the HII
components near Sgr A* with a long time span. Table 1 summarizes the observations
and data that are used in this paper. At 1.3 cm, all the observations were made
in the continuum mode with a total bandwidth of 100 MHz. The flux
density scales for each of the data sets were determined using the primary
calibrators 3C 286 and 3C 48 following the standard VLA calibration procedure
in the Astronomical Image Processing System (AIPS). The complex gains were
calibrated using the quasi-stellar object (QSO) NRAO 530. In order to remove the
time variability of Sgr A*, the flux density of the point source was measured in time bins
of 0.5 hr. Then the time variation in flux density from Sgr A* was accounted
for using the technique described in \citet{zhao91} so that these variations
do not lead to uncorrected sidelobe emission that could affect the proper
motion determinations. In addition, archive data taken by different groups
using different pointing positions slightly offset from Sgr A* are in B1950
or J2000 coordinate systems. We therefore recalculated the coordinates
in each of the data sets with UVFIX in AIPS, converting all coordinate
frames to the J2000 equinox and shifting the phase centers to the position
of Sgr A*. The errors owing to differential aberration caused by the on-line
program were automatically corrected with the off-line program UVFIX.
Further corrections for the baseline-based residual errors were applied
using the gains determined from the model of NRAO 530. Then, the data from
the observations in the consecutive A and B configurations were combined
to form separate epoch data sets for the proper motion measurements. The remaining
residual errors in the complex gains of each data set were further corrected
in both phase and amplitude using the self-calibration technique. Weighting
by the number of visibilities in each combined data set, we determined effective
dates of the three combined data sets to be MJD 53419 (2005 February 18), MJD 51422
(1999 September 01) and MJD 48485 (1991 August 17), spanning 13.5 years. Hereafter, we
refer to these epochs' data sets as 2005K, 1999K, and 1991K, respectively.

A dirty image at 1.3 cm  was constructed by applying an FFT of the 2005K data
with  robustness weighting of R=0. The dirty image was cleaned with the
Clark--Steer hybrid algorithm and the clean component image was convolved with
a Gaussian beam and the resultant FWHM beam is 0.\arcsec2$\times$0.\arcsec1~
(P.A.=11\arcdeg). The rms noise of the ``cleaned'' image (Fig. 1) is 20 $\mu$Jy
and the peak flux density is $>$1 Jy beam$^{-1}$. The dynamical range of the
image is $>$50,000:1. With higher system temperatures at the earlier epochs,
the images of 1999K and 1991K have higher rms fluctuations of 40 and
50 $\mu$Jy, respectively. The delay beam in the image at 1.3 cm is
92\arcsec$\times$46\arcsec~(P.A.=11\arcdeg) and the source offsets from
the delay center are all less than 16\arcsec~in the measurements. Thus,
the effects due to the delay beam can be neglected.

\subsection{Data at 3.6 cm}
At 3.6 cm, a total of nine observations was acquired from the VLA archive. All
the observations were made in the spectral line mode for the H92$\alpha$ line.
The flux density scale was determined using 3C 286 and 3C 48. The calibration
for complex gains utilized NRAO 530 following the AIPS procedure. In addition,
we also corrected for the bandpass shape using 3C 84 and NRAO 530. We corrected
flux density variations of Sgr A* using the method discussed by \citet{zhao91}.

The on-line effect of differential aberration was corrected with the same
procedure as used for the data at 1.3 cm. The phase centers of all the data
sets were shifted to the same common position for Sgr A*. We combined
two data sets taken in the BnA configuration on 2 consecutive days to
form four epochs' data sets (2002X,1999X,1993X and 1990X). The effective
dates of the four data sets --- MJD 52415.5 (2002 May 22), MJD 51468.5 (1999 October 18),
MJD 49030.5 (1993 February 13) and MJD 48075.5 (1990 July 04)--- span nearly 12 years.

Combining all the data at 3.6 cm, we constructed a 8192$\times$8192 dirty
image with robustness weighting R=0 and  the multi-frequency synthesis
technique, which avoids the bandwidth smearing effect. Thus, the frequency
dependence of the $uv$ coordinate was used to provide better $uv$ coverage and
to minimize  frequency smearing. The cleaned image shown in Fig. 2 was
achieved with the Clark--Steer hybrid deconvolution algorithm, convolving
with the synthesized beam FWHM = 0.\arcsec70$\times$0.\arcsec57 (57\arcdeg).
The rms noise is 20 $\mu$Jy and the peak flux density is 0.8 Jy beam$^{-1}$,
giving a dynamical range of 40,000:1.

\section{Measurements of three-dimensional velocities}

\subsection{Proper motion}
Both the $K$-band and $X$-band  data sets were used for proper motion
measurements. In order to eliminate  confusion from the extended, diffusion
emission in Sgr A West, we filtered out the short baseline data in the
imaging process. We constructed images at each epoch with the visibility
data at  projected baseline lengths $>$ 100 $k\lambda$ at both 1.3 and
3.6 cm. The cleaned images were convolved to the common synthesized beams
of $0.^{\prime\prime}2\times0.^{\prime\prime}1$ (P.A.=0\arcdeg) and
$0.^{\prime\prime}6\times0.^{\prime\prime}5$ (P.A.=0\arcdeg) at 1.3 and 3.6 cm,
respectively. Then, we fitted each of the compact HII components with a single
Gaussian and a slope that removes the continuum baseline. The peak position
offsets ${\rm \Delta\alpha,~\Delta\delta}$ from Sgr A* were determined in
the J2000 coordinate system along with 1$\sigma$ errors in the least-square
(LSQ) fitting. All source positions were determined as offsets from Sgr A*.
The motions of the HII components with respect to Sgr A* can be determined
from the difference in the position offsets between two epochs. In order
to minimize the systematic errors, we made the best fit to all the measurements
($\Delta\alpha_i, \Delta\delta_i$) at each epoch ($t_i$) using a linear regression.
The slopes $\mu_\alpha$ and $\mu_\delta$ corresponding to proper motions in RA
and Dec, along with the position offsets ($\Delta\alpha_0$, $\Delta\delta_0$)
at reference time $t_0$, can be determined from the linear fitting. Fig. 3
shows the linear fitting to the position offsets and the determination of
the proper motions. Table 2 summarizes the measurements of the proper motions.
Columns 3 and 4 in Table 2 list the peak position offsets at epochs 2005K
and 2002X for 1.3 and 3.6 cm, respectively. The deconvolved sizes of the major
($\theta_{maj}$) and minor ($\theta_{min}$) axes and the position angle (P.A.)
of the sources, along with their 1 $\sigma$ errors, are given in column 5.
The measurements of the proper motions
($\mu_\alpha$, $\mu_\delta$) are given in  columns 6 and 7. The proper
motion vectors determined from both the 1.3 and 3.6 cm data are overlaid
on the continuum image of Sgr A West at 3.6 cm (Fig. 2).

\subsection{Radial velocity}
\subsubsection{Construction of the H92$\alpha$ line cube}
The H92$\alpha$ line ($\nu_0=8309.393$ MHz) observations were centered
at two radial velocities (see Table 1), 0 km s$^{-1}$ at the early epochs
(before 1992) and $-200$ km s$^{-1}$ at the epochs after 1993. The observations
can be calibrated to form two line cubes at 0 km s$^{-1}$ and $-200$ km s$^{-1}$,
respectively.
Both data cubes have 31 channels, with a channel width of 0.3906 MHz,
corresponding to 14.1 km s$^{-1}$ in velocity resolution. Excluding the
first channel due to poor bandpass signals in the correlator configuration,
each of the cubes covers a velocity range of 423 km s$^{-1}$. Due to the
broad velocity distribution of the H92$\alpha$ line in the range from --350
to +350 km s$^{-1}$ in the Galactic center region, none of the observations
covers the full extent of the line emission. This limitation makes it
difficult to construct a continuum-free line cube. The final line cubes
were made using the following technique: (1) for the $-200$
km~s$^{-1}$ data cube, we used  channels 29 and 30 at velocities of
$-383$ and $-397$ km~s$^{-1}$ to represent the line-free channels
and concatenate them to the other end of the $-200$ km s$^{-1}$ cube;
(2) using UVLIN, the continuum emission was linearly interpolated and
the fitted continuum emission was subtracted from the $uv$ data across
the line cube to produce continuum-free line data. For the 0 km s$^{-1}$
cube, there are essentially no line-free channels. However, the two
line cubes overlap in the velocity range 0 to $-200$ km s$^{-1}$. We
averaged the four overlapping channels at velocities ranging from $-169$
to $-212$ km~s$^{-1}$. In the same velocity range, the line emission
can be determined from the $-200$ km~s$^{-1}$ cube. A line-free channel
was created by subtracting the line emission from the averaged channel.
Then, the line-free channel was attached to both ends of the 0 km~s$^{-1}$
cube and the continuum level was interpolated linearly across the line
cube. Again the fitted continuum  was subtracted from the visibility data
to form the line (continuum-free) cube. We note that this technique works
only if the change ($\Delta S$) of the continuum flux density ($S$) over
the  velocity range ($\Delta V=550$ km~s$^{-1}$ or $\Delta \nu=15.3$ MHz)
is less than the noise-to-signal ratio,
namely,
$\displaystyle {\left|{\Delta S \over S}\right| \approx \left|\alpha
{\Delta \nu \over \nu}\right| < {\sigma_{\rm ch} \over S},}
$ where
$S \propto \nu^{-\alpha}$ and 1 $\sigma_{\rm ch}$ noise in each channel.
For the optically thin free-free emission from Sgr A West, $\alpha\sim 0.1$ and
${\left|\displaystyle{\Delta S \over S}\right|\approx 0.002 \alpha}=0.0002$.
The uncertainties introduced from the continuum subtraction is much less than
the thermal noise.

At this point, we regridded the visibility data by interpolating the velocity
so that the velocities at the adjacent channels between the
0 km s$^{-1}$ and $-200$ km s$^{-1}$ cubes are matched. The final
velocity separation between channels is then resampled to 15~km s$^{-1}$.

Furthermore, the two image line cubes were constructed from the 0 km
s$^{-1}$ and $-200$ km s$^{-1}$ image line data cubes  with robustness
weighting ($R=0$). Using the robustness parameters of 0 and 2, we achieved
the synthesized beams of $1.^{\prime\prime}0\times0.^{\prime\prime}95$
(19\arcdeg) and 1$.^{\prime\prime}0\times0.^{\prime\prime}83$
(3\arcdeg) for the 0 km s$^{-1}$ and --200 km s$^{-1}$ image
line cubes, respectively. The two image cubes were combined to form the final
high-resolution line image cube by convolving the synthesized image to
a circular beam of 1.25$^{\prime\prime}$. We also convolved the
line image cube to a large circular beam (2$^{\prime\prime}$) to detect
a low-surface brightness structure at larger scales. The rms fluctuations
over the cube were not uniform with values with 0.15 mJy
beam$^{-1}$ for the channels from the $-200$ km~s$^{-1}$ data cube and 0.27 mJy
beam$^{-1}$ for the 0 km~s$^{-1}$ data cube.

Fig. 4 shows the channel images covering the velocity range  --415
to 200 \kms. The current data are in good agreement with the data of
\citet{rob93} except for the ``Bar'', the Mini-cavity and the IRS 6
region where the high negative-velocity range ($V_{\rm LSR} <-212$ km~s$^{-1}$)
was not covered by these authors. The high negative-velocity components were
imaged separately and discussed by
\citet{rob96}.

\subsubsection{Radial velocity in the three mini-spiral arms}

Fig. 5a shows the image of the integrated H92$\alpha$ line intensity. This
clearly delineates the three well-known kinematic features of Sgr A West:
the Northern Arm, Eastern Arm and Western Arc. The H92$\alpha$ line spectra
at the positions marked by the circles in each of the streams (Fig. 5b)
are shown in Fig. 5c. We determined the kinematic parameters (radial velocity
and line-width) from the spectra at these locations using Gaussian fitting.
Table 3 summarizes the results. Columns 1, 4 and 7 are the identification
of the locations in the three arms. Columns 2, 5 and 8 are the RA and Dec
offsets from Sgr A*. Columns 3, 6 and 9 list the LSR velocity and FWHM
line-width of the velocity components from the LSQ fitting.

\section{Results}
\subsection{Three-dimensional velocities of the winds from supergiants IRS 7 and IRS 8}
Fig. 6 shows the finding chart for the IR sources in the radio image of
Sgr A West.

{\bf IRS 7.} IRS 7 is the brightest near-IR source at the Galactic center, associated
with an M supergiant \citep{woll82,lebo82}. In our high-angular-resolution
map at 1.3 cm (Fig. 7a), the head of IRS 7 was resolved into several bright
components in a shape consistent with a bow shock and a tailed structure
$\sim$2\arcsec~(0.1 pc) north of the head. The shape of the bow shock is
in good agreement with that observed with lower resolution by \cite{yusef92}
at 2 cm. The bridge between the head of the bow shock and the emission knot
in the tail is resolved out at our  resolution of 0.1\arcsec$\times$0.2\arcsec.
Fig. 7c shows the detailed structure of the radio emission from the bow shock.

We overlay the IRS 7-SiO maser position of \citet{reid07}, and star positions
from several IR measurements on the radio images for comparison in Fig. 7a.
The IRS 7-SiO maser appears to be surrounded by radio continuum emission in the
high-resolution image at 1.3 cm, and agrees with the centroid position of the
radio emission in the low-resolution image at 3.6 cm (contours in Fig. 7a) within
an offset $\le 0.1\arcsec$. The centroid position at 3.6 cm at epoch 2002X is
in good agreement with that determined by \citet{yusef89} at 2 cm at an early
epoch, after correction for proper motion. The positions of the IR star determined
in the IR measurements by a number of IR groups \citep{blum96,genz00,vieh06}
show  offsets ($\sim$0.\arcsec1-0.\arcsec2) from the radio positions (Fig. 7a). The
IRS 7-SiO maser, believed to be located close to the M supergiant ($<10$ mas),
has been used for the position registration in the coordinate frames at IR and
radio wavelengths \citep{ment97, reid03, reid07}. Therefore, we use the position
of the IRS7-SiO maser measured at 2006.23 \citep{reid07} as the reference position
for the star of IRS 7, that is, the IR positions used in this paper have been
corrected for the offsets between the position of the IRS 7 star from various
published catalogs and that of the IRS 7-SiO maser at 2006.23.

The proper motion of IRS 7, $\mu_\alpha=-1.5\pm1.2$ mas y$^{-1}$
and $\mu_\delta=-5.4\pm0.6$ mas y$^{-1}$ at the epoch 2002X,
was determined from the four epochs' data at 3.6 cm,
giving ${ V_x = -56\pm44}$ \kms~and  ${V_y = -205\pm21}$ \kms,
agreeing well with the proper motion of the IR star from \cite{genz00}.
The radial velocity determined from the H92$\alpha$ line
is $V_{\rm LSR} = -123\pm7$ \kms~(Fig. 7b), which is in good agreement with
that derived from [NeII] emission line \citep{sera91}.
The total velocity of the ionized gas,
${V=\sqrt{V_x^2+V_y^2+V^2_{\rm LSR}}}= 246\pm20$ \kms,
agrees with the results measured from the SiO maser
within 3$\sigma$ \citep{reid07}. Based on the cometary morphology,
\citet{yusef91}  proposed that the radio structure (Fig. 7c) is
caused by the ram pressure of a nuclear wind or by radiative pressure
arising from the IRS 16 cluster of stars surrounding Sgr A*.
The current observations agree with the models discussed by
\citet{yusef91} and \citet{yusef92}.

{\bf IRS 8.} IRS 8 was detected at 2.2 $\mu$m by \citet{beck75},
with an estimated luminosity  $\sim1\times10^{5}~L_\sun$. The bow-shock
structure of radio continuum emission in the high-resolution image of
IRS 8 at 1.3 cm (Fig. 8) is in excellent agreement with
the IR structure and the location of the IRS 8 star  at $\Delta\alpha=$1.\arcsec2~and
$\Delta\delta=$29.\arcsec3~\citep{geba04}. The position of
the radio continuum peak agrees with that of the IR apex in the
bow-shock. The proper motion of the radio peak is measured to
be $\mu_\alpha=1.8\pm0.3$ mas y$^{-1}$,
$\mu_\delta=-1.1\pm0.5$ mas y$^{-1}$, or $V_{\rm t} =\sqrt{ V_x^2 +V_y^2}=
80\pm14$ \kms~(P.A.$=121\arcdeg\pm24\arcdeg$).

In the lower resolution ($\theta_{\rm FWHM}=2^{\prime\prime}$) channel image
in H92$\alpha$, a symmetrical line emission has been detected at $-10$ km s$^{-1}$
in the IRS 8 region. We integrated the velocity from $-25$ to 5 km s$^{-1}$
to show the integrated-line-flux image (contours in Fig. 9a). We refer to this
structure, which has a size of 5\arcsec~(EW) by 6\arcsec~(NS) (blue), as the
``IRS 8 nebula'' since its radial velocity is consistent with that of the IRS 8
star \citep{geba06}. In Fig. 9a, the IRS 8 nebula is compared to the pseudo-color
image of the integrated-line emission from the Northern Arm in the velocity
range 35--170 km s$^{-1}$. The intensity-weighted velocity images are also
shown in Fig. 9b, for the negative-velocity gas in the IRS 8 nebula. Fig. 9c
shows the intensity-weighted velocity distribution of the redshifted gas in
the Northern Arm. A high-spatial-resolution (1.\arcsec25) spectrum in Fig. 9d
was created from region 1 with the dominant line emission at $-18\pm4$ \kms~from
the IRS 8 nebula and much weaker line emission from the Northern Arm. A spectrum
of the line emission at $87\pm7$ \kms~from region 3 in the Northern Arm is shown
in Fig. 9e. In Fig. 9f, the spectrum (black) from region 2 is compared to the
spectrum (red) from the position of the radio continuum peak in the bow shock.
The H92$\alpha$ spectra in the bow-shock region show both a broad, redshifted
feature at $V_{\rm LSR}=80\pm28$ km s$^{-1}$ with $\Delta V_{\rm FWHM}=137\pm53$
km s$^{-1}$ and a somewhat narrower feature at $V_{\rm LSR}=-14\pm 5$ km s$^{-1}$
with $\Delta V_{\rm FWHM}=52\pm17$ km s$^{-1}$. The H92$\alpha$ line spectra
in the shocked region agree with the spectrum of [Ne{\rm II}] at IRS 8 in a
larger area \citep{geba04}. Furthermore, a comparison of H92$\alpha$ line
spectra shows that line emission from region 2 (in the tail of the IRS 8
bow shock) is a factor of 1.5 stronger than that from the position at the
continuum peak (the head of the IRS 8 bow shock). We derived line-to-continuum
ratios (L/C) of 5$\pm1$\% and  2.5$\pm0.5$\% from the tail and head of the
bow shock, respectively. The significant difference in L/C between the head
and the tail suggests that the local thermodynamic equilibroum (LTE) electron
temperature in the head
($T_e\sim1.3\times10^4$ K) is higher than that in the tail ($T_e\sim7.0\times10^3$
K), if the gas is optically thin. The suggested higher electron temperature
in the head of the bow shock may result from a strong shock interaction
of the IRS 8 nebula with gas in the Northern Arm. Fig. 9a also shows that
at the position of region 2, both the positive-velocity emission from
the Northern Arm (color) and the negative velocity emission from the IRS 8 nebula
(contours) are enhanced, possible evidence that the ionized gas in both
the velocity components may be compressed due to their collision. If the
interaction can be verified with improved data, we would conclude that
both the IRS 8 star and the nebula are located close to the Northern Arm
and approach the Mini-spiral arm from the far side with respect to Sgr~A*
considering their opposite radial velocities.

Fig. 9g shows a spectrum toward IRS 8 nebula, integrated over
a region of size 6\arcsec$\times$5\arcsec~(P.A.=0\arcdeg) centered at an offset
from Sgr A* of $\Delta\alpha=-$1.\arcsec19, $\Delta\delta=$26.\arcsec3.
The IR star is located $\sim$4\arcsec~NE of the nebula center. We fit two
Gaussian components to the integrated spectrum, giving $S_{\rm L}=34\pm5$ mJy,
$V_{\rm LSR}=-12$ \kms, $\Delta V_{\rm FWHM}=46\pm20$ \kms~from the IRS 8
nebula and $S_{\rm L}=26\pm4$ mJy, $V_{\rm LSR}=75\pm24$ \kms,
$\Delta V_{\rm FWHM}=122\pm50$ \kms~from the Northern Arm stream.
The two components are clearly separated in the integrated spectrum.
For the IRS 8 nebula (the negative-velocity component),
the emission measure (EM$\approx 8\times10^6$ cm$^{-6}$ pc) and
the mean electron density ($n_e\approx 6\times10^3$ cm$^{-3}$)
are inferred assuming that the H92$\alpha$ line is optically thin.
Based on the derived excitation parameter ($U\approx 35$ cm$^{-2}$ pc),  the
rate of ionizing photons ($N_{Lyc}\approx1.5\times10^{49}$
phot. s$^{-1}$) is inferred on the assumption that only 10\% of
the Lyman continuum flux contributes to ionizing the IRS 8 nebula owing
to the fact that the ionizing star is located on the edge of the nebula.
Thus, the ionizing source is equivalent to an O5.5-6 zero-age
main sequence (ZAMS) star \citep{pana73}, which agrees well
with the spectral type inferred from the IR spectrum \citep{geba06}.
The location of the IRS 8 star with respect to the edge of the nebula,
displaced by 4\arcsec~($\sim0.15$ pc) from the center, is striking. This
displacement suggests that the star runs away from the progenital ionized
cloud (as delineated by the blue contours in Fig. 9a) into a dense medium,
the Northern Arm (as scaled with  color in the same figure). The shape
and the location of the observed bow shock with respect to the IR star
also agree with this scenario. The velocity of the star is probably
similar to the bow-shock velocity, that is, $V_{\rm bs}\sim\Delta V_{\rm FWHM}=46$
\kms~with respect to the nebular center which is at a velocity of $\sim$0 \kms.
The observed transverse velocity $V_{\rm t} =80\pm16$ \kms~(P.A.=121\arcdeg$\pm$25\arcdeg)
from our proper motion measurement of the apex corresponds to
the velocity of the medium flow in the Northern Arm shocked by the stellar wind
from IRS 8. The time
for the star to move from the center to the edge of the nebula would be
$>3\times10^3$ y if the star has the same velocity as that of the bow
shock ($V_{\rm bs}$).

\subsection{Motions of the sources in the Northern Arm}
{\bf IRS 5SE1.} A bright radio source, X7 (S$\sim$7 mJy at 3.6 cm),
can be identified in the IRS 5 field. Within the errors, this source
agrees with the mid-IR position of IRS 5SE1 of
\cite{vieh06} (we note that the IR position reported by \cite{perg08}
is offset by more than 1\arcsec~from X7). The radio emission  X7 is resolved
at 1.3 cm (Fig. 10a \& Fig. 22) showing a triangular structure
0.\arcsec5~in size pointing toward Sgr A*. The radio morphology of IRS 5SE1
agrees with the structure of the dust tail observed in the $L\arcmin$ band by \cite{perg08}.
The proper motion data of X7 at 3.6 cm suggest that the source  moves
toward the SW with a transverse velocity of $V_{\rm t}=313\pm31$
km s$^{-1}$ (P.A.$=-148\arcdeg\pm7\arcdeg$),  nearly perpendicular
to the proper motion vector of IRS 5SE1 determined from 2.18 $\mu$m
astrometry \citep{perg08}.
The H92$\alpha$ line spectrum shows a spatially extended, broad spectral feature
at $V_{\rm LSR}=72\pm16$ \kms~with $\Delta V_{\rm FWHM}= 116\pm41$ \kms~(Fig. 3c).
The radial velocity is consistent with the velocity of the Northern Arm but
the transverse velocity is 2 times large. Based on the radio observations,
IRS 5SE1 appears to run into the Northern Arm.

{\bf IRS 10W.} IRS 10W is located in the Northern Arm. A shell-like radio
continuum source
(K8 in Fig. 10b) is revealed in the high-resolution image at 1.3 cm,
suggesting an association with a bow shock. We note that the orientation
of the radio bow shock appears to be very different (by $\sim$120\arcdeg) from
that determined from the near-IR observations \citep{tann05}. The apex of
the radio bow-shock emission appears to be located SW with respect to
the mid-IR source IRS 10W \citep{vieh06}. Proper motion measurements of
the radio bow shock imply a southward
motion of $V_{\rm t}=73\pm30$ km s$^{-1}$ (P.A.$=171\arcdeg\pm20\arcdeg$).
The H92$\alpha$ line spectrum at K8  shows a prominent line emission feature
at $V_{\rm LSR}=67\pm2$ km s$^{-1}$ with  $\Delta V_{\rm FWHM}=49\pm4$ km s$^{-1}$
(Fig. 3a),
suggesting that this radio source is associated with the Northern Arm.

{\bf IRS 21.} In the high-resolution 1.3-cm radio image, the core of the ionized
gas surrounding IRS 21 is resolved with a deconvolved size of
0.\arcsec24$\times$0.\arcsec15~(P.A.=98\arcdeg) and a total flux density
of 9.0$\pm$0.5 mJy (Fig. 10c); the source is slightly resolved at 3.6 cm with
a total flux density of 10$\pm$1 mJy.  The measurements are consistent
with a free--free origin of  the radio  emission from the externally
ionized winds of the IRS 21 star. The morphology of the ionized gas appears to be in
good agreement with the dust emission structure observed in the IR bands
\citep{tann02}. The proper motion measurements suggest that the radio source (K36)
of IRS 21  moves SW with a transverse velocity of
$V_{\rm t}=114\pm17$ \kms~(P.A.$=-127\arcdeg\pm15\arcdeg$). The H92$\alpha$ line
spectrum (K36 in Fig. 3c) shows a radial velocity of
$V_{\rm LSR}=-92\pm4$ km s$^{-1}$ with $\Delta V_{\rm FWHM}= 97\pm10$ \kms.
The moving direction of the radio source K36 appears to be similar to that
of the Northern Arm gas at this location
($V_{\rm z}=-130$ \kms, $V_{\rm t}=401$ \kms with P.A.$=-132$\arcdeg)
as predicted from the Keplerian model (see Section 5) but the magnitude of total velocity
appears to be significantly less than (by a factor of $\sim$3) the model values.
This discrepancy suggests that the radio source K36 of
IRS 21 might be in an orbit significantly different from that of the Northern Arm.

{\bf CXOGC J174540.029003.} This  X-ray transient was discovered by the Chandra X-ray
observatory \citep{muno05, porq05}, while a double radio source was found to be
associated with the X-ray source \citep{bow05}. The double radio source (at the 2005
epoch during the burst) is shown in Fig. 10f. The SW component was present in all three
epochs with  varying flux densities of 1.1$\pm0.1$, 1.1$\pm$0.1 and 3.4$\pm$0.1 mJy
in 1991K, 1999K and 2005K, respectively. The position of the SW component agrees with
the X-ray source within the uncertainties, suggesting that this component is associated
with that of the X-ray source, presumably a low-mass X-ray binary. The NE component was
present only in the  2005K epoch with flux density 3.5$\pm$0.1 mJy and was not detected
at the 3$\sigma$ level of 0.11 and 0.14 mJy beam$^{-1}$ in the 1999K and 1991K images,
respectively; this suggests that the NE component was a hot spot associated with the
head of the jet ejected from the persistent, radio-variable star. The SW component shows
a large proper motion, with the transverse velocity of $V_{\rm t}= 468\pm60$
\kms~(P.A.$=-35\arcdeg\pm6\arcdeg$) toward the NW (Fig. 10). The radial velocity of the
gas in this direction, as determined from the H92$\alpha$ line data, is
$V_{\rm LSR}=-182\pm19$ \kms. Both the value of radial velocity and the vector of a
transverse velocity are consistent with the velocity predicted in the numerical model
for the Northern Arm stream (see Figs. 21b and 21c and Section 5). Of course, there are no
reasons that the X-ray transient CXOGC J174540.029003 should share the motion of the
Northern Arm. The agreement between the transverse velocity of the radio source
associated with the X-ray transient and the kinematics of the gas in the Northern
Arm might be just a coincidence. Also, the X-ray transient is shown to be located within
0.\arcsec15 (1$\sigma$) of IRS 33SW (marked with a plus in Fig. 10f) which was detected
in the mid-IR \citep{vieh06}. The positional error ($\pm$0.\arcsec15) in the mid-IR
appears to be large. The position coincidence between the X-ray transient and the
mid-IR source deserves to be further investigated.

Assuming that the NE component was ejected from the  X-ray source located at  K40,
a proper motion of $\mu_\alpha>89$ mas y$^{-1}$ and $\mu_\delta>58$ mas y$^{-1}$ is
inferred, that is, the velocity of the NE component with respect to K40 is $>$4000 \kms.
The jet velocity ejected from the radio transient is about an order of magnitude greater
than its orbital velocity of $\sim$500 \kms~in this region, as observed and predicted
from the orbital model for the Northern Arm (see Fig. 21c).

\subsection{The sources in the Eastern Arm}
Fig. 11 shows the radio components in the Eastern Arm.  One of the striking radio features
in the Eastern Arm is the arc at $\Delta \alpha=$10.\arcsec6~ and $\Delta \delta=-$6.\arcsec0
with a width of 0.\arcsec2 and  a length of at least 3\arcsec~(Fig. 11a). The same morphology
is observed at both 1.3 and 3.6 cm (Figs. 1, 2 and 6). The IRS 28/IRS 4 star is located close
to the location where this radio arc is bent. The structure is resolved at 1.3 cm and proper
motion measurements at this wavelength give a large uncertainty; therefore, we use the 3.6 cm
data for our reported proper motion measurements. The proper motion derived from the radio
component X18 near the center of the arc indicates that it moves westward at
$V_{\rm t}=89\pm12$ \kms~(P.A.$=-102\arcdeg\pm56\arcdeg$). At this location, the radial
velocity is $V_{\rm LSR}=154\pm4$ \kms.
These gas motions contrast with those of the star IRS 28:
$V_{\rm t}=215$ \kms~(P.A.$=159\arcdeg\pm4\arcdeg$)
and $V_{\rm LSR}=-55$ \kms~determined from the observations of the SiO maser \citep{reid07}.
Thus, the ionized gas and the evolved star are probably unrelated. On the other hand, an He I
star (He I 17) in the IRS 4 region shows a broad line profile ($\Delta V_{\rm FWHM}\sim 500$
\kms)~centered at $V_{\rm LSR}\sim130$ \kms~\citep{krab91}, which agrees with that of X18.
We raise the possibility that the high-velocity wind from He I 17 has shocked the ambient
gas in the Eastern Arm, and has thereby produced the arc of radio emission.

The component K66 appears to be associated with the mid IR source VISIR 12
\citep{vieh06}, showing an arc-like structure with a NW proper motion,
$V_{\rm t} = 87\pm20$ \kms~(P.A.$=-29\arcdeg\pm13\arcdeg$) and $V_{\rm LSR}=163\pm4$
\kms~(Fig. 11c). The H92$\alpha$ line shows a radial velocity gradient of 5 km s$^{-1}$ per
arcsec across this feature. There is no obvious velocity discontinuity. It is possible
that K66 is a continuation of the arc feature described above.

In the IRS 9 region there are two ``head-tail'' radio components
(K57 and K59) located NE and SW of the IR star (IRS 9N) (Fig. 11b),
which is located at the southern rim of the  Eastern cavity
\citep{zhao98}. Both radio components move generally SW,
with $V_{\rm t}=101\pm27$ \kms~(P.A.$=-110\arcdeg\pm50\arcdeg$) and
186$\pm19$ \kms~(P.A.$=-168\arcdeg\pm4\arcdeg$) for K57 and  K59,
respectively. The radial velocities of $V_{\rm LSR}=133\pm4$
\kms~and $145\pm4$ \kms~from the H92$\alpha$ observations are
consistent with the values measured from other lines such as Br-$\gamma$
\citep{paum04}, but differ greatly from  that of the IRS 9-SiO maser:
$-342$ \kms~\citep{reid07}, suggesting that IRS 9  is not
associated with the Eastern Arm.

The radio complex (K48, K50, and K51) may well be associated with
IRS 9NW (Fig. 11d). The mean proper motion of the complex is
$\overline \mu_\alpha=-4.25\pm0.38$ mas y$^{-1}$ and
$\overline \mu_\delta=2.15\pm0.34$ mas y$^{-1}$,
implying $\overline V_{\rm t}=181\pm14$ \kms~(P.A.$=-63\arcdeg\pm9\arcdeg$).
The H92$\alpha$ line spectra (Fig. 3b) show multiple velocity components
at $V_{\rm LSR}=-70\pm15$ \kms~and $98\pm92$ \kms~from K48,  $V_{\rm LSR}=-76\pm22$
\kms~and $91\pm15$ \kms~and $163\pm21$ \kms~from K50, and
$V_{\rm LSR}=98\pm20$ \kms~and $163\pm21$ \kms~from K51, suggesting
the presence of more than one velocity stream along the line of sight.
We also note that any redshifted components at V$_{\rm LSR} > 200$
\kms~would not be covered by the observations.

The Eastern Arm may in fact have several kinematic components. In the H92$\alpha$
line profiles along the portion of the Eastern Arm (see E1-E5 in Fig. 5c)
that  \cite{paum04} termed the ``Ribbon'', one can clearly see the positive velocity
features around +70 to +110 \kms~that correspond to what Paumard et
al. (2004) called the ``Eastern Bridge'', a separate kinematic
component. In addition, a weak negative-velocity feature at $\sim-$100 km s$^{-1}$
is also present (see E7-E9 in Fig. 5c). Unfortunately, our H92$\alpha$ line data
cube does not contain the high positive velocities ($>$ 220 \kms) that are found
in the ``Tip'' feature, which may be related to the Eastern Arm (see
Vollmer \& Duschl, 2000),
although the two are quite distinct in the Br-$\gamma$ spectra of Paumard et al
(2004). While Paumard et al. (2004) drew a distinction between the Eastern Arm
(their ``Ribbon'') and the Bar, we find that the quasi-continuity in
the position and velocity of the gas in the Eastern Arm (positions E1 to
E11) and the Bar (positions E13 to E17; see Figs. 5 and 20) reinforces
the possibility that these features can be unified as a single
dynamical entity, as was suggested by \cite{liszt03}.
He advanced
a circular ring model, which connects the dynamics and placement
of the innermost parts of the Eastern Arm with those of the Bar, but
does not appear to reproduce the outer structure of the Eastern Arm.
Indeed, we show below in Section 5 that the radial
velocities and positions are consistent with motion around a single
Keplerian orbit.  However, the continuity is unclear at around
position E12, so the coherence of this feature remains to be
demonstrated.

\subsection{The sources in the Western Arc}
The radio emission from the Western Arc (Fig. 6) is weak and only a few sources
are compact and bright enough ($S>1.2$ mJy beam$^{-1}$) for proper motion
measurements. Fig. 12 shows radio components with measurements of proper motion
in the Western Arc. A compact radio component, X6, in the Northern part of the
Western Arc shows a double structure (Fig. 12a). It shows a NE-ward motion with
an implied transverse velocity of $V_{\rm t}=299\pm36$ \kms~(P.A.$=66\arcdeg\pm12\arcdeg$),
and the radial velocity from the H92$\alpha$ line is $V_{\rm LSR}=31\pm11$ \kms~at
this location. Somewhat to the east of the Western Arc, the compact radio component
X24 is identified with the IR star MP-9.0-14.4 (Fig. 12b). The proper motion
measurements suggest that X24 moves SW-ward with $V_{\rm t}=244\pm43$
\kms~(P.A.$=-147\arcdeg\pm9\arcdeg$) and $V_{\rm LSR}=-18\pm8$ \kms.
In the Western Arc (Fig. 12c), the filament X23 shows a NW-ward motion with
$V_{\rm t}=537\pm74$ \kms~(P.A.$=-25\arcdeg\pm6\arcdeg$) and
$V_{\rm LSR}=-44\pm4$ \kms. Located 5\arcsec~NE to X23, X21 shows nearly W-ward
motion with  $V_{\rm t}=187\pm44$ \kms~(P.A.$=-72\arcdeg\pm26\arcdeg$).
The H92$\alpha$ line of X21 shows a double profile with peaks at
$V_{\rm LSR}=-51\pm5$ \kms~and $-110\pm7$ \kms. The weaker component,
X19, shows NE-ward motion with $V_{\rm t}=244\pm63$ \kms~(P.A.$=64\arcdeg\pm23\arcdeg$)
and $V_{\rm LSR}=-30\pm4$ \kms. We note that the proper motions of the
three components (X19, X21 and X23) appear to be inconsistent with each
other, which could result from a substantial contribution of non-orbital
motions. If non-orbital motions are random, a vector average could help
reduce the effect of non-orbital motion in the orbital fitting program
discussed in Section 5. The mean proper motion in this region obtained
by vector averaging the three components  is $\overline \mu_\alpha=-3.61\pm0.74$
mas yr$^{-1}$ and $\overline \mu_\delta=2.52\pm0.49$ mas y$^{-1}$,
corresponding to $\overline V_{\rm t}=167\pm25$ \kms~(P.Ai.$=-55\arcdeg\pm13\arcdeg$)
NW-ward.

\subsection{The sources near Sgr A*}
Fig 13 shows the radio images at 1.3 cm (color for the epoch 2005K) and 3.6 cm
(contours for the epoch 2002X ) along with the positions of the IR stars in
the IRS 16 region. The most prominent feature in both the 1.3 and 3.6 cm
images is the linear feature ($\sim4$\arcsec~in length, $<0.$\arcsec5~in width),
located at the NW edge of the Northern Arm. In the middle of the linear feature,
there is an elongated  radio component, K20. The radio source K20 may be
associated with the HeI star (HeI-N2), which shows a P-Cygni HeI profile
 \citep{paum01}. The radial velocity of the star determined from IR line
observations, $-97^{-64}_{+56}$ \kms, is similar to that of the Northern Arm
gas in the same direction, as determined from the H92$\alpha$ line. However,
this coincidence may just be fortuitous. On the other hand, K20 appears to be
the compressed, ionized edge of the Northern Arm, which was also observed clearly
at 3.8 $\mu$m with the VLT \citep{muzi07}. This compression plausibly results from
the collective winds and radiation pressure from all of the high mass stars in the
IRS 16 cluster.

In addition, we searched the literature and only
found that MP+2.37--0.29 \citep{genz00} is close to HeI-N2, with
proper motion measurement. The magnitude of the star velocity agrees
well with that of K20 but the P.A. of the transverse
velocity between the two objects differs more than 100\arcdeg.
K20 shows a SW-ward proper motion of $V_{\rm t}=354\pm19$
\kms~(P.A.$=-136\arcdeg\pm4\arcdeg$), which is consistent with this compressional
front being caused by the IRS 16 stars. Two Gaussian components were fitted to the
broad spectrum of the H92$\alpha$ line at K20, the dominant one being at
${V_{\rm LSR}=-41\pm11}$ \kms~with ${\Delta V_{\rm FWHM}} = 137\pm37$
\kms. The total velocity is then $V=356\pm20$ \kms. Considering the fact that
the gas in the Northern Arm stream is located behind Sgr A* based on the LSQ
fitting and numerical calculations in Section 5.5, the velocity vector of K20 suggests
that the source moves toward its periapse in an orbit that carries it around
Sgr A*. If the proper motion of the linear feature indicates the track of the
gas motion governed by the gravity of the SMBH, we would expect the velocity of
K20 to increase as it approaches Sgr A*. A comparison between its motion and
what the dynamical models (Section 5) predict for the transverse velocity would
be helpful in understanding the accretion process occuring
in the immediate vicinity around Sgr A*.

\subsection{Mini-cavity and IRS 13}

Fig. 14a shows the locations of a dozen  IR stars in
the Mini-cavity region, including the IRS 13 and IRS 2 complexes
to the West and the IRS 33 complex at the Eastern edge of the cavity.
The proper motions
of the compact continuum components are shown (Fig. 14b),
suggesting that the bulk motion of the ionized gas in this region
is toward the West. The source $\varepsilon$  \citep{yusef91} (K22),
the closest component to Sgr A* (offset 1.\arcsec6), has a proper motion of
$\mu_\alpha=-8.8\pm0.5$  mas y$^{-1}$ and $\mu_\delta=-1.4\pm1.5$
mas y$^{-1}$ or $V_{\rm t} = 338\pm21$  \kms~(P.A.$=-99\arcdeg\pm61\arcdeg$)
to the SW, almost directly away from Sgr A*. We note that this is consistent
with the model of \cite{ward92}, who postulated that source $\varepsilon$
has resulted from the confluence of gravitationally focused winds from the IRS 16 stars.

The mean proper motion of the components K25, K28, K33, K40, and K45 in the
IRS 33 region (NE rim of the ``Mini-cavity'') is
$\overline \mu_\alpha=-9.3\pm0.2$ mas y$^{-1}$
and $\overline \mu_\delta=1.4\pm0.3$ mas y$^{-1}$
($\overline V_{\rm t}=355\pm8$ \kms, P.A.$=-81\arcdeg\pm12\arcdeg$),
while for components K32 (source $\zeta$), K41 and K42 (source $\eta$) \citep{yusef90}
in the middle of the ``Mini-cavity'',
$\overline \mu_\alpha=-5.5\pm0.2$ mas y$^{-1}$ and $\overline \mu_\delta=1.7\pm0.5$
mas y$^{-1}$ ($\overline V_{\rm t}=218\pm9$ \kms,
P.A.$=-73\arcdeg\pm16\arcdeg$). The components K47, K49, K53 and K54
around the SW rim show $\overline \mu_\alpha=-5.1\pm0.2$ mas y$^{-1}$ and
$\overline \mu_\delta=-1.2\pm0.4$ mas y$^{-1}$ ($\overline V_{\rm t}=199\pm8$ \kms,
P.A.$=-103\arcdeg\pm19\arcdeg$). The magnitude of the transverse velocity
determined from proper motion measurements appears to be comparable to that
of the radial velocity observed from the H92$\alpha$ line.

The most surprising region is the IRS 13 complex (Fig. 15), with proper motion
vectors pointing in many directions, suggesting that the local stellar winds
might be playing a significant role in the motion of the ionized gas
\citep{zhao98,muzi08}. However, averaging over the proper motion vectors
from the HII components (K21, K23, K24, K26, K27, K29, K31, and K35) in
IRS 13, the resultant vector is to the NW, that is, $\overline \mu_\alpha=-2.91\pm0.04$
mas y$^{-1}$ and $\overline \mu_\delta=2.50\pm0.07$ mas y$^{-1}$,
corresponding to $V_{\rm t}=145\pm2$ \kms~(P.A.$=-49\arcdeg\pm1\arcdeg$).

On the other hand, the observations of the H92$\alpha$ line show
that in the ``Bar'' region, a bright emission feature south of
Sgr A* \citep{eker83}, there are two distinct velocity components,
one associated with the Northern Arm  and the other related to
the ionized stream in the Eastern Arm \citep{rob93}. These components
are also shown in the Br-$\gamma$ line observations \citep{paum04}
although the authors did not regard the bar emission as part of Eastern Arm.
Fig. 16 shows the spectra at the HII components in the ``Mini-cavity''
region covering the velocity range from --415 to 200 \kms.
Around the NE rim, the positive velocity associated with the
Eastern Arm stream is prominent while the negative-velocity
component associated with the Northern Arm stream is weak with
broad-line profile ($\Delta V_{\rm FWHM} > 100$ \kms). In the Mini-cavity,
the spectra close to Sgr A* are dominated by components with positive
radial velocity. For example, the source $\varepsilon$ (K22) has a broad
component at $V_{\rm LSR} =37\pm7$ \kms~with $\Delta V_{\rm FWHM}=63\pm16$
\kms~and a narrower ($\Delta V_{\rm FWHM}=22\pm15$ \kms)
feature at a high positive velocity ($V_{\rm LSR}=165\pm5$ \kms).
Of course, possible lines at $V_{\rm LSR} > 200$ \kms~may
have been missed due to the limited velocity coverage.
The negative-velocity component at $-275$ \kms~becomes
strong about 5\arcsec~to the SW of Sgr A* and peaks at the Southern rim
(K47) of the Mini-cavity. Along the Western rim, the negative-velocity
gas shows a trend similar to that in the Mini-cavity, {\it i.e.}
it appears to be strong, broad and localized at the SW rim (K43) and
it becomes weak as it moves closer to Sgr A*. In comparison with the
negative-velocity component, the positive-velocity ($\sim$+50 \kms)
component becomes stronger and broader as it gets closer to Sgr A*.
The H92$\alpha$ line observations
also suggest that the Mini-cavity was created by strong interactions between
various flows. \citet{morr87} proposed that the Mini-cavity might be due to the
winds from massive stars in this region. Other  interactions, such
as the interaction between the  Eastern and Northern Arm streams
or the interactions between outflows from Sgr A* and the streams might also
cause high temperature and therefore a depression in the radio free--free
emission. The high LTE temperature ($T_e^*$) in the Bar reported by
\cite{rob93} might be owing to such an interaction.

\subsection{The IRS 6 and IRS 34 region}
Fig. 17 shows the radio sources in the IRS 6/IRS 34 region,
which is located 6\arcsec~NW of Sgr A* (Fig. 6). In Fig. 18,
the H92$\alpha$ line shows a noticeable gradient in radial velocity
from $V_{\rm LSR}=-102\pm10$ \kms~at (K19)
to $V_{\rm LSR}=-184\pm5$ \kms~at (K11).
This velocity gradient was also detected by \citet{rob96}. The velocity
gradient observed in the H92$\alpha$ line agrees well with that observed
in the Br-$\gamma$ line (see Fig.A.2b of Paumard et al. 2004). The H92$\alpha$
line spectrum at K19 (Fig. 3a) contains at least
three Gaussian components. Averaging the vectors from the HII components
(K10, K11, K13, K14, K17 and K19) in the IRS 6 region, we derive the mean
proper motion of $\overline \mu_\alpha=-3.4\pm0.2$ and $\overline \mu_\delta=1.4\pm0.2$
mas y$^{-1}$, suggesting a bulk motion toward the NW
($V_{\rm t}=139\pm8$ \kms, P.A.$=-68\arcdeg\pm8\arcdeg$).

High velocity of the Bullet (X12) was reported early based on
proper motion measurements at 2 and 1.3 cm \citep{yusef98,zhao98}.
At 1.3 cm, the structure is resolved  to at least three knots with
varying peak intensities in time, which results in large uncertainties in proper
motion measurements.  Instead, we use the low-resolution data at 3.6 cm
to determine the proper motion of the centroid position of the source.
We confirm that the source moves NW but the magnitude of the transverse
velocity is reduced by a factor of $\sim$3: $V_{\rm t}=319\pm37$
\kms~(P.A.$=-53\arcdeg\pm12\arcdeg$). The revised transverse velocity appears
to be consistent with the velocity of the ionized flow in the Eastern
Arm at this location. However the radial velocities of the
two spectral features, $V_{\rm LSR}=-25\pm9$ \kms~and
$V_{\rm LSR}=70\pm13$ \kms (Fig. 3c),
deviates significantly from the value at this location predicted from the Keplerian model.

\subsection{The overall three-dimensional velocity field}

We imaged the peak radial velocity values derived from the H92$\alpha$ line in
the central 80\arcsec$\times$80\arcsec~(Fig. 18). The mean transverse velocities
along the $x$ and $y$ axes  of the radio knots in the three ionized arms
were determined by averaging the proper motions of several individual
radio knots given in Table 2. The mean values of the transverse velocities
with respect to Sgr A* ($\overline{V}_{x}$, $\overline{V}_{y}$),
the mean radial velocity with respect to the LSR ($\overline{V}_{\rm LSR}$) and
the mean position offsets from Sgr A* (${\rm \overline{\Delta \alpha}}$,
${\rm \overline{\Delta \delta}}$) were derived and are summarized in Table 4.
Column 1 lists the name of the region in which the three-dimensional velocities
were determined. The radio IDs in column 2 indicate the radio knots that were
included in the averaging. Column 3 gives the IRS names of the sources in the corresponding
regions. Fig. 18 shows the images of the vectors of the transverse velocities
superimposed on the image of peak radial velocities in the  ionized arms
based on the VLA  observations of the H92$\alpha$ line. The proper motion
vectors determined from the VLA observations suggest that all three streams
appear to move around Sgr A* in the sense of counterclockwise rotation, as viewed
from  the Earth.

\section{Dynamic models for the ionized streams}
\subsection{Three bundles of Keplerian orbits}

In the case of elliptical motion, adopting the distance ($D=8$ kpc), there are
six orbital parameters ($a$, $e$, $\Omega$, $\omega$, $i$, $M_{\rm dyn}$)
to completely describe an orbit projected onto the plane of the sky. Here $a$
is the size of the semi-major, $e$ is eccentricity, $M_{\rm dyn}$ is
the dynamical mass, $\Omega$ is the longitude of the line of nodes,
$\omega$ is the angle of periapsis with respect to the line of nodes,
and $i$ is the inclination angle. Based on the assumptions that the positions
determined in Section 3, which follow the locus of the stream in each of the arms,
are located along a single, Keplerian orbit, and that the central mass
is fixed at the location of Sgr A*, the orbital parameters ($a$, $e$,
$\Omega$, $\omega$, $i$) for the orbital geometry can be determined with
LSQ fitting to those positions. The dynamical mass
($M_{\rm dyn}$), on the other hand, can be subsequently determined by
fitting the radial velocities in each of the streams. The detailed procedure
for determining  the orbital parameters is developed and described
in the Appendix.

We apply this technique to Sgr A West. Fig. 19 shows the fits (solid ellipses)
to the observed loci (dots) for each of the three streams. For the loci along
each stream, four sets of solutions for the orbital parameters ($a$, $e$,
$\Omega$, $\omega$, $i$) can be derived from the LSQ fitting of the quadratic
equation (A1). The first two geometrical parameters ($a$, $e$) are the same
for all the solutions. The four combinations of the three angular parameters
($\Omega$, $\omega$, $i$) correspond to the two mirror images about the sky plane,
and in each of these, the direction of flow can be clockwise or counterclockwise.
The proper motions can be used to decide between clockwise and counterclockwise,
and the sign of the radial velocities determines which of the mirror images is
correct.

Fig. 18 shows the  measured vectors of the transverse velocities distributed
in each of the three streams, showing that the ionized streams are in
counterclockwise rotation around the dynamical center. The remaining degeneracy of the
two mirror images can be solved by the radial velocity determined from the
H92$\alpha$ line. Thus, we can unambiguously determine the orbital parameters
for the three major streams in Sgr A West.

There is no principle dictating that the gas arrayed along any given
stream must all be on the same Keplerian orbit. Indeed, gas in a tidally sheared
cloud, which may describe these streams, will in general be different orbits,
depending on where it was located in the original cloud. However,
except under unusual circumstances, such as a radially infalling
cloud, the orbits assumed by the different parcels of gas within a shearing
cloud will be rather similar, and the ensemble of orbits will be a family
of similar orbits. We therefore adopt the simplification of a single
orbit in order to characterize the orbit family. The assumptions underlying
this procedure are somewhat vindicated by our success in
fitting single orbits to the streams.

Table 5 summarizes the LSQ solutions of the orbital parameters
for the three streams from the best fits. Both the Northern Arm and
Eastern Arm streams appear to be in Keplerian motion on high-eccentricity
elliptical orbits of $e=0.83\pm0.10$ and  $0.82\pm0.05$, respectively.
Our best fit for the Western Arc stream indicates that it is in a nearly circular
orbit ($e=0.20\pm0.15$), consistent with what has previously been suggested
\citep{rob93,lacy91}. Constrained by  proper motion measurements which show that
all  three streams rotate in a counterclockwise sense  around Sgr A*, the
inclination angles must be greater than 90\arcdeg. From the best-fitted
solutions above, we can unambiguously determine the inclination angles to be
139\arcdeg$\pm10$\arcdeg, 122\arcdeg$\pm5$\arcdeg~and 117\arcdeg$\pm3$\arcdeg~for
the Northern Arm, Eastern Arm and Western Arc, respectively.

\subsection{Dynamical mass in Sgr A West}

The above analysis does not yield information on the mass.
In order to determine the dynamical mass, velocity information is required.
If the radial velocity of Sgr A* with respect to the LSR,
the transverse velocity of Sgr A* with respect to that of the
dynamical center and the position offsets of Sgr A* from the
dynamical center can be neglected, then  $V_z=V_{\rm LSR}$
and the location of Sgr A* defines  the dynamic center.
For a given total velocity $V=\sqrt{V_x^2+V_y^2+V_z^2}$
at position ($x,y,z$), the dynamical equation relating $V$ to the mass
($M_{\rm dyn}$) is

\begin{equation}
V={M_{\rm dyn}^{1/2}\left(\frac{2}{r}
-\frac{1}{a}\right)^{1/2}},
\end{equation}
\noindent where $r$ is the radial distance from  the dynamical center,
which can be expressed as a function of the
projected coordinates ($x,y$) in  Equation (B2).

In principle, the dynamical mass in Sgr A West can be derived by
fitting the total velocity to Equation (1). Since only a few measurements
of proper motion in the outer region of Sgr A West are available, the fit
of the measured total velocities leaves a sizeable uncertainty in the
determination of the dynamical mass. On the other hand, our radial velocity
measurements from each of the three orbits cover a large fraction of the
complete orbits of each flow, so we can use the radial velocities to
constrain the dynamical mass with Equation (B1). With the best-fit
orbital parameters ($a$, $e$, $\Omega$, $\omega$, $i$), we solve Equation
(B1) using our orbit models for three values of the central
mass, that is,  $M_{\rm dyn} =1.2,~4.2,~10\times10^6$ M$_\odot$,
and compare the predicted radial velocities to those measured at
each position along the orbits. Fig. 20 shows the results of fitting in
each of the three streams. In general, the model with a mass of
$M_{\rm dyn}=4.2\times 10^{6}$ M$_\odot$ fits the data, consistent
with the prevailing view  that the mass of Sgr A*  determined by
fitting the orbits of the IR stars \citep{ghez08,ghez03,scho02}
dominates the central dynamics. However, not surprisingly, there are
some deviations between the model and data (see Fig. 20). The deviations
of the radial velocity in the inner region  can be attributed  to some local
non-gravitational effects such as winds, MHD flows, magnetic pressure
gradients, and possibly interactions between streams.
Deviations at larger radii might result from the increasingly
important contribution of stars to the enclosed mass as
the radius increases, thus causing deviations from pure
Keplerian orbits. Of course, many of these apparent deviations could
simply result from the failure of the basic assumption in this analysis:
that each of the three streams follows a unique Keplerian orbit.
In any case, the total dynamical mass in the central 3 pc appears
to be $\sim1\times10^7$ $M_\odot$.

\subsection{Model calculation and three-dimensional location of the three streams}
The fitted parameters are summarized in Table 5 for the three streams in
Sgr A West. Using these parameters, we have modeled
these streams as the  model of three bundles of
Keplerian orbits. In addition to the best-fitted orbital parameters
(Table 5), we also used  the  dynamical mass of
$M_{\rm dyn}=4.2\times10^6$ $M_{\odot}$ and a dispersion of
$\Delta a =\pm 0.25a$ in the semi-major axis
to roughly match the width of the orbits in
each of the streams. The ranges of the true anomaly
192\arcdeg -- 460\arcdeg, 195\arcdeg -- 430\arcdeg, and
130\arcdeg -- 420\arcdeg, were used to calculate the three
streams for~the Northern~Arm,
the Eastern~Arm, and the Western~Arc, respectively.

The comparison between the observed kinematics of Sgr A West and
the calculation based on the best-fitted orbital model is shown in Fig. 21.
The radial velocities ($V_{z}$) of the streams are plotted in
Fig. 21b. The vectors of the transverse velocity ($V_{ x},V_{y}$)
are illustrated in Fig. 21c. The three-dimensional velocity field calculated from
our model appears to be in good agreement with the observations.
In other words, the three bundles of  elliptical orbits along with
the orbital parameters ($a$, $e$, $\Omega$, $\omega$, $i$)
derived from the LSQ fitting are consistent with the model
calculations.

The locations of the three streams along the  line of sight are shown in
Fig. 21d, suggesting that most of the orbiting ionized gas in the ``Bar''
region is located behind Sgr A*. The highly inhomogeneous distribution of
the ionized gas allows  the low-frequency ($\nu\sim0.3$ GHz)
radio emission from Sgr A*, which is subject to strong free--free absorption,
to pass through the gap in the ionized streams, as was suggested from
the VLA and Giant Metrewave Radio Telescope (GMRT) observations \citep{ant05}.

The total velocity and kinetic energy per unit mass were also calculated and
are shown in Figs. 21e and 21f, respectively. The figures show that
the specific kinetic energy of both the Northern and Eastern Arms reaches a maximum in
the ``Bar'' region. The high specific kinetic energy density there emphasizes the possibility
that the Mini-cavity was created by strong shocks resulting from the collision
of the two streams.

\section{A magnetically determined morphology in the Northern Arm?}
The dynamical model discussed above is based on a spherical gravitational
potential centered on  Sgr A*.  However, the magnetic field in the Northern
Arm might be strong enough to cause observable deviations from the kinematics
determined by gravity alone. Polarization measurements at 12.5 $\mu$m of
thermal dust emission arising in the Northern Arm indicate that the dust
grains in this structure are extremely well aligned by a uniform magnetic field
oriented along the long axis of the arm \citep{aitk98,glas03}.
The uniformity  of the field direction is attributed to shear in the direction of the flow
\citep{aitk91}, which is inevitable, given that the finite breadth of the
Northern Arm gives rise to a significant differential gravitational
force across the arm. The magnetic field strength estimated from dynamical
considerations and from the application of the method of \citet{chan53}
is $\gtrsim$ 2 mG.

Our high-resolution image at 1.3 cm (Fig. 22) reveals a  suggestive
sinuous structure in the Northern Arm that  could have a magnetic origin.
Although we do not know the line-of-sight structure of this feature,
the morphology is consistent with a projected helix having 1.5--2 well-defined
wavelengths between declinations (J2000) of --29\arcdeg~00\arcmin~17.\arcsec5 and
--29\arcdeg~00\arcmin~22\arcsec. To illustrate this, we show model-projected
helices in Fig. 22 for comparison with the observed feature.
The velocity ($V_x=-18$ \kms,
$V_y=-223$ \kms, $V_z=70$ \kms) at this location ($\Delta x =7$\arcsec,
$\Delta y =10$\arcsec) is obtained from the orbital model. The tilt (the
angle of the velocity vector with respect to the line of sight)
of this Northern Arm fragment is arccos$(Vz/V)\sim$72\arcdeg,
which is reasonably consistent with the best-fit projection angles of the model
helices.  A helix is a natural morphology for a twisted magnetic field frozen
into a plasma; the twist could result, for example, from torques exerted on the
plasma by reconnection between the Arm field and the ambient field at the surface of
the Northern Arm. This process is important in the Earth's magnetotail, and results
from the ``draping'' of the solar wind field around the Earth's magnetosphere.
It is possible that a similar process occurs in the Northern Arm where the
head of the Northern Arm plows through the ambient Galactic center field.

A sinuous morphology in the Northern Arm had previously been noted by \cite{yusef89}
in a lower-quality 2-cm VLA image (see, e.g., Fig.  1 of
\cite{yusef90}) and this structure is evident in Fig. 22 of
this paper.  However, in that case, the wavelength was suggested
to be 0.4 pc, much larger than the 0.12 pc wavelength of the feature
considered here. \cite{yusef93} interpreted this longer wavelength waviness in
terms of Rayleigh--Taylor or Kelvin--Helmholtz instabilities caused by winds from the young
stars in the IRS 16 cluster. Perhaps there is a homologous structure at multiple
scales in the Northern Arm, or perhaps there is an evolution toward
increasing wavelength from N to S along the arm as the gas accelerates
toward the black hole. In order to investigate this possibility, we
considered a model helix in which the wavelength of the helical turns
increases southward along the Northern Arm as Sgr A* is approached. This is illustrated by
the model helix superimposed on the right side of Fig. 22. Although the observed structure
becomes more diffuse to the south, there is a good correspondence between this model
and the observations.

Observations of the mid-IR polarization vectors and
of the velocity field with spatial resolution comparable to that in Fig. 22
would provide a test of the hypothesis that a strong magnetic field imposes
a helical geometry on the otherwise laminar flow of the Northern Arm.
If the pitch angle of $\sim$15\arcdeg~reflects the ratio of
velocities perpendicular to and along the arm, $\sim$0.25, then velocity perturbations
as large as 60 km s$^{-1}$ are predicted, using a total flow velocity of ~250 km s$^{-1}$
at this location.  In radial velocity only, the perturbation may be only a few tens of
km s$^{-1}$. In addition the mid-IR polarization vectors should everywhere be
tangent to the helix.

\section{Summary and Conclusion}

Using the VLA, we have observed the Galactic center with
an angular resolution of 0.\arcsec1 at 1.3 cm. Along with the data
obtained at previous epochs at 1.3 and 3.6 cm, we measured the proper
motions of 71 compact HII components in Sgr A West. Using VLA archival data,
we constructed an H92$\alpha$ line image cube with angular and velocity
resolutions of 1.\arcsec25 and 15 \kms, respectively, covering
the velocity range from +200 \kms~to --415 \kms.

With the observed proper motion and  radial velocity measurements
from the ionized gas, we have investigated the three-dimensional velocity distributions
in the central 3 pc. The loci and motions of the three well-known
ionized streams in Sgr A West can be modeled with Keplerian motions in
three bundles of elliptical orbits. We developed a procedure using a
least-square fit of the loci of the ionized streams at the
Galactic center. The orbital parameters ($a$, $e$, $\Omega$, $\omega$, $i$)
were determined confirming that the three ionized streams corresponding to
the three radio continuum features (Northern Arm, Eastern Arm and Western Arc)
are confined within the central 3 pc. The dynamics appear to be
dominated by the SMBH at Sgr A*, and the total dynamical mass within a
radius of 1.5 pc is $\lesssim1\times10^7$ M$_\odot$.
With the Keplerian model and the fitted orbital parameters,
we numerically calculated the kinematics and spatial distribution of the
ionized gas. The calculated three-dimensional velocities are in good agreement with the
observed velocity distribution, based on the observations
of  proper motions and radial velocities. This numerical model
confirms that three bundles of elliptical orbits with the orbital parameters
($a$, $e$, $\Omega$, $\omega$, $i$) derived from our LSQ fitting and an assumed mass
for the SMBH
of 4.2$\times10^6$ M$_\odot$ at the dynamical center are
a good approach to modeling the dynamics of the ionized gas
in the central 3 pc.

With the determined orbital parameters for the ionized
streams, our numerical calculations suggest that the Northern and
Eastern streams might have collided in the ``Bar'' region located
5\arcsec~SW of Sgr A*. Such a substantial interaction between the two
streams could  have  contributed to the formation  of
the Mini-cavity.

In the IRS 16 region located 2\arcsec~E of Sgr A*, the
high-resolution observations reveal a linear radio feature (K20).
The collective stellar winds and radiation
from the IRS 16 cluster are likely responsible for compressing the
edge of the Northern Arm at this location, and causing it to be
particularly bright.

In the IRS 8 region, a radio bow-shock structure is observed,
similar to that revealed by IR observations. A shell-like nebula
is revealed by the H92$\alpha$ line image showing
a narrow feature ($\Delta V_{\rm FWHM} =52\pm17$ \kms) at
$V_{\rm LSR}=-12$ \kms. The H92$\alpha$ line observations show that
the NE part of this nebula physically interacts with the Northern Arm.

Finally, from the high-resolution VLA observations, a helical structure
is revealed in the Northern Arm, suggesting that, in addition to the
predominantly Keplerian dynamics attributable to the central mass, MHD effects
play a role in the production of the detailed structure in the orbiting ionized
gas. The predictions from the MHD model are testable with future high-resolution
observations of the mid-IR polarization vectors and the velocity field.
\acknowledgments
The VLA is operated by the National Radio Astronomy
Observatory (NRAO). The NRAO is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.
M.R.M. has been partially supported in this work by NSF grant AST-0406816 to UCLA.
T.A. has been supported by the NSFC (10503008).

redpajama_set_name: RedPajamaArXiv


DORMA's new range of EM hold-open magnets provides the perfect complement to a technically and aesthetically advanced range of fire and smoke check door products. These new market-orientated developments are characterized by their ease of fixing and functional elegance. And thanks to comprehensive quality assurance, they also offer maximum reliability and service life.
The statutory regulations which apply in many countries allow fire and smoke check doors to be held open for a limited period of time by electro-magnetic hold-open devices which, in the event of a fire, are de-energized to release the door so as to enable automatic closing.
It must also be possible to manually release any hold-open device. According to the applicable guidelines for hold-open systems, a manual release pushbutton is necessary when employing electromagnets in such applications. The pushbutton employed must be red, carry the wording "Close door", be located in the immediate vicinity of the door, and must not be hidden when the door is in its hold-open position.


text:
UNODC Survey: Peru coca crop increases but still at lowest rate in the Andean region
5 December 2017 - The surface used to grow coca leaf crops in Peru in 2016 increased by 9 per cent, which is the lowest increase in the region, according to the latest Peru Coca Survey, launched in Lima today. The area under cultivation grew by more than 3,500 hectares (ha) in 2016, compared to 2015. The report, jointly produced by UNODC and the country's Government, indicates that the area used for cultivating the raw material for cocaine production increased from 40,300 hectares to 43,900 hectares.
Speaking at the event, UNODC's Representative in Peru, Kristian Hölge, highlighted that since there had been an increase in coca cultivation in the region "we need to be on alert and strive to improve methodologies and use of new technology, as well as promote new research initiatives in support of the implementation of the National Strategy against Drugs 2017-2021."
Under the country's plan for reducing the illegal coca growing area, according to the Peruvian Government eradication in 2016 was still high at 30,151 ha. The areas impacted by these eradication actions are Aguaytia, Alto Huallaga, Pichis-Palcazu-Pachitea, San Gabán and Orellana. The Apurimac, Ene and Mantaro River Valleys (known for its Spanish acronym of VRAEM), which is the top coca producing area in Peru, showed an increase of 11 per cent in the coca leaf cultivated surface.
Additional analysis contained in the survey focuses on addressing the extent of coca crops in national protected areas and in Amazon native communities' lands. In this period, 168 hectares of coca crops in production have been detected on national protected areas, and about 5,600 hectares on their buffer zones. Concerning native communities, Shimpenchariato and Gran Shinongari were the most affected with 703 hectares and 292 hectares of coca respectively.
Production of sun-dried coca leaves in 2016, which are used by drug traffickers to produce coca paste and cocaine hydrochloride, stood at some 105,960 metric tons (MT), an increase of 10 per cent compared with 2015. As in previous years, 10,728 MT of the total production is used for the traditional practice of coca leaf chewing and 163 MT for industrial production, according to official data, while the remaining 95,069 tons of coca leaf were linked to drug trafficking. The VRAEM region accounted for 77 per cent of this production.
The average farm-gate price of dry coca leaf showed a decrease of 21 per cent, from US$ 3.9 to US$ 3.1 per kilogram (kg). Coca paste price saw a rise of 14 per cent - from US$ 745 to US$ 847 per kg - and the average price of cocaine hydrochloride increased 14 per cent between 2015 and 2016, from US$ 1,133 to US$ 1,289 per kg. Seizures of the latter, meanwhile, increased from 8,465 kg in 2015, to 13,958 kg in 2015, an increase of 65 per cent. Seizures of coca paste increased 20 per cent in the same period, from 11,738 kg to 14,035 kg.

redpajama_set_name: RedPajamaCommonCrawl


text:
from graphql import graphql

from .schema import StarWarsSchema

def test_correctly_mutates_dataset():
    query = '''
      mutation AddBWingQuery($input: IntroduceShipInput!) {
        introduceShip(input: $input) {
          ship {
            id
            name
          }
          faction {
            name
          }
          clientMutationId
        }
      }
    '''
    params = {
        'input': {
            'shipName': 'B-Wing',
            'factionId': '1',
            'clientMutationId': 'abcde',
        }
    }
    expected = {
        'introduceShip': {
            'ship': {
                'id': 'U2hpcDo5',
                'name': 'B-Wing'
            },
            'faction': {
                'name': 'Alliance to Restore the Republic'
            },
            'clientMutationId': 'abcde',
        }
    }
    result = graphql(StarWarsSchema, query, variables=params)
    assert not result.errors
    assert result.data == expected

redpajama_set_name: RedPajamaGithub


Roger Sutton Nelthorpe died on 4th May 2000 after a lifetime of service to his country, his county and his family estates.
He was especially devoted to the Territorial Army and in particular to the Sherwood Rangers Yeomanry, a regiment with which he was associated for more than fifty years. He joined in October 1937 at the invitation of his friend and neighbour the Earl of Yarborough, who was then Commanding Officer.
The Regiment was mobilised at the outbreak of war as a horsed regiment in the 1st Cavalry Division which was sent to Palestine on public order duties. It was there that he took part in a cavalry charge down the main street of Tel Aviv to quell a riot.
The Regiment was soon diverted to more warlike tasks, initially as coastal defence artillery in Tobruk and Crete before being converted to an armoured regiment, and Nelthorpe saw his first action with tanks at the battle of Alam El Halfa, where Rommel's last attempt on Egypt was defeated.
After that battle, he took over command of the Regiment's HQ Squadron, a position he retained until the end of the War two and a half years later. It was his responsibility to supply the Regiment with everything it required and especially with great quantities of fuel and ammunition as it advanced a thousand miles from Egypt to Tunisia and again from Normandy into Germany. During this time, all administrative problems tended to fall on him, a responsibility which he discharged with unfailing skill and good humour.
Perhaps his greatest task was that of totally re-equipping the Regiment during the five short months between its return home from North Africa and its landing in Normandy on D Day. In recognition of his services he was awarded a military MBE.
In 1947, when the Regiment was re-formed, he immediately re-joined, becoming second in command and then Commanding Officer from 1959 to 1964. He was awarded the TD with three clasps.
He devoted much time to public service in the county of Lincoln, being a Governor of the Sir John Nelthorpe School in Brigg, a Justice of the Peace and a Deputy Lieutenant.
His interests in agriculture, and in forestry in particular, are evidenced by the improvements he brought to his estate and he gave much time to numerous committees and organisations connected with these activities.
He was also a General Commissioner of Income Tax and Vice-Chairman of the Lincolnshire Territorial and Auxiliary Forces Association.


text:
Conor MacNeill né le  à West Belfast dans le Comté d'Antrim (Irlande du Nord) est un acteur de télévision et de cinéma.

Filmographie
 2008 : Peacefire
 2008 : La Guerre de l'ombre ()
 2008 : La Cité de l'ombre
 2009 : Cherrybomb
 2010 : An Crisis
 2012 : Saving The Titanic de Maurice Sweeney : Frank Bell
 2017 : The Current War : Les Pionniers de l'électricité (The Current War) de Alfonso Gomez-Rejon  : William Kemmler
 2020 : Artemis Fowl de Kenneth Branagh : un lieutenant des Goblins
 2020 : Industry (série télévisée)
 2022 : Operation Fortune: Ruse de guerre de Guy Ritchie : Bodhi

Liens externes

Naissance en juillet 1988
Acteur nord-irlandais

redpajama_set_name: RedPajamaWikipedia


text:
DIDHD provides timeline on COVID vaccine rollout in UP
Many are wondering when the COVID-19 vaccine will be available to them. The COVID-19 vaccine has been distributed to many provider organizations across Michigan and continues to be distributed and received as supply allows.
Your local public health department encourages all citizens age 16 and older to get vaccinated against COVID-19. In consideration of limited supply, COVID-19 vaccine distribution must follow strict guidance from the U.S. Centers for Disease Control and Prevention and the Michigan Department of Health and Human Services in order to ensure those with the most critical need receive vaccination first.
To get a better picture regarding when you may be able to receive COVID-19 vaccination, listed below are the rollout phases and estimated starting times for each phase for the COVID vaccination process in the Upper Peninsula.
When reviewing this information, it is important to be aware that:
— These time frames of availability are strictly estimates and are entirely dependent upon vaccine supply and distribution to local vaccine providers. As such, time frames of availability are subject to change.
— Those individuals included in each phase may change based on additional information and guidance from national and state experts.
— Public service announcements will be widely distributed prior to the start of each phase.
— There is no need to make a reservation in advance to receive the vaccine unless you are directed to do so by your provider or the health department.
— Vaccination allocation within Michigan varies in quantity by region, and within regions, based upon metrics determined by MDHHS. As such, the quantity of vaccine available within the Upper Peninsula may vary among local health department jurisdiction. As a result, it is possible for one area to be slightly ahead of another in moving through the vaccination phases within their region.
Timeline estimates regarding when you may receive the COVID-19 vaccine are:
December and January
Already started; given by hospital and health department personnel.
— Phase 1A Priority One: Keep critical health care infrastructure open and functioning — i.e., hospitals, critical care units and emergency medical response systems.
Given by CVS and Walgreens and health department personnel.
— 1A Priority Two: Prevent outbreaks and protect residents in long-term care facilities and nursing homes.
Mid-January
Done by multiple vaccination providers from this point forward.
— 1A Priority Three: Health care infrastructure not included in Phase 1A Priority One, such as clinics, dentists and pharmacies.
Mid- to end of January
— Phase 1B: Frontline essential workers and those age 75 and older. Frontline essential workers are those that interact with the public and whose jobs cannot be performed at home. Examples are firefighters and police; education (teachers, support staff, daycare); corrections workers; grocery store workers; public transit workers; food and agriculture; manufacturing; U.S. Postal service workers.
Mid-February
— 1C Priority Group: Ages 65 to 74; those 16 to 64 with medical problems that increase their risk of severe illness from COVID; other essential workers who are non-frontline essential workers.
Adults of any age with these conditions that make for an increased risk of severe illness, hospitalization, admission to the ICU, intubation or mechanical ventilation, or death from the COVID-19 virus: Cancer, chronic kidney disease, chronic obstructive pulmonary disease or COPD, heart conditions, immunocompromised states, obesity, pregnancy, sickle cell disease, smoking, type 2 diabetes
End of March/early April
Phase 2 is a mass vaccination campaign for all those older than age 16 not previous immunized.
— Dickinson-Iron District Health Department
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Appreciates Daily News coverage
From Karen Klenke, president, Niagara Area Historical Society, Niagara, Wis.: Can't thank The Daily News enough ...
Scammers using fake letters in tax collections scam
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Capitol Commission oversteps Legislature by banning open firearms
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Ban on Capitol open carry wise but did not go far enough
The Michigan State Capitol Commission earlier this week banned the open carry of firearms in Michigan's ...


Results demonstrate that properly using the data generated by the systems used to operate your business will help improve operational execution. Why? Because you and your teams will have accurate and actionable information available, enabling you and your managers to set, as well as execute, against those expectations correctly. Equally important is holding workers accountable for their actions that will translate into more successful outcomes for your business.
Leverage Data: Key Performance Indicators ('KPI') are extremely important to optimizing operational execution, such as labor allocation, overtime, food cost, customer satisfaction, speed of service, theft, and employee turnover. These are critical metrics when looking for revenue and profit building opportunities. KPI's are only one step in tying back to your list of best practices. Sharing their importance and holding your team accountable is essential to successful performance.
Share: Leverage the information that your data has provided, to your advantage. How? By sharing the key metrics with your teams. Sure, Daily Sales Reports (DSR) are shared out every day and while they're helpful, they're static and often hide the important message. Each recipient of the DSR has to take the time to review it looking for anomalies that will produce improvements and drawing their own conclusions about what actions should be taken. Going beyond the DSR, Exception-Based Reporting is the best method I know to quickly and concisely communicate key issues directly to those team members responsible for taking action. Labor is one area where knowledge is power. Being notified that 'right now' your location has more labor than needed to meet the customer demand enables you to make a decision, in near real-time, about labor allocation that can have an immediate impact on the bottom line.
Ranking: One of the benefits of being able to see data for every location is that you can compare one store's performance to another. Why are some stores using far more, or for that matter far less, labor for the same or similar amount of sales dollars? Thay can't both be right. Right? Why do some stores sell more or less than other similar locations? Generally, answers to these and many other questions can be found in your data, (SLPH, demographic, mystery shop, guest feedback, or cleanliness ratings). Having the opportunity to quickly and easily combine these different data points will help you pinpoint the outliers. Additionally, operators using advanced reporting and analytic solutions should not only have the ability to compare store performance across their locations they should also have the ability to see how their operations stack up against other brands.
These capabilities enable restaurant management to go beyond simply knowing WHAT happened by helping to understand WHY it happened. Using their data and analysis, restaurants can generate fact-based answers to questions, and those answers can prove or disprove the factors that caused yesterday's results. With this knowledge, operators can either stop doing or do more of whatever is needed to improve performance.
Contests: The ability to see Key Performance Indicators related to individual cashiers, servers and bartenders is important. Ranking staff on items meaningful to your business can help identify contests to drive positive, performance-enhancing behavior in your workplace. Not only can these drive new levels of performance, information generated from these contests can help you identify weaker team members and point out, learn from and share best practices of your best performers.
Trends: While I'm a big believer in exception-based reports because they're concise and can help quickly pinpoint a specific issue I'd also suggest that you take the time to review weekly, monthly and longer time periods to help you spot trends that would otherwise go unnoticed. We're all familiar with the need to look at Same-Store Sales as they have a way of telling you how you're doing over time. But other issues also dictate that you use a longer time window before drawing a conclusion. One example is employee theft. An employee who appears to have suspicious activity (lots of voids, deletes, etc.), for a given day, may, in fact, just have had a bad day. However, if that same employee has a long history of similar suspicious activity then (where there's smoke there's generally fire) you need to take the next step and discuss their behavior with them.
Mismanagement: Another area to consider is Food Cost/Waste but oftentimes this is difficult to control. However, with proper training, the kitchen staff will know what's expected when preparing/portioning each order. Still, without the proper visibility, you could be misled by your management staff. I say that after recently seeing how check level analysis provided by our Enterprise reporting/analytic tool showed what appeared to be possible fraudulent activity. Tickets containing multiple orders of one specific item were being repeatedly rung up and then the checks were being manager comped. This was taking place at more than one site and generally just before the end of the day. One answer, they were Manager Comping and putting the cash in their pockets. The real answer was that they had miscalculated the amount of a particular protein and by falsely creating tickets containing the protein followed by a Manager Comp to get rid of the revenue, their Food Cost magically fell in line. Pretty clever, huh?
When it comes to operational execution there are many other areas, beyond those mentioned, to pay attention to (Labor Turnover, Allocation, Overtime, and Guest Satisfaction). But to pull all this off successfully across all your properties every day you need to properly communicate your expectations, break them down into measurable activities and then actively monitor them to ensure they're being acted on as expected. That brings me back to - inspect what's expected - and I'll add rewarding those that are hitting the mark while coaching those that come up short - will pay dividends in traffic, revenue and profit improvements.
How are you inspecting what you expect?
If you enjoyed this blog, please share using the social buttons at the top of the page and make sure to leave your thoughts in the comment section below!


text:
Influencer Marketing in China
Delivered September 30, 2019. Contributor: ChristineD
Identify case studies of successful influencer marketing campaigns in China with a focus on how creator studios and influencer incubators work. The information will be used to determine how this marketing tactic has developed in China.
INFLUENCER INCUBATOR CASE STUDY
Zhang "BB" Xi is a Gen Y influencer in China with around 300,000 followers in all her social media accounts.
She posts beauty vlogs and tutorials on these platforms.
Even if she has many fans in her social media accounts, she was not able to make a dent yet in the highly-competitive influencer industry.
Still, her legions of fans attracted talent scouts from one of the country's biggest "key opinion leader (KOL)," Ruhnn Holding.
Ruhnn Holding is considered as an influencer management firm or an influencer incubator.
The firm's scouts go through various social media accounts to look for amateurs with over 5,000 followers who have the potential to scale.
The company typically evaluates around 800 people on a monthly basis.
The prospective candidates were then made to take several tests.
One test require identifying best-selling items from 100 pictures to gauge the potential candidate's marketing clout.
This is considered as a significant test as these influencers typically build their own e-commerce stores to sell items to their followers.
The company will also provide a small funding amount to test if many people will signify their interest.
Ruhnn will typically grant 2,000 yuan or around $279.78 on campaigns to try to bring in 10,000 people to each candidate's social media profiles.
If these people became followers, the company became more secure in their decision to take the influencer into their fold.
This ultra-commercialized level of talent search shows the multi-layered strategy of the country's influencer industry.
It is seen to be a potential business model that can be emulated by social media influencers from other countries.
Ruhnn typically offers a contract for 5-10 amateur influencers out of the 800 that it evaluates.
The binding contract will then give the firm sole portrait rights and the privilege to manage the social media platforms and online stores of the influencer.
The chosen influencers will then collaborate with the company to determine which products to sell.
In return, the firm will provide a support group and four months of heavy training to the chosen influencer.
The training will include lessons such as camera presence techniques, types of videos, product-selling, and other relevant topics.
Based on an assessment from a USC associate professor and author of the Social Media Entertainment book, China's influencer industry "has accelerated far more quickly and provides more lucrative careers for its creators" even if it is still in its early stages compared to Western models.
Once Ms. Xi was chosen by Ruhnn from among thousands of accounts, her follower count jumped from 300,000 to almost 1 million across all her social media accounts.
Her number of followers is still increasing and she hopes to further leverage other media types.
Ruhnn's first investment was for an influencer named Dayi Zhang who was known for being "the queen of e-commerce."
Ms. Zhang was able to sell over 1 billion yuan ($145 million) worth of products through her e-commerce store. Her store releases around 1,000 products annually.


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Home>Technologies>Digital Health
Abbott Wins Nod to use Patient Controller App on Apple Mobile Devices
TAGS: Neurological
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The Abbott Park, IL-based company said the approval allows patients living with neurological conditions the ability to manage therapy directly from their personal smartphone.
Omar Ford | Jul 24, 2020
Abbott Laboratories's most recent FDA nod will allow the use of the company's Patient Controller app on compatible personal Apple smartphone devices.
The Abbott Park, IL-based company said this approval allows patients living with neurological conditions, including chronic pain or movement disorders, the ability to manage therapy directly from their personal smartphone.
The approval eliminates the need to carry a separate patient programmer device is eliminated, streamlining the patient's experience and seamlessly integrating therapy management into their life.
Abbott said the Patient Controller app will be integrated into Abbott's broader NeuroSphere Digital Care connected care management platform, which became available in May. It is compatible with Abbott's suite of neuromodulation technologies.
"For physicians who are prescribing and implanting neuromodulation technologies, the ability to integrate therapies into one's everyday life is key," Alexander Escobar, MD., Clinical Assistant Professor of Anesthesiology and Pain Medicine at The University of Toledo, OH, said in a release. "The COVID-19 global health crisis has demanded access to virtual treatment options, especially for those individuals with chronic medical conditions that may have difficulty coming to see their physician or would prefer not to leave their own home. To ensure our patients are receiving the care they need in the appropriate setting, close follow up is critical. Physicians have the ability to remain engaged with their patients through the Apple device, allowing them to interact and treat debilitating chronic pain."
Neuromodulation was a bright spot in Abbott's most earnings. Previously, Abbott's offerings had been impacted by COVID-19.
"Over the course of the second quarter, we saw steady improvements in procedure volumes across our cardiovascular and neuromodulation portfolio," Robert Ford, Abbott's CEO said according to a Seeking Alpha transcript of the earnings call. "For example, at the end of June, our procedure volumes had rebounded to approximately 90% of pre-COVID levels on average in the U.S., which represents a significant recovery compared to procedure activity at the beginning of the second quarter."
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December is busier than I want it to be. Both of my girls' birthday's are this month. (I know, I know. We should have planned better. We should have planned period!!!) This weekend is my youngest's party and next weekend is my oldests. Throw in the other festivities of the season and we are in full blown party mode!
That's a good break from holiday music. I have to say, I have an issue with a particular holiday song. If I hear "Christmas Shoes" one more time I'm going to blow. That song pisses me off! This guy has done everything he could to make us cry; dying mother, sad son who wants to buy her shoes before she goes to met Jesus, the boy doesn't have enough money... CRAP! I will NOT cry! Bad songwriter, BAD Songwriter!
In honor of my youngest birthday that happens to fall on Pearl Harbor Day let's make the namesake drink.
I'm not normally a sweet drink gal, so I just might skip the fruit and just go for the vodka. Cheers!
Let's have a little Optical Illusion fun with our friend Jesus. Try this out!
Now go mingle at our Virtual GNO. When someone leaves a comment, or signs lovely Mr. Linky, go visit their blog and leave a comment. And when your blog is visited, go visit your guests blog. Keep the party going. And invite some of your blog pals!
Come back though, it's a party!