text:
\section{INTRODUCTION}

Fast Radio Bursts (FRBs) are short duration (100~$\mu$s-100~ms)
radio flashes that are extremely bright and appear highly dispersed, and hence thought to be arising from extragalactic distances. Although a
promising Galactic analogue has been found in SGR~1935+2154
\citep{chime2020b, bochenek+20}, the origin of these enigmatic
bursts remains a mystery.  A wide range of FRB models have
been proposed \citep[see, e.g.,][]{Platts2019}, but none have been conclusively
proven.  It is not even known yet if there is a single class of
FRB progenitor or multiple different ones that produce a similar
observational phenomenon.

The discovery of repeating FRBs \citep{Spitler2016, scholz2016} marked a
paradigm shift in FRB research. Repeaters provide an enormous opportunity
to study individual FRB sources in great detail.  Collecting a large number
of bursts from a given source can reveal interesting burst structure
\citep[e.g.,][]{hessels+19}.  Furthermore, since the dispersion measure (DM)
of the bursts is known for repeaters, data from observations can be coherently dedispersed. This allows us
to examine the bursts at extremely high time resolution to explore the
emission mechanism and constrain progenitor models \citep{Nimmo+2021, Majid+2021}.
Repeating FRBs also allow for periodicity searches on a wide range of time scales.
The discovery of a 16.35-day cycle in the burst activity of \riii\
\citep{chime2020a} not only provides an important insight into the progenitor
source of FRBs, it also allows for highly efficient targeted observations
\citep[e.g.][]{marthi+20} to be conducted at the precise times at which
the source is most likely to be active.  A much longer activity cycle has
also been proposed for FRB20121102A\ \citep{20Rajwade, Cruces+2021}, although
it remains to be seen if any other repeaters show this cyclic activity.
Repeating FRBs are also useful targets for searching for short timescale
periodicities of the order of $\sim$ 1~ms to 1~s that would indicate a
neutron star origin.  No pulsar-like periodicity has been detected in any
FRBs \citep{Zhang2018,Li+2021}, but CHIME/FRB recently discovered several
FRBs with sub-second periodic separations of burst components
\citep{chime-subsecond-periodicity-2021}.  This result provides further
evidence in favor of a neutron star origin for FRBs and strongly motivates
deep searches for pulsar-like periodic emission in repeating FRBs.

Precise, sub-arcsecond localization of FRBs allows for unambiguous association
with galaxies and the environs in which they reside. These associations inform
the choice of the models invoked to explain particular FRBs, as they
constrain their genesis and evolution, especially through the interplay between
the progenitor and the circumburst environment
\citep[e.g.][]{Thompson2017, Margalit2018, Thompson2019}. As an example, the
evolution of the rotation measure (RM) of the repeating FRB20121102A\ has led to
some interesting constraints on the properties of the circumburst environment
\citep{Hilmarsson2021} and comparison with predictions
\citep{Piro2018, Margalit2018}.

On 2021-March-31, the Canadian Hydrogen Intensity Mapping Experiment
Fast Radio Burst (CHIME/FRB) collaboration reported that \rss\ was in
a very high burst activity state \citep{CHIMER67ATel}.  Based on this
report, we proposed for and were allocated Director's Discretionary Time
(DDT) to observe with the upgraded Giant Metrewave Radio Telescope
(uGMRT; \citealt{uGMRTpaper}) on 2021-April-5.  Subsequent detections by
the Commensal Real-time Australian Square Kilometre Array Pathfinder
(ASKAP) Fast Transients (CRAFT) survey confined the positional uncertainty
of the source to $\sim 10\arcmin$ \citep{ASKAP-firstATel, ASKAP-secondATel},
which meant we could cover the entire uncertainty region with one GMRT
primary beam at Band-4 (550-750 MHz).  Our observations with the uGMRT,
along with independent campaigns with ASKAP
\citep{ASKAP-localization-ATel, ASKAP-lowband-loc-ATel, Fong2021arXiv}
and the VLA \citep{VLA-localization-ATel, Ravi2021arXiv},
localized the FRB to its present coordinates.

This paper is the first in a series of three detailing our studies
of \rss\ with the uGMRT. Here, we describe the observations and detection
of 48 bursts from \rss\ and present the burst properties.
In \citealt{main+2021} (hereafter P-II), we present the first
ever scintillation timescale measurement of an FRB using combined uGMRT
and 100-m Effelsberg Radio Telescope observations.
Finally, in Wharton et al. (2021, \emph{in prep.}; hereafter P-III),
we detail the precise localization of \rss\ bursts and continuum imaging
of the host galaxy.

This paper is organized as follows. Section~\ref{sec:observations}  describes the observations and the telescope configuration, as well as the burst detection and characterization. In Section~\ref{sec:results}, we describe the results of our DM optimization, burst localization, fluence completeness, short timescale periodicity search and the various properties of the bursts, such as the fluence distribution, the distribution of the burst widths, the statistics of the waiting time between bursts and the burst spectral energies.

\section{OBSERVATIONS AND DATA}\label{sec:observations}
The uGMRT observations of \rss\ were carried out with the Band-4 receivers
on 28 of 30 antennas available at the time, tuned to 550-750 MHz, on 2021-April-05 from
12:30~UTC to 16:30~UTC. The primary beam full width at half maximum (FWHM)
in this band is  $\sim$ 52\arcmin - 38\arcmin.
At the time, the best localization radius of 10\arcmin\ for \rss\ was provided
by ASKAP \citep{ASKAP-secondATel}, which is within the 88\% sensitivity contour
of the GMRT primary beam. We therefore recorded the incoherent array
(IA; \citealt{uGMRTpaper}) beam.

For the observations reported here, we use the IA beam, in which the voltages from each antenna (and each polarization) are first detected and then added. The root mean square (RMS) noise in the beam is hence $\sqrt{N_A}$ times better than a single antenna. The IA beam has a field of view as large as that of a single GMRT dish. In contrast, the phased array (PA; \citealt{uGMRTpaper}) beam is the sum of the voltages from each antenna (for the two polarizations separately) added in phase before detection. As a result, the RMS noise of the PA beam is $N_A$ times better than that of a single GMRT dish. The size of the beam is hence the same as the synthesized beam of the interferometer. The PA beam is hence $\sqrt{N_A}$ times more sensitive than the IA beam.

The GMRT Wideband Backend (GWB) FX correlator was deployed in the 200-MHz Stokes-I interferometer and 8-bit beamformer mode. An FFT of every 4096 samples of the real-valued voltage time series consumes 10.24~$\mu$s of data. Sixty-four contiguous FFTs are integrated for the two polarizations individually from each antenna to obtain a 2048-channel spectrum every 655.36~$\mu$s, which was adequate for temporally resolving the bursts. The polarizations are finally added in quadrature to obtain Stokes-I beam.

Interferometric visibility spectra were concurrently recorded with the fastest possible integration time of 671~ms to ensure adequate temporal sampling of the dispersed burst pulses, to aid in their imaging. Ideally, the shorter the visibility integration time, the better, as it is crucial for a clear isolation of the bursts and subsequent high fidelity imaging. The radio source 3C138 was used as a flux and phase calibrator due to its relative proximity to the region of pointing, resulting in relatively small slewing overheads. The array phases were tied together on 3C138 before every 40-minute scan on the target. The phase corrections for the antennas, referred to a reference antenna, were estimated from the visibilities. The rephasing scans were also used for flux calibration. A 2-minute test scan on the Crab pulsar served as a control beam for dedispersion. In all we have $\approx$ 180 min of on-target exposure.

\subsection{Detecting the bursts}\label{ssec:detection}
We performed a standard \texttt{PRESTO}\footnote{\href{https://github.com/scottransom/presto}{https://github.com/scottransom/presto}}\ \citep*{Ransom2002} search on the incoherent array. The data were visually inspected for radio frequency interference (RFI) and bad channels were manually flagged. The first round of dedispersion was performed with the DM of 414 $\mathrm{pc~cm}^{-3}$ for detecting bright bursts. The data were then dedispersed with a DM of 411\,pc\,cm$^{-3}$, based on visual inspection of the brightest burst.
The 16-bit unsigned integer (\texttt{uint16}) filterbanks as provided by uGMRT were converted to unsigned 8-bit (\texttt{uint8}) filterbanks, which were searched using standard \texttt{PRESTO}\ based pipeline. A large amount of RFI caused the down-conversion to be sub-optimal. Therefore, in addition to above, the \texttt{uint16} filterbanks were de-dispersed and searched using \texttt{single\_pulse\_search.py}.
Candidates with a signal-to-noise (S/N) $\geq 8$ (around 6000 in number) were plotted and manually vetted. A large $\rm S/N$ cutoff was used owing to an excess of residual RFI in the data.
In all we detected 48 bursts over the full exposure time of 180 minutes.

\begin{figure*}

    \centering
    \includegraphics[width=\linewidth,keepaspectratio]{Figures/burst_panorama_gray.pdf}

    \caption{Burst profiles and dynamic spectra in chronological order. Each panel shows the dynamic spectrum of a burst from Table~\ref{tab:fluences} dedispersed to 411\,pc\,cm$^{-3}$, with the upper sub-panel showing the frequency-averaged burst profile. The dynamic spectrum has been binned $5\times$ in frequency and $2\times$ in time. The profile, given at the top sub-panel for each burst, is binned $3\times$ in time. We count bursts 2, 13 and 22 as single bursts, owing to difficulty in determining if they are truly different bursts. While it is not apparent in this figure, there is a faint bridge of emission between the components in burst 22, resulting in an end-to-end width of $\sim315$~ms. A similar argument is applied to the components in burst 2, which also is counted as single. The profiles have been cleaned for RFI by subtracting a smooth off-burst baseline through the burst. }

    \label{fig:burstpanorama}
\end{figure*}

\begin{table*}
    \centering
    \begin{tabular}{r|c|r|r|r|r|r}
    \hline
    Burst  & Barycentric  & Burst width  & Burst width & Peak  & Fluence & Error    \\
       \#  &         TOA  & (zero-crossing) & (boxcar equivalent)  & flux  &     \\
           &   MJD59309+  & ms            & ms &   Jy &   \,Jy\,ms      &  \,Jy\,ms       \\
    \hline
 1 & 0.54335787 & 45.6 & 17.0 &  1.1 &  18.1 &  1.7 \\
 2 & 0.54591884 & 163.8 & 34.3 & 0.8 &  30.1 &  2.4 \\
 3 & 0.54659070 & 91.3 & 23.0 &  1.8 &  41.3 &  1.9 \\
 4 & 0.54761242 & 48.6 & 13.6 & 0.7 &   9.3 &  1.7 \\
 5 & 0.55935229 & 58.5 & 17.8 & 0.7 &  12.8 &  1.7 \\
 6 & 0.57848970 & 65.5 & 14.3 & 0.7 &   9.7 &  1.6 \\
 7 & 0.58136744 & 126.0 & 38.4 & 0.8 &  31.9 &  2.2 \\
 8 & 0.58187302 & 94.3 & 21.4 & 1.2 &  25.8 &  2.5 \\
 9 & 0.58418835 & 57.5 & 16.0 & 1.3 &  20.2 &  1.8 \\
10 & 0.58529781 & 33.7 &  7.5 & 0.6 &   4.8 &  0.8 \\
11 & 0.58921682 & 36.7 &  9.5 & 1.1 &  10.5 &  1.7 \\
12 & 0.59043137 & 33.7 &  10.1 & 0.9 &   9.3 &  1.6 \\
13 & 0.59576209 & 212.3 & 59.3 &  1.0 &  58.4 &  2.9 \\
14 & 0.59626756 & 95.3 & 22.3 & 0.7 &  16.4 &  2.4 \\
15 & 0.59639863 & 19.8 &  6.1 & 0.4 &   2.6 &  0.8 \\
16 & 0.59783325 & 103.2 & 25.2 & 2.1 &  52.9 &  1.8 \\
17 & 0.59870353 & 40.7 & 11.4 & 0.7 &   7.9 &  1.6 \\
18 & 0.61101660 & 69.5 & 19.1 & 1.0 &  19.0 &  1.7 \\
19 & 0.61108629 & 75.4 & 27.9 & 3.9 & 108.0 &  1.6 \\
20 & 0.61256996 & 69.5 & 14.1 & 0.7 &   9.3 &  1.9 \\
21 & 0.61412899 & 33.7 & 7.5 & 0.7 &   5.4 &  1.4 \\
22 & 0.61761505 & 315.5 & 42.1 & 1.6 &  66.5 &  3.8 \\
23 & 0.61763151 & 112.1 & 38.3 & 0.8 &  29.0 &  2.2 \\
24 & 0.62024508 & 79.4 & 23.7 & 0.9 &  21.7 &  2.5 \\
25 & 0.62099280 & 48.6 & 11.9 & 0.8 &   9.0 &  1.5 \\
26 & 0.62315829 & 41.7 & 16.5 & 0.6 &   9.3 &  1.6 \\
27 & 0.62398148 & 86.3 & 25.4 & 0.8 &  20.4 &  2.1 \\
28 & 0.62409520 & 18.9 & 0.7 & 0.0 &   0.0 &  0.1 \\
29 & 0.62932227 & 52.6 & 13.7 & 0.7 &   9.6 &  1.8 \\
30 & 0.63120928 & 84.3 & 22.9 & 1.3 &  29.7 &  1.8 \\
31 & 0.64163927 & 59.5 & 17.2 & 0.7 &  11.9 &  1.6 \\
32 & 0.64281245 & 61.5 & 15.4 & 2.0 &  31.3 &  1.6 \\
33 & 0.64447160 & 51.6 & 13.3 & 0.8 &  10.0 &  1.5 \\
34 & 0.64848111 & 36.7 & 15.3 & 0.6 &   8.9 &  1.6 \\
35 & 0.65177353 & 43.7 & 10.7 & 0.7 &   7.4 &  1.7 \\
36 & 0.65382734 & 44.6 & 15.7 & 0.5 &   7.2 &  1.6 \\
37 & 0.65603984 & 51.6 & 13.1 & 0.9 &  12.1 &  1.7 \\
38 & 0.65638858 & 82.4 & 18.6 & 1.0 &  18.9 &  1.9 \\
39 & 0.65702755 & 68.5 & 15.6 & 0.5 &   8.5 &  1.8 \\
40 & 0.65930498 & 62.5 & 14.8 & 0.8 &  11.2 &  1.6 \\
41 & 0.66312276 & 54.6 & 18.7 & 0.7 &  12.4 &  1.9 \\
42 & 0.66338438 & 63.5 & 16.8 & 1.1 &  17.8 &  1.9 \\
43 & 0.66415983 & 93.3 & 25.1 & 0.9 &  22.2 &  1.8 \\
44 & 0.66577462 & 92.3 & 29.5 & 1.1 &  32.5 &  2.4 \\
45 & 0.67941141 & 45.6 & 15.7 & 0.7 &  11.4 &  1.9 \\
46 & 0.67978340 & 63.5 & 20.9 & 0.7 &  14.7 &  1.9 \\
47 & 0.68965288 & 42.7 & 12.1 & 0.6 &   7.0 &  1.7 \\
48 & 0.68973336 & 53.6 & 10.3 & 0.5 &   5.4 &  1.6 \\
\hline
\end{tabular}
\caption{Time-ordered burst measurements: the ToA is referenced to 550 MHz, the bottom of the band. While burst 28 was detected after RFI cleaning, its fluence could not be estimated reliably.}
\label{tab:fluences}
\end{table*}

\subsection{Flux density calibration}
\label{section:fluxcal}
The detected bursts were isolated for calibration and fluence estimation
using 1~sec of time-frequency data centered on the dedispersed burst peak.
First, the mean `off-burst' emission was estimated in every spectral channel, which was then subtracted and divided by, to establish bandpass correction. Similarly, the corresponding phasing scan on 3C138 and an off-calibrator scan were used to measure the deflection on the calibrator. This deflection was scaled appropriately for the spectral shape of the flux density model \citep{Perley2017}. The frequency-averaged time series of the burst and the calibrator scan were then compared to set the flux scale for the bursts, from which we read off the peak flux and estimate the fluence. The time of arrival (ToA) for each burst is measured at the peak, referred to the lowest frequency of the band, 550~MHz. Since the localized position of the FRB  is less than 2.5\arcmin\ away from the antenna boresight (see Section~\ref{ssec:localization}), no primary beam correction has been applied for our fluence estimates, given that the GMRT FoV at Band-4 is $\sim40\arcmin$. The gallery of the detected bursts is shown in Figure~\ref{fig:burstpanorama}. The ToA, burst width, peak flux, fluence and errorbar on the fluence are all listed in Table~\ref{tab:fluences}.

\section{RESULTS AND PROPERTIES}
\label{sec:results}

\subsection{DM optimization with the power spectrum}\label{ssec:dmopt}
In detecting the bursts, as well as estimating their fluences, widths and ToAs, we use have used DM = 411\,pc\,cm$^{-3}$. However, as we noted in \cite{marthi+20}, the DM that maximizes the peak S/N gives a profile that is degenerate with intrinsic temporal substructure. For bursts that consist of multiple components, a reasonable assumption to consider is that the individual components have no intrinsic drift, while there is only a bulk drift between the components \citep[e.g. in][they make a similar argument]{hessels+19}. One would expect that for the DM that aligns each component perfectly across frequency, it maximizes the total energy in the substructure of a frequency-averaged burst profile. We employ the same method outlined in \cite{marthi+20} to determine the DM that maximizes the energy in the substructure, but we expand on it here for completeness.

We incoherently de-disperse the brightest burst for DMs between 410.00\,pc\,cm$^{-3}$\ to 412.00\,pc\,cm$^{-3}$\ in steps of 0.01\,pc\,cm$^{-3}$. The steps undertaken to determine the DM that maximizes substructure energy are as follows: (i) A singular value decomposition (SVD) of the burst dynamic spectrum is taken. The leading mode eigenfunction of frequency for both of the on- and off-pulse, as a weighting function across the frequency, is applied to the dynamic spectrum, and the time-series data determined. (ii) an FFT of the time-series data produces the power spectrum across Doppler frequencies for both of the on- and off-pulse. The power spectrum of the off-pulse is subtracted from that of the on-pulse, giving us the noise-subtracted power spectrum. (iii) the noise-subtracted power spectrum, which we rebinned from 200 Doppler frequencies into 16 in log-scale, is examined from low to high log-Doppler frequencies to determine the cut-off Doppler frequency when the power across DM shows a Gaussian maximum. For the brightest burst, the power versus DM at the cut-off log-Doppler frequency 0.18 kHz is shown in Figure~\ref{fig:dmfit}. (iv) a Guassian profile is fit to the power versus DM to determine the optimal DM and the error, at the peak and the FWHM, respectively.
The DM thus identified is $410.78\pm0.54 (1\sigma)$ \,pc\,cm$^{-3}$.

We ran {\tt DM\_phase}\footnote{\href{https://github.com/danielemichilli/DM_phase}{https://github.com/danielemichilli/DM\_phase}} \citep{DM_phase_pub}, the DM optimization routine that maximizes the coherent power across the bandwidth, for comparison with our SVD-based method on the brightest burst. It returned a DM of $410.33\pm1.15 (1\sigma)$ \,pc\,cm$^{-3}$, which is in agreement within the error bars with the DM optimized by our method.

\begin{figure}

    \includegraphics[width=\linewidth,keepaspectratio]{Figures/GMRT-burstvsDM.pdf}\\
    \includegraphics[width=0.5\linewidth, keepaspectratio]{Figures/2b.pdf}
    \includegraphics[width=0.49\linewidth, keepaspectratio]{Figures/2c.pdf}\\

    \caption{DM estimation from burst 19 using the SVD method. \emph{Top Left}:  The frequency-averaged burst profile as a function of DM. Note that the S/N peaks at $\sim$418\,pc\,cm$^{-3}$, but that it compromises the substructure. \emph{Top Right}: The power spectrum as a function of the DM. \emph{Bottom Left}: S/N of the burst power at 180 Hz, following the steps outlined in Section~\ref{ssec:dmopt}. \emph{Bottom Right}: The waterfall and the profile for DM=410.78\,pc\,cm$^{-3}$. }

    \label{fig:dmfit}
\end{figure}

\subsection{Burst localization and persistent radio emission}\label{ssec:localization}
At the time of observation, the best localization \citep{ASKAP-secondATel} for \rss\ had an uncertainty of $15\arcmin$ in right ascension and $5\arcmin$ in declination. This is well within the primary beam of the uGMRT, with excellent prospects for simultaneous localization with the visibilities. Our proposal to observe with the uGMRT focused on the localization of the bursts by using its simultaneous interferometric and beamformer capabilities. We observed with the boresight pointing at (J2000) RA: $05^{\rm h}07^{\rm m}55^{\rm s}$, Dec:$+26\degr02\arcmin00\arcsec$.

After identifying the time of arrival (ToA) of the bursts in the beam, the
visibilities of the brightest burst (Burst 19) were imaged and the burst was
localized to sub-arcsecond precision \citep{GMRT-localization-ATel}.
The position was consistent with the earlier VLA localization
\citep{VLA-localization-ATel} and subsequent localizations with
the ASKAP low-band \citep{ASKAP-lowband-loc-ATel} and the
EVN \citep{EVN-localization-ATel}.
In addition, we detect persistent radio emission of $0.7\pm0.1$~mJy
at 650~MHz \citep{GMRT-PRS-ATel} coincident with both the burst position and the galaxy
SDSS J050803.48+260338.0. The persistent radio emission was later found
to be resolved on milliarcsecond scales \citep{EVN-localization-ATel}
and likely associated with star formation in the host galaxy
\citep{Ravi2021arXiv,Fong2021arXiv}.
The complete analysis and findings of the uGRMT burst localization are
described in P-III. These observations provide a proof-of-concept for
future burst localizations of active repeating FRBs with the uGMRT.

\subsection{Spectral energy}
The most energetic burst in our observations has the largest peak flux. At 108\,Jy\,ms, this bright burst is detected with a S/N of $\sim$40, $\sim 4\times$-$5\times$ lower than ideal due to RFI. This burst would have been detected with a S/N of $\gtrsim$200 with the phased array beam under the same RFI conditions, considering the $\sqrt{N_A}$ boost in sensitivity accrued from co-adding the voltages in phase.
At a luminosity distance of 451~Mpc (with $h = 0.7, \Omega_\Lambda = 0.7, \Omega_m = 0.3$) \citep[$z=0.098\pm0.02$][]{R67-redshift-Atel, Fong2021arXiv, Ravi2021arXiv}, the isotropic equivalent spectral energy of burst 19 is $2.63\times10^{31}\ \mathrm{erg}\ \mathrm{Hz}^{-1}$. The faintest burst is 2.6\,Jy\,ms, or  $6.33\times10^{29}\ \mathrm{erg}\ \mathrm{Hz}^{-1}$, and is still more than 3 orders of magnitude more energetic than the Galactic FRB SGR~1935+2154 \citep{bochenek+20, chime2020b}. This is roughly two orders of magnitude more than the $10\times$-$25\times$ energy gap for the faintest 0.1\,Jy\,ms\  burst from \riii\ \citep{marthi+20}, but it is not surprising: even for a faint 0.1\,Jy\,ms\ burst that might have been detected with the PA beam, the larger distance of \rss\ means that only those bursts above a threshold spectral energy of $2.43\times10^{28}\ \mathrm{erg}\ \mathrm{Hz}^{-1}$ are automatically selected. We note that the computed spectral energies are lower limits for two reasons: one, often the bursts do not occupy the full band and in addition, there is an unknown beaming factor. The key to bridging the energy gap with the Galactic FRB lies in detecting extremely close FRBs, such as \RGC\ \citep{Bhardwaj2021, Kirsten2021arXiv}.

\subsection{Burst widths}\label{ssec:widths}

We define the boxcar equivalent width of a burst as the ratio of the fluence to the peak flux, measured in ms: this number therefore represents the width of a boxcar window whose height is equal to the peak flux to give the measured fluence.
The burst widths measured between the zero crossings of a running mean profile, obtained with a 16-bin boxcar kernel, along with the boxcar equivalent width, are given in Table~\ref{tab:fluences}.  However, we use the equivalent width as the basis for simulating events in our completeness analysis in Section~\ref{ssec:completeness}.

We do not attempt to determine the underlying probability distribution function of the burst widths, as there are no physical models that can inform our choice. Instead, we merely attempt to derive an empirical fit to the data, to aid in the completeness analysis.

\begin{figure}
    \centering
    \includegraphics[width=1.02\linewidth, keepaspectratio]{Figures/gamma-burst-width-PDF.pdf}
    \caption{The histogram of the boxcar equivalent burst widths and the PDF of the best-fit Gamma distribution $f_\mathrm{\mathbf{W}}(w; \alpha, \beta)$. The $W>35$~ms bursts are excluded from the fit as they arise from multiple distinct components counted as a single burst.

        }
    \label{fig:burst-width-PDF}
\end{figure}

Figure~\ref{fig:burst-width-PDF} shows the histogram of the burst width $W$. The errors on the histogram are binwise Poissonian. We find the best fit Gamma distribution for the burst width histogram, which is continuous in the random variable $W$. The Gamma distribution is a general two-parameter family of continuous distributions, of which the exponential, chi-square and Erlang distributions are special cases. The PDF of the Gamma distribution is
\begin{equation}
    f_W(w; \alpha, \beta) = \frac{\beta^\alpha w^{\alpha -1} e^{-\beta w}}{\Gamma(\alpha)}
    \label{eqn:gamma-PDF}
\end{equation}
where $\alpha$ is the shape parameter and $\beta$ is the rate parameter. The best fit values are $(\alpha, 1/\beta)=(5.9, 3.0)$, obtained after excluding bursts with $W$ > 35~ms. The mean of the PDF is given by $\mu = \alpha/\beta = 17.5$~ms, the standard deviation is $7.2$~ms, and the empirically determined mean width is $\sim$ 17.2~ms. The larger widths correspond to instances where multiple bursts are counted as a single event (see e.g. Figure~\ref{fig:burstpanorama} and Table~\ref{tab:fluences}, burst 2, 13 and 22).

The burst widths of \rss\ are, on average, larger than those from other known repeaters. The majority of bursts from repeaters detected by CHIME/FRB have durations $<$25~ms \citep{2021arXiv210604356P}. We additionally note that the widths of detections of \rss\ at 1.4~GHz are also unusually large \citep{Hilmarsson2021arXiv}. Also, note that since our data are incoherently dedispersed, there is an intra-channel smearing of $\sim2$~ms at the lowest frequency.

\subsection{Fluence distribution}
\begin{figure}
    \centering
    \includegraphics[scale=0.62,trim=0.0cm 0.0cm 0.0cm 0.92cm, clip=True]{Figures/R67_fluence_power_law.pdf}
    \caption{Cumulative burst rate function of the detected bursts. The bursts are complete up to a fluence limit of 10\,Jy\,ms\ (vertical yellow line). The red line is the best-fit power law excluding bursts below the completeness level. The rate function is $R(>\!F) =  10~{\rm hr}^{-1}\left(F/10\mathrm{\,Jy\,ms}\right)^{-1.2}.$ Only the blue data points ($F>$10\,Jy\,ms) are included in the fit, while the black data points are fainter than the completeness limit.}
    \label{fig:fluence-CDF}
\end{figure}

Figure~\ref{fig:fluence-CDF} shows the cumulative burst rate function
of the burst fluence, $R(>\!F) \propto F^{\gamma}$, which gives the
rate of bursts above a fluence $F$.  The power-law index, $\gamma$, was
determined using a maximum likelihood estimator
\citep[][and references therein]{james+2019} and excluding bursts below
the completeness limit. Our fit yielded the power-law index of
$\gamma = -1.2 \pm 0.2$, by setting a visually identified completeness
limit of 10\,Jy\,ms. We performed a more rigorous analysis with this $\gamma$
that gives a completeness limit of 7\,Jy\,ms\ (described in
Section~\ref{ssec:completeness}). The cumulative burst rate function
inferred from our observations is

\begin{equation}
R(>\!F) =  10~{\rm hr}^{-1} \left(F/10\mathrm{\,Jy\,ms}\right)^{-1.2}.
\label{eqn:CDF}
\end{equation}

The power law index determined here is shallower than that of the well-studied FRB20121102A\ at 1.4~GHz, where it is a steep $\gamma = -1.8\pm0.3$ \citep{Gourdji2019}, although there is evidence for bi-modality in this source \citep{Li+2021} that can not be well-described by a single power law. CHIME/FRB  determined $\gamma = -1.3 \pm 0.3 \pm 0.1$ for \riii{} at observing frequencies comparable to ours \citep{20R3Period}, which is consistent with our measurement of FRB 20201124A. For comparison, Crab super giant pulses show steeper distributions:  $\gamma =-1.8$ to $-2$ \citep[e.g.][]{ramesh10,Bera2019}.

Repeating FRBs are subject to strong selection effects on $\gamma$.  Since there are more faint bursts than bright ones, nearby FRBs are more likely to be detected than far away ones.  For $\gamma<-1.5$, the expected distance diverges nearby, meaning we expect to be dominated by nearby FRBs, while for $\gamma>-1.5$ the event rate is dominated by far away ones.  For the observed event rates to converge, we conclude that the intrinsic population has $\gamma>-1.5$ above some luminosity $L_0$, and $\gamma<-1.5$ below.  In a flux limited survey, most FRBs will be detected near $L_0$, and have an apparent $\gamma \sim -1.5$, which is indeed the case for FRB 20201124A.

\subsection{Fluence completeness}\label{ssec:completeness}
For the GMRT incoherent array beam, the RMS noise in 10~ms is $\sigma_\mathrm{IA}\approx30~{\rm mJy}$. For a burst with a peak flux of $S_\mathrm{p}=300~{\rm mJy}$ and pulse width of $W=10~{\rm ms}$, we get a 10$\sigma$ detection:

\begin{equation}
{\rm S/N}_{\rm IA} = 10 \left(\frac{S_{\rm p}}{300~{\rm mJy}}\right)
                              \left(\frac{W}{10~{\rm ms}}\right)^{0.5}
\end{equation}
For a fluence $F_{\rm p} = S_{\rm p} W$ = 3\,Jy\,ms,
\begin{equation}
{\rm S/N}_{\rm IA} = 10 \left(\frac{F_{\rm p}}{3~\rm{\,Jy\,ms}}\right)
                              \left(\frac{W}{10~{\rm ms}}\right)^{-0.5},
    \label{eqn:detection-likelihood}
\end{equation}
we should be able to detect 10~ms bursts at 10$\sigma$, with brighter, narrower bursts being more likely detected.

The faintest burst we detect in our observations  has a fluence of 2.6\,Jy\,ms, an $\sim 11\sigma$ detection as defined by Equation~\ref{eqn:detection-likelihood}. However, the completeness fluence limit is likely much higher, which we determine as follows.
\begin{figure}
    \centering
    \includegraphics[scale=0.618]{Figures/completeness-eq-width.pdf}
    \caption{The completeness fluence limit is 7\,Jy\,ms. All bursts that fall in the shaded green region are detected, while only a fraction of those below the limit, in the shaded red region, are detected. The missed fraction is $\sim$80\% in the 1-7\,Jy\,ms\ range denoted by the shaded red region. The $F_p=3$\,Jy\,ms\ line is the reference fluence for a 10$\sigma$ detection of a 10~ms wide burst, according to Equation~\ref{eqn:detection-likelihood}

    The scatter points represent the detected bursts, for which the S/N are computed according to Equation~\ref{eqn:detection-likelihood}. }

    \label{fig:completeness}
\end{figure}

We draw a random sample of $10^3$ bursts from the cumulative fluence distribution of Figure~\ref{fig:fluence-CDF}, using the  empirically determined Equation~\ref{eqn:CDF}.
The lower limit to the fluence is set to 1\,Jy\,ms. Next, we draw a random sample of $10^3$ burst widths given by the Gamma distribution with the best fit ($\alpha, \beta$). Assuming $W$ and $F_p$ are independent, we compute the S/N for every pair (obtained as an outer product) using Equation~\ref{eqn:detection-likelihood}. For a cutoff S/N, defined as $\sigma_c$=(S/N)/$\sigma$=11 (see Figure~\ref{fig:completeness}), we find that the lowest fluence for which bursts of all widths are detected is $\sim7$\,Jy\,ms.

\begin{figure*}
    \centering
    \begin{minipage}{0.45\linewidth}
    \hskip 0.26in
    \subcaptionbox{Burst time positions within each scan\label{fig:scaninfo}}{\includegraphics[scale=0.565,trim=0.0cm 0.2cm 0.0cm 0.0cm, clip=True]{Figures/scaninfo.pdf}}\\

    \subcaptionbox{Burst waiting time\label{fig:wait-time}}{\includegraphics[scale=0.42]{Figures/waiting-time-combined-statistics.pdf} }
    \end{minipage}
    \begin{minipage}{0.45\linewidth}
    \subcaptionbox{Burst pair interval\label{fig:pair-sep}}{\includegraphics[scale=0.4]{Figures/separation-stats-colour.pdf} }
    \end{minipage}
    \vspace{2mm}
    \caption{(a): The occurrence of the bursts within each scan. The first four scans are $\approx$40 minutes long each, and the last one is 20 minutes, with 5, 12, 13, 14 and 4 bursts respectively. (b) Histogram of the burst waiting time, with the Poissonian error bars. The histogram of simulated bursts are shown as points with error bars. The shaded region represents the family of exponential mass function curves given by Equation~\ref{eqn:exponPDF} for $40 \leq N_b \leq 50$ with $\lambda = 1/t_w$ (where $t_w = 2.91$ min) from which is drawn the simulated bursts. (c) Burst pair intervals, before (\emph{top}) and after (\emph{bottom}) correcting for relative exposure. The error bars are Poissonian.}
\end{figure*}

We are now specifically interested in the missed fraction of bursts below the completeness limit, up to a reasonable fluence limit. We can compute this quantity as a fraction of the $F_p$ < 7\,Jy\,ms\ events that satisfy the S/N < $\sigma_c$ as well as $F_p > F^\mathrm{th}_p$ condition. For a fluence detection threshold $F^\mathrm{th}_p = 1$\,Jy\,ms, we find that our observations would have missed $\sim80$\% of all bursts 1\,Jy\,ms\ < $F_p$ < 7\,Jy\,ms.
However, our observing conditions were far less than ideal due to the RFI susceptibility of the IA beam. The missed fraction we determine here is hence a lower limit, as we consider 10\,Jy\,ms\ as the more conservative completeness limit.

From the scatter points overlaid on the $W$-S/N space in Figure~\ref{fig:completeness}, it is obvious that bursts with lower widths tend to have lower fluence values. It raises the possibility that the large fraction of bursts being missed could have had intrinsically small burst widths. However, the burst widths follow a Gamma distribution, with the mean burst width being $17.5\pm7.2$~ms, suggesting an inherent deficiency of narrow bursts. On the other hand, it is likely that the burst width distribution itself is biased towards the wider burst population, influenced by the limited sensitivity to narrow bursts (lower fluences).

\subsection{Burst rate and arrival times}
The number of bursts detected in each scan is respectively 5, 12, 13, 14 and 4. The first four exposures are 40 minutes (see Figure~\ref{fig:scaninfo}), while the last one is 20 minutes long.  Considering all bursts above the $\sim11\sigma$ limit of 2.6\,Jy\,ms\ have been detected, we get a burst rate of $\sim$16 per hour, which is likely to be a lower limit due to the incomplete fraction <10\,Jy\,ms. The rate is 10 per hour above the completeness limit of 10\,Jy\,ms. Unlike \riii\ which shows a highly variable burst rate \citep{marthi+20}, \rss\ appears to burst at a more uniform rate at least up to the fluence limit of 2.6\,Jy\,ms. A more sensitive observation with the fully phased beam, which is roughly 5$\times$ more sensitive, could reveal a population of bursts which could revise both the overall burst rate as well as its uniformity. For the PA beam, given an $8\sigma$ threshold of 0.5\,Jy\,ms, the empirically determined CDF of Equation~\ref{eqn:CDF} returns a phenomenal rate of $\sim360$ per hour, if the power law still holds good at the PA beam $8\sigma$ fluence threshold. If confirmed observationally, \rss\ would qualify as the most prolific and active repeating FRB known as yet. \cite{Li+2021} observe a peak rate of 122 hr$^{-1}$ but falling sharply subsequently, suggesting a variable burst rate in FRB20121102A. In \rss, it remains to be seen if the highly optimistic burst rate obtained from an extrapolation of the power law to 0.5\,Jy\,ms\ as well as the uniformity over several epochs hold. It is also likely that our observations occurred at a time when \rss\ was in an extremely active state. Analysis of the cumulative rate distribution from different, widely spaced observations may shed more light on whether the burst rate is evolving.

The longest gap between the scans (see Figure~\ref{fig:scaninfo}) is $\approx$11.7~min, while the typical gap is 8-9~min long. This would skew the histogram of burst wait times slightly, resulting in undercounted bursts for wait times $\lesssim$10~min, while overcounting ones >10~min, assuming a small number of bursts occurred in the scan gaps. In the absence of any priors on the underlying PDF, we cannot account for bursts missed in the rephasing intervals between the scans. One way to circumvent this difficulty is to exclude the pairs that straddle the scan gaps. This results in only a loss of 4 of the 47 waiting times, but results in a more truthful histogram. The mean waiting time between bursts, excluding the 4 inter-scan pairs, is $t_w\sim2.91$ minutes. Figure~\ref{fig:wait-time} shows the histogram of the wait times between successive bursts with the errorbars obtained from the barycentered ToAs, excluding the 4 pairs as described above.

We ran a simulation by drawing waiting times from an exponential mass function with the empirically determined mean waiting time $t_w$,
\begin{equation}
    f(t;t_w) = N_b \frac{1}{t_w} e^{-(t/t_w)},
    \label{eqn:exponPDF}
\end{equation}
generating $N_b = 50$ bursts in each run. These bursts were distributed within the observation as if they were observed with the same scan durations and intervals shown in Figure~\ref{fig:scaninfo}. Those bursts which fell in the scan intervals, as well as at the book-end bursts in each scan, were excluded before obtaining the histogram. The mean and the errorbar in each bin was determined from 1000 iterations: however, increasing the number of iterations beyond $\sim50$ has very little effect on the mean and the Poissonian errorbars as they tend to converge. We note that the simulated waiting times drawn from an exponential distribution agree well with the burst waiting time histogram, suggesting a good match of the data with the distribution. The outputs from the simulation are plotted as points with errorbars. Curves for the exponential mass function are overplotted for $40 \leq N_b \leq 50$ (see Figure~\ref{fig:wait-time}).

An exponential distribution for the waiting time suggests an underlying Poisson point process with a rate parameter $\lambda = 1/t_w$. This is expected for bursts detected within a single observation, as seen for FRB20121102A\ \citep{Cruces+2021}, which is known to follow a Weibull distribution over a longer time with a clustering factor of $k=0.34^{+0.06}_{-0.05}$ \citep{Oppermann2018}. With only 48 bursts, of which only a fraction is complete (30 of 48 bursts, above 10\,Jy\,ms), there may be pitfalls to modelling the burst waiting time distribution. At this juncture, we limit our discussion to the empirical fit of the distribution. The statistics should benefit significantly from sensitive PA beam detections with a much deeper completeness limit. In addition, continued monitoring over long periods should assist in identifying temporal clustering behaviour if any, considering that it has recently entered a state of heightened activity.

\cite{Li+2021} report waiting time statistics for FRB20121102A\ using a collection of $\sim$1600 bursts. They find the waiting time between bursts to be well fit by a log-normal distribution. Their waiting time histogram shows two peaks, with the largest mean waiting time being $\sim 70\pm12$~s, which they consider to be an upper limit to any periodicity, and a separate $\sim 220\pm100$~s limit to the periodicity of the high energy ($ > 3 \times 10^{38}$ erg) bursts. They conclude that these values are consistent with the mean values for the respective samples, and therefore consistent with underlying stochasticity \citep{Li+2021}. While we do find a few bursts with multiple components separated by $\sim$90~s or $\sim$180~s, we do not have sufficient sensitivity to identify them as distinct and independent bursts. Such closely separated bursts deserve keen attention to determine if they truly arise from a different distribution peaking at a shorter mean waiting time, such as seen for FRB20121102A\ by \cite{Li+2021}.

In addition, we derive a histogram of the pairwise intervals between all burst pairs, to investigate any trends for a preferred separation time, or multiples thereof, between bursts that might hint at longer periodicity timescales or burst rate modulation. The raw histogram is
shown in the top panel of Figure~\ref{fig:pair-sep}. This, however, is biased by the relative exposure between pairs. The relative exposure as a function of burst pair separation is obtained as the autocorrelation function (ACF) of the scan windows (see Figure~\ref{fig:scaninfo}), scaled for the number of burst pairs at zero separation (which is the total number of detected bursts). Obviously, shorter pair separations have a higher relative exposure than longer ones. The peaks in the relative exposure correspond to the $\sim45$-minute interval between successive scan start times. The normalized histogram is given in the bottom panel. We find no evidence for a preferred pair separation time that might indicate longer periodicities or rate modulation of $\sim$minutes timescales.

\subsection{Spectro-temporal drift}
The incoherent array beam is very susceptible to radio frequency
interference (RFI).  Broadband, zero DM RFI bursts show a characteristic
reverse dispersion sweep after dedispersion. A singular value decomposition
of the contaminated, but dedispersed, burst dynamic spectrum breaks the
reverse-swept RFI features and distributes it across a very large number
of modes. While the total energy in the RFI is very high, often much more
than the burst itself, it does not dominate the rank-ordered singular values.
The dominant orthogonal modes of the dedispersed burst dynamic spectrum can
thus purely represent the burst. This filtering method works well for bursts
with reasonably high S/N, but becomes progressively less effective with
deteriorating S/N. This is not surprising, as the ability to exclude the
reverse-swept RFI modes depends on their rank ordering in the presence of
the compact representation of the true burst modes.

\begin{figure}
    \includegraphics[scale=0.445]{Figures/burst-19-drift-ACF-marginalized.pdf}
    \vspace{-3mm}
    \caption{2D ACF of burst 19, used for measuring the drift rate. The upper and the right panels show respectively the frequency- and time-averaged 2D ACF. }
    \label{fig:ACF}
\end{figure}

As an example, in Figure~\ref{fig:ACF} we show the 2D ACF and the estimated drift rate for the brightest burst, as it has more than twice the S/N of any other burst. For this burst (burst 19), we find that, using the SVD mode filtering described above, the first six modes adequately represent the burst, allowing us to exclude all the subsequent modes and thus nearly fully eliminate the swept broadband RFI features. The reconstructed dynamic spectrum was used to obtain the 2D ACF, allowing us to estimate a drift rate of $\Delta f/\Delta t = -2\ \mathrm{MHz}\  \mathrm{ms}^{-1}$. Other bursts show drift rates between $\sim-0.75~{\rm MHz~ms}^{-1}$ and $\sim-20~{\rm MHz~ms}^{-1}$.

All the bursts in our sample show a downward drift or a ``sad trombone'' effect, as is known for repeaters \citep{hessels+19, Caleb2020, Chawla2020}, although some anomalous drifting behaviour has been seen in \riii\ \citep{Pleunis2021}. In \cite{marthi+20}, we see two instances of potential upward (or positive) drift in \riii, but it is not clear if these are from the same or separate bursts. \cite{Platts2021} consider the possibility of such upward drift arising from lensing events in FRB20121102A.

We defer an analysis of the drift-rate vs burst width relation to a future paper, after including more sensitive burst detections. \cite{Chamma2020arXiv}   posit the linear relation between the quantities as a possible universal relationship for repeating FRBs. \cite{Hilmarsson2021arXiv} find the relationship between drift rates and burst widths in 1.4~GHz Effelsberg Radio Telescope observations to be consistent with the results of \cite{Chamma2020arXiv} except for an offset. The primary constraint for a similar but robust analysis of the sample presented in this paper is the unfavourable RFI contamination of the bursts, especially the weaker ones.

\subsection{Scattering and scintillation}

Figure~\ref{fig:diagnostics} shows the dynamic spectrum of burst 9 on the left, burst 16 in the middle and that of the brightest burst (19) on the right. These bursts have a clearly identifiable decaying exponential profile: we choose bursts 9 and 16 particularly for their apparent lack of spectro-temporal drift. We consider the low frequency portion of the bursts, where a single component of the multi-component burst 19 is isolated by defining a cut-off frequency (here, 575~MHz). The other two bursts have a single component, but the cut-off frequency is defined and the analysis is done identically for consistency. The bottom panel shows the frequency-averaged (550-575~MHz) profile, which shows
what appears to be an exponential tail. We fit to all the three bursts a Gaussian convolved with a decaying exponential, but constraining the decay time constant to be identical. If we interpret this as a scattering tail, we can set an upper limit of $\tau_\mathrm{sc} \leq 11.1$~ms  to the scattering time. The scattering time $\tau_\mathrm{s}$ is measured as the time constant of the decaying exponential $e^{-t/\tau_s}$, which includes the uncorrected 2-ms dispersion delay in a single 96-kHz channel at the lowest frequency. The error bar in each burst shown in Figure~\ref{fig:diagnostics} is taken as the half-width at half-maximum of a Gaussian of appropriate amplitude.

In addition, the bandpass-normalized dynamic spectrum shows scintillation, evident from the peaks in the $t<0$ and $t>0$ spectra of burst 19: we measure a scintillation bandwidth of 0.1-0.2~MHz at 550-750~MHz. Some of these features appear to be blended at the lower part of the band, whereas they appear to be adequately resolved $\gtrsim$620~MHz. At the frequencies at which we observe, the scattering tail appears to be scintillating with a characteristic bandwidth of $\sim$0.1~MHz but barely resolved: this might be an overestimate as the features appear to be blended. We hence have a case analogous to that of \cite{masui+15} where the scattering is thought to occur in the host galaxy, while the scatter-broadened burst still appears ``unresolved'' at a screen in the Milky way, as the scintillation appears constant throughout the scattering tail. We present a more detailed analysis of the scattering and scintillation in P-II, combining the measurements obtained from these Band-4 uGMRT and 100-m Effelsberg Radio Telescope L-band observations.

It is necessary to distinguish the scattering time constant from the scintillation bandwidth. In our case, the scattering time constant is not inversely related to the measured scintillation bandwidth, leading to our hypothesis that the two measurements are distinct and the two phenomena are mutually independent. In fact, the scattering time constant is roughly 2 orders of magnitude larger than that expected from the scintillation bandwidth. P-II develops the hypothesis that the scattering arises from a screen that is located much closer to the FRB, possibly within the host galaxy, and that the scintillation is being imparted by a scattering screen in the Milky Way.

Importantly, the fact that both scattering and scintillation are seen in this FRB allows us to place constraints on the locations of the screens and measure a velocity of the Milky Way scattering screen. The inferred scattering screen transverse velocity is $30$-$40\, \mathrm{km\,s^{-1}}$ for a screen located at 2~kpc, and much smaller for a 0.4~kpc screen, when the velocity of the scintillation pattern has a larger contribution from Earth's velocity. For a screen located so close to Earth, its large contribution to the scintillation velocity is expected to manifest as a strong annual modulation of the scintillation timescale. If the scattering arises at the host galaxy, we expect the scattering timescale to be constant throughout the annual scintillation modulation cycle.

\begin{figure*}
    \centering
     \includegraphics[width=0.325\linewidth, keepaspectratio]{Figures/burst-diagnostics-burst9.pdf}
     \includegraphics[width=0.331\linewidth, keepaspectratio]{Figures/burst-diagnostics-burst16.pdf}
     \includegraphics[width=0.325\linewidth, keepaspectratio]{Figures/burst-diagnostics-burst19.pdf}
    \caption{The SVD-filtered dynamic spectra of bursts 9, 16 and 19, dedispersed to 411\,pc\,cm$^{-3}$\ and binned 4$\times$ in frequency for plotting. For all the three bursts, the top panel shows the mean profile integrated between 554~MHz and 731~MHz. The bottom panel shows the low-band profile cut off at 575~MHz. The red curve is the best fit obtained by convolving a Gaussian with a decaying exponential, giving a scattering time constant of 11.1~ms along with the respective 1$\sigma$ error bar, which are 2.9~ms, 5.1~ms and 2.5~ms respectively for bursts 9, 16 and 19. Below this panel are the residuals of the fit. The left and right sub-panels respectively show the burst spectrum at $t<0$ and $t>0$.}
    \label{fig:diagnostics}
\end{figure*}

\subsection{Periodicity search on small timescales}

A {\tt PRESTO} search for periodicities on short timescales was done with acceleration and jerk on the full dedispersed data, as well as on multiple 10-minute and 20-minute segments. No significant candidates were detected. Additionally, a Fast Folding Algorithm (FFA) search was performed on the IA beam data using {\tt riptide}\footnote{\href{https://github.com/v-morello/riptide}{https://github.com/v-morello/riptide}} (\cite{Morello20}). However, that again revealed no significant candidates. Some bursts show multiple peaks, as in bursts 2, 13 and 22. It is not clear if these are distinct components of the same burst or are different bursts, due to the poor S/N of the IA beam. Their separations appear to be $\sim$ 90~ms or $\sim$180~ms. We verified through an autocorrelation analysis that the separations have no periodic relationship between the bursts.

The detection of periodicity in the range of typical pulsar periods in FRBs would be unassailable evidence for a neutron star origin for the emission and repetition. While longer periodicites of $\sim$ several days, such as known for \riii\ \citep{chime2020a} relies on models like orbital motion \citep{16DaiOrbit, 20IokaOrbit} or precession \citep{20LevinPrecession}, smaller periodicities in the 1~ms to 1~s range are thought to arise from rotation. \cite{chime-subsecond-periodicity-2021} have discovered multiple bursts which appear clustered with sub-second separations, from FRB~20191221A ($\sim217$~ms), FRB~20210206A ($\sim3$~ms)  and FRB~20210213A ($\sim11$~ms), consistent with typical periods expected for magnetospheric emission. This provides strong motivation for follow-up observations of active repeaters like \rss\ with longer exposures, specifically  with the ability to track the source in the sky.
Observations such as those described here have the potential to detect many more such clustered bursts.

In this context it is interesting to note the possibility of ultralong period (ULP) magnetars as FRB candidates. \cite{Beniamini2020a} invoke a simple long rotation period explanation for the $\sim$16-day periodicity of \riii. In their model, ULP magnetars arise from three distinct possibilities, such as mass-loaded charged-particle winds, loss of angular momentum due to kicks from giant flares and long-lasting accretion discs \citep{Beniamini2020a}, citing the example of the Galactic magnetar candidate with a $\sim$7h period, 1E~161348–5055. However, they note that such progenitors would be extremely rare, accounting for the paucity of scales of periodicity similar to \riii.

\section{SUMMARY AND CONCLUSIONS}\label{sec:summary}
We report the observations at Band-4 of \rss\ with the upgraded GMRT and the detection of 48 bursts in 3 hours of exposure. These observations were carried out with the dual purpose of localizing the FRB as well as detecting associated persistent emission, based on the initial, non-interferometric localization reported by ASKAP \citep{ASKAP-secondATel}. This necessitated only a single pointing with the GMRT. We localize the FRB and detect persistent emission at 650~MHz.

We estimate the DM that maximizes the frequency-averaged substructure energy to be $410.78\pm0.54$\,pc\,cm$^{-3}$, similar to that obtained from {\tt DM\_phase}, $410.33\pm1.15$\,pc\,cm$^{-3}$. Both these DMs are consistent with the fiducial value of 411\,pc\,cm$^{-3}$\ used throughout this paper. A larger number of high S/N bursts from high sensitivity observations with the PA beam are essential to constrain any burst-to-burst DM variability within the observation, or for searching for systematic trends in DM variability over longer timescales \citep[e.g.][seen in FRB20121102A]{Hilmarsson2021}. We find that the mean burst width is $17.5\pm7.2$~ms, but find that they are larger than the widths for other known repeaters. The isotropic equivalent burst spectral energies are $\sim10^{29}\mathrm{-}10^{31} $~erg\,Hz$^{-1}$.

The bursts range in fluence from 2.6\,Jy\,ms\ to 108\,Jy\,ms, following a power law distribution with an index of $\gamma=-1.2\pm0.2$ and an overall burst rate of 16 per hour for these observations, which is a lower limit. We estimate a completeness limit of 10\,Jy\,ms\ for these observations, after empirically modelling the burst width distribution. Our observations might have missed $\gtrsim$80\% of the bursts in the fluence range 1-10\,Jy\,ms. The burst waiting time distribution agrees broadly with an exponential distribution with a mean waiting time of $t_w \sim 2.9$~min, suggesting an underlying Poisson point process that is expected for bursts occurring within a short observation. There is no evidence for longer (minute to several minutes) periodicity or, more specifically, burst rate modulation with those characteristic timescales, inferred from the distribution of pairwise burst intervals in our observations. More sensitive observations with a tighter fluence completeness limit might revise these statistics considerably.

With a DM=411\,pc\,cm$^{-3}$, we measure a range of bulk spectro-temporal drift rates between $-0.75$ and $-20~{\rm MHz~ms}^{-1}$. We measure an upper limit to the scattering time of $\leq$11.1~ms, as well as detect scintillation across frequency.
No small timescale, pulsar-like periodicity was detected in acceleration and jerk searches as well as with FFA.

The simultaneous localization of \rss\ adds strength to the proof-of-concept method adopted from our earlier work \citep{marthi+20}. This could serve as a potential model for all our future localization and follow up of unlocalized repeating FRBs.

More sensitive PA beam observations will likely yield an order of magnitude higher burst rate, if \rss\ continues in its present active state. This holds enormous promise for detailed studies of its polarization properties that would allow us to test between competing emission models, as well as study any systematic evolution of RM as reported in \cite{Hilmarsson2021}. Regular long-term monitoring would enable us to construct a putative trend for an annual scintillation timescale modulation, and hence to locate and study the Galactic scattering screen responsible for the scintillation. Variation or modulation of burst rate or activity over longer timescales would have to be adequately sampled to search for evidence for clustering, as is known for FRB20121102A. Finally, although we have reported only radio observations, extremely active, localized repeating FRBs such as \rss\ are the best targets for extended multi-wavelength campaigns that can considerably advance our current understanding of the origins of FRBs.

\section{ACKNOWLEDGEMENTS}
We thank the anonymous reviewer for comments which have helped improve the manuscript. VRM thanks Jayaram Chengalur and Apurba Bera for insightful discussions. We thank the staff of the GMRT who have made these observations possible. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. VRM acknowledges the support of the Department of Atomic Energy, Government of India, under project no. 12-R\&D-TFR-5.02-0700. We acknowledge use of the CHIME/FRB Public Database, provided at \url{https://www.chime-frb.ca/} by the CHIME/FRB Collaboration. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (funding reference number RGPIN-2019-067, CRD 523638-201). We receive support from Ontario Research Fund - Research Excellence Program (ORF-RE), Canadian Institute for Advanced Research (CIFAR), Canadian Foundation for Innovation (CFI), Simons Foundation, Thoth Technology Inc. and Alexander von Humboldt Foundation.
Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. LGS is a Lise Meitner Indepdendent Max Planck reasearch group leader and acknowledges support from the Max Planck Society.

\section{DATA AVAILABILITY}
The data underlying this article will be shared on reasonable request to the corresponding authors.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


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text:
Q: Formula for linear transformation of cross product Motivated by this question and by my own calculations where I try to find what is the curvature of a rigid transformation to my curve I get to the following equation ($\alpha$ is a curve, $\phi$ a linear transformation):

$\phi(\alpha') \times \phi(\alpha'') = \phi(\alpha' \times \alpha'')$

I wonder if it is true and conjecture that it is true because $\phi$ is an orthogonal linear transformation. So that the more general formula:

$Ma \times Mb = \det(M)(M^T)^{-1} (a \times b)$

holds. Now, what I ask you for is to prove this last formula (fix it if it is not true) or at least give a reference where I can encounter it.

A: The general formula is correct. Your original one holds only when $\phi$ is a proper (orientation-preserving) orthogonal linear map. What underlies all of this is (a) the way linear maps act on the exterior algebra:
$$(\Lambda^2M)(a\wedge b) = Ma\wedge Mb$$
and (b) the Hodge star isomorphism $\star\colon \Lambda^2\Bbb R^3 \to\Bbb R^3$. So the underlying action on the cross product of two vectors $a\times b$ is found by chasing around $\star (\Lambda^2M)(a\wedge b) = \star(\Lambda^2M)(\star(a\times b))$.
We don't need to be so fancy. The crucial thing is the "classical adjoint" formula
$$M^{-1} = \frac1{\det M}(\text{cof }M)^\top,$$
where $\text{cof } M$ is the matrix of cofactors. Here is the typical computation:
\begin{align*}
Me_1 \times Me_2 &= \sum m_{k1}e_k \times \sum m_{\ell 2}e_\ell = \sum_{k<\ell} \left|\begin{matrix} m_{k1} & m_{k 2} \\ m_{\ell 1} & m_{\ell 2}\end{matrix} \right| e_k\times e_\ell \\
&= \sum (\text{cof }M)_{i3}e_i = (\text{cof }M)e_3 = (\det M)(M^{-1})^\top e_3\\
&= (\det M)(M^{-1})^\top(e_1\times e_2).
\end{align*}

redpajama_set_name: RedPajamaStackExchange


Indian Mounds Drive South West is a street located in Grandville, Michigan. In total, there are about 299 houses, condos, apartments or land on the street of Indian Mounds Drive South West. Note that housenode is a real estate database based on public data, for listings of properties for sale please refer to your local realtor in Grandville.
You can find Indian Mounds Drive South West together with 299 other real estate properties on Indian Mounds Drive South West in Grandville. Sometimes we have access to extended information about the residence, such as operating costs, charges, postal code and output prices at previous sales. This information is or has been the audience at the previous sale of the residence, however, such information may be outdated or incorrect so see it more as an indication. The value is based on previous starting price and sale price in the area.


Careers - I cover career development and personal growth.
Stress is like a double-edged sword. There's the good kind that keeps you motivated—like when you're close to landing a job offer or graduation is around the corner—and the kind that's too overwhelming (and actually harmful) to work with.
No one likes dealing with bad stress. But it's an inevitable part of life. As we go through changes—an unexpected layoff, a new move or more responsibilities—we are likely to experience it on a recurring basis. While we may not have a say in the timing of these events, we can control the way they affect us. And we can do this sustainably by building a strong system for managing stress.
While everyone handles it differently, there are some common patterns to the various methods of coping. I spoke to Cheryl Sutherland, founder of empowerment company PleaseNotes, and she nails them down to these five tips.
Change your perspective. A lot of our stressors are temporary, but we often overestimate how long they'll last. When something causes you stress, ask yourself, "Will it matter in a few months or years from now?" For example, if your boss micromanages your work and this gives you anxiety, before you react, think about whether or not this is a job you'll have for a long time. If the answer's yes, have an honest conversation with her and figure out ways to compromise. If the answer's no, focus on what you can do to land your dream job sooner instead. Remember, the more importance we give something, the bigger the impact it has on us.
Break it down. Suppose you get assigned a huge project at work and you have no idea where to start. You also have a short deadline and it's keeping you up at night. Totally understandable! In this case, work backwards and figure out the small steps involved in the execution of the project. If you have to plan your organization's annual gala, maybe you can start with researching local venues and reaching out via email. Start with the small tasks and gradually move to the more challenging steps. Doing this makes you feel more in control and gives you the courage to keep going. This strategy will also help you in the future, as you'll be better trained to assess the scope and needs of a project.
Practice appreciation. Obsessing over what's not working only adds to your stress, and makes you fidgety and unproductive. Draw energy from the things that are working instead. If a project is taking you longer to finish and you're tempted to beat yourself up about it, redirect your thinking to feel gratitude for the work you're doing (assuming it's what you love to do) and the way it's helping you live the life you want. Things rarely go as planned; embrace the detours and think of the big picture. If you're building a business and you're going through the ups and downs of entrepreneurship, think about the way you're carving your own path and making money on your own terms. This will not only empower you to keep going, but also help you channel the stress into the completion of the project.
Take a break. When you hit a wall or are struggling through a difficult phase, it's okay to take a step back and disconnect for a bit. Whether it means working out every morning, going on a midday walk, doing yoga on weekends or signing up for a crafting class, give yourself the gift of a well-deserved break. Taking time to recharge will be beneficial in the short-term as well as the long run.
Breathe. Practicing breathing in the midst of a stressful situation shifts your brain from the "fight or flight" mode and lessens the impact of the associated anxiety. It may not be intuitive to do so—especially when faced with a life threatening event, but getting in the habit will make you less impulsive and more pragmatic over time, and help you better handle pressure.


Our next meeting is '''Tuesday, August 10th'''.
'''The August meeting scheduled for August 10th has been cancelled!''' Our next meeting is '''Tuesday, September 14th'''.
The August meeting scheduled for August 10th has been cancelled! Our next meeting is Tuesday, September 14th.


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Q&A: Claire Martin
Which living person do you most admire? Probably my Mother in Law and Sister in Law. Both very grounded woman who put family first. I'm not like them at all. But I could change… What is the trait you most deplore in yourself? I'm never content. What is the trait you most deplore in others? Never really thought about it. I generally like people. The book or the movie? I hate to admit it but the movie. Does the modern world impress you? Yes and no. I'm glad it is impressive to others and I'm happy to benefit from all the great things about modernity but I'm happy being a luddite. Would you prefer to have children or the nobel prize? What a terrible question. Both of course. If you had to align yourself with a leader in history, who would it be? While I'm agnostic i'd have to say Jesus, a hot carpenter who hangs out with whores and turns water into wine, while fixing all humanities problems? Awesome! What will replace humans? zombies. The flu or a black eye? The flu is for wimps – definitely a black eye. Is disappointment healthy? For sure – life is suffering so they say. Is it healthy to meet your heroes? Different strokes for different folks, it could be the demise of some and the making of others. What is the next book you want to read? Grimms fairy tales.
Is flirting a kind of cheating? Not really. What moment have you most wished you'd had a camera when you hadn't?I can't think of any. I'm not really a single image random moment kind of photographer. I like to tell a story and when I do, I go right into it so in those instances I always have my camera. All other times, I never carry a camera, I just enjoy my life and am happy to see things with my eyes and remember them with my brain. Name something that you would be willing to shorten your life by ten years to receive right now. I'm tempted to say millions of dollars, but maybe I'll be a happy old person and really want those 10 years back, but maybe I'd be happy because I got rich young selling my soul to the devil and lived the good life. Maybe to see loved ones who've passed away one more time, but that could send you crazy too. I think I"ll leave this question at undecided. Is western society still capable of full-scale revolutionary acts? Anything is possible.
What essential life skills are schools neglecting to teach our children? I think the next generations have a weird sense of entitlement. Like they don't have to work for anything, they deserve things just because they exist. I think it's an unhealthy and unrealistic mentality. I don't really think that's up to schools though. Are you satisfied with your level of physical strength? No, I have terrible upper body strength. I've never been able to do a chin up! Have you ever won a fight when you shouldn't have? So many weird questions…. I can't think of any, but I'm really great at cheating, I do it often and I consider it a skill. In a way it's like winning when you shouldn't. What do you think is the most plausible of the supernatural? Intuitive psychic ability. Pick an historic moment from the last hundred years to bring a camera to. Woodstock. I've always had a thing for the psychedelic hippy freak out thing. A museum of natural history and a museum of contemporary art are on fire. Who gets the water? For humanity I'd say the museum of natural history, for myself I'd say the museum of contemporary art for sure!
Claire Martin – From the series Petionville Club.
Q&A: Kristine Potter
Pick a field of science to be an expert within. Psychology. What moment have you most wished you'd had a camera when you hadn't? That happens more often than I'd like to admit. Choose a job you would be willing to do…
Friday Fry Up: Kial Menadue — Speedway 3460
Full Throttle Love World War II finished and the gum trees that grew out of a Daylesford mining gully were razed. 1955 – veterans with undiagnosed PTSD found refuge in the dust laden gully basin now known as the Daylesford…
Friday Fry Up: Meg Porteous
In 2016 Meg Porteous was selected as one of ten artists internationally to attend the Shiro Ono Artist Residency in Japan. The works in Departure Melody, produced during this time, continue the artist's exploration into daily life and contemporary culture….

redpajama_set_name: RedPajamaCommonCrawl


In Drimnagh Castle we enjoy reading books in our school. There are plenty of books to read.
In 2nd and 6th class they do paired reading when they read a book with their parents at home for homework for 15 minutes.
In every classroom there is a small library at the back of the class with a selection of books for the pupils to read.
On Monday the mobile library comes for 4th and 5th to get a book from the library if they have a library card.
I interviewed Ms O Connor and she is big on reading and she said she would like it if boys go to their local libraries more often. She said the librarians will help you renew a book.
Some boys from different classes are going to write book reviews every month on the blog about books they read.


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Zeus, '27 Is The New 17′
Our latest Download of the Week comes from Toronto indie band Zeus. "27 Is the New 17" comes off the band's third album "Classic Zeus," out earlier this month on Arts & Crafts.
Mike Flanagan describes this fuzzy nod to the 70s as such: "Imagine Jimmy Buffet searching for direction on Gorillaz' Plastic Beach in a territory staked out by Electric Light Orchestra."
Download "27 Is the New 17" above!


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Incest, Abuse of a ...
Incest, Abuse of a Dead Body, and Necrophilia
People Crime reports that a 33-year-old Florida woman was recently charged with incest after she gave birth to a child that had severe medical issues. After the mother failed to properly fill out paperwork for that would allow the child to be placed in a home for children with complex medical issues, the hospital performed DNA testing and determined that the father was of close relation to the mother. The defendant eventually told police that the father was her brother, and that the two had been living together as a couple for more than five years and had had sexual intercourse as recently as the night before her eventual arrest. During that arrest, she allegedly kicked and spit at officers, potentially adding to the offenses that she faces.
Incest is a Third Degree Felony
Incest is defined as knowingly marrying or having sexual intercourse with a close relative, such as a sister, brother, aunt, uncle, niece, or nephew. Incest is a third degree felony, penalized by up to five years in prison and a maximum fine of $5,000, as per Florida statute 826.04. Intercourse is defined as the penetration of the female sex organ by the male sex organ, no matter how slight. Emission is not necessary in order to violate this statute. In addition to being a social taboo, incest is a crime because the offspring of incest, called inbreeding, face serious health issues and birth defects due to genetic disorders. Inbred children have a much higher chance of cognitive disorders, disability, and death than other children.
Abuse of a Dead Body
A 32-year-old Florida man was arrested by police after he failed to convince them that a dead human body found in his closet was not his girlfriend, but a life sized sex blow up doll made of flesh, as reported by the New York Post. He was charged with murdering his girlfriend, as well as mutilating a dead body. The body was found with a disemboweled, lacerated stomach; intestines were found in the garbage can. Under Florida statute 872.06, necrophilia or "abuse of a dead body" is defined as:
Mutilating a dead body;
Anal or vaginal penetration of a dead body by the defendant's sexual organ, or any other object;
Contact or union of the penis, vagina, or anus of a person with the mouth, penis, vagina, or anus of a dead body; or
Contact or union of a person's mouth with the penis, vagina, or anus of a dead body.
Grossly abusing, sexually abusing, or mutilating a dead body is a second degree felony, punishable by up to 15 years in prison and a fine of $10,000.
Call an Experienced, Aggressive Criminal Defense Lawyers
Abuse of a dead body and incest are two serious crimes that demand the full legal attention of an experienced West Palm Beach criminal defense lawyer. The legal team at the Skier Law Firm is unmatched in experience when it comes to Florida law, and we are here to get started on your case immediately.


First McKinney's mission is to LIVE and LOVE like Jesus...so that our neighbors, the nations and the next generation will follow Jesus. First McKinney's vision is to ignite a movement of multicultural people who engage their neighbors, the nations of the world and the next generation with the Gospel of Jesus Christ. Through dynamic teaching and missional leadership First McKinney is leaving a legacy here and around the world. Family-focused ministries and events are the core to a missional church that seeks to impact both the people within the walls of the church, and the community outside. Through focused activities, including 15 missions trips a year, countless service projects, and thousands of donors who give to benevolent causes, we seek to be a blessing in action and words to those who are not blessed.


Happy Hippo the Hippopotamus Snuggle Blankey Security Blanket PDF Crochet Pattern - IraRott Inc.
FORMAT: PDF, 10 pages, 3.3 MB (mobile devices friendly). Language - English. This pattern is written row-by-row, using US crochet terms. It also includes many step-by-step photos and diagrams (easy to follow).
SKILLS: Chain, slip stitch, single crochet, double crochet, picot, working in rows & in the round, increasing, decreasing, sewing.
GAUGE: 8 dc sts X 3 rows = 2" X 2" (5 X 5 cm), using hook 3.75 mm (F).
Approximately 16" (40.5 cm) from the ears down to the bottom edge, and 22" (51 cm) in diameter.


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Łuczyce (ukr. Лучиці) – wieś na Ukrainie, w rejonie czerwonogrodzkim obwodu lwowskiego.

W II Rzeczypospolitej do 1934 samodzielna gmina jednostkowa. Następnie należała do zbiorowej wiejskiej gminy Tartaków Miasto w powiecie sokalskim w woj. lwowskim. W związku z poprowadzeniem nowej granicy państwowej na Bugu, wieś wraz z całym obszarem gminy Tartaków Miasto znalazła się w Związku Radzieckim.

Bibliografia

Przypisy

Wsie w obwodzie lwowskim
Rejon sokalski

redpajama_set_name: RedPajamaWikipedia


PHILADELPHIA – One of the oldest black institutions in the country is marking its bicentennial in Philadelphia this week.
The African Methodist Episcopal Church is holding its general conference in the city. The denomination was also founded in Philadelphia by Richard Allen, a former slave who broke with the Methodist Church over racism in the late 1700s.
The church flourished after the Civil War and has been central to the struggle against injustice and inequality for blacks. It has also historically emphasized economic empowerment and education, starting several historically black colleges.
The AME Church was in the spotlight last year after nine black worshippers at Mother Emanuel AME Church in Charleston, South Carolina, were killed by a white gunman who targeted the church for its historic significance.


Of course, the focal point of your further education is the costs and the financing. Because it brings you nothing that there are theoretically meaningful further education, which you can hardly pay in practice. But how much is training and what are your options for financing it? Unfortunately, statistical surveys and comparison tables are also missing here. The costs of continuing education can be very different and can be difficult to compare with each other, also because of different contents, objectives and duration.
This should pay attention to you!
The Federal Institute for Vocational Education and Training has determined a few average values for the costs of further training in a study in which 2000 people were interviewed. According to this, the costs, which are directly related to further training (as participation fees, teaching material, etc.) per year and person are on average 568 Euro.
In many cases, participants often do not pay for themselves, but are reimbursed in part - for example, by the employment agency or the employer. On average, this refinancing accounts for approximately 36%. In the end, the participants will pay 375 Euro themselves. The main part of this will be the registration fees and the travel costs. In addition, there are indirect costs, such as the loss of earnings of 137 Euro per participant, whereby costs are reimbursed to a lesser extent (on average about 7%). Eg by subsistence allowances. But these indirect costs can not only be calculated in euros: in any case, you must also take into account the amount of time, the time that you may have to rework at work.
On average, 138 hours are spent annually on further education. 74 hours of this do not come into the working hours, but cost free time. Additional 59 hours must be spent on overtime (due to further education), information, preparation and follow-up, as well as travel times.
In addition, there are significant differences in terms of the costs of continuing education among the individual groups of participants: Persons who take part in non-company continuing education spend considerably more money each year with 856 Euro than with participants in further training programs - namely 285 Euro. This is because employers often pay the costs, while non-company training participants receive only 14% reimbursement.
Employees are much more likely to be offered free training than those who are unemployed or self-employed. Socio-demographic characteristics also play a role: Young participants up to 24 years are more often free of charge, participants between 25 to 34 and 55 to 64 spend on average the highest costs for further education. Training also plays a role: the higher the level of education, the higher the average cost of training, because those who already have a higher level of basic education are more willing to invest in a higher-qualifying and correspondingly expensive further education.
Depending on the type of further training, the costs are very different and also vary widely between the individual participants: Approximately 45% of the respondents do not have to pay any costs themselves. 14% will have costs up to about 99 Euro, 28% will bear costs between 100 and 999 Euro. 13% of participants must shell out more than 1.000 Euro and 2% even have costs of more than 5.000 Euro. The highest costs are caused by classical course forms: in addition to participation fees, there are also travel and, if necessary, accommodation costs. In addition, the loss of earnings must be taken into account.
Although participation fees often seem higher, eLearning and self-organized learning are altogether a bit cheaper: the learning and work tools (books, PC, telephone and internet access, etc.) are the most important ones. On the other hand, these forms of learning require the least amount of time; the travel costs are eliminated and the loss of earnings is lower.
When planning an advanced course, think about what this costs and how these costs will affect you both financially and time-wise. In any case, please inquire about the total costs of the respective course. Take into account all direct and indirect costs, thus providing you with a broad overview of the various offers. Look carefully! How many lessons have the course? How are these distributed, is this suitable for you? Here the time factor mentioned above is also important! Note that lesson time is not the same as the lesson: In general, one is from 45 minutes per lesson, but some providers may be more or less. In any case, you must take this into account when comparing.
Example: In a crafting chamber, you would pay 33 Euro for a course in Spreadsheet I: MS Excel (330 lessons in three days). A private education provider requires 2007 for a basic Excel 207,64 course (duration: l day with seven lessons). However, only a maximum of eight participants are admitted per course, which promises a better learning atmosphere. An English language course with the same provider costs between 420 Euro (for simple language courses) and 500 Euro (for professional language courses and conversation) - all courses with a total of 60 lessons.
For comparison, the prices of a public school: 26 lessons, no matter what level, cost 72,80 Euro, if 10 people take part in the course, the price drops to 52 Euro. Larger classes are, of course, again bad for learning and national colleges generally do not have the best reputation. But maybe you only pay for the image with your private provider?
Incidentally, it is significantly more expensive if you want to make up a whole education: a training as a European secretary with a total of about 4.800 lessons (30 months full-time) costs at one institute 12.000 Euro, at another provider 10.400 Euro - however, only about half at lessons. An extra-occupational intensive training course for Fachkaufmann Personalfachwesen (duration: 4 months, approx. 12 hours / week) suggests a provider with 3.000 Euro, in the competition you would pay for a six-month course (total 460 lessons) but only 2.875 Euro. If you then want to add the business economist to the specialist trader, you can, for example, For example, for a class with 700 lessons, expect 3.579 Euro.
In some courses the examination with the fees is already included, but with other providers you have to pay them extra. In the case of the examples presented here, the examination fee is between 260 Euro and 450 Euro, depending on the type of financial statements.
Some providers offer the possibility of an installment payment; usually at least a part of the sum has to be paid in advance. If the total amount has to be paid before the start of the action, there may be problems with the refund afterwards. Therefore, you should be careful with such terms of contract.
Incidentally, whether you receive at least part of your money if you do not like it depends on the individual terms of the contract. So read the fine print carefully. For longer-term measures, you should arrange for a quarterly or monthly form of payment - this can save you a lot of financial trouble if you want to terminate early. Tip: tax deductible The costs of continuing professional education are usually tax deductible if you do not receive any grants.
[Founder Report] Careerfoundry: eLearning for the Career and Learning Model of the Future?
Social Media Manager: Social Media can be everyone !?


Former France international Patrick Vieira has continued to criticise the French Football Federation, ahead of the FIFA World Cup in Brazil.
Former France captain Patrick Vieira has criticised Didier Deschamps for leaving Samir Nasri out of his FIFA World Cup squad.
Manchester City coach Patrick Vieira called on the club's senior figures to lead from the front to deliver Premier League success.


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Best Cryptocurrency Stocks To Invest In Right Now As Bitcoin Hits $50,000? 5 To Check Out
Aug 31, 2021 Bitcoin, Check, cryptocurrency, Hits, Invest, Stocks
1 5 Trending Crypto Stocks To Watch Right Now
2 Top Cryptocurrency Stocks To Buy [Or Sell] This Week
3 Marathon Digital Holdings Inc.
4 Robinhood Markets Inc.
5 MicroStrategy Inc.
6 Square Inc.
7 Coinbase Global Inc.
5 Trending Crypto Stocks To Watch Right Now
As we begin another trading week, cryptocurrency stocks seem to be in focus in the stock market today. For the most part, this would be thanks to the flagship digital currency Bitcoin. Earlier today, the cryptocurrency crossed the $50,000 mark and continues to hold steady. This would indicate a notable 3-month high for the digital coin. As you can imagine, all this would see investors eyeing some of the top cryptocurrency stocks again.
Now, with the hype around cryptocurrencies this year, more organizations have and continue to jump on the trend. For starters, we could look at fintech companies such as PayPal (NASDAQ: PYPL) and Mastercard (NYSE: MA). Both companies now offer consumers access to cryptocurrencies and provide related services. More importantly, they are also actively bolstering their cryptocurrency-related offerings now.
In particular, PayPal is launching its cryptocurrency service in the U.K. this week. Earlier today, the company announced the first international expansion of its crypto product. According to PayPal's general manager for crypto and digital currencies Jose Fernandez, the company is confident of its ability to perform in the region. Fernandez cites PayPal's success in the U.S. crypto space as a supporting factor. All in all, the cryptocurrency industry continues to grow and expand. On that note, here are five top cryptocurrency stocks to consider in the stock market now.
Top Cryptocurrency Stocks To Buy [Or Sell] This Week
Marathon Digital Holdings Inc.
Marathon Digital Holdings is a cryptocurrency company that focuses on building the largest mining operation in North America with one of the lowest energy costs. In essence, it helps investors gain exposure to Bitcoin in their portfolios without having to deal with the complications of holding the asset directly. MARA stock currently trades at $36.85 as of 10:31 a.m. ET and has enjoyed gains of over 1,400% in the past year alone.
On August 3, 2021, the company announced its Bitcoin production and mining operations updates for July 2021. Notably, its monthly Bitcoin production increased by 66% month-over-month to 442.2 BTC in July. Total Bitcoin holdings grew to approximately 6,225.6 BTC. Marathon has also received approximately 19,401 S19 Pro ASIC miners from Bitmain year-to-date with an additional 4,287 miners currently in transit.
Impressively, its existing mining fleet consists of 19,395 active miners producing 2.09 EH/s. On August 1, 2021, the company also announced the purchase of an additional 30,000 miners from Bitmain. All things considered, will you consider MARA stock a buy right now?
Robinhood Markets Inc.
Another name to consider in the crypto space now would be Robinhood Markets. In essence, the California-based company provides consumers with stock brokerage services. Notably, Robinhood users can do so via the company's proprietary app with no account minimums. Regarding our list today, Robinhood also offers digital currency-related services via its Robinhood Crypto arm. With all the buzz around cryptocurrencies in the market this week, I could see investors eyeing HOOD stock.
Now, the company's shares currently trade at $43.54 a share as of 10:45 a.m. Since its IPO earlier this month, HOOD stock is now looking at gains of over 25%. Regardless, the company seems to be gaining ground in terms of its crypto offerings. Just last week, Robinhood reported that cryptocurrency transactions accounted for more than half of its sales in the quarter. 62% of said gains are thanks to the hit popularity of Dogecoin among retail investors.
Overall, Robinhood raked in a total crypto transaction revenue of $233 million, a major leap from $5 million in the year-ago quarter. With the company gaining momentum on this front, would you consider HOOD stock a cryptocurrency player to invest in now?
[Read More] Best Communication Stocks To Watch Right Now
MicroStrategy Inc.
Following that, we will be taking a look at MicroStrategy (MSTR). To begin with, it is a major name in the analytics and business intelligence industry. Through its platform, the company provides organizations across the globe with best-in-class enterprise analytics. Notable names among its clientele would include Amazon (NASDAQ: AMZN) Web Services, 3M (NYSE: MMM), and Accenture (NYSE: ACN). More importantly, the company is well-known for its growing treasury of bitcoins. This would be where MSTR stock comes into play amidst the current Bitcoin hype.
Now, the company's shares currently trade at $722.58 as of 11:00 a.m. ET. Namely, this is after skyrocketing by over 360% in the past year. The real question now is whether MSTR stock is worth investing in at this current price point. Well, if you are among the Bitcoin bulls looking to invest in cryptocurrency stocks, the answer could be a yes.
Evidently, CEO Michael Saylor revealed that MSTR currently holds over 105,000 bitcoins. Adding to that, Saylor also mentioned that the company is keen to increase this figure moving forward. Given all of this, will you be keeping an eye on MSTR stock this week?
[Read More] Hot 5G Stocks To Buy As The Stock Market Rebounds? 3 In Focus
Square Inc.
Square is a company that specializes in digital payments. The company allows its Sellers to use its platform to reach buyers online and in-person, manage their businesses, and access financing. Through its Cash App, users can send cryptocurrency and fiat money to one another. SQ stock currently trades at $269.21 as of 11:10 a.m. ET. On August 1, 2021, the company announced its second-quarter 2021 financial results.
Diving in, the company reported a total net revenue of $4.68 billion, up by 143% year-over-year. Excluding Bitcoin, total net revenue in the second quarter was $1.96 billion. Gross profit was $1.14 billion for the quarter, up by 91% year-over-year.
In particular, Cash App delivered strong growth for the quarter, generating $3.33 billion of revenue and $546 million of gross profit. Its gross payment volume (GPV) reached an impressive $4.1 billion, more than doubling year-over-year. Given the impressive financials, is SQ stock worth adding to your portfolio right now?
[Read More] 4 Robotics Stocks To Watch Amid Rising Shifts To Automation
Coinbase Global Inc.
Next on this list, we have Coinbase, a crypto company that operates a cryptocurrency exchange platform. Its company boasts over 68 million verified users and has a quarter traded volume of $462 billion. The company's exchange is available in over 100 countries and it employs over 2,000 employees. COIN stock currently trades at $269.51 as of 11:25 a.m. ET.
Last week, the company announced that it will be investing $500 million of its cash into a diverse portfolio of crypto assets. It also plans to allocate 10% of its quarterly net income into this same portfolio. The company says that it will increase its allocation over time as the crypto economy matures.
It also says that it is a long-term investor and all trades will be executed via its over-the-counter desk or away from its exchange to avoid any conflict of interest with its customers. For these reasons, will you buy COIN stock?
New traders crack regular mold when investing, says CNBC survey
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Individual Finance Chief Quicken Inc. Announces New Majority Financial commitment from Aquiline Capital Companions LLC
PharmaCyte Biotech to Participate in H.C. Wainwright 23rd Annual World Investment decision Convention


Nanna Lysholt-Hansen (Denmark, 1980) is a visual artist based in Copenhagen and Athens and has since 2003 used her body as a tool to investigate relationships between the body, location, situation and time. She is the founder of NLHspace in Copenhagen and holds a MFA in Fine Arts from the Royal Academy of Fine Art, Copenhagen and BFA of Fine Arts from Kingston University of London.
Trine Mee Sook Gleerup (Denmark/South Korea, 1978) is a visual artist based in Copenhagen. Her interests range from post-colonial and race-related perspective as she debates cultural and racial structures and representation. Trine Mee Sook Gleerup holds an MFA in Fine Arts from The Royal Academy of Fine Arts, Copenhagen, and is the co-founder of the Scandinavian artist group, UFOlab (Unidentified Foreign Object laboratory).
Maline Casta (Sweden, 1978) is a visual artist based in Stockholm and has since 2007 worked with performance, looking into site specificity, creating visual and poetic tableaux which quietly examines and questions the realm of reality. She has a background in stage design and has created a large number of opera, theatre and dance productions in the US and Europe. She holds a MFA from Tisch School of Arts, New York and MA in Storytelling from Konstfack, University College of Arts, Crafts and Design.
Melanie Jame Wolf (Germany/Australia, 1977) is an interdisciplinary artist principally making performance based works under the name Savage Amusement and a member of Triage Live Art Collective. Her performances are often made for small audiences and deal with questions of love, distance, intimacy, language, memory and the animal. She holds a Master in International Performance Research from University of Helsinki and is currently a PhD candidate at Victoria University, Melbourne (AU).


Q. What is the benefit of Natural Gas vs. Propane? Can I get either of these from Brenner?
The most significant benefit is cost. Natural gas costs $12.18 per million btu vs. Propane which costs $20.47 per million btu. Another benefit of Natural Gas is the delivery system. Natural Gas is direct to the user were Propane is delivered by truck into a tank at the users location which then either the buyer or seller has to monitor inventory and order as needed. Brenner does not currently sell or deliver Propane or Natural Gas.
Q. Why do gas prices fluctuate so much?
There are many reasons that cause gas to fluctuate from Geo-political and weather to simple supply and demand. I believe there are three main reasons that should be at the top of the list.
The first would be Supply and demand. Supply and demand can be affected by available Crude Oil for making refined products such as gasoline. The petroleum infrastructure needs to operate at levels to meet demand. If it does not a shortage will occur which in turn will cause prices to increase. Demand is a good indicator on the health of the world economy. When demand is up it could also put pressure on inventories which can cause price spikes.
The second factor that affects volatility in prices is that Crude oil and refined products are traded as commodities. Energy has become an asset class. Investors from privately held portfolios to 401k funds buy and trade contracts on the NYMEX for their clients.
The third main influence is Retail strategy. The convenience store owner prices gas on a number of different factors that range from their cost to competitive pressure.
Q. What does oil have to do with gas?
Q. How does Brenner help preserve our environment?
Brenner Oil Group was at the fore front of Ethanol and Bio-Diesel blending in the Midwest. All of us at Brenner are committed to preserving the environment through the products we sell and the energy we use to sell them. We are focused as a company to find new ways to reduce the energy we and our customers use while achieving the same productivity.
Q. Where does Brenner get its gas? How?
Brenner has relationships with all of the major suppliers in our Marketing Area. We purchase or transport fuel from these supplier terminals to our customers typically by truck.
Q. How many gallons of fuel does Brenner deliver on any given day?
More than 1.3 million gallons.
Currently but not limited to all of the state of Michigan, northern Indiana and eastern Illinois.
Q. Do you supply factories with their oil/energy?
If the factory is one of our customers we supply them with their fuel needs.
Q. Is Brenner an American Company?
Yes. Brenner was started in 1930 and is currently lead by its third generation, brothers Jerry and Doug Brenner.
Q. Do you sell gas to just large chains or can individual operators participate too?
We sell to anyone from the home heat customer to large retail chains. We have many single store owners who we are proud to supply. We have wholesale, retail, municipal, marine and industrial customers.
Are you responsible for my fuel prices fluctuating?
Brenner Oil does not determine fuel product prices. These prices are regulated through stock exchanges located all over the world. Brenner Oil can estimate fuel-futures in order to give our customers the best product rates we can.


text:
SEGAN
Software Name: SEGAN
Legacy software from 1978 for the analysis of curved segmentally erected prestressed concrete box girder bridges, including time dependent effects, so that deflections and stresses can be computed at any stage during the construction or service life of the bridge. Source code in FORTRAN and related reports can be downloaded from the earthquake engineering online archive maintained by University of California Berkeley.
SEGAN: Analysis of Curved Segmentally Erected Prestressed Concrete Box Girder Bridges
Van Zyl, Stefanus F.
Department of Civil Engineering, University of California, Berkeley, 1978,
This program permits the analysis of curved segmentally erected prestressed concrete box girder bridges, including time dependent effects, so that deflections and stresses can be computed at any stage during the construction or service life of the bridge. The segments can be either precast or cast in place. The bridge cross section must consist of a single box section with vertical or inclined webs and have cantilever flanges. Width and depth dimensions can vary along the bridge span. Time-dependent material changes, such as creep and shrinkage of concrete, as well as environmental effects such as humidity and temperature changes, are accounted for. However, other concrete material nonlinearities such as cracking or inelastic behavior and geometric nonlinearities are not included in the analysis. Prestressing in the longitudinal direction can be included in the analysis. Tendons can be located in either the webs or flanges and can have a linear or parabolic profile. Stressing and release operations, slip in of tendons, and restressing and removal of tendons are included. A procedure is included for specifying the structural configuration and the erection sequence. Operations used in segmental construction, such as addition of segments, prestressing, changing of support boundary conditions, application or removal of construction loads, and prescribed displacements can be analysed. At each construction stage, the current structure is analyzed and the incremental and total displacements, stresses, and strains are obtained. The complete structure can also be analyzed for a variety of live loads and time steps.
Bridge Design, Incrementally Constructed Bridges
segmental bridge
http://nisee.berkeley.edu/elibrary/Software/SEGANZIP