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ASX:MBH
Introducing Maggie Beer Holdings (ASX:MBH), The Stock That Zoomed 169% In The Last Year
December 15, 2020 • Updated February 01, 2023
When you buy shares in a company, there is always a risk that the price drops to zero. But if you pick the right stock, you can make a lot more than 100%. For example, the Maggie Beer Holdings Limited (ASX:MBH) share price had more than doubled in just one year - up 169%. Also pleasing for shareholders was the 76% gain in the last three months. On the other hand, longer term shareholders have had a tougher run, with the stock falling 68% in three years.
See our latest analysis for Maggie Beer Holdings
Maggie Beer Holdings isn't currently profitable, so most analysts would look to revenue growth to get an idea of how fast the underlying business is growing. When a company doesn't make profits, we'd generally expect to see good revenue growth. Some companies are willing to postpone profitability to grow revenue faster, but in that case one does expect good top-line growth.
In the last year Maggie Beer Holdings saw its revenue grow by 72%. That's a head and shoulders above most loss-making companies. And the share price has responded, gaining 169% as we previously mentioned. That sort of revenue growth is bound to attract attention, even if the company doesn't turn a profit. Given the positive sentiment around the stock we're cautious, but there's no doubt its worth watching.
You can see below how earnings and revenue have changed over time (discover the exact values by clicking on the image).
ASX:MBH Earnings and Revenue Growth December 15th 2020
We like that insiders have been buying shares in the last twelve months. Having said that, most people consider earnings and revenue growth trends to be a more meaningful guide to the business. It might be well worthwhile taking a look at our free report on Maggie Beer Holdings' earnings, revenue and cash flow.
It's good to see that Maggie Beer Holdings has rewarded shareholders with a total shareholder return of 169% in the last twelve months. That certainly beats the loss of about 8% per year over the last half decade. We generally put more weight on the long term performance over the short term, but the recent improvement could hint at a (positive) inflection point within the business. While it is well worth considering the different impacts that market conditions can have on the share price, there are other factors that are even more important. For instance, we've identified 3 warning signs for Maggie Beer Holdings (1 makes us a bit uncomfortable) that you should be aware of.
Maggie Beer Holdings is not the only stock insiders are buying. So take a peek at this free list of growing companies with insider buying.
Please note, the market returns quoted in this article reflect the market weighted average returns of stocks that currently trade on AU exchanges.
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This article by Simply Wall St is general in nature. It does not constitute a recommendation to buy or sell any stock, and does not take account of your objectives, or your financial situation. We aim to bring you long-term focused analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Simply Wall St has no position in any stocks mentioned.
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Have feedback on this article? Concerned about the content? Get in touch with us directly. Alternatively, email editorial-team@simplywallst.com.
About ASX:MBH
Maggie Beer Holdings
Maggie Beer Holdings Limited manufactures and sells food and beverage products in Australia.
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Online video juggernaut YouTube continues to get bigger.
After years of claiming more than 1 billion monthly users, YouTube now says that it reaches 1.5 billion logged-in viewers each month. CEO Susan Wojcicki made the announcement Thursday during her annual presentation at VidCon, the online video conference that happens in Anaheim every summer. She also disclosed that YouTube viewers spend an average of more than one hour each day watching YouTube videos on their mobile devices.
YouTube, which in late 2015 launched a subscription streaming platform called Red, has been mum about subscribers' viewership on the platform, but on Thursday afternoon, the company disclosed that its first 37 original series and movies have generated nearly 250 million views.
"We are excited about working with creators to help them create incredible content that delights their fans," said Wojcicki. YouTube has 12 new projects in the works for Red, including comedies from Rob Huebel and Ryan Hansen.
Other big announcements during the VidCon keynote, in which Wojcicki was interviewed onstage by online creators Rhett & Link, included the launch of a new video format for 180-degree videos. The feature is seen as a less-expensive step to creating full 360-degree videos.
YouTube is also making its live TV bundle, called YouTube TV, available in more markets. The service, which launched in April in select markets including New York and Los Angeles, will soon be available in 10 new cities, including Dallas, Houston, Atlanta and Phoenix.


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Aritic PinPoint introduced its brand new audit log feature. This audit log feature is available to its users and for integration purposes. It allows enterprises as well as SMBs to track updates made to the contact list. One can track various information such as who did it, the updated changes and the time of updated changes.
Tracking the changes:
Quite a few companies give access to multiple users to edit and update the information such as contacts, notes and reminders. At some point in time, one needs to update additional information like phone, address, date of birth, etc. Native Aritic PinPoint integrations allow these functions which cause false information to circulate. This false information can be problematic and one needs to control it. This is where the data audit feature plays a role. One can view the entire history of all user-related changes or integrations. To enable this, the addition of an audit tab and an integration tab is made to the contact details page.
Contact Audit log and integrations audit:
One can check information like which contacts are connected to which integrations. In this way, it enables your organization to keep a tab on information of a contact such as its source and furthermore the connection of the contact with CRM, Social Networks, and so on. Aritic PinPoint also displays information like the date of the last synchronization with CRM, the date of addition of the contact, and even the contact ID in the CRM instrument.
Audit log for users:
As for the individual users, they are free to make changes through forms, pixel interactions and changes made by the colleagues. Other information like the date on which it updated the contact and the progressions made from that point forward is available by simply tapping on the icon of the first column of the list you can receive a report referring to the update.
The feature is beneficial for companies as one cannot afford false information to circulate. A user has to think twice before feeding into inaccurate information. This financial certainty will help the people understand the ascertained workplace. It recognizes all the possible pieces of evidence that evaluates and formulates the opinion on the basis of communication they carry that out.

redpajama_set_name: RedPajamaCommonCrawl


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AIBECS: Bridging the Gap Between Ocean Modeling and Field Research
UCI oceanographers design an open-source program for in-depth ocean modeling.
Sarah Ruttenberg
The AIBECS (Algebraic Implicit Biogeochemical Elemental Cycling System) logo.
Benoît Pasquier
In a paper published earlier this year in the Journal of Open-Source Software, a group of oceanographers describe a computer program developed at UCI that models biogeochemical cycles on a global scale. The program, called AIBECS (Algebraic Implicit Biogeochemical Elemental Cycling System), is the first open-source tool for ocean modeling that is both easy enough for field researchers to use and powerful enough to provide publication-quality data processing.
François Primeau, Professor of Earth System Science at UC Irvine and co-creator of AIBECS, said the program does "state of the art mathematical modeling of ocean processes. It solves millions of equations, non-linear equations and millions of unknowns – things that are challenging for anyone."
Before the development of computational modeling, or before there was acute interest in the state of the ocean, minimal analysis was necessary to publish data collected in the field. Today, with the ever-growing threat of climate change, collecting data from the ocean and understanding its role in biogeochemical cycles is an urgent and complex endeavor; such cycles have dozens of factors contributing to them, and most of those factors are relevant to multiple cycles. This makes computational modeling a necessity to fully understand the data's significance.
"A lot of problems are not being done simply because there is no easy computational way to take them on," said Primeau.
Modeling of the ocean is now at a level of complexity close to matching the real world. However, this type of modeling typically requires high-level expertise to perform – something most field researchers lack. This creates what Primeau describes as a division of labor between those who model the ocean and those who collect data in the field.
"One piece of data is inadequate to tell any kind of story about what is going on physically in the ocean," Primeau says. "Lots of the things we are learning is by combining many measurements made by different labs by different people and very often over a long period of time because the environment is changing, so measurements that were made 30 years ago and measurements made today have to be combined."
Under Professor Primeau's guidance, former UCI postdoc Benoît Pasquier designed AIBECS to bridge this gap. AIBECS is a powerful package for inverse modeling, which is the practice of inferring immeasurable parameters from measurable data. Initially, Pasquier developed the program to run simulations of marine tracers – or indicators of ocean circulation – to model biogeochemical cycles. Eventually, other members of Professor Primeau's Lab used the program to study a "biological carbon pump." This "pump" is the cycle of oceanic phytoplankton taking in carbon dioxide from the atmosphere, converting it into mineral carbon, and excreting it into the deep ocean. You cannot directly measure the rates of this cycle, and so you must infer them based on multiple related factors that are measurable. By inputting such data into AIBECS, you can determine the rates, and thus estimate their greater impact on Earth's climate.
While AIBECS allows for the input of such equations if desired, the most current models of the oceans' circulation are already loaded into the program and can be swapped in and out with updated data as it becomes available. This flexibility and compatibility makes AIBECS an infinitely extendable tool.
In 2019, Pasquier took a postdoctoral position in Professor Seth John's lab at the University of Southern California. That lab quickly adopted AIBECS to model the role of trace metal nutrients like nickel and cadmium in ocean lifecycles. Using the model, members of the lab integrated the most current ocean models using data collected around the world over hundreds of years. Since Pasquier's departure from the lab, Professor John continues to use the program regularly, describing it as "incredibly powerful," and "approachable for people who haven't done modelling before."
AIBECS is also an open-source tool, available for free on GitHub. When asked about their decision to open-source the program, Dr. Pasquier said "science should be done for the benefit of all, and its dissemination should be optimized, public and free." Professor Primeau added that both scientists and academic journals are moving towards open sourcing because access to all collected data, past and present, is necessary for accurate and reproducible science, especially in computational modeling. This is especially pertinent considering the increasing rates of climate change. According to NOAA, Earth's temperature has risen by 0.14° F (0.08° C) per decade since 1880, and the rate of warming over the past 40 years is more than twice that: 0.32° F (0.18° C) per decade since 1981. Creating accurate models is imperative for understanding how the climate is changing and preventing further harm from coming to it.
Primeau anticipates the development of training workshops to give researchers the confidence to use the program in their work. He hopes that "field-going oceanographers who would normally not have done this kind of mathematical modeling feel empowered to do it because the tools are available."


Washington Drug and Alcohol Treatment Facilities.
Are you looking for Washington Drug and Alcohol Treatment Centers? Our listings listed below can help.
Not only are lots of drugs sold in Washington but large amounts are imported from Canada with the sole purpose of being distributed throughout the United States. Marijuana and ecstasy are amongst the most popular drugs shipped in for this purpose. BC Bud, a high potency form of marijuana, is one of the predominant drugs in the Canadian/Washington drug trade.
The crystal meth market in Washington, however, is controlled mostly by Mexican drug trafficking organizations. The drug availability and consumption of this drug is widespread and is one of the most problematic for the state.
Cocaine and crack can be found throughout Washington as well. Crack cocaine is mostly sold and used by those in inner-city, low income areas. The trade of this drug is dominated by Mexican drug trafficking organizations as well.
The type of heroin that is most popular in Washington is Mexican black tar. It has origins in Mexico but is often directly imported from California. Methamphetamine use has proven to be quite problematic. It is abused by those from all socioeconomic backgrounds and ethnicities. The most popular form is crystal meth. It is the most potent, addicting and dangerous. Mexican drug trafficking organizations are the most influential meth traffickers in the state. There are some domestic laboratories in Washington, however, their production has decreased because there are laws on the books which limit how much pseudoephedrine and other necessary chemicals to make the drug, can be purchased.
Most of the ecstasy abused in Washington comes from Canada and is shipped directly into the state. LSD and GHB are also fairly popular club drugs.
Marijuana can be found throughout Washington. It is either of the Mexican variety or BC Bud from Canada. BC Bud is considered to be of higher quality and is more potent then other types of marijuana.
The abuse of prescription medications such as Percodan, Oxycontin, Percocet, Lortab, Vicodin, Methadone and even anabolic steroids have all proven to be problematic and of great concern to law enforcement agencies. These drugs are being purchased online, obtained via forged prescriptions, doctor shopping and theft.
Choose a City to Find Addiction Help in Washington.


The Steve Morgan Foundation has handed over a cheque for £373,000 to The Reader to improve the lives of children in the North West.
The major investment, which was announced in 2017, will significantly improve the life chances of children living across the region by building a culture of reading for pleasure that will empower them for life.
Working with a range of organisations across the region, The Reader will embed their 'Shared Reading' initiative into public provision for families most in need, by providing training and support for staff and volunteers at a grassroots level.
Jane Harris, Director of Regional Funding with the Steve Morgan Foundation, said: "We first worked with The Reader back in 2010 and we're delighted that they are the first recipient of one of our new Major Grants for uplift funding.
"Our Trustees were very by impressed the team and their entrepreneurial approach to what they are trying to achieve.


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En breves publicaremos una newsletter para los consumidores. Si quiere atraer más compradores a su página web además de promocionarse de una manera sencilla, por favor, no dude en contactarnos.
We are working with several networks for display advertising. If you are interested in advertising on Scamadviser, please feel free to contact our agency Webads (+31 (0)20 62 616 34 or adverteren@webads.nl).
Our newsletter not only offers information on the latest scams and hoaxes but also the best online shopping deals for consumers worldwide.
If you like to attract more shoppers to your website and have a great offer or deal to promote, please feel free to contact us.
Interested in reaching 2.5 million unique visitors - a month - by advertising on Scamadviser? Please contact us.


Who was it who posted the entry about what kind of gross things you'll do when it comes to your kids? Because I was just holding Alden over my head and he drooled right into my mouth. And yet I did not move out of the red zone, because he was laughing and it was totally worth it.
42 responses to this post.
But I'm here to tell you that you'll do gross things for any kid you love very much. On more than one occasion I have picked food out of Anya's teeth with my very own fingernail – I did it last week, in fact. And I've picked Ezra's nose several times. There's no telling how many times the Georgelets have been the recipients of my, er, affection.
This time it was , although there is no shortage of grossness in my LJ.
I do recall a day when my goddaughter was about three and she leaned over and barfed up a bellyful of blueberries all over my lap. And I was weirdly… flattered.
Right! So funny. I suspect I'm well on my way to being able to write an entire survey of my own.
Right now Sabrina gets the biggest kick out of feeding other people things, but she is still completely unaware of how gross her food offerings are after she's gummed them a bit. I let her feed me a few pieces of bread this morning. Totally gross. Totally worth it.


A typed sign hanging on the door was all the notice that many received about today's closure of Bottega Americano, an ambitious Italian-inspired restaurant and specialty food marketplace that opened in San Diego's East Village in Summer 2014.
The first venture from four notable partners in San Diego's dining scene, Bottega Americano was the brainchild of owners Giuseppe Ciuffa, founder and CEO of Giuseppe Fine Restaurants & Fine Catering; avid foodie, investor and East Village resident Chad Ruyle; restaurateur Greg Van de Velde, who most recently managed the iconic Bertrand at Mister A's restaurant; and noted chef David Warner formerly of San Diego's beachfront hotspot JRDN (who returned to JRDN's employ last year). The restaurant and market launched at the base of the Thomas Jefferson School of Law building in August 2014. The 8,000-square-foot dining hub has reportedly been on the market for some time due to difficulties with the location. There is no word yet on who will be moving into the unit.


Wondering where to find eco-friendly Rubbish Removal Company in Upton Park Newham London E6?
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As a part of our mandate to assist the Atlantis Impact Economic Investment Development Forum create sustainable businesses in the local community, the Caban Investments team have been visiting the area every second week and advising the Forum Board on the next steps and receiving detailed reports on activities.
Since the signing of the MOU, the Forum has gone form strength to strength. The original 500 members that were present for the signing ceremony have now swelled to over 7 500 and this number is set to increase in the coming months. The Forum have also engaged successfully with local businesses to secure small contracts. The Forum is also conducting a skills audit of all members which is bringing to the fore the incredible talent that lies within the community and unearthing a large number of existing and potential entrepreneurs.
The Caban team have reviewed the business plans put forward by the Forum and are now in the process of registering the various businesses and securing a factory in which most of these companies will be incubated. The holding company is in the process of being registered and the name and logo of the new company will be announced soon!
We are extremely proud to be associated with this initiative and look forward to growing with the Forum. Read more here.


text:
\section{Introduction}

 Charged lepton flavor violation (CLFV) is a smoking gun signature of physics beyond the Standard Model (SM)  and is one of the most sought-after signals  at the intensity frontier~\cite{Kuno:1999jp,Marciano:2008zz,Bernstein:2013hba,deGouvea:2013zba}. Important search channels involving the lightest two lepton generations are $\mu \rightarrow 3e$, $\mu\rightarrow e\gamma$, and nucleus-catalyzed $\mu\rightarrow e$ \cite{Kuno:1999jp,Bernstein:2013hba,deGouvea:2013zba,Marciano:2008zz,Calibbi:2017uvl,Galli:2019xop}. The current best limits on $\mu\rightarrow e$ come from SINDRUM-II \cite{Kaulard:1998rb,Bertl:2006up}.

 The upcoming Mu2e~\cite{Bernstein:2019fyh} and COMET~\cite{Lee:2018wcx} experiments will either probe or discover CLFV at unprecedented levels of precision. Both experiments expect on the order of $10^{18}$ muon capture events, and plan to measure the ratio, $R_{e\mu}$, of $\mu\rightarrow e$ events to total muon captures, at the level of $10^{-17}$.

 %
 \begin{figure}\centering
    \subfloat[][]{\includegraphics[height=0.33\linewidth]{RMC.pdf}}%
    \qquad
    \subfloat[][]{\hspace{20pt} \includegraphics[height=0.33\linewidth]{RMC-ee.pdf}}
    \caption{Radiative muon capture on a nucleus (double lines) resulting in (a) a real photon and (b) a virtual photon that mediates the production of an electron positron pair. In this work we study how the $e^+$ (or $e^-$) spectrum in (b) is related to the photon spectrum in (a). \label{int-vs-ext}}
 \end{figure}
 %

 Importantly, the Mu2e setup is ``charge symmetric'' such that the detection efficiencies for electrons and positrons are comparable. Thus, Mu2e will serve as a testing ground not just for the discovery of CLFV, but also for the discovery of lepton \emph{number} violation (LNV). Specifically, on a nucleus (e.g.\ aluminum), the reaction
 %
 \begin{equation}
    \mu^-  + [A,Z] \rightarrow e^+ + [A,Z-2]~,
 \end{equation}
 %
 becomes a viable target for observation (see also \cite{Kaulard:1998rb}).

 While neutrinoless double beta ($0\nu\beta\beta$) decay is often touted as the most promising direction for the discovery of LNV, there do exist extensions of the SM that predict a more competitive signal in the $\mu e$ sector than in the $ee$ sector (cf. \cite{Geib:2016atx,deGouvea:2019xzm,Berryman:2016slh} and references therein). There also remains the looming possibility that $m_{ee}\approx 0$ (cf. Fig.~4 of \cite{Avignone:2007fu}), rendering $0\nu\beta\beta$ insensitive to LNV if it is mediated by a light Majorana neutrino. The fact that Mu2e is charge symmetric by design yields a new handle on LNV ``for free''.

 Unfortunately, the charge-changing nature of $\mu^-\rightarrow e^+$ can result in a substantially lower positron energy compared to the electron energy in the CLFV channel $\mu^-\rightarrow e^-$. This is driven by the mass difference between $[A,Z]$ and $[A,Z-2]$~\cite{Yeo:2017fej}, and causes the signal region to approach, or overlap with, poorly-understood SM backgrounds.  The most important of these backgrounds is radiative muon capture (RMC),
 %
 \begin{equation}\label{reaction}
    \mu(k) + [A,Z](p) \rightarrow \nu_\mu(k') + [A,Z-1](p') + \gamma(q) \,,
 \end{equation}
 %
 where, for definiteness, we assume the final state nucleus is in its ground state\footnote{This assumption can be easily relaxed and a generic set of final states summed over as discussed in \cref{inclusive-X}.} (in the case of $^{27}$Al the final state would be $^{27}$Mg).

 In searches for CLFV or LNV, incoming muons are the  source of both the $\mu \to e$ signal and the RMC background.  It is therefore critical to constrain  the energy spectrum of electrons and positrons from RMC in order to discriminate signal from background.

 There are two ways that RMC can contaminate the signal window in a CLFV or LNV search:
 %
 \begin{enumerate}
    \item External conversion: a (real) photon is produced and interacts with surrounding material ultimately pair-producing an electron positron pair.
    \item Internal conversion: a virtual photon mediates the production of an electron positron pair.
 \end{enumerate}
 %
 These two possibilities are shown schematically in \cref{int-vs-ext}. Both cases are subject to nuclear model dependence.\footnote{The RMC rate and spectral shape for capture on hydrogen has been studied in heavy baryon chiral perturbation theory~\cite{Meissner:1997mq,Ando:1997es}.
Nuclear corrections substantially alter the spectral shape of RMC photons~\cite{Fearing:1988mu,Fearing:1991je,Bergbusch:1999ms,Cheoun:2003ah},
especially near the end-point \cite{Christillin:1979fa}.
}

 In the case of external conversion, nuclear model uncertainties can be circumvented at either Mu2e or COMET by directly measuring the real photon spectrum from RMC on aluminium. With this information in hand, dedicated Monte Carlo simulations (including the full detector geometry) can be used to predict the resultant electron and positron spectra. In this sense, the collaborations (Mu2e and COMET) control their own fate and can empirically constrain the external RMC backgrounds relevant for their own experiment.

 Internal conversion is a more formidable challenge.  Early work by Kroll and Wada~\cite{Kroll:1955zu} investigated the ratio of $e^+e^-$ production relative to single photon production for a $1\rightarrow 2$ process. The results of their investigation showed, unsurprisingly, that the ratio is \emph{not} calculable without microscopic theoretical input. Rather, somewhat heuristically, they suggested that the infrared enhancement of the virtual photon favours small virtualities and argued for an approximation in terms of real photon matrix elements.
 \begin{figure}\centering
    \includegraphics[width=\linewidth]{Error-Estimate-Fold.pdf}
    \caption{Spectrum of positrons/electrons as compared to real photons near the end-point assuming that the photon spectrum is given by $\dd \Gamma/ \dd E_\gamma \propto (1-2x+2x^2)x(1-x)^2$ with $x=E_\gamma/q_\text{max}$ and $q_\text{max}=100$ MeV. This corresponds to the closure approximation spectrum used in the analysis of RMC data on various nuclear isotopes in \cite{Bergbusch:1999ms}. The electron/positron spectrum is computed using \cref{P-int-dE,main-result} below. The spectrum is softened relative to photons because 1) the end-point is shifted by $m_e=0.511$ MeV, and 2) the probability of producing an $e^+e^-$ pair rises sharply as one moves further from the end-point as shown in \cref{main-plot}. Errors due to virtual-photon nuclear matrix elements (gray band) are estimated by treating $C_L$ and $C_T$ (see \cref{Error-Estimates}) as independent random variables drawn from a Gaussian distribution with unit variance.
    \label{photon-vs-positron}    }
 \end{figure}
 %

 In this work we critically re-examine this problem focusing specifically on the viability of using measurements of the (real) photon spectrum to predict the internal positron (or electron) spectrum. The main conclusion of our work is that the real photon spectrum is sufficient to predict the internal spectrum of positrons \emph{near the end-point} as shown in \cref{photon-vs-positron}.  This observation implies that if the real photon spectrum is measured, then the full (internal + external) electron and positron spectra can be predicted. If the photon spectrum cannot be measured, then Mu2e and COMET could use direct measurements of the total electron or positron spectrum to infer the RMC photon spectrum.

 The rest of the paper is organized as follows. In \cref{Nuclear-RMC} we define the  non-perturbative matrix element that governs the emission of real photons and discuss how this same matrix element also governs the emission of electron positron pairs at leading order in $\alpha$.  Next, in \cref{Real-Photon} we provide an explicit formula for the real photon spectrum, which naturally leads into \cref{Positron-Spectrum} where we provide the corresponding expression for the positron spectrum. In \cref{Near-End-Point} we discuss the near end-point spectrum and demonstrate how the real photon spectrum can be used to predict internally converted positrons. Finally, in \cref{Conclusions} we summarize our conclusions, and suggest future improvements.

 We also provide four appendices. In \cref{Error-Estimates} we discuss how one can parameterize sub-leading corrections to the near end-point approximation discussed above. In \cref{OFPT} we give a formal argument for some power counting details needed to justify the approximation of transversely polarized virtual photon matrix elements by their real photon counter parts. To facilitate a comparison between our work and that of Kroll and Wada we provide a short discussion of the correspondence in \cref{KW-vs-HP}. We also discuss our disagreements with their conclusions there.   Finally in \cref{inclusive-X} we describe how to generalize the analysis presented in the main text to the case of inclusive final states.

 \section{Radiative muon capture on a nucleus \label{Nuclear-RMC}}

The relevant S-matrix element for radiative muon capture is the overlap of an in-state, $\ket{A\mu,\text{atom} }_\text{in}$  containing a muonic atom, with an out state $\ket{A'\nu_\mu \gamma}_\text{out}$ containing a recoiling nuclear system $A'$, a muon neutrino $\nu_\mu$, and a photon $\gamma$:
\begin{equation}
    S_\gamma=  ~~_\text{out}\hspace{-3.5pt}\braket{A'\nu_\mu\gamma}{A\mu,\text{atom}}_\text{in}~.
\end{equation}
This can be expressed via the LSZ reduction formula as
\begin{equation}\begin{split}\label{Sgamma}
    S_\gamma&= (2\pi)^4\delta^{(4)}(\Sigma_3 P) \epsilon^\mu ~~ _\text{out}\hspace{-3.5pt}\mel{A'\nu_\mu}{\hat{\mathscr{J}}_\mu}{A\mu,\text{atom}}_\text{in}~,
\end{split}\end{equation}
where ${\hat{\mathscr{J}}_\mu}$ denotes the electromagnetic current and the notation $\Sigma_3 P$ signifies that this momentum conservation is for three on-shell particles in the final state.

At leading order in $\alpha$, the $S$ matrix for internal pair production is given by (we use  $ \langle \hat{\mathscr{J}}_\mu \rangle \equiv$  $_\text{out}\hspace{-3.5pt}\mel{A'\nu_\mu}{\hat{\mathscr{J}}_\mu}{A\mu,\text{atom}}_\text{in}$ from here on for brevity's sake)
\begin{equation}\begin{split}\label{See}
    S_{ee}
    &=-(2\pi)^4\delta^{(4)}(\Sigma_4 P)  { \langle \hat{\mathscr{J}}_\mu \rangle}_*~ \frac{\sqrt{4\pi\alpha}}{m_*^2} \bar{u} \gamma^\mu v~.
\end{split}\end{equation}
Note that the in-out matrix element in (\ref{See}) is evaluated ``off-shell'', in that $m_*^2\equiv(p_++p_-)^2\neq 0$, where $p_\pm$ refer to the four momenta of $e^+$ and $e^-$ respectively.

Stripping off the four-momentum conserving delta function, we can therefore identify the matrix elements as
\begin{align}
    \label{eq6}
    \mathrm{i}\mathcal{M}_\gamma &= { \langle \hat{\mathscr{J}}_\mu \rangle}_0  \epsilon^\mu~,\\
    \mathrm{i}\mathcal{M}_{ee} &= -{ \langle \hat{\mathscr{J}}_\mu \rangle}_*\frac{\sqrt{4\pi\alpha}}{m_*^2} \bar{u} \gamma^\mu v ,\label{eq7}
\end{align}
where in \cref{eq7} we work at leading order in $\alpha$. The subscript reminds us whether the matrix element has been evaluated for real, ${ \langle \hat{\mathscr{J}}_\mu \rangle}_0$, or virtual, ${ \langle \hat{\mathscr{J}}_\mu \rangle}_*$, photon kinematics.

To calculate the rate of decay we can make use of the standard formula\footnote{The conventional muon capture formula (see e.g.\ \cite{Fearing:1979be})  written in terms of $\abs{\psi_{1\text{s}}(0)}^2$ can be recovered in the non-relativistic limit by constructing the bound state $\ket{1\text{s},A\mu}$ out of plane-wave states $\ket{\mu(k)}$ and $\ket{A(-k)}$ as described in \S5 of \cite{Peskin:1995ev}.}
\begin{equation}
    \Gamma = \frac{1}{2 M_{\text{atom}} }  \int \dd \Phi_n \sumsq{\mathcal{M}}~,
\end{equation}
where $M_{\text{atom}}$ is the mass of the muonic atomic (including binding energy), $\sumsq{\cdot}$
denotes an average over initial-state spins and a sum over final-state spins,
and $\dd \Phi_n$ is $n$-body Lorentz invariant phase space,
\begin{equation}
    \dd \Phi_n = \qty[ \prod_{i=1}^n \frac{\dd^3 p_i}{2E_i(2\pi)^3}  ]  \times  (2\pi)^{4}\delta^{(4)}(\Sigma_n P)~.
\end{equation}
In what follows we consider the spin-averaged matrix element which is rotationally invariant. This allows us to choose our coordinate system to lie with the $\hat{z}$ axis along the direction of the photon's momentum without loss of generality.
\section{Real photon spectrum \label{Real-Photon}}
Let us introduce the tensor
\begin{equation}
\mathscr{J}_*^{\mu\nu} = \sum_{\text{spins}} \langle \hat{\mathscr{J}}^\mu\rangle_* ~\times ~ \langle \hat{\mathscr{J}}^{\nu\dagger}\rangle_*~,
\end{equation}
where an average over initial spin states, and sum over final spin states is performed.

The real photon matrix element squared, $\sumsq{\mathcal{M}_\gamma}$, can be expressed in terms of this tensor  as
\begin{equation}
   \sumsq{\mathcal{M}_\gamma}=  (-g_{\mu\nu}^\perp) \mathscr{J}^{\mu\nu}_0~,
\end{equation}
where we have used $\sum \epsilon_\mu \epsilon_\nu^* = -g_{\mu\nu}^\perp$ for the sum over physical photon polarizations. The differential rate (or spectrum) of real photons in the lab frame is then given by
\begin{equation}
    \dv{\Gamma_\gamma}{E_\gamma} =
     \frac{1}{2 M_{\text{atom}} }  \int \dd \Phi_3 \qty[ \mathscr{J}^{11}_0+ \mathscr{J}^{22}_0] \delta(q_0- E_\gamma)~.
\end{equation}

\section{Positron spectrum \label{Positron-Spectrum}}

The matrix element for $e^+e^-$ creation can be expressed in terms of $\mathscr{J}_*^{\mu\nu}$ as
\begin{equation}
    \sumsq{\mathcal{M}_{ee}} =  \frac{4\pi\alpha}{m_*^4}  L_{\mu\nu} \mathscr{J}_*^{\mu\nu}  ~,
\end{equation}
where the lepton tensor $L_{\mu\nu}$ is defined as
\begin{equation}
L_{\mu\nu} =  \mathrm{Tr}\qty[ (\slashed{p}_-+m_e)\gamma_\mu (\slashed{p}_+-m_e)\gamma_\nu]~.
\end{equation}
The positron spectrum is then given by
\begin{equation}\label{Gamma-ee}
    \dv{\Gamma_{ee}}{E_+} =
     \frac{1}{2 M_{\text{atom}} }  \int \dd \Phi_4  \frac{4\pi\alpha}{m_*^4}  L_{\mu\nu} \mathscr{J}_*^{\mu\nu}  \delta(\mathfrak{E}_+- E_+)~,
\end{equation}
where $\mathfrak{E}_+$ is a function of the phase space variables that will be specified explicitly below in \cref{Funny-E}.

At this point, to make contact with the real photon spectrum, it is important to decompose phase space appropriately. This can be done via \cite{HitoshiPS}
\begin{equation}\label{phase-space-decomp-impl}
    \dd \Phi_4 = \dd \Phi_{3*} \frac{\dd m_*^2}{2\pi} \dd \Phi_2(\gamma_*\rightarrow e^+ e^-)~,
\end{equation}
where $\Phi_{3*}$ is the three body phase space for $A'$, $\nu_\mu$ and a particle of mass $m_*$. Let us compare to the massless case. We will explicitly integrate over the $A'$ system's momentum such that only the energy conserving delta function,  $\delta(\Sigma_{3*} E)$  and the neutrino-photon phase space remain
\begin{align}
    \dd \Phi_{3*} &= \frac{1}{2 E_{A'}}
   \frac{\dd^3 k'}{2 k'  (2\pi)^3} \frac{\dd^3 q}{2 q_0  (2\pi)^3} (2\pi)\delta(\Sigma_{3*}E)
   \label{3star-phase-space}\\
   &= \frac{1}{2 E_{A'}}
   \frac{\dd^3 k'}{2 k'  (2\pi)^3} \frac{ \dd \Omega_q }{ (2\pi)^3} \times
   \frac{\beta_* q_0}{2} \dd q_0 (2\pi)\delta(\Sigma_{3*} E)\nonumber~,
\end{align}
where $\beta_*=q/q_0=\sqrt{1-m_*^2/q_0^2}$, and we have made use of $\dd q/\dd q_0 = 1/\beta_*$. This is to be compared with the case of a massless photon which does not have the factor of $\beta_*$
\begin{equation}\label{3-phase-space}
\dd \Phi_{3}=\frac{1}{2 E_{A'}}
   \frac{\dd^3 k'}{2 k'  (2\pi)^3} \frac{ \dd \Omega_q }{ (2\pi)^3} \times
  \frac{q_0}{2} \dd q_0 (2\pi)\delta(\Sigma_3 E)~.
\end{equation}
The energy conservation condition is (for a recoiling $A'$ of mass $M$)
\begin{equation}\label{energy-conservation}
  \sum_{3*} E=   k+q_0 + \underbrace{\sqrt{k^2 + |\vec{q}|^2 + 2|\vec{q}|k\cos\theta_{\nu\gamma}  + M^2}}_{E_{A'}}- M_{\text{atom}}~,
\end{equation}
where $|\vec{q}|^2 = q_0^2-m_*^2$ and $\theta_{\nu\gamma}$ is the opening angle between the photon and neutrino in the lab frame. Integrating over the neutrino energy introduces a factor of $\qty[ \pdv{\Sigma_{3*} E}{k}]^{-1}$:
\begin{equation}
    \frac{1}{1+\frac{k + |\vec{q}|\cos\theta}{E_{A'} }} = \frac{E_A'}{M_{\text{atom}} - (1-\beta_*\cos\theta_{\nu\gamma}) q_0} ~.
\end{equation}
 The factor of $E_{A'}$ cancels against the factor of $E_{A'}$ in the denominator of \cref{3-phase-space,3star-phase-space} such that the phase space for a massive photon can be related to the phase space for a massless photon via
\begin{equation}\label{3-vs-3*}
    \dd \Phi_{3*}= \dd \Phi_3 \times \beta_* F_*~,
\end{equation}
with $\Phi_{3}$ being independent of $m_*$ and $\dd \Phi_2$, and the variable $F_*$ being given by (cf. Eq.\ (2) of \cite{Fearing:1979be})
\begin{equation}\begin{split}
    F_* &=\qty[\qty(\pdv{\Sigma_{3} E}{k})\bigg/ \qty(\pdv{\Sigma_{3*} E}{k}) ] \times \frac{k'_*}{k'}\\
    &= \frac{M_{\text{atom}} - (1-\cos\theta_{\nu\gamma}) q_0}{M_{\text{atom}} - (1-\beta_*\cos\theta_{\nu\gamma}) q_0}~ \times \frac{k'_*}{k'} ~,
\end{split}\end{equation}
where the various energetic factors in the phase space measure are modified so that they satisfy \cref{energy-conservation}.

In terms of these variables we can then write
\begin{equation}\label{phase-space-decomp-expl}
   \int \dd \Phi_4 = \int \dd\Phi_3 \int_{4m_e^2}^{q_0^2} \frac{\dd m_*^2}{2\pi} \beta_* F_* \int \dd \Phi_2~,
\end{equation}
with $\Phi_2$ the two-body phase space for a virtual photon of mass $m_*$ decaying into an $e^+e^-$ pair. We have inserted the integral symbols explicitly to emphasize the order in which the they must be performed.

Let us now study \cref{Gamma-ee}, performing the integrations sequentially from right to left as suggested by \cref{phase-space-decomp-expl}. Since the decomposed phase space is factorized into independently Lorentz invariant pieces we can carry out the integration in the frame of our choice. The quantity $\mathscr{J}_{\mu\nu}$ is independent of the two-body phase space $\Phi_2$ and so we can first evaluate
\begin{equation}
    \int \dd \Phi_2 L_{\mu\nu} \delta(\mathfrak{E}_+ -E_+) ~,
\end{equation}
in the rest frame of the photon. Two body phase space in this frame is given by
\begin{equation}
    \dd \Phi_2 = \frac{\dd \cos\vartheta \dd \varphi }{32\pi^2} \beta_e~ ,
\end{equation}
where $\beta_e=\sqrt{1-4 m_e^2/m_*^2}$ and coordinates are defined such that $\hat{z}$ is parallel to the boost direction that connects the photon's rest frame to the lab frame.  As already discussed above, this choice can be made without loss of generality because of the spherical symmetry of the spin-averaged matrix element $\sumsq{\mathcal{M}}$.

In terms of these variables the function $\mathfrak{E}_+$ that determines the positron's energy is given by
\begin{equation}\label{Funny-E}
    \mathfrak{E}_+(q_0, \cos\vartheta)=
    \frac{q_0}{2} (1+ \beta_e \beta_*\cos\vartheta)~,
\end{equation}
where $\beta_*=\sqrt{1-m_*^2/q_0^2}$ is (as above) the velocity of the virtual photon.

The delta function is independent of $\varphi$ and so it is convenient to define $\langle L_{\mu\nu} \rangle_\varphi= \int \frac{\dd \varphi}{2\pi}  L_{\mu\nu}$ given explicitly by

\begin{widetext}
\begin{equation}\label{lepton-tensor}
    \langle L_{\mu\nu} \rangle_\varphi= m_*^2  \begin{pmatrix}
         0 & 0 & 0 & 0 \\
         0 & 2-\left(1-\cos^2\vartheta\right) \beta_e^2 & 0 & 0 \\
         0 & 0 & 2-\left(1-\cos^2\vartheta\right) \beta_e^2 & 0 \\
         0 & 0 & 0 & 2 \left(1-\cos^2\vartheta \beta_e^2\right)  \\
    \end{pmatrix}
    \qq{(in photon rest frame)}~.
\end{equation}
\end{widetext}
Then we find
\begin{equation}
   \int \dd \Phi_2 L_{\mu\nu} \delta(\mathfrak{E}_+ -E_+)=  \left. \frac{\beta_e}{8\pi} \frac{1}{q_0 \beta_e \beta_*} \langle L_{\mu\nu} \rangle_\varphi \right\rvert_{\cos\theta}~,
\end{equation}
where we have used (note the different fonts of $\vartheta$ vs $\theta$)
\begin{equation}
\delta(\mathfrak{E}_+ -E_+)= \frac{2}{q_0 \beta_* \beta_e} \delta(\cos\vartheta-\cos\theta)~.
\end{equation}
The emission angle of the positron, $\cos\theta$, is found by solving $E_+=\mathfrak{E}_+(q_0,\cos\theta)$,  being given explicitly by
\begin{equation}\label{cos-theta-func}
     \cos\theta(E_+,q_0,m_*)=\frac{ 2 E_+/q_0 -1}{\beta_*\beta_e} .
\end{equation}
Obviously,  $\cos\theta$ must lie in the interval $[-1,1]$ and so Heaviside functions enforcing this condition should be included:
\vfill
\begin{widetext}
\begin{align}\label{exact-rate-1}
    \dv{\Gamma_{ee}}{E_+}&= \frac{1}{2 M_{\text{atom}}} \int \dd \Phi_3  ~\frac{\dd m_*^2}{2\pi} \times \beta_* F_* \times \frac{4\pi \alpha}{m_*^4}  \times \frac{1}{8\pi}\frac{1}{q_0 \beta_*} \langle L_{\mu\nu}\rangle_\varphi \mathscr{J}^{\mu\nu}_*
    \Theta(1-\abs{\cos\theta})\nonumber\\
    &= \frac{1}{2 M_{\text{atom}}} \int \dd \Phi_3 \frac{\alpha}{4 \pi q_0}\int \dd m_*^2~ F_*\qty[ \frac{1}{m_*^4} \langle L_{\mu\nu}\rangle_\varphi \mathscr{J}^{\mu\nu}_* ] \Theta(1-\abs{\cos\theta})\\
    &=\frac{1}{2 M_{\text{atom}}} \int \dd \Phi_3 \frac{\alpha}{4 \pi q_0}  \int \dd m_*^2 \frac{F_*}{m_*^2}~\qty[\qty(2-\qty[1-\cos^2\theta] \beta_e^2)\qty(\mathscr{J}^{11}_* + \mathscr{J}^{22}_*) +2\left(1-\cos^2\theta \beta_e^2\right) \mathscr{J}^{33}_*]\Theta(1-\abs{\cos\theta}) \nonumber~.
\end{align}
\end{widetext}
In \cref{exact-rate-1} we have contracted  $\mathscr{J}_*^{\mu\nu}$ against the lepton tensor evaluated in the rest frame of the photon.\footnote{If the longitudinal matrix element is evaluated in the lab frame then one finds  $(m_*/q_0) \times[L_*^2]_\text{lab}$ \cite{Kroll:1955zu}. We can relate $[L_*^2]_\text{lab}$ to $[L_*^2]_\text{rest}$ by boosting between frames, and one finds that $[L_*^2]_\text{lab}=(q_0/m_*)\times [L_*^2]_\text{rest}$ such that the factor of $m_*/q_0$ is precisely canceled.}

Now let us define auxiliary variables to condense the notation:
\begin{align}
    T_*^2 &= \frac{[\mathscr{J}^{11}_* + \mathscr{J}^{22}_*]- [\mathscr{J}^{11}_0 + \mathscr{J}^{22}_0]}{\mathscr{J}^{11}_0 + \mathscr{J}^{22}_0}~,\\
     L_*^2 &= \frac{\mathscr{J}^{33}_*}{\mathscr{J}^{11}_0 + \mathscr{J}^{22}_0}~.
\end{align}
The quantities $T_*^2$, and $L_*^2$ are related to the transverse and longitudinal matrix elements respectively. Notice that $T_*^2(m_*=0) =0$ by construction such that $T_*^2\sim O(m_*^2)$ in the small $m_*$ limit.

Having introduced all of the necessary ingredients, we  can now write the positron spectrum as if it were produced by real photons converting ``internally'' via a probabilistic process described by a function $P_\text{int}$
\begin{equation}\begin{split}
\label{P-int-Phi3}
    \dv{\Gamma_{ee}}{E_+}&= \frac{1}{2 M_{\text{atom}}} \int \dd \Phi_3 \qty[\mathscr{J}^{11}_0 + \mathscr{J}^{22}_0 ] P_\text{int}(E_+|q_0, \Pi)~.
\end{split}\end{equation}
The symbol $\Pi$ represents a set of 3-body phase space variables (e.g. the photon-neutrino opening angle $\cos\theta_{\nu\gamma}$), and we have introduced the internal conversion probability
\pagebreak
\begin{widetext}
\begin{equation}\label{P-int-def}
     P_\text{int}(E_+|q_0, \Pi)=
    \frac{1}{q_0 } \frac{\alpha}{4\pi}\int \frac{\dd m_*^2}{m_*^2} F_* \qty[\qty(2-\qty[1-\cos^2\theta] \beta_e^2)(1+T_*^2) +2\left(1-\cos^2\theta \beta_e^2\right) L_*^2]\Theta(1-\abs{\cos\theta})~,
\end{equation}
\end{widetext}
where $ \dd q_0\times  \int P_\text{int}(E_+|q_0, \Pi)\dd\Pi$ can be interpreted as the probability for photons with energy between $q_0$ and  $q_0+\dd q_0$ to produce an electron positron pair.

The functions $T_*^2$ and $L_*^2$ are unconstrained by measurements of the on-shell photon spectrum. As discussed above, $T_*^2\sim O(m_*^2)$ for small virtualities, and so if $m_* \ll q_0$ then we can expect it to be small. In contrast, $L_*$ is expected to be $O(1)$ in the $m_*\rightarrow0$ limit.\footnote{This is qualitatively different than the conclusion of \cite{Kroll:1955zu}. We discuss the origin of these differences in \cref{KW-vs-HP}.} Notice, however, that as $\cos\theta\rightarrow 1$ (or equivalently as $E_+\rightarrow q_0 -m_e$) that the longitudinal matrix elements are suppressed.  We will discuss this in more detail in \cref{Near-End-Point}.

Our definition of $P_\text{int}$ still depends on the unconstrained matrix elements $L_*^2$ and $T_*^2$. As we will show in the next section there exists a limit where $L_*^2$ and $T_*^2$ can be neglected.  In this case \cref{P-int-Phi3} can be re-written by carrying out the integration over all of the 3-body phase space except for $\dd q_0 $ in which case we find
\begin{equation} \label{P-int-dE}
    \dv{\Gamma_{ee}}{E_+}= \int \dd E_\gamma \dv{\Gamma_\gamma}{E_\gamma} P_\text{int}(E_+|E_\gamma)~,
\end{equation}
which allows us to construct the positron spectrum using the measured photon spectrum from the same nucleus, and the calculable function $P_\text{int}(E_+|E_\gamma)$. We now turn our attention to the aforementioned limit in which $P_\text{int}$ is independent of $T_*^2$ and $L_*^2$.

\section{Near end-point spectrum \label{Near-End-Point}}

As discussed in the introduction, for $\mu\rightarrow e$ searches  it is the high-energy tail of the RMC spectrum that is most important. This motivates studying the internal conversion probability in the limit where $E_+\rightarrow E_+^{\text{(max)}}$. This is conveniently parameterized by the dimensionless ratio formed from the electron's kinetic energy to the virtual photon energy,
\begin{equation}
    \delta= \frac{q_0 - (E_+ + m_e)}{q_0}= \frac{E_--m_e}{q_0}~,
\end{equation}
which tends to zero as the positron approaches its endpoint.

Let us now study the integral over $m_*$ in \cref{P-int-def} more carefully. Having restricted ourselves to a specific value of $E_+$, the limits of integration on $m_*$ are supplied by the Heaviside function. This can be understood by plotting plotting $\mathfrak{E}_+$ for $\cos\theta=\pm 1$, as a function of $m_*$ at different fixed values of $q_0$ as depicted in \cref{phase-space-hull}.  At a fixed positron energy $E_+$, the limits of integration over $m_*$ can be found by solving
\begin{equation}
    \mathfrak{E}_+( m_*, q_0, \cos\vartheta=1)= E_+ ~.
\end{equation}
These are given explicitly by
\begin{widetext}
\begin{equation}\begin{split}\label{max-min-mstar}
     m_*^{(\pm)} =   \sqrt{2\qty[m_e^2+E_+( q_0-E_+) \pm \sqrt{\left(E_+^2-m_e^2\right) \left([q_0-E_+]^2-m_e^2\right)}]}    ~.
\end{split}\end{equation}
\end{widetext}
Notice that $m_*^{(-)} \geq 2 m_e$ and consequently $m_e/m_* \leq 1$ over the full range of integration. If we introduce the small parameter
\begin{equation}
    \epsilon=\frac{ m_e}{q_0}~,
\end{equation}
then the maximal value of $m_*$  is set by
\begin{equation}
    m_*^{(+)} = q_0 \qty[2\sqrt{(1-\delta ) \delta } +O(\epsilon)]~.
\end{equation}
We therefore find that $m_*/q_0 \leq O(\sqrt{\delta})$ in the small $\delta$ limit (provided $\epsilon \ll \delta$). Similarly, for a high-energy positron to emerge from a virtual photon, it must be emitted collinear to the photon's momentum, $\cos\theta\approx 1$.  Explicitly,
\begin{equation}\begin{split}
  1- \cos\theta &=1-   \frac{ 2 E_+/q_0 -1}{\beta_*\beta_e}= O(\delta)~,
\end{split}\end{equation}
where we treat $\beta_e\approx \beta_*\approx 1$ (see \cref{Error-Estimates} for details).
Thus, we can re-express the internal conversion probability for $E_+ \rightarrow q_0$ as
\begin{equation}\begin{split}\label{p-int-approx}
     P_\text{int}&=
    \frac{1}{q_0 } \frac{\alpha}{\pi}\int_{m_*^{(-)}}^{m_*^{(+)}} \frac{\dd m_*^2}{m_*^2} F_* \\
    &\quad\quad\quad\quad\quad\quad\times \qty[2 +2 T_*^2- O(\delta)  +O(\delta)\times L_*^2]\\
    &= P_\text{int}^{(0)}(E_+|q_0) + O(\delta)~.
\end{split}\end{equation}
where we have counted $T_*^2\sim O(\delta)$ (see \cref{OFPT} for more details). The longitudinal matrix elements, by contrast, are taken to be $O(1)$ in the $m_*\rightarrow 0$ limit, but are suppressed by  $\left(\cos^2\theta \beta_e^2-1\right)=O(\delta)$.
Therefore at leading order in $\delta$ we find, setting $F_* \approx 1$ as discussed in \cref{Error-Estimates}, that
\begin{equation}\begin{split}\label{main-result}
    P_\text{int}^{(0)}(E_+|q_0)&=
    \frac{1}{q_0 } \frac{\alpha}{4\pi}\int_{m_*^{(-)}}^{m_*^{(+)}} \frac{\dd m_*^2}{m_*^2} \times 2 \\
    &= \frac{1}{q_0}\frac{\alpha}{\pi} \log\qty(m_*^{(+)}\big/m_*^{(-)}) ~.
\end{split}\end{equation}
This function is plotted, along with error estimates discussed in \cref{Error-Estimates}, in \cref{main-plot}.  The small-$\delta$ form of $m_*^{(+)}/m_*^{(-)}$ depends on the relative size of $\epsilon$ and $\delta$.  Explicitly the various scaling limits are given by (always taking $\delta,\epsilon \ll 1$)
\begin{equation}\label{ratio-cases}
    \frac{m_*^{(+)}}{m_*^{(-)}}
    \sim
    \begin{cases}
        2\delta /\epsilon & \delta \gg \epsilon \\
        \qty(\frac{\delta +\epsilon+\delta  \sqrt{1+2 \epsilon /\delta} }{\delta +\epsilon-\delta  \sqrt{1+2 \epsilon /\delta } })^{1/2} & \delta \sim  \epsilon\\
        1+ \sqrt{2 \delta/\epsilon} & \delta \ll \epsilon
    \end{cases}
\end{equation}
If one wishes to straddle these various regimes then the exact expressions for $m_*^{(\pm)}$, as presented in \cref{max-min-mstar}, should be used. This is important for applications at Mu2e and COMET where  energy resolution is of $O(100~\text{keV})$ \cite{Bernstein:2019fyh} such that electron mass effects can be resolved.

\begin{figure}
    \includegraphics[width=\linewidth]{phase-space.pdf}
    \caption{Phase space for radiative muon capture. Varying $\cos\vartheta$ from $-1$ to $1$ at fixed $m_*$ moves from the bottom of the hull to the top of the hull. Changing $E_\gamma= q_0$ changes the size of the hull to be integrated over (i.e. orange dotted curve [$E_\gamma=85$ MeV] $\rightarrow$ blue dashed curve [$E_\gamma=100$ MeV]). If $E_+\rightarrow q_0$ then only the top-tip of the hull contributes to the phase space integration. Units of $E_+$ and $m_*$ are in MeV. \label{phase-space-hull} }
\end{figure}

\section{Conclusions and Outlook \label{Conclusions}}

We have shown that given the photon spectrum from RMC on a nucleus, the spectrum of high energy positrons or electrons can be computed accurately with errors controlled by $\delta= (E_{-}-m_e)/q_0$. This allows for a robust characterization of the internal RMC positron and electron spectra near the end-point. External positrons, stemming from real photons pair producing in surrounding detector material, can be calculated from the real-photon spectrum by dedicated Monte Carlo simulations that include the full detector geometry. Thus, with this present work, a measurement of the real-photon spectrum becomes entirely predictive for the purposes of determining the high-energy positron spectrum. Most importantly, this allows for nuclear physics effects, which have large theoretical uncertainties, to be included empirically with measured data.

 %
 \begin{figure}\centering
    \includegraphics[width=\linewidth]{Error-Estimate.pdf}
    \caption{Probability per differential bin (i.e.\ of width $\dd E_\gamma$) of producing a positron with energy $E_+$ given a photon energy of $E_\gamma=100$ MeV, \cref{main-result,max-min-mstar}. We plot $P_\text{int}^{(0)}$ of \cref{p-int-approx} as well as error estimates (gray band) obtained by considering an ensemble of the two parameters $C_L$, and $C_T$, that capture nuclear structure dependence (see discussion in \cref{Error-Estimates}). We treat $C_L$ and $C_T$ as random variables drawn from independent Gaussian distributions such that $\langle C_L^2 \rangle= \langle C_T^2  \rangle =1$. \label{main-plot}}
 \end{figure}
 %

While our study has emphasized the near end-point positron spectrum, it applies equally well to the near end-point electron spectrum.  The reason that electrons and positrons can be treated on an equal footing is that we have \emph{not} included the influence of the nucleus' strong Coulomb field, which, in reality, will influence the outgoing electron and positron. Near the end-point, for internal conversion, this approximate neglect of Coulomb corrections may be insufficient. A high-energy positron necessarily implies a low-energy electron whose outgoing wavefunction is then substantially distorted by the Coulomb field of the nucleus (as is well known in the theory of beta decay \cite{Wilkinson:1982hu}). This has been discussed in a more general setting in \cite{Schluter:1981cjo}, and we will study this issue in the context of the RMC end-point in future work \cite{Plestid-Future}. We anticipate that our formalism of an internal conversion probability can be readily adapted to account for Coulomb distortion effects.

\section*{Acknowledgements}

We are indebted to Robert Bernstein, Michael Mackenzie, Pavel Murat, and Stefano Di Falco for their consistent availability, enthusiasm,  and willingness to help us understand the details and needs of the Mu2e experiment. We especially thank Pavel Murat for emphasizing the importance of the internal positron spectrum and for the existing gap in the literature surrounding its near end-point behavior. This work was made possible by the Intensity Frontier Fellowship program which supported R.P.'s visit to Fermilab. R.P.\ is extremely grateful for the support and hospitality of the Fermilab theory group. This work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0019095. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.

redpajama_set_name: RedPajamaArXiv


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There are 12 representatives unrelated to 228 Incident. Most of them have outstanding contributions in multiple field, especially in the field of politics, academia, medical, engineering and media. A list of these representatives according their professional field is shown in Table 2.
Some of them are the pioneers with their unflinching belief in Taiwan independence. Some of them are the first and second generations of mainlanders and followers that openly advocate independence after rethinking their national identity. They all share the similar experiences and stories in pursuing the universal values throughout their lifetime perseveringly.


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«Слов'янський Орфей» (, 1992) — драма сербського письменника Зорана Стефановича, в якій стародавній балканській міф інтерпретований мовою геополітики, слов'янських обрядів і наукової фантастики.

Дійові особи
 Орфей, але й «Аполлон» і Поводир-Зловісник;
 Діоніс, але й «Зевс», Арістей-Змія та «Аїд»;
 Еврідіка, але й «Гера»;
 Аполлон;
 Лахесіс, доленосниця
 Атропа, доленосниця
 Клото, доленосниця
 Пан, але й «Кербер»;
 Сивіла;
 Менада-Навіжена;
 Німфи й Сатири, які також є «Богами», «Богинями», «Доленосницями», «Мертвими Душами» й Новобранцями.

Основна інформація
Театральна прем'єра відбулася в Македонському національному театрі «Антон Панов» із Струмиці (1992), а на радіо — в Сербії в Драматичній програмі Радіо Белграда (2002).

Постановка драми «Слов'янський Орфей» режисера Горана Тренчовського (1992) вважається одним із перших пагонів пост-югославської драматургії й театру в Македонії та Сербії.

Драма отримала дуже позитивну оцінку зі сторони вітчизняної та зарубіжної критики й увійшла в зарубіжні енциклопедії та історії драми й театру. Неодноразово публікувалася в друкованому та електронному вигляді, а запис македонської вистави десятки разів транслювався через супутник у 21 столітті.

Переклади: македонський (1992), англійський (2002), український (2010), російський (2011).

На даний момент адаптується в комікс, над яким працює один із найвідоміших авторів південно-східної Європи Зоран Туцич.

Нагороди, подяки
 2010. Італійська енциклопедія «Де Агостіні» включила Стефановича за його «Слов'янського Орфея» до чотирьох найвпливовіших сербських драматичних письменників пост-югославського періоду
 2002: Сербська радіо версія була номінована на «Prix Europa» в Берліні
 1993. Македонська вистава внесена до офіційного списку белградського БІТЕФ-у, але Міністерство культури Македонії не дозволило візит через ембарго Організації Об'єднаних Націй щодо Югославії (яке стосувалося й культури).
 1993: Журнал «Екран», Скоп'є. Вистава струмицького театру номінована на найкращу виставу в Республіці Македонії 1992 року.
 1992: Нагорода «Йосип Колунджич» за найкращу драму на Факультеті драматичного мистецтва (Белград) в 1991-1992 роках.

Із рецензій «Слов'янського Орфея»
 «Вдалий симбіоз стародавнього міфу й сучасного мистецтва.» — Гойко Божович (газета Побједа, Подгориця, 1992)
 «Драматичний текст Зорана Стефановича (...) має кілька надзвичайних особливостей (...) Розповідь про слов'янського Орфея (...) може бути прочитана як обережне етнографічне дослідження слов'янської релігії Веселіна Чайкановича, як політичне есе про актуальний, так званий новий режим, і як будь-який американський науково-фантастичний комікс Френка Міллера.» — Петар Груїчич (газета Борба, Белград 1992)
 «Те, що Стефановича визначає як самобутнього автора і є гарантією його автентичності, (...) — терпкість, гіркота, летальність, пряма провокація. І винні в цьому не роки, а, здається, спадщина насильства варварів, відчуття якогось справжнього мистецького бунту, характерного лише для даного шматка Балкан. Таке поєднання одного середньоєвропейського сприйняття світу й одного насильницького, Міцич би сказав «дикого», духу й імпульсу, то похмурого, то грубого, і є специфікою письменника Стефановича.» — Дубравка Кнежевич (післямова книги Слов'янський Орфей та інші драми, Белград, 1995)
 «(Письменник) вносить в місцеву театральну рутину нетиповий (читай нереалістичний) експеримент, схильну до фантастики й гротеску чуттєвість, яка полонить багатошаровістю й численними значеннєвими площинами.» — Ілля Бакич (журнал Време, Белград 1995)
 «(Очевидним є) існування багатошарового інтелектуального дискурсу, відмінної театральної естетики, а також опори на традицію, яка в історії театру була найвибагливішою.» — Петар Груїчич (рецензія книги Слов'янський Орфей та інші драми, 1995)
 «Поетика Зорана Стефановича є абсолютно диспартною на нашому літературному просторі. (...) Він не фотографує, він оформлює. Він не бере занадто багато із дійсності, але й те, що запозичає, слугує йому як матеріал для пошуків сутності людини і явищ.» —  Володимир Стаменкович (рецензія рукопису книги Слов'янський Орфей та інші драми, 1995)<ref>Стаменковић, Владимир. [http://rastko.rs/rastko/delo/15075 Рецензія рукопису книги Слов'янський Орфей та інші драми Зорана Стефановича], 1995.</ref>
 «Стефанович вміло використовує не лише образні метафори, але й виразну іронію, щоб привести читача прямо до прихованої сутності своїх драм. [...] Він створює певний неоднозначний і товстий рукопис, який цілком незалежно виживає й поза межами театральної сцени. Своєрідним парадоксом є безперечний факт, що, незважаючи на його безсумнівні можливості, п'єси Стефановича до сьогодні правильніше прочитууються за кордоном, а не в Сербії.» — Душан Відакович (журнал Ваљевац, Валєво 1995)
 «Перше, що впадає у вічі, — висока мовна майстерність (...) Стефанович пише соковитою, грайливою сербською мовою, якій додає особливого шарму поєднання старої лексики та синтаксису із сучасними [...] висловлюваннями. Можливо, найбільша цінність Стефановичевих п'єс — у великій легкості, з якою відбуваються дії на різних рівнях: вони просто пливуть і непереборно тягнуть нас за собою.» — Іван Вукович (журнал Погледи, Крагуєвац, 1995).
 «Не важко знайти паралелі із сьогоднішньою ситуацією на Балканах і в світі взагалі (...) І все (у драмі) подано в дотепній і дуже цікавій проекції. » — Ранко Бурич (газета Политика,'' Белград 2002)

Примітки

Посилання
 Зоран Стефанович: Слов'янський Орфей, обрядова подія (драма). Переклад з сербської – Мила Маркевич
 Офіційний сайт драми «Слов'янський Орфей»

Джерела
 Кнежевич, Дубравка. На захист розмаїття: Післямова книги «Слов'янський Орфей та інші драми», 1995.
 Стаменкович, Володимир. Рецензія рукопису книги «Слов'янський Орфей та інші драми», 1995.

Драми
Трагедії
П'єси XX століття
П'єси 1992
Фантастичні твори Сербії
Сербські п'єси
Сербськомовні п'єси
Слов'янська міфологія в популярній культурі

redpajama_set_name: RedPajamaWikipedia


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Q: How do I put a condition inside a filter in power BI (DAX)? I am just getting started with Power BI and am struggling to create a measure. I am trying to count the sum of my column "Repartition", but with some filters.
Here is my current measure:
Nb_Actifs = CALCULATE (SUM(PAIE[Repartition]), FILTER(PAIE, PAIE[REMUNERABLE] = "Oui"), IF(PAIE[PROFIL]="CC", FILTER(PAIE, PAIE[Taux_Contractuel]<> 0)))

The filters that I put before my IF statement are the ones that I want to apply to all rows. The ones after the statement are the filters that I only want to apply to the rows where the condition PAIE[PROFIL]="CC" is met.
However, I get this error message: "A function 'FILTER' has been used in a True/False expression that is used as a table filter expression. This is not allowed."
From what I understand I need to replace the IF function by a filter, but since there are several filters already I get confused as to how to do that in Power BI.
Could someone help me?

A: You can add some logic within your filter to catch all the conditions you need to return:
Nb_Actifs =
    CALCULATE (
        SUM ( PAIE[Repartition] ),
        FILTER (
            PAIE,
            PAIE[REMUNERABLE] = "Oui" && (( PAIE[PROFIL] = "CC" && PAIE[Taux_Contractuel] <> 0 ) || PAIE[PROFIL] <> "CC" )
        )
    )

A: I think a SUMX function would be more appropriate here. You would also want to put all logic into a single FILTER. Try
Nb_Actifs =
    SUMX(
        FILTER(
            PAIE,
            PAIE[REMUNERABLE] = "Oui" &&
                (
                    (PAIE[PROFIL] = "CC" && PAIE[Taux_Contractuel] <> 0) ||
                    (PAIE[PROFIL] <> "CC")
                )
        ),
        PAIE[Repartition]
    )

Regardless of whether you use SUMX or not, putting all of your logic into a single FILTER with corresponding logic would solve your conditional filter problem.

redpajama_set_name: RedPajamaStackExchange


Building a new website for your bank or credit union can be a complicated and time-consuming process. And considering the fact that as much as 80%-90% of your business comes from your website, this process should not be taken lightly.
Each month, we get RFPs from banks and credit unions interested in helping them build a new website.
And each month, we politely inform them we are not interested in responding to the RFP but are happy to help guide them if they are willing to take a different approach to building a website that sells.
Budget: Your website is the heart of your organization, and we often find new website underbudgeted. Remember, you get what you pay for.
Design: While important, design is only one of many elements needed to build a website that sells. Just because you get a new responsive website with a fresh look does not mean you have a website that will have a positive impact on your bottom line.
Technology: We often find website RFPs are simply a tactical checklist of different technology platforms, such as an easy-to-use CMS (content management system). However, as these lists are developed internally, they may lack the perspective needed to truly build a website that sells.
You can simplify the website development process by considering the six following points that go beyond budget, design, and technology.
While a new design might bring a fresh face to your website, this new design will be worthless if you simply copy and paste the content from your old website into your new one.
When working with banks and credit unions to help them build websites that sell, it is not uncommon to find the copy on their current website is 4-5 years old, if not older, as it has been passed from one website to the next with little to no changes.
It is the copy on your website that will help to attract, capture, nurture, and convert leads for loans and new accounts.
Recommendations: When planning to build a website that sells, plan to have each page of content rewritten and simplified. Use the StorySelling process as a guide so that you may go beyond promoting only "great rates" and "amazing service" alongside a commoditized list of product features.
Careful consideration for website content must also be paid when it comes to formatting. For example, a local search engine optimization (SEO) strategy should include the writing of localized H1 and meta tags for each page.
Finally, in addition to writing new content for the website, it is important you plan an ongoing content marketing strategy to help first and sell second as you guide and nurture consumers through the buying process for different products and services. Use the Content Marketing Guidebook to help determine what types of content will be best for you to produce and distribute.
It is important to remember that 80%-90% of visits to your website's home page are from current account holders logging into home banking. Therefore, only 10%-20% of visits to your website are from consumers shopping for financial products.
And with such a small percentage, it is important that every interaction on your website helps guide these consumers from intent to conversion and beyond.
When planning and mapping out digital consumer journeys, remember the average consumer takes 30-45 days, if not longer, when making a decision to open an account. And during this time period, they use 8-10 different resources throughout their buying process.
Use this knowledge to map out digital journeys on your website for your key products. Determine what types of content and information someone needs in the different stages of the buying process. This can include awareness of a need, consideration of products to solve that need, and contemplation of converting and applying for a loan or opening an account.
Recommendations: Mapping digital consumer journeys requires you to first assess the journeys currently established on your website and other digital channels. What's working? What can be improved? What does not exist yet?
To get answers to these questions, we recommend you first start with user testing of the current website. This will require you test your website with current account holders as well as consumers from the markets you serve. Ask them to perform different tasks, such as applying for an auto loan, mortgage, or credit card.
In addition to analyzing qualitative data from live user testing, it is also important to review quantitative data collected from heat maps, click maps, and scroll maps. These maps visualize how consumers are interacting and using your current website when shopping for financial products and services.
Another key element of mapping digital consumer personas is to talk with your sales team. This will include your front line, call center, and business development representative. When preparing Digital Growth Blueprints for clients, we always uncover new opportunities for each of these different sales roles for how a new website and related technology can enable them to sell more.
Finally, once the research has been performed, we recommend using this data to help facilitate the wireframe and UX prototyping phase of a website development process.
Building a website that sells is much more than having a CMS that makes website updates easy to manage. And while a modern, secure, and compliant CMS serves as a solid foundation for your new website, it is only one piece of technology needed to build a website that sales.
Recommendations: As you explore the following technologies, you will find they provide a benefit beyond the marketing department as they enhance your digital sales team while also improving operational efficiencies. It is, for this reason, the budget for these technologies, as well as the website for that matter, should be allocated from each department accordingly.
When preparing Digital Growth Blueprints for clients, we often find they are lacking a content distribution or digital marketing plan. This, in turn, limits the traffic driven to the site. When building a website that sells, ensure you have a digital marketing and content distribution plan in place to ensure you maximize the investment of your new digital asset.
The problem with vanity metrics is they do not impact the bottom line.
There is so much more that goes into building a website that sells than just a pretty design.
And as a strategic focus on digital marketing continues to grow, we have found many bank and credit union executives grow frustrated as they lack the proper training and resources needed to build a successful digital marketing and sales program.
In fact, a study from Adobe found that only 9% of marketers know their digital marketing is working. And another 82% are having to learn digital marketing on the job.
Recommendations: We know you are already extremely busy. And we don't want your pretty new website to go to waste.
That's why it is important to consider your current staff and capacity when building a website that sells. Do they have the proper training? Do they have the capacity to properly manage your website, content, technology, digital ads, reporting, optimization, etc.?
If not, it is important to consider partnering with a digital marketing expert who can continue to train and guide your team along the way to digital marketing success while also assisting digital content production, distribution, reporting, recommendations, and optimization.


Four children have died in a house fire, and two adults and another child are also in hospital.
"Three occupants, two adults and a child, had managed to get out of the property. Tragically, four children from the property were confirmed dead on scene.


Take a photo and upload it, and PhotoID will automatically identify that animal or plant.
It's free and there's no software to install. Just tweet your photo to one of our accounts.
PhotoID can identify butterflies, birds, and wildflowers. Discover the Nature around you!
PhotoID takes the hassle out of identifying species by quickly narrowing the choice down to a few options.
The better your picture, the better the results. Try to take a close up shot with good colors and lighting.
Our butterfly identification bot knows around 50 species from Europe.
Our bird identification bot knows around 256 European species and can even identify juveniles.
Our wildflower bot can identify around 200 species from across Europe.
Within a minute you'll get a reply with two identification suggestions and information.
For a longer list of results, include the hashtag #nolink in your tweet.
Amazing automated photo ID service - tweet a picture of a butterfly, bird or plant and get ids back.
The first step in identification is the hardest. PhotoID takes the hassle out of identifying species by quickly narrowing the choice down to a few options. These can then be checked against other sources to confirm the species.
All you need is a photo of your subject. There's no need to hold it up, snap at a certain angle or have a particular background which some other apps require. PhotoID is part of recent advancements in image recognition, using neural networks inspired by the human brain to allow the bots to learn different species.
PhotoID is free to use, all you need is a Twitter account. There's no software to download. Simply take a photo and tweet it to the right account.
It's quick and accurate. PhotoID covers a variety of species of birds, butterflies and wildflowers across Europe and the UK.
I only wish that something like this had been around when I was studying.
PhotoID was developed by Natural Vision. We'll be very happy to hear from you!


The New Orleans Shakespeare Festival at Tulane will open its 25th summer season with Shakespeare's comedy All's Well That Ends Well for the first time in its history.
Helena, a poor orphan, has her sights set on Bertram, who is the son of a countess. Despite his disinterest in Helena, her efforts to woo and win him as he goes off to war lead to a romantic goose chase that's heavy on dark comedy.
The show's director, Amy Holtcamp, has directed noteworthy productions across the country and currently serves on the faculty at the New Orleans Center for Creative Arts.
The show features some of the region's most celebrated actors, including Liann Pattison - award-winning actress and Broadway veteran, and her real-life husband Silas Cooper - head of NOCCA's Drama Department. The show also stars NOLA Project company members Alex Ates and A.J. Allegra. The full cast list is available here.
Performances will take place on June 1, 2, 8, 9, 15 and 16 at 7:30 p.m. and at 1:30 p.m. on June 3, 10 and 17.
Tickets range from $20-$30 with discounts available for students, teachers, seniors and Tulane employees.


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Home » betting news » Allegri: Napoli are like Barcelona
Allegri: Napoli are like Barcelona
Massimiliano Allegri sees Wednesday's Coppa Italia clash with Napoli as the perfect preparation for Juventus' Champions League tie against Barcelona as he feels the two are similar.
Juventus have a 3-1 lead from the first leg of the semi-final tie as they prepare to take on Napoli at the Stadio San Paolo for the second time in four days after recording a 1-1 draw in Serie A at the weekend.
"Napoli are a team that play in a similar way to Barcelona, making Wednesday's game an even more important test," said Allegri, whose side face Barca in the last eight of the Champions League this month.
"We will need to score in order to be sure of reaching the Coppa Italia final.
"We want to reach our third straight final and we are in a great position to do so.
"We are in a great position on all fronts with just a couple of months of the season left.
"Juventus have achieved a great deal in recent years. We have earned the respect of the rest of Europe."
Allegri plans to make a number of changes to his starting XI for the match as he looks to rest some key players.
Ready for another #NapoliJuve! All eyes on the Coppa Italia semi-final second leg in Vinovo today… #FINOALLAFINE pic.twitter.com/2XfwhuFCx2
— JuventusFC (@juventusfcen) April 3, 2017
"There could be seven or eight changes compared to Sunday's line-up. After all, we are playing every three days at present," he added.
"Neto will definitely play, but I still need to decide about the others.
"[Paulo] Dybala and [Juan] Cuadrado are both available.
"It is unlikely that [Mario] Mandzukic will play. Any one of Alex Sandro, [Stefano] Sturaro or Cuadrado could come in to replace Mario."
4th April 2017 Posted in betting news by bestbettingodds
4 April 2017 13:04 Massimiliano Allegri sees Wednesday's Coppa Italia clash with Napoli as the perfect preparation for Juventus' Champions League tie against Barcelona as he feels the two are similar. Juventus have a	Bet Now


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Bowl barrow on Thorncombe Hill, 1.07km north east of Paradise Farm
A Scheduled Monument in Bicknoller, Somerset
OS Grid: ST130394
Mapcode National: GBR LV.7V3K
Mapcode Global: VH6GX.QD0Q
Entry Name: Bowl barrow on Thorncombe Hill, 1.07km north east of Paradise Farm
Scheduled Date: 18 September 1996
County: Somerset
Civil Parish: Bicknoller
Traditional County: Somerset
Lieutenancy Area (Ceremonial County): Somerset
The monument includes a bowl barrow on the hill top plateau of Thorncombe Hill
on the sandstone ridge of the Quantocks.
The barrow has a low symmetrical mound of 7.5m diameter, and is 0.45m high.
It was first noted by L V Grinsell in 1961.
It includes a 2 metre boundary around the archaeological features,
considered to be essential for the monument's support and preservation.
The area of the Quantock Hills, although small in extent, is one of the few
remaining expanses of open moorland in southern Britain. Its archaeological
importance lies in the existence of a landscape displaying examples of
monuments tracing the exploitation of the hills from the Bronze Age onwards.
Well-preserved monuments from the Bronze Age and Iron Age, including round
barrows, cairns, settlements, hillforts and a trackway, as well as later
industrial remains, give insights into changes in the pattern of land use on
the hills through time. These earthworks are one of the key components of the
Quantocks' broader landscape character.
Bowl barrows, the most numerous form of round barrow, are funerary monuments
dating from the Late Neolithic period to the Late Bronze Age, with most
examples belonging to the period 2400-1500 BC. They were constructed as
earthen or rubble mounds, sometimes ditched, which covered single or multiple
burials. They occur either in isolation or grouped as cemeteries and often
acted as a focus for burials in later periods. Often superficially similar,
although differing widely in size, they exhibit regional variations in form
and a diversity of burial practices. There are over 10,000 surviving bowl
barrows recorded nationally (many more have already been destroyed), occurring
across most of lowland Britain. In excess of 30 bowl barrows can be found on
the Quantock Hills. Often occupying prominent locations, they are a major
historic element in the modern landscape and their considerable variation in
form and longevity as a monument type provide important information on the
diversity of beliefs and social organisations among early prehistoric
communities. They are particularly representative of their period and a
substantial proportion of surviving examples are considered worthy of
protection.
The bowl barrow on Thorncombe Hill survives as a good example of its type,
seemingly without antiquarian investigation, and will contain archaeological
remains and environmental evidence relating to the barrow's structure, period
of construction and environmental conditions.
Grinsell, L V, 'Proceedings of the Smerset Archaeological and Nat.Hist Society' in Somerset Barrows Part 1, , Vol. 113, (1969), 27
Bicknoller
Bowl barrow on Thorncombe Hill known as `Thorncombe Barrow'
Bowl barrow on Thorncombe Hill
Cairn on Thorncombe Hill
Two cairns and two bowl barrows on Weacombe Hill, 440m south of Bicknoller Post
Cairn on Thorncombe Hill, 990m north west of Halsway Post
Bowl barrow on Weacombe Hill, 300m SSW of Bicknoller Post
Bowl barrow on Thorncombe Hill 500m north west of Halsway Post


Thoroughbreds are known as "America's Racing Horse". This breed of horse runs at the race track every single day around the world. History of the Thoroughbred: This breed of horse was originally bred in England due to the English horsemen's desire to have a fast race horse. There are three that founded this bloodline which are: Byerley Turk, Darley Arabian and Godolphin Arabian, named after their respective owners, Thomas Darley, Lord Godolphin and Captain Robert Byerley. All of these stallions were imported to England from the Mediterranean Middle East between 1670 and 1710. The result was an animal that could carry weight with sustained speeds over extended distances.
Approximately ninety percent of modern thoroughbreds have descended from Eclipse whose grandsire was Darley Arabian, who was never beaten in eighteen races. This began a very selective breeding process which has been going on for nearly 250 years. Breeding the best stallions to the best mares to produce fast race horses, giving them superiority and excellence being established on the race track. Around the turn of the 1700's, breeding records for Thoroughbreds were sparse and usually incomplete, and many times, they would not name a horse until the young horse had proven them self worthy. A gentleman named James Weatherby, through his own research and hard work and by the consolidation of his own privately kept pedigree records published the first volume of the General Stud Book.
This was done in 1791. The first publication listed 387 mares, each of which could trace back to Eclipse. The General Studbook is still published in England by Weatherby and Sons, Secretaries to The English Jockey Club. Many years later, as thoroughbred racing proliferated in North America the need for a pedigree registry for American Bred Thoroughbreds, similar to the General Stud Book became apparent. In 1873, the first American Stud Book was published by Colonel Sanders D. Bruce. This man spent almost a lifetime researching the pedigrees of American Thoroughbreds. He followed the pattern of the General Stud Book producing six volumes of the register until 1896 when the project was taken over by The Jockey Club. The integrity of the American Stud Book is the foundation on which all Thoroughbred racing in North America Depends. The first publication of the American Stud Book by The Jockey Club had a foal crop of around 3,000.
In 1986 in had grown to an astonish 51,000. Today The Jockey Club runs an elaborate new computer technology to meet the registration challenges posed by the gigantic number of annual registrations. The Jockey Club owns and operates one of the most sophisticated computer operations in the world today, with its database holding more than 1.8 million horses on a master pedigree file, with names that trace back to the 1800's. This is quite impressive genealogy. As well as bloodlines, this computer system also handles daily racing results of every Thoroughbred race in North America, as well as the ability to process electronically submitted pedigree and racing data from England, Ireland, France and other leading Thoroughbred countries. Another descendant of Darley Arabian is Diomed; he won the first running of the Kentucky Derby in 1780. When he was twenty one years old he was brought to the United States where he produced the male line through his son, Sir Archie. The most world renowned horse race is the Kentucky Derby, being the first race of the Triple Crown. The Preakness and The Belmont follow this historical racing event.
Thoroughbreds are the horse of choice for track racing. Most thoroughbreds are born between January and April, but their official date of birth is January 1 of the current year. During their first year of growth, they are developing size and power with the youngster beginning his training as a yearling. The horse learns to accept a bridle and a saddle and soon after a rider on his back to break the horse and prepare him for the starting gate and the run around the track.


text:
Florida residents with Maine ties prepare for Dorian's arrival
They put hurricane shutters in place as Emera Maine dispatches repair crews to Florida and the American Red Cross of Maine sends volunteers to the Southeast.
By Rob WolfeStaff Writer
Electric utilities, aid organizations and residents with Maine ties are readying for the impact of Hurricane Dorian as it approaches the southeastern U.S.
The powerful Category 5 storm battered the Bahamas on Sunday as it slowly made its way toward Georgia and South Carolina. Current meteorological projections say Dorian may graze the Florida coast instead of making landfall there, and pass by Georgia and South Carolina as late as Wednesday and Thursday.
Still, Nancy Vaughn, a South Portland native who lives in Port Orange, Florida, near Daytona Beach, is taking precautions. She and her husband, Jeff, have bolted their hurricane shutters to the eastern side of their stucco house, just in case the storm meanders their way.
"There's so many variables," she said over the phone Sunday. Though the Vaughns have weathered several hurricanes during their 20 years in Florida, for some of their neighbors, "being in limbo as to what's going to happen is maddening," she said.
The National Hurricane Center issued a hurricane watch for Florida's East Coast from Deerfield Beach north to the Volusia and Brevard county line, The Associated Press reported. Port Orange is in Volusia County.
Maine organizations are doing their part, too.
Emera Maine, the electric utility serving northern and eastern Maine, has sent down two repair crews – 12 workers and a supervisor – to help Florida power companies keep electricity flowing, a spokeswoman said Sunday.
Emera Maine and Central Maine Power are part of nationwide networks that coordinate disaster relief. CMP hasn't yet been called on to help, a spokeswoman said.
At least nine volunteers for the American Red Cross of Maine have already been assigned to different stations in Florida, Georgia and South Carolina, according to spokeswoman Ann Kim. They're expected to fill a variety of roles, including shelter work and psychological "first response."
They are joining a relief effort of more than 1,600 Red Cross volunteers from around the country, with 110 emergency response vehicles and 99 tractor-trailer loads of supplies.
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