Abstract (250 Words Maximum)Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis vestibulum diam a eleifend tincidunt. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Morbi libero risus, pretium ac urna vel, iaculis sagittis nisl. Duis non sapien justo. Quisque elementum, mauris a ullamcorper pharetra, mauris enim ullamcorper urna, sit amet fermentum sem nulla vel nibh. Etiam id urna non leo condimentum egestas pulvinar sit amet ex. Aenean faucibus eget dui at gravida. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vestibulum sodales neque dolor, et mollis turpis viverra non. Sed quam libero, ornare vitae rutrum eu, venenatis et massa. Morbi rutrum vulputate tellus, sit amet placerat arcu fringilla et. Vestibulum condimentum blandit libero eget luctus. Sed suscipit accumsan nibh vel lobortis. Maecenas tellus mi, commodo id odio nec, ullamcorper rutrum neque. Duis tincidunt ut tellus ut sodales. Aenean in massa ac ligula scelerisque viverra.Significance Statement (120 Words Maximum)retra mauris enim ullamcorper urna sit amet fermentum sem nulla vel nibh. Etiam id urna non leo condimentum egestas pulvinar sit amet ex. Aenean faucibus eget dui at gravida. Lorem ipsum dolor sit amet consectetur adipiscing elit. VestiIntroduction (750 Words Maximum)The Introduction should briefly indicate the objectives of the study and provide enough background information to clarify why the study was undertaken and what hypotheses were tested.Materials and MethodsThe materials and methods section should be brief but sufficient to allow other investigators to repeat the research (see also Policy Concerning Availability of Materials). Reference should be made to published procedures wherever possible; this applies to the original description and pertinent published modifications. The sex of subjects should be stated. If the sex of subjects is unknown, this should be stated. All companies from which materials were obtained should be listed. If materials were obtained from an individual, an affiliation for that individual should be listed. A manuscript that presents only a theory may omit the Materials and Methods section.Experimental DesignDescription of experimental design retra mauris enim ullamcorper urna sit amet fermentum sem nulla vel nibh. Etiam id urna non leo condimentum egestas pulvinar sit amet ex. Aenean faucibus eget dui at gravida. Lorem ipsum dolor sit amet consectetur adipiscing elit. VestiStatistical AnalysisDescription of statistical analysis retra mauris enim ullamcorper urna sit amet fermentum sem nulla vel nibh. Etiam id urna non leo condimentum egestas pulvinar sit amet ex. Aenean faucibus eget dui at gravida. Lorem ipsum dolor sit amet consectetur adipiscing elit. VestiResultsLorem ipsum dolor sit amet consectetur adipiscing elit. Duis vestibulum diam a eleifend tincidunt. Class aptent taciti sociosqu ad litora torquent per conubia nostra per inceptos himenaeos. Morbi libero risus pretium ac urna vel iaculis sagittis nisl. Duis non sapien justo. Quisque elementum mauris a ullamcorper pharetra mauris enim ullamcorper urna sit amet fermentum sem nulla vel nibh. Etiam id urna non leo (Figure \ref{333327}) condimentum egestas pulvinar sit amet ex. Aenean faucibus eget dui at gravida. Lorem ipsum dolor sit amet consectetur adipiscing elit. Vestibulum sodales neque dolor et mollis turpis viverra non. Sed quam libero ornare vitae rutrum eu venenatis et massa. Morbi rutrum vulputate tellus sit amet placerat arcu fringilla et. Vestibulum condimentum blandit libero eget luctus. Sed suscipit accumsan nibh vel lobortis. Maecenas tellus mi commodo id odio nec ullamcorper rutrum neque. Duis tincidunt ut tellus ut sodales. Aenean in massa ac ligula scelerisque viverra.

Dear Dr. Berlinsky, Please consider our application for a 1 week visit following the KITP program “Galactic Archaeology and Precision Stellar Astrophysics”. The proposing team wants to meet again to continue some very exciting work that was started at KITP and led to groundbreaking results in the field of stellar physics and asteroseismology. Please find below a brief description of the results that the team achieved during/after the KITP program and the follow up work we intend to perform while together at KITP. A team justification closes this application. We would like to meet at KITP either on 15-22 NOVEMBER (strong preference for this week) or 6-13 December. INTRODUCTION The team members enjoyed a very productive period of collaboration during the Galactic Archaeology and Precision Stellar Astrophysics program at KITP in 2015. That collaboration led to two papers on red giant asteroseismology, recently submitted to Science and Nature. The first paper discussed the ability to measure internal magnetic fields in red giant stars using asteroseismology, and the second used this technique to constrain/measure magnetic fields in the core of thousands of red giant stars. We believe this work has paved the way to a new sub-field of stellar astrophysics that is ripe for additional study. Consequently, there are several research topics which we wish to pursue during a follow-up visit to KITP. PROJECT OVERVIEW The first research topic we intend to investigate is the EXISTENCE OF STRONG MAGNETIC FIELDS WITHIN STARS ON THE RED CLUMP. The previous works only analyzed stars ascending the red giant branch, but similar physics will occur for red clump stars burning helium in their cores. However, identifying the asteroseismic signature of strong magnetic fields in clump stars is slightly more difficult because they are difficult to distinguish from ascending red giants. Collaboration between the team members will allow us to work out the details of this process from the observational end, and what can be learned from these observations on the theoretical end. A second topic of investigation are “DROOPY-LIKE” STARS that show a particular asteroseismic signature that allows for a more precise measurement of their internal magnetic fields. Thus far, only one star KIC 8561221 (“Droopy”) that shows this signature has been analyzed in detail (Garcia et al. 2014). However, more Droopy-like stars likely exist. We intend to identify these stars in the data, measure their internal magnetic field strengths, and use them to trace the evolution of internal magnetic field strengths in red giant stars. Third, we hope to use additional time at KITP to examine the OCCURRENCE OF MAGNETIC FIELDS IN CLUSTER STARS. These stars have nearly identical ages and compositions and provide the perfect testbed to understand evolution of magnetic fields in a uniform population of stars. Red giant cluster stars exist in both Kepler data and recent and upcoming K2 fields, with substantial data already secured by the team. These red giants are found in several clusters (of differing ages and metallicities) and can be used to understand the development of magnetic fields in different populations of stars. As a fourth research topic (time permitting) we will try to CONSTRAIN THE GEOMETRY OF INTERNAL MAGNETIC FIELDS in red giants with suppressed dipoles, using the scattering properties of dipolar gravity waves on the magnetic fields. Proposing Team and Team Justification 1. Lars Bildsten (KITP resident) 2. Matteo Cantiello (KITP resident) 3. Jim Fuller (Caltech) 4. Rafael A. Garcia (CEA, Paris) 5. Stéphane Mathis (CEA, Paris) 6. Dennis Stello (Sydney University) Five of the six team members outlined above are the main authors in the two papers submitted to Science (Theory) and Nature (Observations). Thanks to their complementary expertises, this group of scientists found a remarkable synergy while at KITP. Thanks to the presence of both theorists and observers, we were able to quickly identify an observational puzzle, find a theoretical explanation and test it on brand new data. In the process this led to the discovery of a novel, powerful way to look for magnetic fields in stellar interiors. The team has remained in touch and active after meeting at KITP, but it’s clear that only re-creating a full-immersion atmosphere can lead to rapid progress on the follow-up research program.

On September 15th, 2016 Authorea CEO and Cofounder, Alberto Pepe, encouraged the Reddit science community to ask him anything. Below are a few excerpts from the AMA on the topic of metrics and impact. Click here for the full thread.

Writing research articles is an important part of the scientific process. They are what researchers and the public read, and can impact future experiments and policies. Contrary to popular belief, one may think that writing research articles is taught at the undergraduate and graduate level. However, this isn't the case. With little to no formal training in writing, researchers must learn by doing. Arguably, this lack of training leads to negative consequences in research literature. As you can see below, research articles are becoming harder to read \cite{Plaven-Sigray119370}.

Title of Submission to PLOS Journals Name1 Surname1,2\Yinyang, Name2 Surname2\Yinyang, Name3 Surname2,3¤, Name4 Surname2, Name5 Surname2‡, Name6 Surname2‡, Name7 Surname1,2,3*, with the Lorem Ipsum Consortium¶ 1 Affiliation Dept/Program/Center, Institution Name, City, State, Country 2 Affiliation Dept/Program/Center, Institution Name, City, State, Country 3 Affiliation Dept/Program/Center, Institution Name, City, State, Country \Yinyang These authors contributed equally to this work. ‡These authors also contributed equally to this work. ¤Current Address: Dept/Program/Center, Institution Name, City, State, Country †Deceased ¶Membership list can be found in the Acknowledgments section. * correspondingauthor@institute.edu

This example manuscript is intended to serve as a tutorial and template for authors to use when writing their own AAS Journal articles with Authorea. The manuscript includes a history of   and documents the new features in the previous version, 6.0, as well as the new features in version 6.1. This manuscript includes figure and table examples to illustrate these new features. AUTHOREA FEATURES A RICH TEXT EDITOR SO THAT YOU CAN WRITE IN LATEX, MARKDOWN, OR RICH TEXT AND RENDER DIRECTLY ON THE WEB. AUTHOREA SUPPORTS AND RENDERS THE VAST MAJORITY OF LATEX NOTATION NEEDED FOR AAS JOURNAL ARTICLES. A FEW FEATURES PROVIDED BY AASTEX V6.1. THAT ARE NOT AVAILABLE IN AUTHOREA HAVE BEEN LISTED IN THIS DOCUMENT. Authors are welcome replace the text, tables, figures, and bibliography with their own and submit the resulting manuscript to the AAS Journals peer review system. The first lesson in the tutorial is to remind authors that the AAS Journals, the Astrophysical Journal (ApJ), the Astrophysical Journal Letters (ApJL), and Astronomical Journal (AJ), all have a 250 word limit for the abstract. If you exceed this length the Editorial office will ask you to shorten it.

What’s the deal about public vs. private articles? You can write public articles for free, but you have to pay to write private articles? That’s like saying you can go to the beach for free, but you have to pay to wear a swimsuit. True! But after all, they're not giving away swimsuits for free at Macy's :)We, at Authorea, are a small company with a big vision. We're all recovering researchers (mostly Ph.D.s in physics and computer science) and are on a mission to make research better. We built Authorea because we were annoyed by the slowness and inefficiencies of writing research in collaboration and publishing it, in scholarly journals. We believe that we built a product (you are looking at it) that is both useful (it makes collaborative writing faster, more seamless, and a bit less painful) and also visionary in its nature (we deconstructed LaTeX's old fashioned ways and allowed dynamic, interactive figures and data to be part of scholarly articles). We are one of the few projects that is truly rethinking scholarly writing. We also think that if a product is good enough, researchers and universities should be willing to pay for it. The problem is: what do we charge for? Since we are passionate about Open Science, Open Access and Open Data, we figured that we would charge for privacy so that on the one hand, we have a sustainable business (which is important and great!) and on the other, we are encouraging scientists to write in the open (our mission: equally great and important!). That is in a nutshell, why we are charging for privacy, i.e., "why you are paying for the swimsuit". We have been, from day one, open to suggestions. So I ask you: do you have ideas for alternative business models?

As an undergraduate network science researcher, I use social networking platforms to keep abreast of cutting edge research and publications in my field, engage in larger conversations with leaders in my own and adjacent fields, and enter into personal conversations that have extended beyond social media and into real friendships and mentorships. These opportunities did not exist in the same magnitude before the advent of modern social media, nor did the analogous version of these opportunities have such low barriers to entry.  Because of social networking sites, I have had to the opportunity to expand my peer group, mentorship circles, and overall access to the frontiers of numerous fields of academic research far beyond what was available at my own university and social circle. As a senior in college, trying to figure out what academic path I should take after graduation, the conversations I have had with both groundbreaking academics and PhD students alike, across a broad range of scientific fields, from architecture and urban planning, computational biology, particle physics, and natural language processing, to name just a few, have been extremely fruitful in guiding me toward a broader perspective both in terms of my personal and professional trajectory, and my active research project. For my senior thesis, I am working on a computational and mathematical epidemic model for the spread of the Zika Virus. While my thesis advisor has been tremendously helpful in providing me support and guidance and answering my questions, I have also gained a significant amount of my current knowledge from following the right accounts on Twitter and reading the articles, both general and scholarly, that they tweet out to their followers, as well as the ensuing conversations that occur with other experts on their profiles and the larger social media sphere. When trying to develop a model for the spread of the virus, I stumbled upon papers and comments discussing the spreading phenomenon of memes on twitter and then witnessed their spread firsthand through the very discussion. An experience like that gives deeper and fresher insight into the underlying science than just diving into journal articles with techniques and ideas that are at least 6-months old. Rather than detract from this phenomenon, by alleging that it is without precedent and not in the spirit of scientific discovery, or that it may only serve as a distraction, I embrace the shift to lively discourse on these social networks, where everyone from the top academics in the field, to students, to interested lay-readers can contribute their voice to the conversation and join together to create a vital spirit of science, discovery, and discourse that is the heart of modern scientific research. Improvements to the ad-hoc social networking that is currently done in science could include introducing semi-formal discussion forums that help to foster a sense of community and enrich the discussion by situating it within a digital place and time rather than the current seemingly random diffusion of ideas. This random diffusion is still very valuable and should not be disregarded, but can be enhanced by adding this second, organized component. Cultural attitudes that need to change center around the majority of academics’ disregard of social networking sites as silly and not part of ‘real science.’ Ways to adjust this attitude would be to engage in campaigns on campus to bring more academics into the social media fold by creating accounts with them, showing them relevant sources and people to follow, both within their field of expertise and the larger scientific and popular discourse, and slowly chipping away at the inherent bias against engaging in meaningful discussions online.

Are you looking for an alternative to Google Docs?Choosing the right word processor for your documents is very important. While Google Docs and Authorea are similar in some ways, Google Docs is a great tool for writing general purpose drafts whereas Authorea is more appropriate if you are writing a scholarly manuscript, a student essay, a math heavy manuscript, a technical blog post, or a data-driven document. We list here a few key comparison points that show how Google Docs and Authorea are different.

source  ee  eμ 1 & 50 & 837 & 970 2 & 47 & 877 & 230 3 & 31 & 25 & 415 4 & 35 & 144 & 2356 5  45  300  556

Hello, welcome to the online curriculum for the Authorea hands-on session at ResBaz! This curriculum is intended to walk you through the exercises and challenges that we will cover during the Authorea workshop. You can access it at HTTP://AUTHOREA.COM/18566/.

SEARCH FOR SUSY DECAYS AT $ = 8$ TEV Given the high precision of analysis techniques implemented at the LHC at Cern, there has been increasing opportunity to discover theories beyond the current model of fundamental physics. One such theory for physics “beyond the Standard Model” is known as Supersymmetry and proposes an additional symmetry to be added to space-time, allowing for a family of particles that are an exact duplicate (except for this quantity, labeled R) to those found in the Standard Model. Associated with the extension is a corresponding conservation law in supersymmetric interactions known as ‘R-parity’ . R-parity conserving decays have been in high focus since they provide an explanation for the massive amount of dark energy foundr, estimated to be close to 73% . Since R needs to be conserved, the lightest supersymmetric particle (LSP for short) would not be able to decay to any other particle other than itself and would explain the massive amount of seemingly stable dark matter . For this reason, there has been a large effort to look for data that resemble R-parity conserving modes, without much attention towards R-parity violating decays. Over the past two years, I performed an analysis looking for data that resembles a signal that is consistent with a supersymmetric decay. My target process is a supersymmetric top decaying to oppositely charged W-bosons one of which decays to a positive muon and an anti-b quark, and the second decays to a b-quark and negatively charged muon. I chose to look for a particular decay that resembles a standard model interaction with well understood backgrounds because I assumed that the process would behave similarly, except for this additional symmetry which I ignored as part of the analysis. Therefore, I chose a process whose major backgrounds were well modeled using current Monte Carlo methods. One variable that affects the rate at which this occurs is the mass of the supersymmetric top quark . Since this quantity has not be measured, the goal of my research was to to calculate a cutoff mass at which I can say there is enough data to prove/disprove the theory at a mass lower than a certain value. I did this by performing a comparison between the expected numbers if the theory were true to the numbers found in the data sample. Since the probability at which the decay happens decreases as the supersymmetric top mass increase, there should be a point at which the numbers flip from being too high to too low. The point at which this flip occurs is the “cutoff” point where I can say below which the data does not have enough events to support the theory. The data came from the latest set published by the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider at CERN in Switzerland. At the core of the design is a superconducting solenoid magnet that is 6m in diameter,13m long, and generates a 4T field which is used to determine the charge of the particle. On the outside of the magnet is an electromagnetic calorimeter (ECAL) which is designed to measure electromagnetic deposits. After the products of the decay have passed through the ECAL, they reach the hadronic calorimeter (HCAL) which absorbs most of the energy left in the collision. The particles that do make it through the HCAL are either neutrinos or muons. The muons are detected and collected in a separate configuration around the magnet composed of a drift tube and cathode-strip detector . The result of this analysis will provide future researchers with a better sense of possible values for the mass of the supersymmetric top and possibly allow for the creation of more specialized detectors that focus on higher mass regions than the calculated cutoff. ADDITIONAL SOURCES MEASUREMENT OF TTBARCITEPLACEHOLDER8ID This paper provides a lot of important background information concerning the major backgrounds for the standard model version of my decay. Since it specifically focuses on ttbar production, it discusses many of the issues that I encountered while performing the analsysis. This paper will be useful in both the backbrgound section to provide appropriate info as well as guide me during my analysis of the data. STOPS AND NEUTRINO MASS HIERARCHY CITEPLACEHOLDER9ID This paper outlines the correlation between supersymmetric top decau paramters and the neutrino mass hierarchy. This paper will prove to be useful during the section dedicated towards future research as it shows a way for this analysis to provide guidance towards research in the future. PREVIOUS SERCHES FOR R-PARITY VIOLATION CITEPLACEHOLDER10ID This paper discusses previous searches for R-parity violation and will be used in my background section to discuss the current state of ressearch in the field. A GENERAL SUMMARY OF SUSY SEARCHES AT LHC CITEPLACEHOLDER11ID Whereas the previous paper discusses more current efforts to search for SUSY, this paper provides an outlook on the field when it was first being discuessed. By looking at the original papers, the original reasons for pursuing particular lines of reseaerch becomes much more clear. This paper will be referenced in my introduction for a description of the field before we knew where to look. DARK MATTER CONSIDERING MSSM CITEPLACEHOLDER12ID This paper will also go in my introduction and provides a link between dark matter and the MSSM model. By providing this sort of information, it is clear that the hole I am filling with my research is not commonly considered due to the attractiveness of other theories, increasing the usefullness of my research. DARK MATTER PRIMER CITEPLACEHOLDER13ID This paper will be referenced in my introduction and provides a different viewpoint on the Dark Matter problem as it stands in modern astro physics. By highlighting this issue I am able to drive home the importance of my research. LSP AS DM CANDIDATE CITEPLACEHOLDER14ID This paper describes the viability of the LSP as a dark matter candidate and will be referenced in my introduction to provide additional background material. DETECTOR PHYSICS AT THE LHC CITEPLACEHOLDER15IDCITEPLACEHOLDER16ID These two papers provide a detailed description of the two technologies that are used in the CMS detector. By looking at the details of the construction, I am able to notice possible shortcomings of the experiment and find ways in which it can be improved. This paper will be refernced in my introduction as well as briefly in the section concern data acquisition.

Science Manuscript Template General Instructions on using this template and submitting a manuscript to Science: Thank you for preparing a manuscript for submission to Science. Using this template, or following the guidelines below, will help us in processing your paper. Our goal is to be able to identify each section of your manuscript so that we can accurately record the title, authors, abstract, etc. and also be able to enrich it by including reference links and an accurate layout. Please use the actual template, which starts on page 2. delete the text on this cover page. You can submit your paper at www.submit2science.org Additional instructions are available at http://www.sciencemag.org/site/feature/contribinfo/index.xhtml If you are using LaTeX , please convert your paper into a Word or RTF file if possible. If this is not possible, please use our LaTeX template and upload a PDF version of your paper. Some conversion approaches are available here: http://www.tug.org/utilities/texconv/textopc.html So that we can identify the parts of your paper, and even if you do not use our template, please begin each section with the specific key words listed below, some of which are followed by a colon. Please do not use paragraph breaks in the title, author list, or abstract.

WHAT’S ON YOUR MIND? This is an experimental “article”. I’ll periodically drop citations to papers and news I’m reading, I’ve read, or I’m still thinking about. Dropped citations might have comments, links to related articles/writings, or be effectively untouched. At any point, anyone can comment on anything (please do; it’s encouraged). Maybe you have some insights on a paper, a particular concept, or technique. Maybe you disagree with something. Maybe you have more recommended reading. Maybe you just want to say something is “cool”. Any kind of comment is good because it adds information to the thought-process or discussion. As this is a work very much in progress, organizational changes will be made I’m sure, and if anyone has suggestions or wants to build off anything here, go for it. The goal, while not yet entirely clear, is some kind of radical or innovative collaboration.

Are you looking for an alternative to Hackpad?On July 19, 2017, Hackpad will be shut down. Dropbox acquired Hackpad in 2014 to make Dropbox Paper. If you are a technical writer, it is possible that you'll miss some of the technical features of Hackpad. In this post, we highlight a few key comparison points that show how Authorea can replace some of the features and functions of Hackpad.

Science writing is an important part of the research cycle. Even if findings are sound, poor communication can derail the progress of experiments and policy decisions. We would expect universities to teach science writing to undergraduate and graduate students. But they don't. Instead, researchers "learn by doing". This is having negative consequences as scientific papers become harder to read \cite{Plaven-Sigray119370}.

ResumenEl fenómeno de los clíticos marginales ha sido estudiado en distintas lenguas romances y en lenguas como el griego moderno (Spitzer, 1941; Bibis & Roberge, 2004; Espinal, 2009; Leivada & Grohmann, 2014; entre otros). En español rioplatense, el clítico marginal la ocurre de manera productiva en verbos como zurdearla, kirchneriarla y hipiarla, preferentemente en un registro informal...Palabras clave: clíticos marginales, morfema -ear, español rioplatense, objetos nulos.AbstractThe marginal clitics phenomena has been studied in several Romance languages and languages like Modern Greek (Spitzer, 1941; Bibis & Roberge, 2004; Espinal, 2009; Leivada & Grohmann, 2014; among other authors). In Rioplantense Spanish, the marginal clitic la (3.sg.Acc.fem) occurs productively in verbs such as zurdearla (‘left-ear it’), kirchneriarla (‘Kirchner-ear it’) y hipiarla (‘hippie-ear it’), principally in informal register…Keywords: marginal clitics, -ear morpheme, Argentinean Spanish, null objects.Planteamiento del problemaLorem ipsum dolor sit amet, consectetur adipiscing elit. Proin at massa quis ante hendrerit efficitur eget eu lacus. Phasellus at augue condimentum, imperdiet felis vitae, consequat lectus. Sed posuere semper ultrices. Praesent ac dui purus. Proin rhoncus erat massa, vitae tristique mi tristique vel. Aenean eget mattis dolor, ut blandit enim. Quisque cursus nisi sem, in pulvinar diam iaculis id \cite{Wagner_2010}.In luctus sit amet odio eget venenatis. Donec nunc dui, sagittis sed neque ac, aliquet convallis ligula. Vivamus ornare, sapien in viverra lobortis, odio tortor sagittis tortor, et elementum ex enim at arcu. Pellentesque tincidunt velit non mauris euismod, sed mollis nulla varius. Proin porttitor pretium magna ac congue. Morbi congue pharetra leo et hendrerit. Morbi laoreet varius lectus, eget aliquam ligula venenatis ut. Proin urna mauris, auctor in lacus quis, venenatis rutrum turpis. Maecenas vitae mauris sit amet purus cursus tincidunt nec id mauris.

INTRODUCTION Recently, there has been much interest in the construction of Lebesgue random variables. Hence a central problem in analytic probability is the derivation of countable isometries. It is well known that ∥γ∥=π. Recent developments in tropical measure theory have raised the question of whether λ is dominated by 𝔟. It would be interesting to apply the techniques of to linear, σ-isometric, ultra-admissible subgroups. We wish to extend the results of to trivially contra-admissible, _Eratosthenes primes_. It is well known that ${\Theta^{(f)}} ( } ) = \tanh \left(-U ( }} ) \right)$. The groundbreaking work of T. Pólya on Artinian, totally Peano, embedded probability spaces was a major advance. On the other hand, it is essential to consider that Θ may be holomorphic. In future work, we plan to address questions of connectedness as well as invertibility. We wish to extend the results of to covariant, quasi-discretely regular, freely separable domains. It is well known that $} \ne {}$. So we wish to extend the results of to totally bijective vector spaces. This reduces the results of to Beltrami’s theorem. This leaves open the question of associativity for the three-layer compound Bi₂Sr₂Ca₂Cu₃O10 + δ (Bi-2223). We conclude with a revisitation of the work of which can also be found at this URL: http://adsabs.harvard.edu/abs/1975CMaPh..43..199H.