Authorea Help

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WHAT IS LATEX? LaTeX is a programming language that can be used for writing and typesetting documents. It is especially useful to write mathematical notation such as equations and formulae. HOW TO USE LATEX TO WRITE MATHEMATICAL NOTATION There are three ways to enter “math mode” and present a mathematical expression in LaTeX: 1. _inline_ (in the middle of a text line) 2. as an _equation_, on a separate dedicated line 3. as a full-sized inline expression (_displaystyle_) _inline_ Inline expressions occur in the middle of a sentence. To produce an inline expression, place the math expression between dollar signs ($). For example, typing $E=mc^2$ yields E = mc². _equation_ Equations are mathematical expressions that are given their own line and are centered on the page. These are usually used for important equations that deserve to be showcased on their own line or for large equations that cannot fit inline. To produce an inline expression, place the mathematical expression between the symbols \[! and \verb!\]. Typing \[x=}{2a}\] yields \[x=}{2a}\] _displaystyle_ To get full-sized inline mathematical expressions use \displaystyle. Typing I want this $\displaystyle ^{\infty} {n}$, not this $^{\infty} {n}$. yields: I want this $\displaystyle ^{\infty}{n}$, not this $^{\infty}{n}.$ SYMBOLS (IN _MATH_ MODE) The basics As discussed above math mode in LaTeX happens inside the dollar signs ($...$), inside the square brackets \[...\] and inside equation and displaystyle environments. Here’s a cheatsheet showing what is possible in a math environment: -------------------------- ----------------- --------------- _description_ _command_ _output_ addition + + subtraction - − plus or minus \pm ± multiplication (times) \times × multiplication (dot) \cdot ⋅ division symbol \div ÷ division (slash) / / simple text text infinity \infty ∞ dots 1,2,3,\ldots 1, 2, 3, … dots 1+2+3+\cdots 1 + 2 + 3 + ⋯ fraction {b} ${b}$ square root $$ nth root \sqrt[n]{x} $\sqrt[n]{x}$ exponentiation a^b ab subscript a_b ab absolute value |x| |x| natural log \ln(x) ln(x) logarithms b logab exponential function e^x=\exp(x) ex = exp(x) deg \deg(f) deg(f) degree \degree $\degree$ arcmin ^\prime ′ arcsec ^{\prime\prime} ′′ circle plus \oplus ⊕ circle times \otimes ⊗ equal = = not equal \ne ≠ less than < < less than or equal to \le ≤ greater than or equal to \ge ≥ approximately equal to \approx ≈ -------------------------- ----------------- ---------------

Alberto Pepe

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We're in a crisis  We are in the midst of an unprecedented global crisis. Just weeks since its outbreak, the Coronavirus pandemic (COVID-19) has already affected, and will continue to affect, our daily lives, around the globe, for the foreseeable future. The answers and the solutions to this crisis will come from science. But the crisis affects science, too.It affects students, educators, and researchers; not just their day-to-day lives, social ties, and work routines, but also their ability to actively collaborate, convene in face-to-face meetings, attend academic conferences, teach and learn in an open university setting, pay a visit to the library, work overnight at the laboratory, and so on.But the thing is: science cannot stop. Scientific progress must go on. For each one of the challenges that scientists face in this time of crisis, there is, or there will be, a solution. We believe that the solution is not to be found in a single technological tool, product, framework, institution, funding agency, or company. It is the global cyber-infrastructure of scientific collaboration, built on scientific rigor, intellectual curiosity, and cooperation, that will enable science to advance in such difficult times. The power of scientific collaborationAs scientists, publishers, science communicators and technologists, we believe that: a. Science is the solution to the ongoing crisis. Now more than ever, reliance on the scientific method, rigor and clarity of scientific communication, transparency, reproducibility, and seamless sharing of all research data (including negative results), are fundamental to solving this health crisis and advancing human progress.b. Global collaboration and cooperation, beyond and above national and economic interests, is necessary not only at the scientific level, but also at the political and societal level. We're more interconnected and interdependent today than ever. And such interconnectedness extends to the ecological ecosystem in which we live. A crisis of such scale requires global solidarity, bipartisan political action, civic participation, and long-term thinking.

Dennis

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PREVIOUS “A “MODERN SCIENTIST” MANIFESTO” In the 21st century science is growing more technical and complex, as we gaze further and further while standing on the shoulders of many generations of giants. The public has often a hard time understanding research and its relevance to society. One of the reasons for this is that scientists do not spend enough time communicating their findings outside their own scientific community. Obviously there are some exceptions, but THE RULE IS THAT SCIENTISTS WRITE CONTENT FOR SCIENTISTS. Academia is often perceived as an ivory tower, and when new findings are shared with the outside world, this is not done by scientists, but by the media or even the political class. The problem is that these external agents do not have the necessary background to digest and properly communicate this knowledge with the rest of society. They often misunderstand, over-hype and in some case even distort the results and views of the scientific community. IT’S IRONIC AND SOMEWHAT FRIGHTENING THAT THE DISCOVERIES AND RECOMMENDATIONS FOR WHICH SOCIETY INVESTS SUBSTANTIAL ECONOMIC AND HUMAN CAPITAL, ARE NOT DIRECTLY DISSEMINATED BY THE PEOPLE WHO REALLY UNDERSTAND THEM. At the same time transparency and reproducibility are at stake in the increasingly complex world of research, which is still using old-fashioned tools when packaging and sharing content. This is not only a big problem for research itself, but can give science a bad name in front of the public opinion, which increasingly does not understand and trust the work of scientists. To the average tax-payer science is often cryptic, with most recently published papers behind a pay-wall and the majority of research virtually inscrutable. In this scenario it is hard for the public to access and capture the relevance of scientists’ work. I strongly believe that a society that does not trust its scientists is set on a dangerous course. ACTION ITEMS. To improve the situation 21st century scientists need to: 1. Learn to efficiently share and communicate their research with the public at large. 2. Make their research more transparent and reproducible, so that it can be trusted and better understood by their peers and the public at large. 21st century scientists need to produce “PUBLIC-FRIENDLY OPEN SCIENCE” (PFOS).

Jim Fuller

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The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical (10 M⊙ ≲ M ≲ 20 M⊙) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $P_{\rm min,Fe} \gtrsim 50 \, {\rm s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm min,NS} \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGW during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\rm max,Fe} \lesssim 10^4 \, {\rm s}$ in typical core collapse supernova progenitors, and a corresponding spin period of $P_{\rm max, NS} \lesssim 400 \, {\rm ms}$ for newborn neutron stars. This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGW during shell O/Si burning may thus determine the initial rotation rate of most neutron stars. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope.
The power of the atomAt the beginning of the 20th century, major advancements in our understanding of fundamental physics led scientists to the discovery of nuclear energy. An unprecedented amount of power could in principle be released by combining (nuclear fusion) or breaking (nuclear fission) certain atomic species under special conditions. Nuclear fusion in particular was understood to be the process powering the immense luminosity of stars, including our Sun. Nuclear fusion is the energy source illuminating our Universe.Why so much energy?Burning fossil fuels releases chemical energy. This chemical energy is stored in the mild electromagnetic interactions between atoms in a compound. Nuclear energy, on the other hand, comes from the very central regions of the atom.  As the name suggests, it is stored in the nuclei, which are kept together by the strong force. The strong force is much stronger than all the other forces, including the electromagnetic one. As a result, nuclear fuel has an energy density about ten million times larger than chemical fuel. If your car was running on nuclear fuel, its gas mileage would be something like hundreds of millions of MPG. From light to darknessThe physics revolution that characterized the first three decades of the 20th century and led to the development of quantum mechanics and nuclear physics, was followed by the second World War. In 1942, the United States started a very ambitious project to build a nuclear weapon. The Manhattan Project, led by Robert Oppenheimer and gathering some of the best physicists on the planet, culminated with the successful Trinity experiment in 1945 (Fig.\ref{982837}). The first detonation of a nuclear weapon was the most shocking demonstration of the great power of science and the scientific method. Only less than a month later, two nuclear bombs were dropped over the Japanese cities of Hiroshima and Nagasaki, resulting in the end of WWII and the death of hundreds of thousands of people. The sheer destruction inflicted by the atomic bomb left an indelible mark on humankind's consciousness, formally starting a new era in the history of man. An era of greater responsibility. While no nuclear weapons have been purposely used in war ever since, more than 2000 nuclear tests have been performed after the Trinity, Hiroshima and Nagasaki explosions.