This may be a touchy question but I am considering using ShareLaTeX for a book I am working on.  I am beginner in LaTeX and ShareLaTeX seems very easy to use and user-friendly.  However, since I eventually plan to publish this book I am concerned about security at internet sites like ShareLaTeX.  I am not going use "group" (paid for more than 2) feature if I decide to go with ShareLaTex.  My second question concerns portability.  Can I go back and forth between my own computer (where I have installed TeXshop) and ShareLaTex or are there some issues or concerns I should worry about?  Any thoughts and/or ideas are greatly appreciated.  Thanks in advance.
Background: One of my co-authors faced problem of compiling the paper that I had built using TexStudio and MikteX 2.9 on his Mac Machine running TexLive.   ShareLaTeX Role: So, one solution is to use ShareLaTeX. But the first problem pops in mind is how safe is uploading unpublished article to a publicly accessible portal?  What I did: I googled security and data breach of ShareLaTex and found nothing except some words from the ShareLaTex community about their word to ensure that our data are safe; perhaps this would not be enough.  My 1st Question: To what extent can I trust ShareLaTeX and put my ready-to-publish content there?   My 2nd Question: Is there any alternate way of sharing LaTeX with others around the globe without changing the underlying platform?
Сanonical form of a quadratic form by Lagrange's method This is just an eg. to understand how to solve it.  There is a quadratic form as below we need to bring to canonical form using Lagrange's method and find the coordinate transformation.   Then find the positive &amp; negative indexes, rank of the quadratic form. Finnally, to investigate sign-definiteness of the quadratic form by two ways: according to it's canonical form and the criterion of Sylvester: $4x_{1}^2+2x_{2}^2+10x_{3}^2-4x_{1}x_{2}-12x_{1}x_{3}-8x_{2}x_{3}$  Any clarification on how to do it are very welcomed. Primary ideals of $\mathbb{Z}$ Let $R=\mathbb{Z}$ I must prove that      In $\mathbb{Z}$ the primary ideals s are precisely the ideals $(p^k)$ where $p$ is a prime number and $n\ge 1$.   $$$$ The definition of primary ideal.     Definition. An ideal $I$ of the ring $R$ is called primary if for all $a,b\in R$ $$(ab\in I\quad\text{and}\quad a\notin I)\Rightarrow b^n\in I, \text{for some positive integer $n$}.$$   Therefore I must prove that      $$(n)\;\text{is primary in}\;\mathbb{Z}\iff n=p^k, k\ge1,p\ge2,\;\text{where}\;p\;\text{is a prime}.$$   Proof ($\Leftarrow$) We suppose that $n=p^k$ for same prime $p$ and $k\ge 1$. Let $a,b\in\mathbb{Z}$ such that $ab\in(p^k)$ and $a\notin (p^k)$. Then $p^k\nmid a$, but $p^k \mid ab$ I no longer know how to proceed.  $(\Rightarrow)$ Let $(n)$ a primary ideal and we suppose for absurd that $n$ is not a power of a prime, then? how could I proceed?  Now, let $ab\in (p^k)$ with $a\notin(p^k)$, then $p^k\mid ab.$ Can I conclude that $p^k\mid b$?   How can I set up the other implication? Thanks How do I prove if a set of operations is complete? For example $\{\land, \lnot\}$ apparently forms a functionally complete set as it can form any logical expression.  But I don't really know what this means or how you show it. Do we just show that some set is complete and then in the future if we have a new set, show that we can replicate the known operations with the new ones?  Do you have to find these strategically or is there a systematic way? In  is a proof of Stirling's formula.  I really like most of it, but at a crucial step he uses the integral identity  $$n! = \int_{0}^{\infty} t^n e^{-t}  dt$$  , coming from the Gamma function.  I have a mathematical confession to make: I have never "grokked" this identity.  Why should I expect the integral on the right to give me the number of elements in the symmetric group on $n$ letters?    (It's not that I don't know how to prove it.  It's quite fun to prove; my favorite proof observes that it is equivalent to the integral identity $\int_{0}^{\infty} e^{(x-1)t}  dt = \frac{1}{1 - x}$.  But if someone were to ask me, "Yes, but why, really?" I would have no idea what to say.)  So what are more intuitive ways of thinking about this identity?  Is there a probabilistic interpretation?  What kind of random variable has probability density function $\frac{t^n}{n!} e^{-t}$?  (What does this all have to do with Tate's thesis?)  As a rough measure of what I'm looking for, your answer should make it obvious that $t^n e^{-t}$ attains its maximum at $t = n$.  Edit:  The kind of explanation I'm looking for, as I described in the comments, is similar to  of the beta integral. Apparently I cannot count. I think there are three files in /media  $ tree /media /media ├── foo ├── onex └── zanna 3 directories, 0 files   However, ls -l finds 12.  $ ls -l /media total 12 drwxr-xr-x  2 root root 4096 Jul 31 20:57 foo drwxrwxr-x  2 root root 4096 Jun 26 06:36 onex drwxr-x---+ 2 root root 4096 Aug  7 21:17 zanna   And, if I do ls -la I get only . and .. in addition to the above, but the count is total 20  What's the explanation? How to put terms in lexicographic order? I am trying to prove the following:  In $C[0,1]$ the functions that preserve the rationals (i.e. $f(\mathbb{Q})\subseteq \mathbb{Q}$) are dense.  So far, I have not made much progress- I am aware that $A$ is dense in $B$ iff $A$ has non-empty intersection with each open set $U$ in $B$ but am not sure how to apply this definition. I have also thought about showing that the closure of $X$ (where $X$ is the set of functions that preserve the rationals) is equal to $C[0,1]$ by a double-inclusion proof but I have also made no progress with this approach. Am I on the right track or should I change my approach? fp - How to keep running sum in variable? I have this code in my LaTeX:   \FPset{totalHours}{0}  \newcommand{\entry}[5]{     \FPeval{totalHours}{(totalHours)+#5}     #1 &amp; #2 &amp; #3 &amp; #4 &amp; #5 \\ }   Where \entry is meant to be an entry in a time log. The 5th argument is a number representing the number of hours in that entry. I want to keep a running total of the hours in a variable I can print later on, totalHours.   This seems to do the \FPeval but then totalHours gets reset to 0 by the next time I write \entry. What is the correct way to keep a running total? Thanks. What should a main game loop do? Generally, what are the core things that one should do in the game loop, and what are some things that one shouldn't do in the game loop? I created a model and added some Actions in the DopeSheet editor (more or less 5).  I exported the model to my game engine, saved the .blend file (Ctrl-S) and closed it.  Then I opened it again, and all the actions were gone, it just had the one I was using last.  The same happens with some preferences (for example, I disabled mip-maps on User Preferences -> System, and I have to re-enable it every time I open the .blend file again.  Does somebody knows how to restore the Actions and save everything? Thanks. Sometimes when I'm making a sauce or soup that needs to be a bit spicy, I have no troubles spicing how I want to.  But if the dinner party is a bit late, or I made the sauce in advance to really draw out all the flavors of the spices, vegetables and meat, sometimes I end up with a way too spicy/hot dish.  You can always pour a bit water and try to dilute it a bit, but that also takes away all of the good flavor. So is there some trick that I'm missing I can use, when this happens to me (other than being more careful or using the spices later)? Is there a way to turn off an external Apple Cinema Display remotely and continue to use the computer? Here's the situation: I often access my Mac Pro remotely using Screen Sharing and sometimes TeamViewer. The problem is that when I do this, everything I'm doing can be seen by those near the physical computer. It also uses a considerable amount unnecessary power to have the displays on but not actually being used.  Is there a way to turn them off and not just blank if possible, while still using Screen Sharing or TeamViewer Free? Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable. Let $f:A \to \mathbb R$ and suppose that $$ \sup\Big\{\sum_{a\in F}\lvert\, f(a)\rvert :  F\text{ is finite subset of }A\Big\} &lt; \infty $$ then the set $\{ a \in A : f(a) &gt; 0\}$ is countable.  My try: Define these element of ${ a ∈ A : f(a) &gt; 0}$, then $∑_{n=1}^\infty\lvert\, f(a_n)\rvert$ is determined, regardless of the method of arrangement. In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of the gravitational field".  But I can't find anything concrete to substantiate this claim. As a first check, I did a calculation to compute the gravitational potential energy of a sphere of uniform density of radius $R$ using Newton's Laws and threw in $E=mc^2$ for energy of the sphere, and it was by no means obvious that the answer is zero!  So, my questions:   What is the basis for the claim &ndash; does one require General Relativity, or can one get it from Newtonian gravity? What conditions do you require in the model, in order for this to work? Could someone please refer me to a good paper about this? How to prove that the radial basis function is a kernel? How to prove that the radial basis function $k(x, y) = \exp(-\frac{||x-y||^2)}{2\sigma^2})$ is a kernel? As far as I understand, in order to prove this we have to prove either of the following:   For any set of vectors $x_1, x_2, ..., x_n$ matrix $K(x_1, x_2, ..., x_n)$ = $(k(x_i, x_j))_{n \times n}$ is positive semidefinite. A mapping $\Phi$ can be presented such as $k(x, y)$ = $\langle\Phi(x), \Phi(y)\rangle$.   Any help? Macbook Air - how to install a dual bootable Ubuntu 14.04 LTS On my Macbook Air 10.9.2 without crashing the current setup, how can i install as dual boot: Ubuntu 14.04 LTS ? (can anyone please advise some step by step please) Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$ Clipboard.GetText returns null (empty string) My clipboard is populated with text, but when I run  string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.Text);   I get back an empty string. I've toyed with various forms of the call including:  string clipboardData = Clipboard.GetText(); string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.UnicodeText);   But with the same result.  Am I missing something obvious? $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute Sci-fi novel, scout crash lands on planet, shaman sees competition and wrecks spherical spaceship I read this years ago. A scout in spherical advanced ship lands on a planet. Natives are friendly, but the shaman perceives competition, and sneaks into the craft and scatters potions on the controls, their acid eating into plastics and metals. He can be rescued at the other side of planet, but he has a deadline. Eventually all make airship and he makes it.