I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months?
I am currently visiting the USA from the UK (I am a UK citizen) and am intending on staying here for the full 90 days under the Visa Waiver Program.     How long would I have to stay out of the US at the end of this period before returning again?    Would I have to return to the UK, or could I stay with friends in another country (such as Canada) for a while?
What camera settings should be used to capture sky shots without over exposing the clouds? Are there any Combinatoric proofs of Bertrand's postulate? I feel like there must exist a combinatoric proof of a theorem like: There is a prime between $n$ and $2n$, or $p$ and $p^2$ or anything similar to this stronger than there is a prime between $p$ and $(\prod_p p) + 1$ (Euclid's theorem).  I was trying to prove one by the Sieve on this grid      1     2     3     4 ... p   p+1   p+2   p+3   p+4 ... 2p  2p+1  2p+2  2p+3  2p+4 ... 3p ........................... ........................... ........................... p^2 p^2+1 p^2+2 p^2+3 p^2+4 ...   but it did not work.  Do any good arguments like this exist? I don't expect anything as strong as Prime Number Theorem or even Bertrand, but surely a direct combination proof can prove that there are lots of primes? How to specifically use ntfsundelete to recover directory This is a followup on my original post  which may be deleted in the future.  In the process of backing up my audio books, I "permanently" removed a folder (with subfolders) that I had already exclusively moved to that drive. It's path is /media/gratis/Seagate Expansion Drive/Audiobooks/Jason Dark. The sole folder in that should be called John Sinclair; but I'm not sure about that.  Which tool offers the best chances to recover those files? I haven't written plenty on that drive afterwards; so I hope for the best. It's not that other methods failed; I just cant get my head around what to do and I want to be cautious. It's a NTFS Drive.  According to testdisk it has an "EFI GPT" Partition table.  Disk /dev/sdb - 5000 GB / 4657 GiB - CHS 608001 255 63, sector size=512 - Seagate Expansion Desk, FW:9401   Information According to "Disks" (Ubuntu Standard Software):  NTFS; GUID Partition Table; [...] Partition Type: Microsoft Reserved   Attempt 1: First off, ntfsprogs seems to no longer be in repos (those mentioned by another user); but it is already installed on my machine so no problems there. I always get the error:     Access is denied because the NTFS volume is already exclusively opened. The volume may be already mounted, or another software may use it which could be identified for example by the help of the 'fuser' command. You can use force option to avoid this check, but this is not recommended and may lead to data corruption.   Although I only just plugged it in and even quit Nautilus by force (nautilus -q).   Therefore, I ran sudo ntfsundelete /dev/sdb2 -f. That gave me a list of a bunch of files, 205013 to be exact. Now, what I want is the content of the directory .../Audiobooks/Jason\ Dark/ to be restored. What do I have to do? It's contents are .m4b &amp; .opus files and folders, of course. Is there any way to include an animated GIF directly in either PDFLaTeX or XeLaTeX? I realize the animate package can include animations in a PDF, but it doesn't support animated GIFs and you have to split them up manually into EPS or PNG files as far as I can tell. Changing Screen Brightness Through Keyboard Functions on My Notebook I've installed Ubuntu 16.04 on my Asus X555LJ.  But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness. Apache error "Could not reliably determine the server's fully qualified domain name" Young adult book about a boy(?) who gets sent through a portal to another world which is really the distant future Trying to remember a book about (I think) a boy who goes through a portal (possibly struck by lightning?).   Ends up in a strange, primitive bush/forest land. Alien but somewhat Earth-like plantation everywhere - I believe the grass was purple. There are very primitive humans (or humanoids?) and the main character was possibly made a slave by a tribe? Thinks is on alien planet. It is revealed they are still on earth when someone has a glass bottle which reads "Coca-cola" on it. There was something to do with quicksand which seemed important to the plot.   Probably read sometime around the late 90s, but could have been written earlier.  Was either a short novel or possibly even a short story.  Would be curious if anyone can remember this. Why is the picture not inserted? When I pdflatex the text below it doesn't insert the picture, but writes the name of the file instead (pic).  And the geometry line gives the error  ! LaTeX Error: Missing \begin{document}.   The picture I am using is at  and the floatrow package .  Question  Can anyone see what is wrong?  Text  \documentclass[a4paper]{article} \pdfpagewidth=\paperwidth \pdfpageheight=\paperheight \usepackage{aeguill} \pdfcompresslevel=9 \usepackage[pdftex,colorlinks]{hyperref}  \usepackage{a4} \usepackage{fixltx2e} \usepackage[danish]{babel} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc}  \usepackage[draft]{graphicx} \usepackage{floatrow}  \usepackage{geometry}  \geometry{margin=10pt,paperwidth=\textwidth+20pt,paperheight=\textheight+20pt}  \begin{document}  The first paragraph.  \begin{figure}   \includegraphics{pic} \end{figure}  And the second.  \end{document} How to write uncertainties with the \pm symbol "10 ± 1 K" by using siunitx? Using the siunitx package, if I specify an error with the \pm symbol then it automatically converts it to a form using parenthesis. I would like it to not do this and keep the \pm symbol, but still space the elements of the quantity and symbol in a good way.  e.g. \SI{10 \pm 2}{\kelvin} would produce 10(1) K  I would like it to produce: 10\pm1 K or something similar with spacing taken care of. Every open set in $\mathbb{R}$ is a countable union of closed sets I can't write Chinese characters in edited posts, but OP could when posting Is there a definitive list of which episodes / scenes that they used for the classic doctors in The Day of The Doctor? I have to move a MongoDB Collection (Size: 1TB+) from Sharded MongoDB Cluster to another[5 shards on both clusters]. During this operation, it is assumed that the accompanying program will be offline, so no need to worry about inconsistent data, but I need to minimize the downtime.  I've tried testing it with mongodump and mongorestore, but looks like that is taking ages to finish.  Please share your experiences for such kind of scenarios.  Note: Cluster has only one collection, so I am open at cluster level sync as well. Uncountable well ordered set in $Z^-$ theory. I want to build an uncountable well-ordered set within the theory $Z^\textbf-$. So, I take $A=\omega$ (exists by infinity axiom) and define $$W:=\{(X,R)\in\mathcal{P}(A)\times\mathcal{P}(A\times A):\langle X,R\rangle\ \text{is a well-ordered set}\}$$  With this I consider the set $T:=W/\cong$ (where $\cong$ is isomorphism relation). Note that $W$ and $T$ are sets by power set axiom. So I define for each equivalence class $[x],[y]\in T$ the order  $$ [x]\leq_T[y]\Leftrightarrow \text{type}(x, R_x)\leq \text{type}(y,R_y) $$  Here, $R_x$ means the order of $x$ that make it belongs to $[x]$.   So, $T$ is well ordered by $\leq_T$ and it is uncountable.  Question: I don't pretty sure if I can build $\leq_ T$ without replacement axiom. Another doubt is, Can I take the $R_x$ without AC? Why are integers subset of reals? In most programming languages, integer and real (or float, rational, whatever) types are usually disjoint; 2 is not the same as 2.0 (although most languages do an automatic conversion when necessary). In addition to technical reasons, this separation makes sense -- you use them for quite different purposes.  Why did they choose to say $\mathbb{Z} \subset \mathbb{R}$ in math? In other words, why are 2 and 2.0 considered the same?  When you are working in $\mathbb{R}$, does it make any difference whether some elements, eg. 2.0, also belong to $\mathbb{Z}$ or not? For each positive integer $n$, let $x_n=1/(n+1)+1/(n+2)+\cdots+1/(2n)$. Prove that the sequence $(x_n)$ converges.   This is what I have so far..  Let $\epsilon &gt; 0$ be given to us. We must show that there exists an $N \in \mathbb{N}$  such that $n\ge N \implies \left|\frac{1}{2n} - 1\right| &lt; \epsilon$. Choose $N$ to be any positive integer which is larger than $\frac{1}{\epsilon}$. (So $N&gt;\frac{1}{\epsilon}$.) Then $n\ge N \implies \left|\frac{1}{2n} - 1\right| = |\frac{1-2n}{2n}|$ Upper bound for norm of Hilbert space operator It is a standard result that for a bounded self-adjoint operator $T$ on a complex Hilbert space $H$, we have $\|T\|=\sup_{\|x\|=1}|\langle Tx,x\rangle|:=M(T)$, where $M(T)$ is called the  of $T$. It seems that for any bounded operator on $H$, we have $||T||\leq 2M$. Why is that so? I have the age-old problem of a div wrapping a two-column layout. My sidebar is floated, so my container div fails to wrap the content and sidebar.  &lt;div id="container"&gt;   &lt;div id="content"&gt;&lt;/div&gt;   &lt;div id="sidebar"&gt;&lt;/div&gt; &lt;/div&gt;   There seem to be numerous methods of fixing the clear bug in Firefox:   &lt;br clear="all"/&gt; overflow:auto overflow:hidden   In my situation, the only one that seems to work correctly is the &lt;br clear="all"/&gt; solution, which is a little bit scruffy. overflow:auto gives me nasty scrollbars, and overflow:hidden must surely have side effects. Also, IE7 apparently shouldn't suffer from this problem due to its incorrect behaviour, but in my situation it's suffering the same as Firefox.  Which method currently available to us is the most robust? Can you have a class in a struct? I just discovered Matlab's factor()-function, and I randomly typed in 20081294819, and to my surprise it only had two factors (5099 and 3938281)! I had expected many more factors for such a big number and wondered how normal this was. The following is what I've done in my investigation so far.  In the first figure below, I have plotted the probability that some number below $10^k$ has $m$ indistinct prime factors.  The second figure shows the evolution of the probability of finding a number with $m$ indistinct prime factors as the numbers one is looking at grows, i.e. it is just another way to visualize the same data. I have left out all points of zero probability.  If one looks at the first part of the figure, it seems that the peak of the curve for some $k$ shifts toward higher $m$ as $k$ grows.   My first question is this: Does this behavior (i.e. the peak shifting toward higher $m$ as $k$ grows) continue indefinitely, or will the peak stabilize at some point? The latter seems unlikely but I can't be sure.  My second question is this: Approximately how fast does the peak-value $m_{peak}$ move as $k$ grows?  I briefly looked at the , but this involves distinct primes and I don't really know much number theory, so any help would be greatly appreciated!