Maximum helicopter height
Why can't helicopters reach mount everest?
How do you convert a cake recipe to make brownies? What is the proper way of creating installation media from Ubuntu iso? This is the third time I've tried to install Ubuntu Server 14.04.03 64-bit on the same laptop, and each time it caused different problems.  Each time I wrote the same iso image to a USB flash drive by using a different application and OS.   Universal USB Installer (pendrivelinux.com) from Windows WinImage writer from Windows built-in image writer from Linux Mint 17.2    The iso image is the same in all three cases, the USB flash drive is the same, and the laptop is the same. However each time the installation of Ubuntu gave me different installation options. For example, the last time I installed Ubuntu, it didn't show all the packages to choose while installing (Basic Ubuntu server, etc.). nomencl package : sort by order of appearance In the nomencl package, how can I make the symbols print by order of appearance in the LaTeX code? $\displaystyle\sum_{n=1}^\infty \frac{1}{n^s}$ only converges to $\zeta(s)$ if $\text{Re}(s) &gt; 1$.  Why should analytically continuing to $\zeta(-1)$ give the right answer? I'm a fourth year undergraduate student in a university in the U.S., and this is my last semester. I have already applied to graduate schools, and I'm currently awaiting responses. Since I have already finished all my requirements and am ready to graduate, I wanted to go part time this semester. I am aware of how it affects my financial aid; however, I do not know if it has an effect on my admittance to graduate school. I do not mean whether or not I get accepted (the decisions will happen without knowledge of my current semester), but whether I am eligible to attend graduate school if I have been part time for a semester. That is, will there be any potential issues when the schools that have accepted me see my final transcript and see I was part time? Is there a universal answer to this? Or should I contact each school individually and ask about their policy?   Also, are there any other potential issues with going part time that I haven't mentioned? Anything noteworthy I might have missed? Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$ I need to show that  $$ \int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3} $$  I have already derived the result $\int_0^\infty \frac{\sin^2x}{x^2} = \frac{\pi}{2}$ using complex analysis, a result which I am supposed to start from.  Using a change of variable $ x \mapsto 2x $ :  $$ \int_0^\infty \frac{\sin^2(2x)}{x^2}dx = \pi $$  Now using the identity $\sin^2(2x) = 4\sin^2x - 4\sin^4x $, we obtain  $$ \int_0^\infty \frac{\sin^2x - \sin^4x}{x^2}dx = \frac{\pi}{4} $$ $$ \frac{\pi}{2} - \int_0^\infty \frac{\sin^4x}{x^2}dx = \frac{\pi}{4} $$ $$ \int_0^\infty \frac{\sin^4x}{x^2}dx = \frac{\pi}{4} $$  But I am now at a loss as to how to make $x^4$ appear at the denominator.  Any ideas appreciated.  Important: I must start from $ \int_0^\infty \frac{\sin^2x}{x^2}dx $, and use the change of variable and identity mentioned above Given two separate annulus with centers $[C_1,C_2]$ and their corresponding radii being $[R_1,r_1]$ and $[R_2,r_2]$ respectively, larger radius being $R$. There are methods to look at whether they are overlapping or not. If they overlap how to find the overlapping area. Is there any close form expression for it?  equation of first annulus   $r_1^2&lt;(x-x_{c1})^2 + (y-y_{c1})^2 &lt;R_1^2$   equation of second annulus  $r_2^2&lt;(x-x_{c2})^2 + (y-y_{c2})^2 &lt;R_2^2$  If there are three circles overlapping, we get overlapping area as solution to set of 4 in-equations by least squares approach(Though we don't end up getting total area but, area within tangents of circles ). Predefined Coordinate Systems missing in QGIS 2 in QGis 1.8 were lots of predefined coordinate systems (national projections). Where have they all gone in qgis 2.0? I specifically need the Gauß-Krüger-Projections Zone 1 to 5.  Is there any plugin to load those coordinate systems? How can I vertically center a "div" element for all browsers using CSS? Why do Google search results include pages disallowed in robots.txt? I have some pages on my site that I want to keep search engines away from, so I disallowed them in my robots.txt file like this: User-Agent: * Disallow: /email  Yet I recently noticed that Google still sometimes returns links to those pages in their search results.  Why does this happen, and how can I stop it? Background: Several years ago, I made a simple web site for a club a relative of mine was involved in.  They wanted to have e-mail links on their pages, so, to try and keep those e-mail addresses from ending up on too many spam lists, instead of using direct mailto: links I made those links point to a simple redirector /  script running on my own site.  This script would return either a 301 redirect to the actual mailto: URL, or, if it detected a suspicious access pattern, a page containing lots of random fake e-mail addresses and links to more such pages.  To keep legitimate search bots away from the trap, I set up the robots.txt rule shown above, disallowing the entire space of both legit redirector links and trap pages. Just recently, however, one of the people in the club searched Google for their own name and was quite surprised when one of the results on the first page was a link to the redirector script, with a title consisting of their e-mail address followed by my name.  Of course, they immediately e-mailed me and wanted to know how to get their address out of Google's index.  I was quite surprised too, since I had no idea that Google would index such URLs at all, seemingly in violation of my robots.txt rule. I did manage to submit a removal request to Google, and it seems to have worked, but I'd like to know why and how Google is circumventing my robots.txt like that and how to make sure that none of the disallowed pages will show up in their search results. Ps. I actually found out a possible explanation and solution, which I'll post below, while preparing this question, but  in case someone else might have the same problem.  Please do feel free to post your own answers.  I'd also be interested in knowing if other search engines do this too, and whether the same solutions work for them also. Problem with defining shortcuts for TikZ matrices For  I wanted to define a shortcut for creating a matrix inside a tikzpicture. As a minimal example, consider  \newcommand\mymatrix[1]{     \begin{tikzpicture}         \matrix[matrix of math nodes] {#1};     \end{tikzpicture}% }   which would then be used as  \mymatrix{     a &amp; b \\     e &amp; f \\ }   But LaTeX complains about Package pgfbasematrix Error: Single ampersand used with wrong catcode at the line with the closing brace of \amatrix{}. Why does it do that and how can I avoid it? If $\sum{a_n}$ converges does that imply that $\sum{\frac{a_n}{n}}$ converges? I know if $\sum{a_n}$ converges absolutely then $\sum{\frac{a_n}{n}}$ converges since $0\le \frac{|a_n|}{n} \le |a_n| $ for all $n$ so it converges absolutely by the basic comparison test and therefore converges. However, I cannot prove the convergence of $\sum \frac{a_n}{n}$ if $\sum{a_n}$ converges but not absolutely even though I suspect it to be true. Can you give me a proof or a counterexample for this? LSTM : shape of tensors? I'm trying to understand LSTM, using for instance   I get the overall idea, I guess. But I'm not quite sure I get the maths.  I'll set a very simple problem : I have a sequence of numbers and want to predict next number.   So x_t is of shape (1), and as I understand, h_t will be the prediction, so it should also be of shape (1). (I'm just here ignoring batch size)  Now, the equation producing h_t, using * operation should then have two operands of the same size as the result; that is, C_t and o_t should also be of shape (1).  Following on that idea, equation producing C_t forces also shape of (1) for f_t, i_t and ~C_t.  So... everything reduced to scalar real numbers in that case ?  what am I getting wrong ? because this would just not be able to learn much, would it ? Create tar archive of a directory, except for hidden files? I'm wanting to create a tar archive of a specific directory (with its subdirectories of course). But when I do it, using the tar command, I get a list of files that were included, for example:     a calendar_final/._style.css      a calendar_final/style.css   As you can see, there are two versions of the same file. This goes for every file, and there are many. How do I exclude the temporary files, with the ._ prefix, from the tar archive? If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$ In Windows there’re perhaps only a couple of important folders (by important I mean important in my logical picture of the Windows file system) in the installation drive (in my case C:\). Namely Program Files and Windows. I simply stay away from Windows folder and the “add remove program files” is good enough to handle the program files folder of Windows. Of course there’s a folder named Users where the users (who are not admins) can access only their folders.  Thus there’s a clear picture at some level in my mind of the Windows file system. In Ubuntu, when I reach the location /, there’s a huge list of folders, most of which I have no clue as to what they contain. The /bin folder seems to be the equivalent of the Windows folder in windows. The /usr folder seems like it’s the equivalent of the Users folder in Windows. But even the /home folder looks like it can fit the bill.  Please understand that I do understand, that Ubuntu (Linux) has a different character than that of Windows, i.e., there need not be exact equivalent of Windows functions, in Ubuntu. All I am looking for is a bit more clearer picture of the Ubuntu file system.   This question is a part of a bigger question which I am splitting up to make it more answerable. The original question can be found here: Adjust rounded rectangle radii without creating a new one in Photoshop C6 When I create new rounded rectangles, I see the radii and other information in the properties, but after I work on something else and go back to that layer, the information does not show. How do I adjust the radii of the rounded rectangles without deleting and creating a new one? I am designing the layout for a touchscreen for outside use, What are some good color combination to use that will be visible under the sun light for outside use? Maybe bright neon colors? Get variable from PHP to JavaScript A girl who transcends time I remember quite a bit, but can't seem to find the title or (female) author.   A girl accompanies her father as he captains a mission to travel at near-light speed in order to experience the effects of time dilation and return to Earth 100 years into its future. She leaves behind her boyfriend (Tal or Tel or something), who promises he'll find a way to stay with her despite the time travel that will render him, well, dead before her return. She's accompanied by a close friend who is deaf but lip-reads and speaks so well as to occasionally fool others into believing she is hearing. They spend a lot of time in the ship's garden. I believe he ends up either getting on a different ship to survive into the future via time dilation, or else having himself frozen. Either way, if I recall correctly, Earth isn't doing well at all by the time the mission with the girl returns. There's been a war or some other disaster. There's an extended period of vague, ambiguous, existential crap in which the girl (now a woman) eventually ends up transferring her consciousness into her own daughter, presumably in order to go on living. Everything wraps up somehow and the girl and her boyfriend walk together hand in hand on a desolate planet into the sunset near the end of time.   It was all really rather trashy and silly, I remember, and took itself entirely way too seriously, but I'd like to at least know what it was so I could read it again. Either it'll be worth a laugh, or it'll turn out to be surprisingly good.