Why do we need extra force to pull an upside down mug out of a bucket?
Why is it so difficult to pull an immersed mug out of the water?
Should an image carousel on a mobile site automatically rotate? How can I make a peer-to-peer multiplayer game? How can I make a p2p multiplayer game? I would like to have a server-less multiplayer game. But then, how all the clients know each other?  Why the p2p-protocol is so famous in file transfer but not in multiplayer games? Is there a way to make bash more TAB friendly? I use bash on both my Mac and as my cygwin shell. Overall, I'm quite pleased with it.  My one complaint however is that its TAB completion isn't as good as Windows Command Line TAB completion.   For example, if there are two files with the same prefix, then bash just beeps at me when I try to TAB complete. If I keep nailing TAB, then it will eventually show me a list of potential files.  I definately prefer how Windows will cycle through potential files right on the command line.   Is there a way to get bash to operate similar to Windows Command Line in this regard?  If there isn't (I do not want to switch shells), am I missing something about TAB completion in bash? Is there a more efficient way to use it? The problem from Burton: show that the equation $n^2 + (n+1)^2 = m^3$ has no solution in the positive integers.  So far, I can see that gcd($n$,$n+1$)$=1$ and $m \equiv_4 1$ and $m=a^2 + b^2$ for some integers a,b. I'm guessing I need to reach a contradiction.  At this point, I am stuck. Any hints? AMD GPU Material in "material preview mode" and "rendered mode", is entirely gray as background. Only outline is displayed I don't know why but now, when i go in material preview or rendered (in solid mode it works fine), my object is entirely gray, or invisible idk, because it has the same color of the background. I've been working for days on this project without having this issue, it suddenly showed up. I tried opening other old projects and suddenly they all do the same so i guess it is some blender program setting that applies for all the projects, but idk how it happened cuz i didn't change anything :/, anyone got any tips? Bounded sequence which is not convergent, but differences of consecutive terms converge to zero I have a question that says "Show that there is a bounded sequence $x_n$ which is not convergent but has the property that $x_n - x_{n+1} \to 0$ as $n \to 0$.  What does this mean? Do I need to come up with an example or does the problem actually want me to prove such proposition?  By the way, I see that this sequence looks like Cauchy because of $x_n - x_{n+1} \to 0$ as $n \to 0$, but it is obviously not. I'm asking this because my HDD (Hard Disk) has 5 years, and ultimately (this year) it gave me many headaches. Many moths ago I has Windows 7 (and 10 T.P. since april) and all was good. But after a moment, instantly, all gets reversed: veeery slow, and actions which will take a tiny time, at these moment the time seems frozen (for example, instead a 1 minute boot, it turned to 5-8 minutes boot). I formatted and installed Windows every 2 months because it was the time which runs good before it gets slooww. Seeing the abuse of privacity in W10, I changed to Ubuntu 15.04 and the things lasted more in time... But again, HDD error. Click, trying to read, click, trying to read... And the upper bar (title of window/buttons of volume, language, wifi, etc.) disappeared. The left bar (where are the app's icons) was empty and the file explorer said the resource wasn't available (or something like these error). I restarted and nothing happens. I had to press CTRL+D to boot-up Ubuntu, but after hours... the same error (can't do anything except moving the mouse/cursor).  Welcome to the routine: copy files with live-cd to a pendrive, wipe HDD and install all again. And the things was calmed again... and the errors comes again. And after 2 weeks, I had to do the same. Now my PC works fine, but yesterday I heard a few "clicks" from the HDD.  Now, I remembered this  and I came to Disks and the HDD shows a new value; normally, the problematic number was "pending sectors", always changing, but now, in "irrecoverable sectors", the number is different of zero.  I never had "reallocated sectors". Now, neither. And now, while I write this lines, I've 5 "pending s." and 9 "irrecoverable s.". If this helps, the "read error rate" is 42, 5 for "write error rate".      Very well!! While I was writing "write error rate", I heard 2   clicks. And while writing this, one click more.   And 123 "CRC error rate". So, with this information: is my HDD dying? It'll last days or months? I think this problem will kill the disk in a not very far time.  The drive is a Western Digital Green 1TB-WDC WD10EARS-00Y5B1 (80.00A80) S.N.: WD-WCAV5J301610  PS: When I boot with CTRL+D, many times the system is in "RO mode"; I can't save/download files, Unity doesn't find apps when I write their name {click again, now, while I write the text} and, after a few hours, a crash like the lines above I'm looking for a book I read in Junior High (probably) about a world where everyone was basically the same race.  One genetically pure male and female teenager of each race still exists.  They are transporting a genetically pure boy to meet his genetically pure female counterpart and accidentally introduce him to a genetically pure female of a different race.  And, of course, chaos ensues.  Any thoughts? I am trying to calculate the final velocities of two equal mass 2-dimensional circles after an elastic collision. I have tried to figure it out using formulas I know from high school physics, but nothing seems to work. My known variables are:   initial x and y velocities for each circle x and y distances between the centres of the circles at the time of the collision   The variables I would like to solve for are:   final x and y velocities for each circle   Here are diagrams showing all the variables: Today a student asked me $\int \ln (\sin x) \, dx.$ Calculate the integral $$\int \ln (\sin x) \, dx.$$ My question is in the title. I'm a little lost in how to solve this problem. There is a hint associated with the problem that states the following:   Use a line integral to show that $ |f(z)| \leq A + |z| $ where A = $\max\{1, |f(0)|\}$  Thanks for the help. In languages like Java and C#, strings are immutable and it can be computationally expensive to build a string one character at a time.  In said languages, there are library classes to reduce this cost such as C# System.Text.StringBuilder and Java java.lang.StringBuilder.  Does php (4 or 5; I'm interested in both) share this limitation?  If so, are there similar solutions to the problem available? How can I make a single event handler handle ALL Button.Click events? Suppose there are $2$ permutations given by $p$ and $q$. I need to check whether $p$ belongs to the group generated by $q$, and if so, it's representation in a power of $q$. In other words, I've been given $p$ and $q$, I need to check whether $\exists i \in \{ 0,...,|q|-1 \} \text{ such that } p = q^i$ I know that if $m = \gcd(i, |q|)$, then $|q^i| = \frac{|q|}{m}$. Now, say that such an $i$ exists. Then, $$ |p| = \frac{|q|}{\gcd(i, |q|)} \Rightarrow \gcd(i, |q|) = \frac{|q|}{|p|} $$ Thus, a necessary condition for such an $i$ to exist is: $|p|$ divides $|q|$ Say that this holds, and $\frac{|q|}{|p|} = r$, where r is an integer. Then we just have to solve $\gcd(i, |q|) = r$ for $ i \in \{ 0,...,|q|-1 \}$. Can this be done? If not manually, then by some efficient algorithm? (Note: Just looping over all values of $i$ is not efficient as $i$ may be very large) Edit: Another way I can think of solving this is by writing both $p$ and $q$ as product of disjoint cycles: $$ p = c_1c_2\ldots c_k \text{ and } q = d_1d_2\ldots d_l $$ And thus, as disjoint cycles commute: $$ p^i = c_1^ic_2^i\ldots c_k^i $$ How to proceed after this? How to remove top and bottom whitespace of longtable? I am using longtable instead of tabular environment and noticed that it puts some additional whitespace at the top and at the bottom of the table. Is there some way to remove it (something less hacky than \vskip -\baselineskip before the table)?  Small piece of code for illustration:  \documentclass[12pt]{book} \usepackage{longtable}  \begin{document}  Linelineline  \begin{longtable}{l l} cell1 &amp; cell2 \end{longtable}  Linelineline  \begin{tabular}{l l} cell1 &amp; cell2 \end{tabular}  Linelineline  \end{document}   And that's what I am getting:    Common tabular environment does not have any additional margins, but longtable does. Make "compact view" as a default directory view instead of "icon view" How can I make "compact view" the default for all directory views in File Manager, instead of "icon view" ? Resolve the error "An illegal choice has been detected..." I want to run a script on all files with two specific extensions on a disk with a hierarchy of multiple nested folders.  My script works fine when I choose a folder further down the line with fewer subfolders but I'd like to run it on an entire archive with over a thousand folders.  The AppleScript takes forever to get all the files and then exits without returning anything and without executing the operations after getting the files.  No timeout message, no error message.  And the Finder becomes unresponsive (and remains stuck after the script exits).   set myFolder to choose folder with prompt "Choose a folder:"     tell application "Finder"         try             set eafFiles to (every file in entire contents of myFolder whose name ends with ".eaf") as alias list         on error             try                 set eafFiles to ((every file in entire contents of myFolder whose name ends with ".eaf") as alias) as list             on error                 set eafFiles to {}             end try         end try         try             set pfsxFiles to (every file in entire contents of myFolder whose name ends with ".pfsx") as alias list         on error             try                 set pfsxFiles to ((every file in entire contents of myFolder whose name ends with ".pfsx") as alias) as list             on error                 set pfsxFiles to {}             end try         end try         set myFiles to eafFiles &amp; pfsxFiles     end tell      repeat with CurrentFile in myFiles         set CurrentFile to CurrentFile as string          do shell script "perl /path/to/perl/script.pl " &amp; quoted form of CurrentFile     end repeat USB WiFi dongle device that can emulate a virtual mass storage device for a home video player Is there a USB WiFi dongle device that can:   Emulate a virtual mass storage device for a home video player But in fact shows the files from a network-shared folder? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound.