Proof that if $a^n|b^n$ then $a|b$
Show that $a^n \mid b^n$ implies $a \mid b$
What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out? What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out?   I guess I am confused: If you know the yield and when the dividend will be paid out, why not buy a share an instant before the dividend is paid out and then sell it?  Do you have to have held the share for some amount of time to get the dividend? Is there too much volatility in the instant the dividend is paid out? What are the “spam” and “rude or abusive” (offensive) flags, and how do they work? When flagging, there are two special case options: spam and rude or abusive.   What is spam, and when should I flag content as such? What is considered offensive, rude or abusive content? How does the spam flag differ from the rude or abusive flag? What is the effect of these special flags? When are these flags removed? $3\times3$ linear system organization Free, open-source substitutes for Mendeley? is (mainly) a proprietary social network to share basic citation data and research papers.   Are there any free and open source substitutes for this service?   A technical possibility: users could collect BibTeX data and a hash and share this information.  It would be very useful to have such a free service because every journal provides the citation data in a different format. That includes false field entries, broken files and hidden download buttons on the website. Is ‘half half’ ambiguous? 50-50  Ex) There are half half milk and water. = there are 50:50 milk and water.  1/4  Ex) There is half half water. = there is 1/4 water. Is it right? Analysing Bounce Rate and Time on Page I'm working on an eCommerce site and there's a perceived problem with the bounce rates on product pages. The best performing page (in terms of views), tends to have a very high bounce rate, at about 80%. This page is also targeted with Ads, but in both non-paid and paid traffic, the bounce rate stays high.  What's weird about it is that the time on this page is about 2 and a half minutes. The others pages have a slightly lower bounce rate (between 50% and 75%) with visit times between 1 minute and 2 minutes.  I'm not entirely sure about how to analyse this data. I've checked all the possible technical problems (faulty GA code, JS race conditions, breaks in the chain), and whilst there were some things that need improving, no technical fix budged the bounce rate at all.  The other thing we noticed was that the product pages were getting lots of traffic for very generic and brand based search terms. In these cases the pages come up as sitelinks, could this explain a high bounce rate too?  So in short :  If the page view time is so high, should I be worrying about the bounce rate at all? What's the chances of someone visiting the page and then leaving to compare prices? And how do sitelinks affect bounce rate on eCommerce sites? Cannot install Ubuntu in VirtualBox due to "this kernel requires an x86-64 CPU, but only detects an i686 CPU, unable to boot" error Chrome phishing warning on main Is there any way (such as a command or environmental variable) to determine what window manager is the one actively running in the current session? What is the word that means “that which can be fixed up at home”?   For example, I buy parts from a store, bring the parts home, and then can construct the thing out of those parts by myself. What is the word that means such an object, one that can be made at home in a do-it-yourself style? Script failing with "command not found: ^M" When I try to run the following script in zsh, via the command /bin/zsh ~/.set_color_scheme.sh I get the following error:  command not found: ^M   The script has u+x permissions and it used to work on another machine that also had zsh. Any clues why?   Note: This question is related to  (where I am trying to adapt the script for tcsh)  #!/bin/zsh # Contents of set_color_scheme.sh  export LS_COLORS=$( \ ( grep '\w' | grep -v '^#' | sed 's/#.\+//' | perl -lane 'printf "%s=%s:", shift @F, join ";", @F;' ) &lt;&lt;&lt; "  # HUMAN_FORMATTED_DATA # list one per line  # these are basic filesystem items no 00          # normal fi 00          # file di 01 34       # directory ln 00 36       # link pi 40 33       # pipe so 00 35       # bd 40 33 01 cd 40 33 01 or 01 05 37 41 mi 01 05 37 41 ex 00 91       # executable ow 01 34       # other writables   *.cmd 00 32 *.exe 00 32  # archive, compressed things etc *.gz  00 90 *.bz2 00 90 *.bz  00 90 *.tz  00 90 *.rpm 00 90 *.rar 00 90 *.zip 00 90 *.iso 00 90   *.cpio 00 31    # perl &amp; CODE *.c      33 *.h      33 *.sh     33 *.t      33 *.pm     33 *.pl     33 *.cgi    33 *.pod    33 *.PL     33 *.js     33 *.php    33 #*.xs  # strikethrough *.off 00 9 *.bak 00 9 *.old 00 9   # documents misc, html webstuff # really TEXT *.htm    94 *.html   94 *.txt    94 *.text   94 *.css    94   # MOVIE *.avi    96 *.wmv    96 *.mpeg   96 *.mpg    96 *.mov    96 *.AVI    96 *.WMV    96 *.mkv    96  # images &amp; pdf *.jpg    96 *.jpeg   96 *.png    96 *.xcf    96 *.JPG    96 *.gif    96 *.svg    96 *.eps 00 96 *.pdf 00 96 *.PDF 00 96 *.ps  00 96  *.ai  00 91 # adobe ill *.doc 00 91 # msword   # data, such as .db, .csv *.csv    95 *.dsv    95 *.db     95 *.sql    95 *.meta   95 # CONFS *.xml    95 *.yaml   95 *.yml    95 *.conf   95 # [a-z0-9]*rc ") What are the pros and cons of adding a vapor barrier behind shower backer board? Sharing a Bluetooth Keyboard and Mouse sequentially between two Macs I work out of my house where I have two computers: a mid-2010 Macbook Pro (for my day job) and a mid-2010 iMac (personal). During the workday, my iMac acts as a second display for my Macbook Pro via Mini Displayport.  Currently, I use a USB keyboard and mouse for my work computer and a Bluetooth keyboard and Magic Mouse + Magic Trackpad for use with my personal computer. I'd like to get rid of the wired keyboard and mouse and just use the Bluetooth stuff for both machines (but never simultaneously).   Is it possible to easily share the single set of input devices without having to repeatedly break and reestablish the pairing of the input device to the correct computer? I'm not opposed to buying some type of additional hardware to accomplish this, provided it's not prohibitively costly or cumbersome to use or configure.  It's not clear to me how I would tell the MacBook Pro to leave the devices alone so the iMac can have them for the evening. I want to avoid de-pairing and re-pairing the devices each time I want to shift them back or forth.  Basically is there software or hardware that works as a Bluetooth KVM switch? I have a set of values $x$ and $y$ which are theoretically related exponentially:  $y = ax^b$  One way to obtain the coefficients is by applying natural logarithms in both sides and fitting a linear model:  &gt; fit &lt;- lm(log(y)~log(x)) &gt; a &lt;- exp(fit$coefficients[1]) &gt; b &lt;- fit$coefficients[2]   Another way to obtain this is using a nonlinear regression, given a theoretical set of start values:  &gt; fit &lt;- nls(y~a*x^b, start=c(a=50, b=1.3))   My tests show better and more theory-related results if I apply the second algorithm. However, I would like to know the statistical meaning and implications of each method.  Which of them is better? Dynamic grid with Atlas generation Why are Flash applications so sluggish/crashy? I've noticed that Flash applications tend to be more sluggish under Ubuntu than they do under Windows on the same machine. This is particularly noticeable when watching HD video or playing graphics/physics-heavy games. Are there any ways of improving the performance of Flash under Ubuntu, or is this just an issue with the Linux version that I will have to live with?  Currently I'm just cutting down on the number of tabs open, blocking flash ads, and closing other programs, but I'm looking for ways to affect Flash itself.  Other things I have already been doing include using Youtube's HTML5 feature and playing videos straight from /tmp in VLC. I was wondering if there was some way of streamlining Flash itself though. Perhaps not.  More Specific Question: Is there anything I can do in mms.cfg to boost performance? How to align a  to the middle (horizontally/width) of the page Ubuntu Server 18.04 LVM out of space with improper default partitioning Nearby objects won't move independently? I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. When is it useful to include the code in a thesis? I am writing my master of science thesis and I am not sure whether I should add some of the code I have written: they are not proper programs, but more like input files to be fed to a commercial program (Nastran) very popular in my field.  My concerns are related to the fact that I am not making any discovery, just applying the things I have learned reading the manual. Still, I feel the code will make the effort I put into the thesis to also learn this language clearer.