firefox window size and position
How do I save/remember last-used window position and size for applications?
Problem  Let $n \geq 3$ be an odd number and let $G=\{1,...,2n\}$ be a group of order $2n$. Let $\phi:G \to S_{2n}$ be the morphism defined by $\phi(g_i)(g_j)=g_ig_j$ and let $H=\phi^{-1}(A_{2n})$. Show that $H$ is a proper normal subgroup of $G$.  So basically the result of this problem is that every group of order $2n$, with $n$ odd, is not simple.   The morphism $\phi$ can be seen as the action of $G$ on itself by left multiplication. Since $A_{2n} \lhd S_{2n}$, then $H=\phi^{-1}(A_{2n}) \lhd G$. I am stuck at showing that $H \neq \{1\},G$. All I could think of is that $G$ has an element $g$ of order $2$, then $\phi(g)$ is of order $1$ or $2$, but it is easy to see that $\phi(g)=1$ if and only if $g=1$, so $ord(\phi(g))=2$. I don't know which are the elements of order two in $S_{2n}$. I would appreciate some help to solve the problem, thanks in advance. I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } Windows utility to render which key I am pressing on-screen "I had my house [be] burned down" I have found out that using the verb be in passive constructions such as:      I had my house be burned down    is incorrect, therefore it should be      I had my house burned down.    But is it possible instead of be to use get? E.g.      The wire is passed through the pliers in a specific way to avoid having it get bent.   The rope had its surface wear.   The rope had its surface get worn.   The rope had its surface worn.   The first two sound very odd to me, but just for clarification could you please point out the errors and which ones are correct? Or is using get, be it in -ing or the to infinitive, in any situation along with have incorrect? How align 2 adjacent divs horizontally WITHOUT float? Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$ I've been trying to solve this limit: $$\lim_{n\to \infty} \left(\cos\left(\frac{1}{n}\right)\right)^{n^2}$$ I solved it using l'hopital but I have to try in another way. I tried to make the expression:  $$ \lim_{n \to \infty}\exp\left(n^2\ln\left(\cos\left(\frac{1}{n}\right)\right)\right)$$  but it didn't work out for me... Given that $\displaystyle{a+b\sqrt[3]{2} +c\sqrt[3]{4} =0}$, where $a,b,c$ are integers. Show $a=b=c=0$  Do I use modular arithmetic? How do I set up shared folders in a Windows Virtualbox guest? I have installed VirtualBox OSE on Ubuntu 11.04 and Windows XP pro as the virtual machine. Now I want to have a shared folder which can be accessed on both, my host Ubuntu machine, and my WinXP guest virtual machine.  How can I do that? xslt, javascript and unescaped html entities i have a tiny little problem with xslt, js and html entities, eg. within a template:  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &amp;lt; 5; i++) {         //            ^^^ js error     } &lt;/script&gt;  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &lt; 5; i++) {         //            ^ xslt error     } &lt;/script&gt;  &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     // &lt;![CDATA[     for (var i = 0; i &lt; 5; i++) {         //            ^ becomes &amp;lt;     }     // ]]&gt; &lt;/script&gt;   &lt;script type="text/javascript"&gt;     &lt;xsl:value-of select="/some/node"/&gt;     for (var i = 0; i &lt;xsl:value-of disable-output-escaping="yes" select="string('&amp;lt;')"/&gt; 5; i++) {         // works of course     } &lt;/script&gt;   does anyone have an idea where my problem could come from? i always thought the xslt processor would leave the content of a &lt;script/&gt; element unescaped when using the html output method ...  i run libxslt2 version 1.1.24 on OSX which was installed using macportsports ... How full is too full for mechanical hard drives? I have heard many claim that it doesn't matter how full a drive is until it starts cutting into temp and virtual memory space.  This doesn't make sense to me, given the nature of how the data is transacted on a hard drive. The inside of the platter presents less data per revolution than the outside of the drive does, by significant factors. The inside 40% of the radius of full size hard drive is used for the spindle, so only the outside 60% is used for data storage, but that still means that the inside track of a hard drive presents data 60% slower than the outside track.  By my calculation, a Hard drive that is only 10% full should perform about 2.25 times faster than a hard drive that is 90% full, assuming that the flow is constrained by other factors.  Am I wildly off base here? For all the drives I know, even the top speeds of the first 1% of the drive would be well within the bandwidth provided by a SATA 2 connection. Make all new files in a directory accessible to a group Suppose I have two users Alice and Bob and a group GROUPNAME and a folder foo, both users are members of GROUPNAME (using Linux and ext3).   If I save as user Alice a file under foo, the permissions are: -rw-r--r-- Alice Alice. However, is it possible to achieve that every file saved under some subdirectory of foo has permissions -rwxrwx--- Alice GROUPNAME (i.e. owner Alice, group GROUPNAME)? Browsing  I came across this:  The conjugacy class of an element $g\in A_{n}$:  splits if the cycle decomposition of $g\in A_{n}$ comprises cycles of distinct odd length. Note that the fixed points are here treated as cycles of length $1$, so it cannot have more than one fixed point; and does not split if the cycle decomposition of $g$ contains an even cycle or contains two cycles of the same length.   Anybody with a proof? The  claims that likelihood and probability are distinct concepts.     In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that is the probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes.    Can someone give a more down-to-earth description of what this means?  In addition, some examples of how "probability" and "likelihood" disagree would be nice. Uninstalling Ubuntu from Windows Dual Boot if I don't have Windows recovery CD I installed Ubuntu (I had already had Windows 8.1) from USB (I still have live Ubuntu on it). Is there a way I can uninstall Ubuntu in a way that my Windows will remain bootable? All the tutorials I have seen say that uninstalling ubuntu will delete GRUB also so I will need a Windows recovery CD to boot into it, but I don't have one. Is there a solution? A film or TV series about classic monsters getting together I'm being asked to find 2 subgroups of $S_3$, one of which is normal and one that isn't normal. I guess, to find the non normal subgroup is easier. I would do this by trial and error, but since the group is $S_3$ and easily visualizable, I guess that there should be a geometrical property that makes it easy to find a normal subgroup. Any of you guys know one? Or should I try this by brute force? How to have full bleed between two facing pages Indesign Restore a large number of transaction logs I'm using SQL Server 2008 R2, and I need to restore 36 .trn logs to a database. I have restored the first 4 using the restore transaction log functionality in SSMS (right-click database > tasks > restore > transaction log).   Is there a way to restore them all in order using this tool or with a script? The .trn files are in a folder on a remote server. I do not not need to restore all the files in the folder, only ones between specific dates.  I'm looking for a way to automate this so I don't have to manually restore each individual log.  I access the files using an address like the one below.  \\remote server IP\SQL_Backup\LMSQL02\TLog\file.trn Any way to have CPU temperature in the menu bar? I tried  and  but it does not update the temperature and I do not wish to change the fan speed. I do not have much experience in table design. My goal is to create one or more product tables that meet the requirements below:   Support many kinds of products (TV, Phone, PC, ...). Each kind of product has a different set of parameters, like:   Phone will have Color, Size, Weight, OS... PC will have CPU, HDD, RAM...  The set of parameters must be dynamic. You can add or edit any parameter you like.   How can I meet these requirements without a separate table for each kind of product?