Symmetric algebra and exact sequences
Symmetric powers of modules
Getting full JS autocompletion under Sublime Text What registers to save in the ARM C calling convention? It's been a while since I last coded arm assembler and I'm a little rusty on the details. If I call a C function from arm,  I only have to worry about saving r0-r3 and lr, right?  If the C function uses any other registers, is it responsible for saving those on the stack and restoring them? In other words, the compiler would generate code to do this for C functions.   For example if I use r10 in an assembler function, I don't have to push its value on the stack, or to memory, and pop/restore it after a C call, do I?  This is for arm-eabi-gcc 4.3.0. I met an interesting issue about C#. I have code like below.  List&lt;Func&lt;int&gt;&gt; actions = new List&lt;Func&lt;int&gt;&gt;();  int variable = 0; while (variable &lt; 5) {     actions.Add(() =&gt; variable * 2);     ++ variable; }  foreach (var act in actions) {     Console.WriteLine(act.Invoke()); }   I expect it to output 0, 2, 4, 6, 8. However, it actually outputs five 10s.  It seems that it is due to all actions referring to one captured variable. As a result, when they get invoked, they all have same output.  Is there a way to work round this limit to have each action instance have its own captured variable? Is there a tag in HTML that will only display its content if JavaScript is enabled? I know &lt;noscript&gt; works the opposite way around, displaying its HTML content when JavaScript is turned off. But I would like to only display a form on a site if JavaScript is available, telling them why they can't use the form if they don't have it.  The only way I know how to do this is with the document.write(); method in a script tag, and it seems a bit messy for large amounts of HTML. Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$. Let $X=(0,\infty)$. Define two metrics on $X$ by   $d_{1}(x,y)=|x-y|$ and   $d_{2}(x,y)=|x-y|+|\frac{1}{x}-\frac{1}{y}|$   for all $x, y \in{X}$.   Let $(x_{n})$ be a sequence in $X$ and $x\in{X}$.   Show  $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.  Note: $d_{1}$ and $d_{2}$ are then said to be equivalent metrics on $X$.  Since $d_{1}$ and $d_{2}$ are equivalent metrics, will it be sufficient to show $c*d_{2}(x,y)\leq{d_{1}(x,y)}\leq{C*d_{2}(x,y)}$?  So far I have the following: $d_{1}(x,y)=|x-y|\leq{|x-y|+|\frac{1}{x}-\frac{1}{y}|}=d_{2}(x,y)$. Therefore, $d_{1}(x,y)\leq{C*d_{2}(x,y)}$ where $C=1$. Is there a $c$ that would satisfy the left-hand side of the inequality?  Any help would be appreciated. (this is not homework) What is the easiest way to make a backup of an entire hard disk I got myself a dell laptop from the local computer store. Its a used machine with Windows Vista Home Basic on it. I want to load Ubuntu Desktop 10.10 though so I can do perl development. BUT I want to keep a copy of the entire harddrive with the dell utility partition and Windows Vista in case I want to go back. I was thinking I could image the drive but I not sure what to use, I don't have Ghost or anything, Someone had told me about Clonezilla. Would that work for me? Is it hard to use? Also I want to burn the data to a DVD or something more storable than a harddisk. Suppose $\{a_n\}$ is a sequence such that the subsequences $\{a_{2n−1}\}$ and $\{a_{2n}\}$ converge to the same limit, say $a$. Show that $\{a_n\}$ also converges to $a$. There are two 9-digit numbers on the back of the Global Entry card. The one on the upper left corner is the Known Traveler Number or PASSID. But on the upper right hand corner there is another 9-digit number, slightly larger than the PASSID. What is the purpose of this second 9-digit number? How can we replace $\sup$ with $\max$ in definition of subordinate norm for finite-dimensional vector space? Split a string by a delimiter in python How to produce a longer \sim with a small letter on top Can EU citizens travel to UK after Brexit with just an identity card? Gimp won't allow me to copy and paste a transparent image On the latest version of GIMP on my PC, whenever I try to copy a transparent image from the internet, GIMP will automatically fill in the transparent areas with the background color I have selected.  This is a non-issue on my Mac, but I need to do this work on my PC, so how can I make it recognize the alpha of the image and not fill it with the background color?  The image canvas that I'm working with does have an alpha channel, but that does not seem to make a difference. "Dare speak" vs. "dare to speak" vs "dares to speak" Which is the most appropriate improvement in the following     I am surprised that he dares speak in such a tone to his father.     a) he dares to speak b) he dare to speak c) he dare speak    I think the answer should be 'c' but the book says 'a'. Google map signed api key errors in Android This comes up every time I login, how do I remove this or fix it.  Thanks. Group of order $8p$ is solvable, for any prime $p$ Consider the following question:     Show that a group $G$ of order $8p$ is solvable, for any prime $p$.   I am kind of stuck, but here are my first attempts:  I chose the series of subroups $G&gt;H_8&gt;H_4&gt;H_2&gt;H_1=\{e\}$ where $H_k$ has order $k$. All of these subgroups exist due to Sylow's Theorems. We have the quotients $H_8/H_4\cong H_4/H_2 \cong H_2/H_1 \cong \mathbb Z/2\mathbb Z$, so $G&gt;H_8\rhd H_4\rhd H_2\rhd H_1=\{e\}$. Only the factor $G/H_8 \cong \mathbb Z/p\mathbb Z$ is causing me a headache, because although its of prime order (and hence abelian) I don't know whether $H_8$ is normal in $G$ (unless $p=2$).  If $p\ne 2$, then the number $k$ of Sylow $2$-subgroups is $1$ mod $2$. Since $k$ divides $|G|$ we might have $k=1$ or $k=p$. If we had $k=1$ then $H_8$ would be the only Sylow $2$-subgroup (and hence normal in $G$). But how could we show this?  Or is there even an easier way to approach this problem?  $\ $  edit: I am going to try a different approach: The case $p=2$ is clear. When $p=3$ or $p=7$ the group has order 24 or 56 and since the smallest simple non-abelian group has order 60, the group must also be solvable in these exceptional cases (as Mariano pointed out).  In any other case we get a Sylow $p$-subgroup $H_p$ of order $p$, which is is normal in $G$. The quotient $G/H_p$ has order $8=2^3$; and prime power order implies solvable. So $G/H_p$ is solvable and $H_p$ is also solvable. And since the composition factors of $G$ are those of $H_p$ together with those of $G/H_p$, we conclude that $G$ is solvable iff $H_p$ and $G/H_p$ are solvable, which is the case. Hence $G$ is solvable if $|G|=8p$. Which Jedi have served in the Rebellion? Besides Luke Skywalker, Kanan Jarrus, Ezra Bridger and Ahsoka Tano, which other Jedi, regardless of whether they were survivors of Order 66 or became one at a later point, served within the Rebellion's ranks during the Galactic Civil War?  Looking for both canon and Legends versions.  Edit: ok, just to clarify what would qualify as a Jedi for the answer. Loosely speaking, anyone who follow the ideals of the Jedi philosophy - a practitioner in the ways of the Force, a protector of the galaxy, and an opposer to the dark side - would count.   Only trained Force users, not aligned with the dark side, would count. They need to be able to consciously control their use of the Force to aid the Rebellion. This excludes Leia Members of the Jedi Order of the late Republic would obviously count. However, they need to have survived Order 66 (duh), did not renounce the Jedi ways nor succumbed to the dark side, and become a member of the Rebellion. This excludes the Grand Inquisitor nor Darth Vader, but includes Kanan Jarrus and, in Legends, Rahm Kota. Those who are killed in action after joining the Rebellion also count. However, you don't need to be an official member of the order to be counted. You could be opposed to what was wrong with the late order, but as long as you follow the ideals defined above, and identify with them, you are a Jedi at heart by the count of this question. This counts Ahsoka Tano, Luke Skywalker and Ezra Bridger among its number. They aren't in the old Jedi Order's roster, but they believe in what the Jedi are meant to be, and follow its ways in that regard. Galen Marek in Legends, when he genuinely turned to the ways of the light, even though he was still a user of dark side powers, would be one. It's the thought that counts.   So loosely speaking, that means members of the Rebellion who are trained Force sensitives and genuine good guys. I am trying to perform stepwise regression for variable selection in R.  In matlab, the stepwisefit function is able to work in n &lt; p problems. Trying to use step() for such problems i get the error message AIC is -infinity for this model, so 'step' cannot proceed. Is there a way to modify parameters so i can use step function? I've sometimes seen this construct, used to avoid repetitive handwriting, but I don't even know if it's proper English.  If it is, what is the name of this construct? I have no idea what to search for when looking it up...        Don't forget to buy eggs.   &emsp;"&emsp;&emsp;      "&emsp;&emsp;"&emsp;"&emsp;yogurt.   &emsp;"&emsp;&emsp;      "&emsp;&emsp;"&emsp;"&emsp;milk.