Hard links versus symbolic links: which one is faster / smaller?
Why do hard links exist?
Can't transfer purchases from iPhone to iTunes in iOS 9 After upgrading to iOS 9, I can't transfer purchases from my iPhone to iTunes. It happens to just start the process, then it finishes without transferring anything. However, I can still transfer purchases from my iPad with iOS 8.4 like before.   iPhone 5c, iOS 9 iTunes 12.3 MacBook Pro 13" with Retina Display Mid 2014, OS X El Capitan   Apparently, not many people happen to use this "transfer purchases" feature so it didn't get any real attention. I used it a lot, I used to update my apps on my iPhone, transfer them to iTunes and updated my iPad apps using iTunes. Still, I can update my apps using iTunes and update apps on all my devices. How does Ubuntu partition the disk when we choose "Erase disk and install Ubuntu" during installation? Dual boot with windows 7! I'm using windows 7 right now. I want to install Ubuntu with dual boot. Is is safe? And does the process go safely? Primary ideals in Noetherian rings For an $R$-module $M$ I have the following definition for a submodule $N\subset M$ to be $\mathfrak{p}$-primary: this is the case when $\text{Ass}(M/N) = \{\mathfrak{p}\}$, that is, $M/N$ is coprimary or $(0)$ is a primary submodule.  Now for an ideal $\mathfrak{q} \subset R$ this definition gives that $\mathfrak{q}$ is $\mathfrak{p}$-primary iff $\text{Ass}(R/\mathfrak{q}) = \{\mathfrak{p}\}$. It can be shown that this is equivalent with $\mathfrak{p}^n \subset \mathfrak{q}$ for some $n\in \mathbb{N}$ and the condition \begin{align*} \forall r,s \in R: rs \in \mathfrak{q}, r\not\in \mathfrak{p}\Rightarrow s \in \mathfrak{q}. \end{align*}     Now I suspect that if $R$ is Noetherian, and if $\mathfrak{q}$ is $\mathfrak{p}$-primary, then we have $\sqrt{\mathfrak{q}} = \mathfrak{p}$. I have shown this for PID's, but does this generaly hold?    And if so, is every ideal $\mathfrak{q}\subset R$ then $\sqrt{\mathfrak{q}}$-primary?   Many thanks. Let $Z_i,Z_2,\ldots$ be IID Random Variables with density $f$. Suppose that $P(Z_i&gt;0)=1$ and that $\lambda=\lim_{x \to 0+} f(x)&gt;0$. How can I show that $X_n=n \times \min\{Z_i\}$ has a limiting exponential distribution with mean$1/\lambda$?  I know that the CDF of the first order Statistic is for $t&gt;0$  $$F_{min \{ Z_i \}} (t)= 1- \left[ 1-F(t) \right]^{n}$$  Convergence in distribution requires that $F_n (t) \to F(t)$ for some distribution function $F$ but I cannot quite take the limit of the above, with $t$ replaced by $x/n$, as the distribution is not known. I guess I have to insert the second piece of information somewhere but I do not recognise where.  Could you please give me a hint or two?  Thank you. The thing with these tags is, you can always (or almost always) use a specific product/technology/language tag which would render the company-name tag completely redundant (see Appendix C for sloppy non-proof). For example, what relevant information would  tag add to  already tagged with ? What would  tag add to  already tagged with ? Another way of looking at this: how much useful information do you lose if you don't tag a question with a company name? Note: I'm not talking about brand/company/organizations like , , ,  because those names also refer to websites/web services with which you can interact via API or from which you can extract data. Appendix C: The &quot;about&quot; test The relationship between a tag and a question can be expressed as such  This question is about [tag]  In case of ,  This question is about [microsoft]  Fair enough. But in reality people are using these company-name tags like this  This question is about something developed by or related to [microsoft]  But if that's the case, you might as well just go with  This question is about [something developed by or related to microsoft]  where  can be , , ... you get the idea. Introduction to string theory I have  $m\times n = n + n + \dots + n$    in my text right now, but I would like to put a curly brace under the \dots to emphasize that there are m,n's involved. How would I do this? Short story about aliens who want to trade items for information, stories, jokes etc Does low disk space affect SSD performance? I was wondering if having less than 5-10GB of free space on an SSD would affect performance. Is it specific to SSD or is it more of an operating system aspect?  For example, on an Intel X-25 G2 that has TRIM support (on Windows 7). Equivalence of Categories and of Their Functor Categories Suppose $A, B, C$ are categories. If $A$ and $B$ are equivalent, is it the case that $C^A$ and $C^B$ are equivalent? Also, is it the case that $A^C$ and $B^C$ are equivalent.  I first conjectured that $C^A$ and $C^B$ are equivalent, but then as I tried to prove the conjecture, I started to realize that it might not be the case. So now I'm trying to find a counterexample. So far I have not been able to find one. Maybe I'm stuck with "too complicated" ideas. I strongly believe that there are very simple counterexamples. Please help. (For more detail, I got to the point where I have a cube that I want to be commutative, but I can only show that 4 of its sides are commutative squares. That's when I realize the other two sides may not necessarily commute.)  And of course, there is the second part to the problem that's not just the dual problem. I would like to know about the special case in which $A$ is a preorder and $B$ is a partial order which is the skeleton of $A$. This may have nothing to do with the validity of the statement in question at all, but it is the setting that originated this question. How to install with Wubi when it says "Could not retrieve the required disk image files"? Count if two criteria match while ignoring duplicates I have a simple Sheet with 2 cells that I need to countif 2 conditions match and treat  duplicates as 1.  Column A    Column B Male        closed Female      invalid # Male        exception Male        closed Male        closed Female      new   I would like a formula that counts Male closed and return 1 result (ignoring duplicates) Why is $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$? It seems as if no one has asked this here before, unless I don't know how to search.  The Gamma function is $$ \Gamma(\alpha)=\int_0^\infty x^{\alpha-1} e^{-x}\,dx. $$ Why is $$ \Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}\text{ ?} $$ (I'll post my own answer, but I know there are many ways to show this, so post your own!) In a Silverlight application I'm trying to find out when a property on a usercontrol has changed. I'm interested in one particular DependencyProperty, but unfortunately the control itself doesn't implement INotifyPropertyChanged.  Is there any other way of determining if the value has changed? Question:     Let $f$ be differentiable on $[0,+\infty)$, such as$$\lim_{x\to+\infty}\left([f'(x)]^2+f^3(x)\right)=0$$show that $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$$   I think this problem is similar to  and (the  background)  For my problem I guess that if  $$\lim_{x\to+\infty}\left([f'(x)]^{2m}+f^{2n+1}(x)\right)=0,m,n\in N^{+},n,m&gt;1$$ then we have $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$. KOMA-Classes (scrbook, scrreprt, ... ): Disable chapter separation in \listoffigures and \listoftables I use \listoffigures and \listoftables. Both commands create line breaks for items from different chapters. How can you stop that?  Screenshot: How do I earn SC2's "Hurry up, it's raid night" achievement? The "Hurry up, it's raid night" achievement in Starcraft 2 involves "beating Wings of Liberty, on normal, in 8 hours or less."  Is there a recommended mission path to take? Which mission should I take for the branching paths? Does it count time spent on the Hyperion in between missions, or is it exclusively time elapsed on missions. Does replaying a mission affect the time? General tips / hints from those who've unlocked the achievement?  Edit: Just got this achievement tonight, finally! The answer was perfect. If column matches another file, print every line with match (awk/grep) I’m taking two input files, one with certain ID numbers, and another with a large list of ID numbers and additional columns. The latter file contains multiple lines for each ID number and I need to extract all lines that match an ID from the first file. Those lines then must be printed in a new file.  Edit 1: Replaced sample files with excerpts from actual  Edit 2: Removed extra spaces that were in excerpt, but not actual file. Files likely need to be sanitized in some way, but how is unclear.  file1:  AT1G56430 AT3G55190 AT3G22880   file2:  AT1G01010|GO:0043090|RCA AT1G56430|GO:0010233|IGI  AT1G56430|GO:0009555|IGI  AT1G56430|GO:0030418|IGI   expected output  AT1G56430|GO:0010233|IGI  AT1G56430|GO:0009555|IGI  AT1G56430|GO:0030418|IGI   [[  I have tried:  awk -F'|' 'NR==FNR{c[$1$2]++;next};c[$1$2] &gt; 0' file1 file2 &gt; output.txt   and:  grep -Ff file2 file1 &gt; output.txt   I’m aware that there are many somewhat similar questions posted in these forums and others. However, these don’t mention how the output is handled… nor do they mention duplicates. I’ve tried solutions from 4 of them, have been messing with this for many hours and keep getting the same problem: a blank output file.   I’m new to awk and I greatly appreciate the help. Sorry if this is a simple problem with syntax etc; please let me know. Thanks for the help. I had parked my follower at an inn with a bunch of valuable items that I didn't want to carry. I guess I have been out a bit too long as this message appears:      Your follower tires of waiting and leaves.    There have been other situations where my follower has mysteriously disappeared as well.  How can I find my follower when they get up and leave or disappear into thin air?