How can I add some new tag set in my Stack Overflow account to get notification, if a new question is asked by a user for that particular tag set?
Is there a way to configure your Stack Overflow account so that you receive notification emails when posts are made to specific tags?    Or do you simply have to log on to see new posts?
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$. Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.  I'm not really sure of how I should proceed to show this, and it's pretty un-intuitive as well.  I've managed to manipulate the RHS into  $$\frac{e^{4\beta}}{\sqrt{\pi}} \int_0^\infty \frac{1}{\sqrt{u}} e^{-(\beta+2u)^2/4u} du$$ which now vaguely resembles a Gaussian. However, substituting $v = \beta + 2u$ in in order to to get something like $e^{-x^2}$ doesn't particularly help. I got $$ \frac{e^{4\beta}}{\sqrt{2\pi}} \int_0^\infty \frac{1}{\sqrt{v - \beta}} e^{-v^2/2(v-\beta)} dv. $$  I'm really unsure of how I should proceed; any help would be appreciated. Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$. $|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$. Appending to an ObjectOutputStream How do I use the conditional (ternary) operator? I've always wondered how to write the "A ? B : C" syntax in a C++ compatible language.  I think it works something like: (Pseudo code)  If A &gt; B    C = A Else    C = B   Will any veteran C++ programmer please help me out? Both DHCP and static IP addresses simultaneously on one interface We can use multiple IP addresses for a single interface in Linux (eg. eth0:0, eth0:1). But can we use DHCP and static IP at the same time? eth0:1 should have a static IP address and eth0:0 should be configured using DHCP.  How can we accomplish both? I have a problem understanding the proof of Rencontres numbers (Derangements) I understand the whole concept of Rencontres numbers but I can't understand how to prove this equation  $$D_{n,0}=\left[\frac{n!}{e}\right]$$  where $[\cdot]$ denotes the rounding function (i.e., $[x]$ is the integer nearest to $x$). This equation that I wrote comes from solving the following recursion, but I don't understand how exactly the author calculated this recursion.  $$\begin {align*}  D_{n+2,0} &amp; =(n+1)(D_{n+1,0}+D_{n,0}) \\ D_{0,0} &amp; = 1 \\ D_{1,0} &amp; = 0  \end {align*} $$ How do I prompt for Yes/No/Cancel input in a Linux shell script? How do I get started with 'painting with light' photography? Tunnels being naturally dark may not be the most intuitive choice for a place to take pictures. But I love the '' work that artists such as '' are putting out and they're clearly seeking out places like tunnels, caves, garages... Dark places in other words, to create their works of art. Which brings two questions to mind:   How do I go about finding places that I can accomplish this sort of 'tunnel photography.' What are some techniques that I can use to 'paint with light' in my photography once I have found some locations? Purely "algebraic" proof of Young's Inequality states that if $a, b \geq 0$, $p, q &gt; 0$, and $\frac{1}{p} + \frac{1}{q} = 1$, then $$ab\leq \frac{a^p}{p} + \frac{b^q}{q}$$ (with equality only when $a^p = b^q$).  Back when I was in my first course in real analysis, I was assigned this as homework, but I couldn't figure it out.  I kept trying to manipulate the expressions algebraically, and I couldn't get anywhere.  But every proof that I've seen since uses calculus in some way to prove this.  For example, a common proof is based on this  and integration.  The proof on Wikipedia uses the fact that $\log$ is concave, which I believe requires the analytic definition of the logarithm to prove (correct me if I'm wrong).  Can this be proven using just algebraic manipulations?  I know that that is a somewhat vague question, because "algebraic" is not well-defined, but I'm not sure how to make it more rigorous. But for example, the proof when $p = q = 2$ is something I would consider to be "purely algebraic":  $$0 \leq (a - b)^2 = a^2 + b^2 - 2ab,$$ so $$ab \leq \frac{a^2}{2} + \frac{b^2}{2}.$$ How do you maximize the cycle count of your battery?  There seems to be a debate between:   Leave plugged in 24/7 but do a full cycle once a month Charge to ~100%, drain to ~10%, repeat.   NOTE: Taking your   Which method is better and why? How much of a difference does it really make?  Here are some of the better sources I've found about battery behavior so far. Even still I feel they don't conclusively answer the question above. See my elaborations below:           Elaborating on Option 1  Now IF Apple engineers were smart and optimized for AC draw when plugged in to not use up your charge cycles, then it seem logical to assume that you are using effectively none of your 1000 charge cycles while plugged in. If that's the case, it would seem that the LiPo drop from holding at 100% would be vastly outweighed by the fact you're not using any charge cycles.  However, this is a purely speculative assumption and I could find no evidence to either confirm or deny.  If this is NOT true, and the AC adapter only goes to charging the battery, then there would be no difference. Your battery would drain to 99%, then back up to 100%, then back down to 99%, etc. Those micro-charge cycles would add up at the same rate as 100% -> 0% -> 100%, and you would get no gain. In this case the negative effect of holding LiPo batteries at 100% would outweigh everything else.  Elaborating on Option 2  There are lots of good reasons why Option 2 is the way it is:   Because of known LiPo chemistry issues, holding a 100% charge for a long time causes the battery to degrade Apple specifically recommends not to leave it plugged in all the time  Draining a battery all the way to zero all the time is bad for the cell (Which is why ~10% is used) Heat is a killer, and when plugged in AND charging, you get extra heat that causes damage.   There are a couple reasons why I'm challenging Option 2:   It seems silly that the most intuitive use case for thousands of people that use their macs as primary computers is wrong. If the hypothesis in option 1 is true, you're just burning unnecessarily through your finite charge cycles. It's a pain to have to remember to keep plugging in and plugging out and be worried about whether or not your device is plugged in. Where can I find a list of all the Stack Exchange sites?  I need to ask a question about cars (where my total knowledge is about zero) but I can't find a cars Stack Exchange site - tried guessing all the obvious (and pun based) names.  I assume the list of a dozen or so at the bottom of this page is only a subset? There must be a site on a topic as geeky as cars!  A list of future/beta sites would also be useful - I found a few on topics I'm interested in only after they had been up for a while. Login not redirecting back to page where login link was clicked if account created Please let me know how to remove certain repositories in Ubuntu 11.04. I am getting the following errors while updating.  sudo apt-get update  Err http://ppa.launchpad.net natty/main Sources                                      404  Not Found Err http://ppa.launchpad.net natty/main i386 Packages                                404  Not Found ......  E: Some index files failed to download. They have been ignored, or old ones used instead. Does iOS have a firewall? Does iOS support a built-in firewall like macOS does? I don't see anything about it in Settings. What is the noun for someone who receives a referral? When a referrer (noun) gives a referral (noun) to another person, what is the term (noun) used for the recipient of the referral? "The referred" may work, but am I missing another term? "Referred" indicates past-tense, but I intend to use the term in future and present tense as well. My computer name in System Preferences &gt; Sharing is set to &quot;archos&quot;, but is showing as &quot;iphone&quot; on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this? Is the function $\mbox{tr}(XAX')$ convex? Is the function $\mbox{tr}(XAX')$ convex, where $A$ is a positive semidefinite (PSD) matrix? I know that for a general $A$, the above trace function is not convex. But for a PSD $A$, is the function convex? java.lang.IllegalArgumentException: The servlets named [X] and [Y] are both mapped to the url-pattern [/url] which is not permitted I'm trying to move some data over and to start with I'd like to make sure that the size is ok. I run into a problem however, if I check the folder with   du -sh  myfolder/ 780M    myfolder/   but   du -sh * .. 71M     myfolder ..   I thought it might be something to do with hidden files but this particular folder does not have any inside.  Am I missing something?