Java Collections: which collection to use and when?
Which Java Collection should I use?
What do I do? I looked at a similar question to mine and there was an answer saying to make sure Java is allowed past the firewall. So I checked and it already is. I've tried uninstalling and installing both Minecraft and Java but nothing has changed.  says that all services are fine, so what's going on? I bought a 2nd account to use as an alternative in-game account and now I can't log in.  (I cleared the email and password boxes for obvious reasons in this screenshot: security purposes) Grub rescue after installing Ubuntu on a external HDD from USB Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$ Prove that      $$ \int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}\,dx = \ln\left(\frac{a}{b}\right) $$   My Attempt:  Define the function $I(a,b)$ as  $$ I(a,b) = \int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}\,dx $$  Differentiate both side with respect to $a$ to get  $$ \begin{align} \frac{dI(a,b)}{da} &amp;= \int_{0}^{\infty}\frac{0-e^{-ax}(-x)}{x}\,dx\\ &amp;= \int_{0}^{\infty}e^{-ax}\,dx\\ &amp;= -\frac{1}{a}(0-1)\\ &amp;= \frac{1}{a} \end{align} $$  How can I complete the proof from here? Transfer from JFK Terminal 2 to Terminal 4 I have family who does not speak English.  They are changing planes in JFK Airport and will most likely be transferring from Terminal 2 (Delta) to Terminal 4 (China Southern Airlines).  At first I thought that directing them to use the Airtrain would be best.  However, in doing more reading my understanding is that the Airtrain would mean they would need to go through security again.  I found this on Delta's site:   If they use the JITNEY Shuttle to change from Terminal 2 to Terminal 4, does that mean they would not need to re-clear Security?  Edit: They are flying TO China. They are going from Tampa -> NY JFK -> China. List creation/manipulation Can "mustn't" be used for conclusions? I heard this sentence in an American film a while ago as I was watching it on DVD (the part after but is verbatim):  "I'm doing my best but I mustn't be doing it right."  This is something I occasionally hear in American films: phrases like "he mustn't have done it" or "she mustn't be studying now", where a logical conclusion is expressed. So far I've thought that the normal thing to say is "he can't have done it" or "she can't be studying now".  My question is: Can mustn't be used to express a logical conclusion when the speaker is certain that something didn't happen or isn't happening, at least in informal speech? Is this an American usage? (I've never heard this usage in British English, but this doesn't mean it doesn't exist.) Is there a change going on in the usage of the particular modal verb?  Note: All the references I've checked don't even mention this use of mustn't. Google books aren't of help either.   EDIT: I should clarify that I'm asking this question because if I wanted to express that I'm certain I'm not doing something right (as in the sentence quoted from the film) I'd say "I'm doing my best but I can't be doing it right". I would think that the use of mustn't/must not wouldn't be standard usage (although the meaning is perfectly clear to me; I never mistook it for an injuction). Use laptop trackpad as graphics tablet I have this problem I'm working on. Hints are much appreciated (I don't want complete proof):  In a normed vector space, if $ x_n \longrightarrow x $ then  $ z_n = \frac{x_1 + \dots +x_n}{n} \longrightarrow x $   I've been trying adding and subtracting inside the norm... but I don't seem to get anywhere.  Thanks! XGBoost Loss function Approximation With Taylor Expansion As an example, take the objective function of the XGBoost model on the $t$'th iteration:  $$\mathcal{L}^{(t)}=\sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)}+f_t(\mathbf{x}_i))+\Omega(f_t)$$  where $\ell$ is the loss function, $f_t$ is the $t$'th tree output and $\Omega$ is the regularization. One of the (many) key steps for fast calculation is the approximation:  $$\mathcal{L}^{(t)}\approx \sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)})+g_tf_t(\mathbf{x}_i)+\frac{1}{2}h_if_t^2(\mathbf{x}_i)+\Omega(f_t),$$  where $g_i$ and $h_i$ are the first and second derivatives of the loss function.   What I'm asking for is convincing arguments to demystify why the above approximation works:  1) How does XGBoost with the above approximation compare to XGBoost with the full objective function? What potentially interesting, higher-order behavior is lost in the approximation?  2) It's a bit hard to visualize (and depends on the loss function) but, if the loss function has a large cubic component, then the approximation will likely fail. How is it that this doesn't cause problems for XGBoost? Isomorphism of $S^1$. A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$ An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal This result appears to be ubiquitous as an algebra exercise. How do you prove this result?     Let $A$ be an integral domain with field of fractions $K$, and let $A_{\mathfrak{m}}$ denote the localisation of $A$ at a maximal ideal $\mathfrak{m}$ considered as a subring of $K$. Prove that $$A = \bigcap_{\mathfrak{m}} A_{\mathfrak{m}}\,,$$ where the intersection is taken over all maximal ideals $\mathfrak{m}$ of $A$. Reputation graph not interactable with a touch screen What is the method for converting radians to degrees? I run into this occasionally and always forget how to do it.  One of those things that pop up ever so often.  Also, what's the formula to convert angles expressed in radians to degrees and back again? Any way to find out what US Customs & Border Protection has in their database on me? I travel from the US to Canada occasionally (about once per year on average) with my family. We are all US citizens and travel with US passports. Every time we re-enter the United States, I am given extra scrutiny.  Most recently, we used an automated check-in procedure at the airport. These are terminals where you scan your passport &amp; fill out a customs declaration online and it prints a receipt which you take to the customs agent. When I got my receipt, it had a big "X" printed on it and we were directed to a line to talk to an agent.  In the past, I've had questions directed at me or my family: "Have you ever been to New York?", "Do you own any firearms?", and once "Where is your daddy?" directed at my then 4 year old son. The agents also seem to examine my photo &amp; my face more closely than the other members of my family.  We get through customs OK, but it gives me a some anxiety. I suspect that there's someone out there with the same name (I have a pretty common name) who is on a "no fly" list or something.  My question is this: is there any way to find out what they're looking for when they scan my passport &amp; see my name? Like a Freedom of Information request or something? I know I could/should ask when I'm in the line, but as I said, it makes me pretty anxious. Keyboard shortcut for switching between different keyboard layouts in Ubuntu Mate Is there a pre-assigned keyboard shortcut for switching between different keyboard layouts in Ubuntu Mate? Cannot find hard drives after installing Ubuntu 13.10 When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation) I need an appearing effect for text like the one (in javascript) here .  However I don't know how to insert js code into LaTeX (apart from using the AcroTeX Bundle) and that would also force me to use Acrobat Reader, so I'd like to implement a similar effect in Beamer. Is it possible?  (of course I would love to see alternative approaches to this) Activating 'missing' standard GRASS utilities in QGIS Processing toolbox