We are (4) travelers flying from Charlotte, North Carolina (Lufthansa) to Munich, Germany then on to Pisa, Italy.  All will have carry-on bags only. Is 1 1/2 hours enough time to get through customs in Munich?
I'm heading to India next week and have a connection in Munich, Germany. I made the mistake of booking a flight with only an hour and a half layover (freaking out!) and I'm wondering if I'll have to go through customs in Munich or if I can pass right on through.
Showing a set is closed under inverses Let $G$ be a finite group, say a group with $n$ elements, and let $\emptyset \neq S \subseteq G$. Suppose $e \in S$, and that $S$ is closed with respect to multiplication. Prove that $S$ is a subgroup of $G$.    Let $G = \{a_1, \ldots, a_n\}.$ Let $a_i \in G.$ Then any number of $a_ia_1, a_ia_2, \ldots, a_ia_n \in S,$ since $S$ is closed under multiplication. One of those $a_ia_j$ is $e$ since $e \in S.$ Then either $a_i$ or $a_j$ is $a^{-1}.$ Would this argument work? Is there a keyboard shortcut to "unselect" in Windows Explorer? I've had a very strange Finer error caused by recent macOS High Sierra betas that affected Macs running macOS 10.13 as well as macOS 10.12 Sierra. This error causes an entire Finder window to show visual artifacts when opening certain folders on either an APFS or HFS+ volume.  After moving the cursor or the affected Finder window, the window may look something like this;    Attempting to use Disk Utility to repair the affected volume does not resolve this issue, nor does restarting the affected Mac (even in Safe Mode).  Without formatting this disk, how can I prevent Finder from exhibiting this graphical error when opening particular folders? Can't log in using Firefox in Stack Overflow What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse(&quot;Active&quot;);  but that isn't a valid code. I have the two PGF nodes foo and bar positioned in a row.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document}   \begin{tikzpicture}[node distance=0.2cm,mynode/.style={rectangle,draw}]     \node[mynode] (foo)                {foo};     \node[mynode] (bar) [right=of foo] {bar};   \end{tikzpicture} \end{document}   How can I create a third node below those two nodes with the width of foo, bar and the node distance between them? Is there a way to do this with the fit library or is this the wrong approach? I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra dimensions, and all these dimensions need to fit together in a way such that the extra dimensions are compactified (with a Calabi-Yau or $G_2$ structure).   My question, however is not about the possible $10$, $11$ or $26$ dimensional manifolds that may be possible, but about whether string theorists consider space-time as somehow quantized (or discrete), or rather as a continuous manifold, or are both options possible? In other words, can strings move continuously through space, or are there a discrete set of locations where strings can be, and does string theory rule out one of the options?  How about the same question in loop quantum gravity (LQG)? Should I think of the spin networks in LQG as describing a discrete space-time?  Thanks for your insight, or any references you may be able to provide! Is there only a single Skywalker family? Given the size of the Empire, it seems highly probable that names would be reused. Although I'm not aware of any in canon, there must be other Skywalkers in the galaxy, leading me to my question.  Are there other Skywalkers in the galaxy, and are they mentioned in canon? Does Luke have any third cousins twice removed (etc.)?  Bonus points if you can attest to force sensitivity among the surname. How to animate multiple lines I wonder what would be the best way of animating multiple 2 dimensional lines in blender.  Lets say I have lots of line, that are parallel and have some sort of rule, kind of like a PCB board with hundreds of circuits.  The starting frame would be when nothing is visible and during the animation the lines would slowly build up from nothing all the way to the end forming the finished lines.  I have a couple of ideas that might work, but all include heavy hand animation, like:   grease pencil animation, drawing them one by one, converting to curve, then build up modifier some dynamic paint hack   There maybe other more efficient methods that I don't know of and if so, please let me know. What are Extension Methods? What are extension methods in .NET?    EDIT: I have posted a follow up question at add transistor model to LTspice I'm trying to add the mmbt3904lt1g model to LTspice. - I've copied its data from the MMBT3904LT1.LIB.txt in the standard.bjt library. - I've added an NPN to my schematic then I've changed its value to mmbt3904lt1g  - through the Edit->spice directive I've pasted the path to this library I thought it was all to use this device but no simulation is achieved.. I get only: Can't find definition of model "MMBT3904LT1g"  where I'm doing wrong ? Cancelling upvote on comment? As mentioned on :     For something that can be done so   easily by accident, there should be   the ability to undo mistakes.   I know that I have clicked several times on a comment up-vote without actually wanting to.  I would suggest being able to cancel the up-vote (maybe only for a couple of minutes or even less than a minute, no problem, as long as I can undo a miss-click). $$\sqrt{x + \sqrt{x + \sqrt{x + \cdots}}}= 5$$ I installed the latest Ubuntu today, 15.04. Spotify has stopped working. How can it be made to work again?  The Unity bar flashes green 4 or 5 times and then stops flashing. There are no error messages. It was installed successfully and played well on 14.10 till the upgrade a few hours ago. It just does not appear on the screen. Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$ Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$ Let $F$ be the field $\Bbb Q(\alpha_1,...,\alpha_k)$ where  $\alpha_i^2\in\Bbb Q\ \forall i$  I want to show that $\sqrt[3]{2}\notin F$  I thought if $\sqrt[3]{2}\in F$ then $\sqrt[3]{2}\in\Bbb Q\cup(\alpha_1,...,\alpha_k)$ but this is not a disjoint union so I'm not sure what to do... taking the square of $\beta:=\sqrt[3]{2}$ gives $2^{2/3}=\sqrt[3]{4}\notin\Bbb Q$ but that doesn't really advance things  So I'm looking for a hint How can I force a program to open in a specific desktop? I've created an environment where I use 3 different desktop configurations, but every time I reboot, I have to manually open each program in that target desktop to make it look like it did before.   So, I'd like to write a .bat file that can get all my programs running in their appropriate desktops. I'm wondering if something like this is possible:  "C:\Program Files (x86)\Mozilla Firefox\firefox.exe" -desktop:2 "C:\Program Files\My\Other\Software.exe" -desktop:3 ...etc.   Obviously, this example is not real, but I hope there's something similar. I don't care if it's hacky :) Finding Radii of Convergence for $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ Setting: Let $\sum a_n z^n$ have radius of convergence $R$.  We have that  $$ R = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} $$  via Hadamard's formula for the radius of convergence.  Question: What are the radii of convergence for (i) $\sum a_n z^{2n}$ and (ii) $\sum a_n^2 z^n$?  Attempt for $\sum a_n^2 z^n$:   For ease of notation, let $R_1$ and $R_2$ denote the radii of convergence for power series $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ respectively. From Hadamard's formula, we then have  $$ R_2 = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n^2 \right|^{1/n}} = \left( \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} \right)^2 = R^2 $$   But what about $R_1$? When you create a script via the Unity editor, it generates a script with some pre-formatted code.  using System.Collections; using System.Collections.Generic; using UnityEngine;  public class GenericClass : MonoBehaviour {      // Use this for initialization     void Start () {      }      // Update is called once per frame     void Update () {      } }   When I create a script, I am generally guaranteed to use additional code, such as a namespace or a custom editor. Furthermore, I almost always delete content from the automatically-generated script. Is there a way to change the automatic code generated by Unity? Continuous footnote numbering I would like footnote numbering to continue over pages and chapters. In my document it's reset every chapter. I'm using the report documentclass.