Can a non-EU citizen travel freely within the Schengen area without passport?
Travel in schengen countries without carrying passport for non EU citizen
Help with proving that $\pi$ is irrational Why does the natural ring homomorphism induce a surjective group homomorphism of units? I'm trying an old problem here:   Suppose $n\mid m$, and I have a natural ring homomorphism $\varphi\colon \mathbb{Z}/m\mathbb{Z}\to\mathbb{Z}/n\mathbb{Z}$ defined by $\varphi(j)=j\mod{n}$. I can verify that this is a ring homomorphism, but why does it induce a surjective group homomorphism on the unit groups $(\mathbb{Z}/m\mathbb{Z})^\times\to(\mathbb{Z}/n\mathbb{Z})^\times$?  My question in particular is why is it surjective? I take $k\in(\mathbb{Z}/n\mathbb{Z})^\times$. Then there exist integers $s,t$ such that $sn+tk=1$. Since $n\mid m$, I can also write $m=na$. So multiplying through I get $sm+tka=a$. I'm lost here. How can I find a unit in $(\mathbb{Z}/m\mathbb{Z})^\times$ which maps to $k$ to show surjectivity? How variance is defined? Diagonalizable Operators and characteristic polynomials Can I change the color of the last selected face, so that it is the same as the other selected faces?  Here, I've selected the left face then the right face. Note the right face is some sort of checkered or dithered pattern, and just the outline has the nice orange 'selected' color.    Here I've selected the top face, note the right face has now the nice color.    And here I've deselected the top face. Now, both of the remaining selected faces have the nice color. This is the result I'd rather see instead of image 1. Are planets actually moving in elliptical orbits around the Sun or do they move in circular orbits around their center of mass? In every derivation of Kepler's Laws that I have seen, we assume that the sun is stationary. However, in other places I have read that celestial bodies move about their barycentre (center of mass). So are planets actually moving in elliptical orbits around the Sun or do they move in circular orbits around their center of mass? I go to the Minecraft menu and click on singleplayer to test out the 1.9 update. I made a new world (no mods), it said downloading terrain and then it crashes every time (I've tried about 20 times now).  Has anyone else experienced similar issues and know what the fix may be?  Here is the launcher log:  Completely ignored arguments: [--nativeLauncherVersion, 301] [00:35:12] [Client thread/INFO]: Setting user: Teddy_Cromwell [00:35:12] [Client thread/INFO]: (Session ID is &lt;censored&gt;) [00:35:14] [Client thread/INFO]: LWJGL Version: 2.9.4 [00:35:14] [Client thread/WARN]: Removed selected resource pack resources (no region and battle music).zip because it's no longer compatible [00:35:14] [Client thread/INFO]: Reloading ResourceManager: Default [00:35:15] [Sound Library Loader/INFO]: Starting up SoundSystem... [00:35:16] [Thread-5/INFO]: Initializing LWJGL OpenAL [00:35:16] [Thread-5/INFO]: (The LWJGL binding of OpenAL.  For more information, see http://www.lwjgl.org) [00:35:16] [Thread-5/INFO]: OpenAL initialized. [00:35:16] [Sound Library Loader/INFO]: Sound engine started [00:35:18] [Client thread/INFO]: Created: 1024x512 textures-atlas [00:35:26] [Server thread/INFO]: Starting integrated minecraft server version 1.9 [00:35:26] [Server thread/INFO]: Generating keypair [00:35:27] [Server thread/INFO]: Preparing start region for level 0 [00:35:28] [Server thread/INFO]: Preparing spawn area: 5% [00:35:29] [Server thread/INFO]: Preparing spawn area: 8% [00:35:30] [Server thread/INFO]: Preparing spawn area: 15% [00:35:31] [Server thread/INFO]: Preparing spawn area: 21% [00:35:32] [Server thread/INFO]: Preparing spawn area: 27% [00:35:33] [Server thread/INFO]: Preparing spawn area: 34% [00:35:34] [Server thread/INFO]: Preparing spawn area: 42% [00:35:35] [Server thread/INFO]: Preparing spawn area: 48% [00:35:36] [Server thread/INFO]: Preparing spawn area: 56% [00:35:37] [Server thread/INFO]: Preparing spawn area: 66% [00:35:38] [Server thread/INFO]: Preparing spawn area: 74% [00:35:39] [Server thread/INFO]: Preparing spawn area: 81% [00:35:40] [Server thread/INFO]: Preparing spawn area: 91% [00:35:41] [Server thread/INFO]: Preparing spawn area: 98% [00:35:42] [Server thread/INFO]: Teddy_Cromwell[local:E:6d7525a7] logged in with entity id 301 at (244.5, 69.0, 244.5) [00:35:42] [Server thread/INFO]: Teddy_Cromwell joined the game # # A fatal error has been detected by the Java Runtime Environment: # #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x00007fffcf6e6b37, pid=15456, tid=12424 # # JRE version: Java(TM) SE Runtime Environment (8.0_25-b18) (build 1.8.0_25-b18) # Java VM: Java HotSpot(TM) 64-Bit Server VM (25.25-b02 mixed mode windows-amd64 compressed oops) # Problematic frame: # C  [ig8icd64.dll+0x16b37] # # Failed to write core dump. Minidumps are not enabled by default on client versions of Windows # # An error report file with more information is saved as: # C:\Users\Connor\AppData\Roaming\.minecraft\hs_err_pid15456.log # # If you would like to submit a bug report, please visit: #   http://bugreport.sun.com/bugreport/crash.jsp # The crash happened outside the Java Virtual Machine in native code. # See problematic frame for where to report the bug. # AL lib: (EE) alc_cleanup: 1 device not closed Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release AMPscript Error with XML I have a Partner sending some data to a Triggered Email/Data Extension which includes a column for XML data.   The trigger is erroring and not allowing the data to get to the Data Extension.   Below is what they are sending over. Is the formatting of the XML incorrect?  XML data that I've used in the past in Data Extensions starts with....   &lt;?xml version="1.0" encoding="UTF-8" standalone="yes"?&gt;   This version of XML starts with... {"XML":  Could that be it?  {"To": {"SubscriberKey": "test@acme.com", "ContactAttributes": {"SubscriberAttributes": **{"XML":** "&lt;root&gt;&lt;ITEM&gt;&lt;ITEM_PRODUCT_NAME&gt;dark chocolate nuts &amp; sea salt&lt;/ITEM_PRODUCT_NAME&gt;&lt;ITEM_PRODUCT_SKU&gt;15127&lt;/ITEM_PRODUCT_SKU&gt;&lt;ITEM_PRODUCT_URL&gt;https://www.test.com/15127.html&lt;/ITEM_PRODUCT_URL&gt;&lt;ITEM_PRODUCT_IMG_URL&gt;https://www.test.com/images/nuts.png&lt;/ITEM_PRODUCT_IMG_URL&gt;&lt;ITEM_QTY&gt;1&lt;/ITEM_QTY&gt;&lt;ITEM_SUBSCRIPTION_PRICE&gt;12.59&lt;/ITEM_SUBSCRIPTION_PRICE&gt;&lt;ITEM_TOTAL&gt;12.59&lt;/ITEM_TOTAL&gt;&lt;/ITEM&gt;&lt;ITEM&gt;&lt;ITEM_PRODUCT_NAME&gt;crunchy peanut butter&lt;/ITEM_PRODUCT_NAME&gt;&lt;ITEM_PRODUCT_SKU&gt;41800&lt;/ITEM_PRODUCT_SKU&gt;&lt;ITEM_PRODUCT_URL&gt;https://www.test.com/images/butter.png&lt;/ITEM_PRODUCT_IMG_URL&gt;&lt;ITEM_QTY&gt;1&lt;/ITEM_QTY&gt;&lt;ITEM_SUBSCRIPTION_PRICE&gt;11.37&lt;/ITEM_SUBSCRIPTION_PRICE&gt;&lt;ITEM_TOTAL&gt;9.55&lt;/ITEM_TOTAL&gt;&lt;/ITEM&gt;&lt;ITEM&gt;&lt;ITEM_PRODUCT_NAME&gt;pear cinnamon &amp; pecan&lt;/ITEM_PRODUCT_NAME&gt;&lt;ITEM_PRODUCT_SKU&gt;17227&lt;/ITEM_PRODUCT_SKU&gt;&lt;ITEM_PRODUCT_URL&gt;https://www.test.com&lt;/ITEM_PRODUCT_URL&gt;&lt;ITEM_PRODUCT_IMG_URL&gt;https://www.test.com/images/apples.png&lt;/ITEM_PRODUCT_IMG_URL&gt;&lt;ITEM_QTY&gt;1&lt;/ITEM_QTY&gt;&lt;ITEM_SUBSCRIPTION_PRICE&gt;12.59&lt;/ITEM_SUBSCRIPTION_PRICE&gt;&lt;ITEM_TOTAL&gt;12.59&lt;/ITEM_TOTAL&gt;&lt;/ITEM&gt;&lt;/root&gt;", "SHIPPING_LNAME": "Tester", "FIRST_NAME": "Test", "LAST_NAME": "Tester", "ORDER_TOTAL_SAVINGS": -5.97, "MERCHANT_ORDER_ID": "1810002352", "SHIPPING_ADDRESS_STATE": "NY", "ORDER_PLACE_DATE_LONG": "Fri 11 January 2019", "SHIPPING_ADDRESS_ZIP": "10004", "ORDER_SHIPPING": 0.00, "CARD_TYPE": "Visa", "ORDER_SUBTOTAL": 47.32, "ORDER_PLACE_DATE_SHORT": "01/11/2019", "SHIPPING_FNAME": "Test", "SHIPPING_ADDRESS_TOWN": "new york", "ORDER_TOTAL": 47.32, "CARD_EXPIRE": "12/2027", "CARD_HOLDER": "Test Tester", "SHIPPING_ADDRESS_1": "75 broad st", "SHIPPING_ADDRESS_2": "fl 23"}}, "Address": "acme@test.com"}}   AMPSCRIPT IN EMAIL Calling the XML....  %%[   var @LOOPINGAPPENDIX  set @LOOPINGAPPENDIX = AttributeValue("LOOPINGAPPENDIX")  set @productRows = BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM", 0)  ]%%   %%[   for @j = 1 to RowCount(@productRows) do       set @productXML = Concat("", Field(Row(@productRows, @j), "XML"), "")      set @ITEMPRODUCTNAME = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_NAME", 0), 1), "Value"))      set @ITEMPRODUCTSKU = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_SKU", 0), 1), "Value"))      set @ITEMPRODUCTURL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_URL", 0), 1), "Value"))      set @ITEMPRODUCTIMGURL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_PRODUCT_IMG_URL", 0), 1), "Value"))      set @ITEMQTY = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_QTY", 0), 1), "Value"))      set @ITEMSUBSCRIPTIONPRICE = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_SUBSCRIPTION_PRICE", 0), 1), "Value"))      set @ITEMTOTAL = Trim(Field(Row(BuildRowSetFromXML(@LOOPINGAPPENDIX, "/root/ITEM/ITEM_TOTAL", 0), 1), "Value"))      set @rowColor = Iif(Mod(@j,2) == 0, "#efefef", "#ffffff")   ]%%   %%[endif]%%   %%[next @j]%% Do Hutts find humanoid females attractive, and if so why? Jabba the Hutt kept scantily clad humanoid slaves.  Jabba even tried to kiss Leia.  But IIRC Hutts are hermaphrodites and of course should by all biological reasoning not be attracted to creatures of a specific sex (don't recall sexy dudes hanging around) with radically different body design.  So do Hutts find humanoid females hot, and if so why?  Or do they just do this for status and to show off to the largely humanoid populations that surround them? Browsing the internet from the command line How can I browse the Internet from the command line in Ubuntu? It confuses/blows my mind that the Binomial has variance proportional to $p(1-p)$. Equivalently, the Fisher information is proportional to $\frac{1}{p(1-p)}$. What is the reason for this? Why is the Fisher Information minimized at $p=0.5$? That is, why is inference most difficult at $p=0.5$?  Context:  I'm working on a sample size calculator, and the formula for $N$, the sample size needed, is an increasing factor of $p(1-p)$, the result of a variance estimation in the derivation. How to modify font for all text fields? How to solve this integral? $I=\int{e^x \Big(2\log x+\frac{1}{x}+\frac{1}{x^2}\Big)dx}$ $$I=\int{e^x \Big(2\log x+\frac{1}{x}+\frac{1}{x^2}\Big)dx}$$ I have tried to use many methods of substitution  But I am aware of a formula  $$I=\int{e^x[f(x)+f'(x)]dx}=e^xf(x)+C$$  but can this formula be applied to the above equation What is the best choice for .NET inter-process communication? Should I use Named Pipes, or .NET Remoting to communicate with a running process on my machine? Is there a way to simulate a numeric keypad on apple wireless keyboard in OSX? I'm tempted to get an Apple Wireless Keyboard but the lack of a number pad is a concern. I'm interested whether there is some form of software you can use where for example you hold some control keys down and you can use a set of keys like the following as a substitute numeric keypad:   7890 uiop jkl; m ./ How many regenerations does the Doctor have after The Time of the Doctor? In The Time of the Doctor, the Doctor says that he has a "new regeneration cycle". Does this mean he has another set of 12 regenerations, or just the one? Intuition behind the definition of a measurable set This week I saw the definition of a measurable set for an outer measure.     Let $\mu^*$ be an outer measure on a set $X$. We call $A \subseteq X$ measurable if $$\mu^*(E) = \mu^*(A\cap E) + \mu^*(A^c\cap E)$$ for every $E \subseteq X$.   This is not the first time I've seen this definition. Unlike most other things in mathematics, over time I have gained absolutely no intuition as to why this is the definition.   The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not comfortable with it is that you require a measurable set to break up sets which, according to this definition, are non-measurable; why would you require that? Of course, you can't say what a non-measurable set is without first defining what it means to be measurable so I suppose no matter what your condition is, it will have to apply to all subsets of $X$.     Is there an intuitive way to think about the definition of measurable sets? Is there a good reason why we should use this definition, aside from "it works"? Terminal prompt not wrapping correctly I have an issue where if I type in very long commands in bash the terminal will not render what I'm typing correctly. I'd expect that if I had a command like the following:  username@someserver ~/somepath $ ssh -i /path/to/private/key myusername@something.someserver.com  The command should render on two lines. Instead it will often wrap around and start writing over the top of my prompt, somewhat like this:  myreallylongusername@something.somelongserver.comh -i /path/to/private/key  If I decide to go back and change some argument there's no telling where the cursor will show up, sometimes in the middle of the prompt, but usually on the line above where I'm typing.   Additional fun happens when when I Up to a previous command. I've tried this in both gnome-terminal and terminator and on i3 and Cinnamon. Someone suggested it was my prompt, so here that is:  \[\033[01;32m\]\u:\[\033[01;34m\] \W\033[01;34m \$\[\033[00m\]  Ctrll, reset, and clear all do what they say, but when I type the command back in or Up the same things happens.  I checked and checkwinsize is enabled in bash. This happens on 80x24 and other window sizes.  Is this just something I learn to live with? Is there some piece of magic which I should know? I've settled for just using a really short prompt, but that doesn't fix the issue. I have over 400 open-ended responses. The total has been coded by one rater, and a 10% identical sample of the total has been coded by 2 raters. There is a choice of 14 nominal codes, of which the rater can use any number per case, though most cases have between 1-4 codes. Which statistical test is the most appropriate to determine if I have inter-rater agreement on the 10% sample?   Also am I right in assuming that I will need to treat each code as a variable and look for the level of agreement for each variable?   I'm using SPSS 21.  Much thanks, Kellie Every time I try to install "WINE" VIA the Software Center on Ubuntu 12.10, I get this error:  The following packages have unmet dependencies:  wine1.4: PreDepends: dpkg (&gt;= 1.15.7.2~) but 1.16.7ubuntu6 is to be installed          Depends: libc6 (&gt;= 2.14) but 2.15-0ubuntu20 is to be installed          Depends: wine1.4-amd64 (= 1.4.1-0ubuntu1) but 1.4.1-0ubuntu1 is to be installed          Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not going to be installed   When I try installing it VIA the terminal, this is what I get:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine1.4 : Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not installable            Recommends: gnome-exe-thumbnailer but it is not going to be installed or                        kde-runtime but it is not going to be installed            Recommends: ttf-droid            Recommends: ttf-mscorefonts-installer but it is not going to be installed            Recommends: ttf-umefont but it is not going to be installed            Recommends: ttf-unfonts-core but it is not going to be installed            Recommends: winbind but it is not going to be installed            Recommends: winetricks but it is not going to be installed E: Unable to correct problems, you have held broken packages.   how do I fix this?