There are tags such as  and  which clearly seem to be eclipse versions and there are already tags for them .  There are no users who have starred these tags and neither are there any questions posted under it. Shouldn't they be marked as synonyms or deleted?

During the re-tagging of questions, tags sometimes become orphaned from existing questions.  Are these zombie tags ever removed from the ?  What if a tag is misspelled and needs to be removed? How do we get rid of it?


How can you prove that $S_n$ is generated by $(1\space 2)$ and $(1\space 2\space 3\space ... \space n))$ for $n\geq 2$?

How do I prove that $S_5$ (the permutation group on five letters) can be generated by a two-cycle $(12)$ and a five cycle $(12345)$?


I have Ubuntu 14.04 LTS installed on Virtualbox and I wannted to upgrade it to the latest version (16.04 LTS).  I Upgrade it using my software updater, I restart my system. But, after restarting the system I found myself with the same old version (14.04). What's wrong guys?  Any suggestions?  /* Why my question is different to .  My question is totally different to the question identified as a possible duplicate. Because I was able to complete the update till the end and the OS asked me to restart the PC to finish the installation.  */

Question is about Ubuntu release process. Are migrations from n to n+1 releases expected?  Assuming we have server with installed Ubuntu 14.04 LTS. Will it be smoothly upgradable to Ubuntu 16.04 LTS via apt-get upgrade ?  Assumptions:   scope is software therefore we assume that given hardware is supported on both releases (upgrading from and to) that's why, always before upgrade you are asked to make backup to be able to revert in case of failure


I am level 13 and I would really like to know from anyone if I could fully upgrade an equinox with range to fly from Madrid-New York or New York-London? Thanks

I'm based in North America and have a bunch of major airports on the Eastern Seaboard.  I'm level 14 and just unlocked the Pearjet, but I still don't have a plane with enough range to make it across the Atlantic.  What's the first plane I'll get that will let me make that crossing?  Or more specifically, what's the range from New York (or Boston) to London (or Lisbon) - the smallest range that'll get me across?


Is it true that the only way two irrationals can sum to a rational is if they sum to zero?  Thanks!

I understand that the set of irrational numbers with multiplication does not form a group (clearly, $\sqrt{2}\sqrt{2}=2$, so the set is not closed). But is there a proof or a counter-example that the irrationals with addition form (or do not form) a group?  Thank you!  Edit: In particular, I am wondering if the set is closed with respect to addition.


I have a lists of list, and I would like to append data to each sublist independently.  When I append to one, it seems like ALL of the sublists are getting the same data appended.  Here is my code:  Code:  parent = [[]] * 2 data = [1]*4 parent[0].append(data) print "sublist 0:", parent[0] print "sublist 1:", parent[1]   Output:  sublist 0: [[1, 1, 1, 1]] sublist 1: [[1, 1, 1, 1]]   Expected Output:  sublist 0: [[1, 1, 1, 1]] sublist 1: []   What am I doing wrong or not understanding here?

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


I'm trying to change the font of the template in  .  For that, I need to use XeLaTeX and, as I understand, set  \usepackage{fontspec} \setmainfont{Baskerville}  \renewcommand*\namefont{\fontspec{Baskerville}\fontsize{40}{48}\selectfont} \renewcommand*\titlefont{\fontspec{Baskerville}\fontsize{20}{24}\selectfont} \renewcommand*\addressfont{\fontspec{Baskerville}\selectfont} \renewcommand*\sectionfont{\fontspec{Baskerville}\fontsize{20}{24}\selectfont}   Unfortunately, when I try to compile with XeLaTeX I get  "kpathsea: Running mktexmf FontAwesome  [Some stuff here, and, finally]  Package fontspec Error: The font "FontAwesome" cannot be found. "   On the other side, when I run with LaTeX, everything goes fine.   By the way, I'm using a macOS High Sierra 10.13.6.  So, what's the problem. Do I have to install this font or something like this? If so, why LaTeX identify somehow this font? Furthermore, how can I install such font if that's the case?  An example as required in the comments  \documentclass[11pt,a4paper,sans]{moderncv}       \moderncvstyle{casual}                             \moderncvcolor{blue}      \usepackage{fontspec}                            \setmainfont{Baskerville}  \renewcommand*\namefont{\fontspec{Baskerville}\fontsize{40}{48}\selectfont} \renewcommand*\titlefont{\fontspec{Baskerville}\fontsize{20}{24}\selectfont} \renewcommand*\addressfont{\fontspec{Baskerville}\selectfont} \renewcommand*\sectionfont{\fontspec{Baskerville}\fontsize{20}{24}\selectfont}   \name{John}{Doe} \title{Resumé title}                               \address{street and number}{postcode city}{country}  \begin{document}  \makecvtitle  \section{Education} \cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description}  % arguments 3 to 6 can be left empty \cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description}  \section{Master thesis} \cvitem{title}{\emph{Title}} \cvitem{supervisors}{Supervisors} \cvitem{description}{Short thesis abstract}  \end{document}   For some reason, it also works for LuaLaTeX also as suggested by Herbert in the comments.     Thanks in advance.

I'm using the latest version of MacTeX 2013 on OS X 10.8.4. All of my Tex Live packages are fully up-to-date. Tex Live also lists the fontawesome package as installed. I'm trying to use the FontAwesome font with XeLatex or LuaLatex and getting font-not-found errors. The exact message is: kpathsea: Running mktexmf FontAwesome ! I can't find file `FontAwesome'.  There's a longer traceback which I am omitting for brevity. Let me know if it's needed to resolve this problem. I have already tried running the following commands, to no avail: sudo -H mktexlsr sudo -H updmap-sys  Other than the above two commands, this is a 100% new out-of-the-box installation, with no modifications whatsoever. Here's a minimal broken example: \documentclass{article} \usepackage{fontawesome}  \begin{document} \faTwitter \end{document}  How can I add this missing font? Edit (Q1 2021): Please see Justin Curry's answer regarding an update to the package name from fontawesome to fontawesome5.


with the new update IOS 7 there is a itunes radio. well i've updated my iphone with the IOS 7 and the itunes radio has not shown up. i was told that it only works for the USA users and not the canadian or other users. now why is that?

I just have a quick question regarding the iTunes radio function. My girlfriend and I updated our iPhone 5 at the same time. She got the iTunes Radio, and mine is nowhere to be found. I open iTunes and cannot seem to find it anywhere. Anyone else experienced this?  I currently live in Norway with a Norwegian account, if that matters :)


If I give my 1/1 creatures +3/+3 in response to my opponent getting  out, then my opponent cast  and I give my creatures indestructible. Will my creatures live or will they die?

Can I hit a 4/4 indestructible creature with a  (3 damage) and give it -1/-1 with  to kill it? (Does it matter which way around I cast those?)  I read  here and it says, damage is removed in cleanup step, so it should be on the creature still after both spells.     702.12. Indestructible   702.12a Indestructible is a static ability.   702.12b A permanent with indestructible can’t be destroyed. Such permanents aren’t destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage (see rule 704.5g).   702.12c Multiple instances of indestructible on the same permanent are redundant.


I have installed Ubuntu 14.04 LTS . During installation on my Windows PC using VMWARE Player, it asked a username and I provided one. But now after successful installation, I also want to login as the root user. But unfortunately I don't know how to retrieve the root password or change it.  How can I log in as the root user?

I would like to enable the root account on my Ubuntu installation.  I realize the security implications of this.


I am learning about pointers. I don't understand what the difference between the char variables is.  #include <stdio.h>  int main() {     char *cards = "JQK";     char cards2[] = "JQK";      printf("%c\n", cards[2]);     printf("%c\n", cards2[2]); }   I experimented with them in the printf() and they seem to be working the same way except that cards2[] can't be resigned while cards can. Why is this the case?

The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.


I'm have listView which show Name of book and first Author:  <ListView.View>         <GridView>             <GridViewColumn Header="Name" Width="Auto" DisplayMemberBinding="{Binding Name}" />             <GridViewColumn Header="Author" Width="Auto" DisplayMemberBinding="{Binding Authors[0].Name}" />         </GridView>     </ListView.View>   But i need to show not only name first author, but all author in collection separated by commas. This is my Model:  public class Book : IModel     {         public Book()         {             Authors = new List<Author>();             Tags = new List<string>();         }         public string Name { get; set; }         public List<Author> Authors { get; set; }         public string ISBN { get; set; }         public int Pages { get; set; }         public List<string> Tags { get; set; }         public int PublicationYear { get; set; }         public PublicationHouse PublicationHouse { get; set; }     }   And code behind XAML:  public partial class BooksView : ListView     {         public BooksView()         {             InitializeComponent();             ItemsSource = FilesManager.books.Values;         }     }

does anyone know if there is a simple way to bind a textblock to a List. What I've done so far is create a listview and bind it to the List and then I have a template within the listview that uses a single textblock.  what I'd really like to do is just bind the List to a textblock and have it display all the lines.  In Winforms there was a "Lines" property that I could just throw the List into, but I'm not seeing it on the WPF textblock, or TextBox.  Any ideas?  did I miss something simple?  Here's the code  <UserControl x:Class="QSTClient.Infrastructure.Library.Views.WorkItemLogView" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"          Width="500" Height="400"> <StackPanel>     <ListView ItemsSource="{Binding Path=Logs}" >         <ListView.View>             <GridView>                 <GridViewColumn Header="Log Message">                     <GridViewColumn.CellTemplate>                         <DataTemplate>                             <TextBlock Text="{Binding}"/>                         </DataTemplate>                     </GridViewColumn.CellTemplate>                 </GridViewColumn>             </GridView>         </ListView.View>     </ListView> </StackPanel>     and the WorkItem Class  public class WorkItem {     public string Name { get; set; }     public string Description { get; set; }     public string CurrentLog { get; private set; }     public string CurrentStatus { get; private set; }     public WorkItemStatus Status { get; set; }     public ThreadSafeObservableCollection<string> Logs{get;private set;}   I'm using Prism to create the control and put it into a WindowRegion          WorkItemLogView newView = container.Resolve<WorkItemLogView>();         newView.DataContext = workItem;         regionManager.Regions["ShellWindowRegion"].Add(newView);   thanks


I've been just introduced to Zermelo-Fraenkel set theory, and I don't know the proper way to approach this exercises yet.   Here I'm being asked to prove that $B^{A}$ (i.e. the collection of all maps between the sets $A$ and $B$) is a set itself.  I know the axioms but it's hard for me now to figure out which axiom do I have to start with to attack this exercise.  I'd appreciate any hint.  Thanks for your time.

Can we say "the set of all functions between two sets" as easily as we could say "the set of all real numbers", for example?


In C# this would work -  String[] elements = sample.Split((char)30);  What is the java equivalent?

What regex pattern would need I to pass to  java.lang.String.split()  to split a String into an Array of substrings using all whitespace characters (' ', '\t', '\n', etc.) as delimiters?


I saw a video in which a guy from IBM was explaining (very generally) quantum computing, it's difference with classical computing etc.  The talk was not technical at all, it was intended for a broad audience.  At some point he told that, if we need to represent our position on the planet with only one bit, we could only tell for example if we are on the North or South hemisphere, but with a qubit we could tell exactly where we where.  He did this example to explain the difference in how much information can a bit and a qubit contain and to give a little idea of what a superposition is (I think).  Now, my question:  From what I know a qubit has more than one state, but when I read it I can only have one or zero, so why this example was made? From what I can understand a qubit can hold more information but I can't read it, so basically it's useless.

I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a single qubit. I'm not sure I completely comprehend this.    Here's how I rationalized it: You take all the information you want to store, put it in binary form, and make it the real component of $\alpha $ or $\beta$ (the coefficients of the computational basis states).   Now I'm not sure if I've understood it right, but since it's still fuzzy in my head it would be great to get some kind of ELI5 explanation or possibly a more detailed picture of how this would, even theoretically, be possible.    Apologies if the question doesn't meet standards. I'm new to the forum and would be open to feedback regarding asking questions or answering them.


I have come across a problem in a book on elementary mathematics that I am unable so solve. The problem statement is : "Show that the numbers $\sqrt{2}$, $\sqrt{3}$, and $\sqrt{5}$ cannot be terms of a single arithmetic progression" When I look at the hint for the problem in the back of the book it provides a partial proof by contradiction. They say : assume we have an arithmetic progression such that $m,n,p \in \mathbb{N}$ with : \begin{align} a_{m} & = \sqrt{2} \\ a_{n} & = \sqrt{3} \\ a_{p} & = \sqrt{5} \end{align} Here we know $m$, $n$, and $p$ must be pairwise distinct. They then tell the reader to use the formula for the general term of an arithmetic progression to compute $\frac{n-m}{p-m}$. The formula referenced here is : \begin{equation} a_{k} = a_{1} + (k-1)r \;\; \forall k \geq 1 \end{equation} Where $(a_{i})_{i \geq 1}$ is the progression and $r$ is the common difference between adjacent terms. I am able to compute $\frac{n-m}{p-m}$ using the formula, but I do not understand why computing this can allow proving what the problem requests of the reader. Can someone help me with this ?

In a sequence $a_1, a_2,\dots$ of real numbers it is observed that $a_p=\sqrt{2}$, $a_q=\sqrt{3}$, and $a_r=\sqrt{5}$, where $1\leq p<q<r$ are positive integers. Then $a_p$, $a_q$, $a_r$ can be terms of (A) an arithmetic progression (B) a harmonic progression (C) an arithmetic progression if and only if $p$, $q$, and $r$ are perfect squares (D) neither an arithmetic progression nor a harmonic progression  I have tried using the definition of AP and argued that if the first option is true then $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{5}-\sqrt{3}}=\frac{q-p}{r-q}$  is true which implies that the left hand side is an rational number. I don't know whether the left hand side is a rational number or not. I am stuck here. Also, I don't know how correct this approach is. How do I approach and solve this problem?


I recently tried to create a model for predicting what class a sample belongs to out of 160 possible classes. These classes of the target variable are just simple strings describing workouts like "Push-ups", "Sit-ups" etc. I used sklearn's method LabelEncoder to transform the target variable, and it assigned every class a number between 0 and 159. I know that the reason why we are supposed to do one-hot encoding for categorical features is to avoid telling an algorithm something nonsensical like "blue is greater than red". My question then becomes, doesn't LabelEncoder tell the sklearn algorithm that "push-ups" is less than or greater than "sit-ups" if both of them are assigned distinct numbers between 0-159? Why or why not? This feels like a very stupid question, but I had real trouble finding an answer anywhere online.

In a classification problem when the response variable has multi-class, e.g., "sunny","rainy","cloudy", how should we encode it? I know that for predictors like this, usually we do , and if a predictors have too many classes, then we might just use the .   When this multi-class issue occurs in the response variable, I guess we can just use LabelEncode() rather use using One Hot encoding right? Because if we use One Hot encoding, then we will have 2 variables as the response variable, and the machine learning algorithm in sklearn usually expects the response variable not to be a vector right? (I mean it expects a long 1D vector with length equal to the number of observations but not a 2D matrix). But on the other hand, if we just map "sunny", "rainy","cloudy" to {1,2,3} or {0,1,2}, or whatever 3 numbers, that will create a less than or greater than relationship among "sunny", "rainy","cloudy", which is not inherited in the original problem.


Consider the an infinitesimal coordinate transformation $x^{\mu}\mapsto x'^{\mu}:=x^{\mu}+\epsilon^{\mu}(x)$. The appropriate changes in the metric manifest as: $$g'_{\mu\nu}=\frac{\partial x^{\alpha}}{\partial x'^{\mu}}\frac{\partial x^{\beta}}{\partial x'^{\nu}}g_{\alpha\beta}= g_{\mu\nu}-(\partial_{\mu}\epsilon_{\nu}+\partial_{\nu}\epsilon_{\mu})+\mathcal{O}(\epsilon^2).$$ Now, for the transformation above to qualify as a conformal transformation, the $\mathcal{O}(\epsilon^1)$-term must be proportional to the metric $g_{\mu\nu}$ and the proportionality factor can be determined by taking a trace of the resultant expression. All in all, $$\partial_{\mu}\epsilon_{\nu}+\partial_{\nu}\epsilon_{\mu}\overset{!}{=}\frac{2}{D}\partial\cdot\epsilon g_{\mu\nu},\quad(*)$$ where $D:=n+m$ is the dimensionality of the semi-Riemannian manifold $\mathbb{R}^{n,m}$. The main problem I am facing here is using (*) to get to, $$(g_{\mu\nu}\square +(D-2)\partial_{\mu}\partial_{\nu})(\partial\cdot\epsilon)=0,\quad(**)$$ where $\square$ is the d'Alembertian [1]. According to a lecture by Prof. Tobias Osborne, "it is due to the equality of mixed partial derivatives [...] up to third order ..." [2]. The method I have adopted is to evaluate $\partial_{\alpha}\partial_{\beta}\times(*)$ and note that the RHS(*) is $\propto g_{\mu\nu}$ and therefore it is sufficient to consider $\partial_{\mu}\epsilon_{\nu}=\partial\cdot\epsilon g_{\mu\nu}$ to get $$(2\partial_{\alpha}\partial_{\beta}\partial\cdot\epsilon)g_{\mu\nu}=\frac{2}{D}\partial_{\alpha}\partial_{\beta}\partial\cdot\epsilon g_{\mu\nu},$$ which appears a fairly bogus result. How do I get to (**)? [1]  [2]

It is known as a fact that conformal maps on $\mathbb{R}^n \rightarrow \mathbb{R}^n$ for $n>2$ are rotations, dilations, translations, and special transformations while conformal maps for $n=2$ are from a much wider class of maps, holomorphic/antiholomorphic maps. I was wondering to know if there is any topological or geometrical description for this.   To show what I mean, consider this example: in $\mathbb{R}^n$ for $n>2$ interchanging particles can only change the wave function to itself or its minus. It is related to the fundamental group of $\mathbb{R}^n-x_0$ ($x_0$ is a point in $\mathbb{R}^n$ and $\pi_1(\mathbb{R}^n-\{x_0\})=e$ for $n>2$) but this is not true for $n=2$.   I want to know whether exists any topological invariant or just any geometrical explanation that is related to the fact that I mentioned about conformal maps on $\mathbb{R}^n$.


Let $A$ be an integral domain. Then $\forall m$ where $m$ is maximal ideal in $A$,$\; A_{m}$ is integrally closed$\implies$ $A$ is integrally closed.  This fact is proved in Atiyah-MacDonald in a different way. I am trying to prove it in the following way and hoping to complete it:  The field of fractions of $A_{m}$ is same as the field of fractions of $A, K_{A}.\;$Then we want to prove that $a/b \in K_{A}$ is integral over $A\implies a/b\in A.\;$ Now, $a/b$ satisfies some monic polynomial over $A$ means it satisfies some monic polynomial over $A_{m}, \forall m.\;$ Hence, $a/b$ is integral over $A_{m},\forall m.\;$ Now I just have to prove that $b\notin m,\forall m.$ Suppose, $b\in m$ for some maximal ideal $m$. Then $a\in m.$  After that I'm stuck. Thanks in advance!

I've managed [with help from the wonderful people lurking on this site :)] to prove that for an integral domain $A$, if $A$ is integrally closed, then $S^{-1}A$ is integrally closed for all multiplicatively closed subsets $S$ of $A$.  The problem that I want to apply this to is:     $A$ is integrally closed if and only if $A_{P}$ is integrally closed for all maximal ideals $P$ of $A$.   So far:  $(\Rightarrow)$ If $P$ is a maximal ideal of $A$, then $A\setminus P$ is multiplicatively closed, because maximal ideals are prime. So by the result mentioned above, $A_{P} = (A \setminus P)^{-1}A$ is integrally closed.  Update:  Attempting to prove the contrapositive.  Assume there is some $\frac{r}{s}$ in $F$ (the field of fractions of $A$) such that $\frac{r}{s}$ is integral over $A$ but not in $A$.  I feel like I haven't done hardly anything at all with your hint, but I suppose that I would want to somehow get a maximal ideal of $A$ from this $\frac{r}{s}$ such that $A_{P}$ is not maximal, thus proving the converse.


I have a function get_board to fill a 2d list with increasing numbers.  size= int (input("Size"))  def get_board(size):    i=0    num=0    board = [[0] * size] * size    for i in range(size):       j=0       for j in range(size):         board[i][j]=num         num+=1    return board  board= get_board(size)  print (board[0][0])   I cant get the correct values. If the size is 3, board starts with 6 7 8. The example board[0][0] is equal to 6. I didnt get that.

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


In the past three weeks alone, the number of people displaced inside Ukraine itself has doubled to at least 260,000, according to the UN's Vincent Cochetel in Geneva.   Is this "two hundred sixty thousand" or "two hundred sixty thousands"?

I'm having problems with hundred and thousand.   If someone asks you, How many trees are in this forest? Would you answer seven thousand or seven thousands, because thousands are countable?  I know that you usually say seven thousand, but I also know that thousands are countable, so wouldn't that make it seven thousands?  And when you are talking about multiple countable nouns, you would make it plural, but the plural isn't thousand, it's thousands, so it couldn't be that thousand is the plural.  Why isn't it a few thousands? Is it because of an exception in English? Any help would be appreciated.


Let $T_1$ be a circle with centre at the point $O$ and radius $R$. Two other circles $T_2$ and $T_3$ with centres at $O_2$ and $O_3$ respectively are tangent internally to $T_1$ and meet each other ($T_2$ and $T_3$) at the points $A$ and $B$. Find the sum of the radii of $T_2$ and $T_3$. $R_2$ + $R_3$, if $\angle OAB = \pi/2$.  [OP's thoughts, added by Brian Tung] I got $O_2AO_3B$ is a Kite. Also if extend $OA$ and intersects $T_3$ to point $W$ in $T_2$ for example, and extend $AO$ to $T_2$ then intersect $T_2$ to $V$, can get $O_2O_3$ equal to half of $WV$.  If I can approve $WV$ is paralleling to $O_2O_3$ or $OO_3$ is paralleling to $WB$, may get the result of $R_2 + R_3 = R$. Not sure if this is the right direction?

Let $T$ be a circle with centre at $O$ and radius $R$. Two other circles $T_1$ and $T_2$ with centres at $O_1$ and $O_2$, respectively, are tangent internally to $T$. $T_1$ and $T_2$ intersect one another at the points $A$ and $B$. Find the sum of the radii of $T_1$ and $T_2$, $R_1 + R_2$, if $\angle OAB = \pi/2$. The answer should be expressed in terms of $R$ and the coordinates of the points $O_1$ and $O_2$ (relative to $O$).  (This was a question posted by someone who subsequently deleted his/her account. The question originally generated a lot of comments - and was eventually put on hold - because the OP hadn't made it clear enough. Some of us thought the question is sufficiently interesting to be re-opened so I've cleaned it up and re-posted it anew. The original question is found  but may have been deleted by the time you read this)


How can i write text between some pre-defined coordinates in tikz?. As shown in the attached figure, i want to write text between a-b-c-d coordinates.

I am designing a poster, which has some geometrical shapes (TikZ paths) surrounded by some text. I would like the text to flow neatly around these shapes. I bet there's some clever TikZ magic that could do this.  EDIT: This is the sort of effect I want, sorry to not be clear:    \documentclass[a4paper]{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw (0,0) to (2,-2) to (2,-4) to (4,-4) to [out=up, in=down] (6.5,0); \node [text width=6cm, anchor=north west] at (0,0) { \hspace{5pt}  This is the sort of effect I want to \\ \hspace{23pt} achieve, with text automatically \\ \hspace{36pt} constrained by some \\ \hspace{46pt} geometrical form. Here \\ \hspace{55pt} it's just a curve, \\ \hspace{57pt} but this could \\ \hspace{57pt} also be the \\ \hspace{57pt} text label \\ \hspace{57pt} of a node.}; \end{tikzpicture} \end{document}


Is it allowed to set the noun after the verb?  An example from Wikipedia where this is used:     and I've also noticed this in some films and texts.

It's very common to say:   "Here he comes."  "Here comes the man."    But what about:   "Here comes he."  "Here the man comes."    Is there a rule about the order of noun and verb in inversion? It will be too much if all the inversions are considered, so let us talk about adverb inversions only, such as:   "Here comes the rainbow."  "Off we go."  "In the room is the man lying."


This is a contest math problem which I was not able to solve. A hint toward the solution would be helpful as well.   Problem: Show that there are infinitely many powers of 2 starting with the digit 7.  Thanks in advance.

Prove that for any finite sequence of decimal digits, there exists an $n$ such that the decimal expansion of $2^n$ begins with these digits.


I'm fairly new to programming and web dev and up until now I haven't worked on any projects that I felt were large enough to warrant using proper version control. However, I am now working on a project that is getting bigger and bigger (very exciting!). I think it would be prudent to use some kind of version control. At the moment I work alone, but if this project gets where I want it to then I expect at some point I am going to need (and want!) some other people to come on board.  My problem is because I've never used version control, I don't really know what it is, how it works etc etc.  I hope this question isn't classed as subjective. I'm not asking for people to tell me which version control they think is best, I'm quite happy to spend some time looking around and trying them out for myself.  I'm really wanting some people to either give me a quick run down of how a standard version control system works (I know they'll all be different, but I'm talking basics here) and if possible, in a non-subjective way, to explain the differences between some of the major players. ie what is the difference between mercurial and git, not which is better - I'll decide that for myself thank you!

After being told by at least 10 people on SO that version control was a good thing even if it's just me I now have a followup question.  What is the difference between all the different types of version control and is there a guide that anybody knows of for version control that's very simple and easy to understand?


In Harry Potter and the Order of the Phoenix, there’s a point in the Department of Mysteries where two prophecies get smashed and are able to be heard. But these two prophecies are not about anybody present. Couldn’t one of the Death Eaters do this for the prophecy about Harry and Voldemort? Just smash the prophecy off the shelf and listen to it?

Towards the end of 'Order of Phoenix', it is revealed that Lord Voldemort is trying to steal the prophecy regarding him and Harry from the Ministry.  The book mentions the accessibility rules of the prophecy orbs in two places:   Only people the prophecy is about can lift it from the shelf If anyone else tries, they go mad.   But later, we see orbs falling off the shelves as curses hit them. This means that either they aren't magically impossible to dislodge by others, or the curses break the magic if they are.  Moreover, when they break, a ghostly shadow appears and recites the prophecy.  Since Voldemort aim was to hear it once, not preserve it, why didn't he simply had the prophecy orb broken. (Even if he couldn't be there in person, there are surely other ways in the magical world to listen. Sirius's two-way mirror comes to mind. And this is the (2nd?) greatest wizard alive we're talking about. Who had for almost a whole year to try new things.)  The only answer I could come up with is that Voldemort wasn't aware what would happen if the prophecy orbs got broken. But I'm not sure about that.  Is there any canon explanation?


Please, I'm not sure how in American English this "direct speech inside another direct speech" should be written properly. Here it is this sentence:     "He was five and a half meters from her and he was talking to her, softly. He told her: 'Please, try to calm yourself down. Everything will be OK'."   The use of the quotation marks is it correct? Thank you everybody in advance for your help!  Andrea Iovinelli

How would embedded quotations be used when quoting from passages/sources within an essay? What would be the difference between normal quotations and embedded quotations?


How does the "is:answer" search order the answers when sorted by relevance?  On here, Meta.SE, they are clearly sorted by votes:        On Ask Ubuntu they are neither sorted by votes or date or views, and if I click relevance again, the order changes. There is a variance in votes between 0 and 18, but none less than 0:        Skeptics may be ordered by date? Although I can't actually check for some reason - the tool tip isn't working. And anyway, they're all Feb 25th / 26th, and today is the 22nd of March.        So how is this being ordered by default, and why does it vary site to site?

I frequently prefer to look for questions on superuser .    I have never been able to determine how these search results are ordered.  Typically, search results are returned in order of relevance and the search help says they are "weighted heavily towards question title matches", but in this case, you would think that the search would order them based on whatever tab is currently selected (newest, hot, active)?  I ordinarily never stray outside of 'newest', but it's clear the results are not sorted by age.


$$x^2<\sin x \tan x \quad as \; x \to 0$$  I made the substitution $x \to \arctan x$ .   $\arctan^2 x<x\sin (\arctan x)$  $\arctan x < \large \frac{x}{(x^2+1)^{\frac 14}}$  There are two functions $f(x)$ and $g(x)$ . $f(0)=g(0)$ . If $f'(x)>g'(x)$ on the interval $(0, a)$ , then that implies that $f(x)>g(x)$ on the interval $(0, a)$ . Therefore if $RHS'>LHS'$ , then $RHS>LHS$ .   $LHS'=\large \large \large \frac {1}{x^2+1} <RHS'=\frac {x^2+2}{2(x^2+1)^{\frac 54}}$  $\large \large \large \frac {1}{x^2+1}<\frac {x^2+2}{2(x^2+1)^{\frac 54}}$  $1<\large \frac {x^2+2}{2(x^2+1)^{\frac 14}}$   Using standard techniques (such as first derivative test) we can show that the $RHS$ has a minimum at $(0, 1)$ so we have proved the inequality.  I have two questions:   $1)$ Is my proof correct?   $2)$ Are there nicer ways of doing this inequality (without involving math higher than calc 1)? I have tried AM-GM and others but I think it is very hard to do it very elegantly because the $RHS$ is such a good approximation of the $LHS$ as $x \to 0$ .

Find $$\lim_{x\to0}  \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$$ where $\lfloor\cdot\rfloor$ is greatest integer function   I am a high school teacher. One of my students came up to ask this limit.  For $\lfloor\frac{\sin x}{x}\rfloor$, I have used $\sin x > x$ using increasing decreasing functions.  I tried to prove $x^2 > \sin x \tan x$ using increasing /decreasing  function but I am not getting it.


I've grown up in my grandparents house my entire life. They lived two miles away my entire life. Sleep overs, dinners, barbecues, etc.  It's been the plan since I was a kid to buy the house when I got older.  The house is a 4-bed 2-bath, and it's getting to be too empty for them.  They've lived in the house for nearly thirty years. The value of the house is about $340,000. They have about $160,000 left on the mortgage.  They came to me with a proposition for me to buy the house for less than market value, and take the difference, buy a trailer and put it on another piece of property they own and live there.  The current proposition is that I get a mortgage for less than the current market value of the house, probably about $260,000. They then sell me the house for that amount. They pay off the $160,000 mortgage, and take the remaining $100,000 to get them setup on their other property (buy a trailer/fifth wheel, garage, carport, etc).  Are there any concerns with this plan? Do they have to do anything special to facilitate this? Do I?

I own a property that recently appraised for $350,000 in the state of Maryland that I purchased for $300,000 7 years ago. I wish to sell this property for a value of $240,000. Here are my questions:   Is this legal? The state of Maryland has a transfer/recordation tax of 1.5% for each, the buyer and seller. Would this be computed on the appraised or sale value? Will this pose any problem if the buyer needs financing? Would I be able to deduct a capital loss on my tax return?     From comments: I should have mentioned - the buyer is a sibling.


I am new to ubuntu .  I have a python file . i just want to execute it in every 15 min .  any body can tell, how i can do it ?  with all basic steps  Thank you

I want to schedule a task to run on a regular basis and have heard that Cron is the way to do this.  How do I add Cron jobs in Ubuntu?


Can we prove that the eigenvalues of an $n\times n$ orthogonal matrix are $\pm 1$ from the definition of orthogonal matrix alone?   An $n\times n$ matrix $A$ is orthogonal iff $AA^T=A^TA=I$.  Is it possible to use solely this definition, without using the result proven from this definition which says orthogonality preserves length, to show that the eigenvalues of $A$ is $\pm 1$?

what are the possible eigenvalues of an orthogonal matrix?  I got the answer key which says its 1 and -1 but it doesn't explain well


The default defuse node missing from node editor - i have tried repairing / did a reinstall -- changed the cycles render // chose use node editor from the material tab. Blender 2.78c. I cannot insert or create a new node.  here is the screen shoot.

I have been following  tutorial until I started adding nodes. The problem is that he has completely different nodes than I have. Even nodes that are created at start are different (I have Material and Output and he has Render Layers and Composite). Have I missed something or should I use different nodes than he?


I am looking to find a way using SDO Geometry to overlay two polygons, Polygon A and Polygon B. I consider Polygon A to be my bottom layer. Wherever Polygon B overlaps Polygon A, I want to cut that geography out of Polygon A. Basically, the geography of Polygon B will take precedence over Polygon, without getting rid of all of Polygon A.  My intent is to throw the now-modified Polygon A and Polygon B into a new Feature Class. This Feature Class will eventually be made into an ArcGIS Service.  Some Visuals:  Blue = Polygon A  Red = Polygon B    When we place Polygon B on Polygon A. We'll cut out where Polygon B is. If we think of this example as 1 layer, this would also be the intended end result.    Polygon A after we remove the chunk where Polygon B was.    Edit: This was marked as a duplicate. Although I can see how this is a duplicate from an ArcGIS Perspective, the answer that was marked as duplicate did not mention anything about SDO Geometry. I would like to see if there is an option available via SDO Geometry as well,(Even if it's not the best solution) in the event that I must end up using SDO. I've removed the references to ArcMap to designate this as more of an SDO Question.

I am working on a project doing spatial analysis at a statewide level. I am looking at a form of transportation coverage in a state, and part of my analysis involves buffers and drive time polygons. I am using a geodatabase (therefore ArcGIS) for all my work, so new features will be exported as feature classes in feature datasets. To visualize: I have said state border, and some dissolved buffer rings around some points, and they cover parts of the state. I want to create a feature class for the parts of the state these buffer rings don't cover, AKA gap areas. Is there a tool I can use or create to do this? I know I could draw them in manually in editor, but I am unsure if that's the most precise way to generate these feature classes. To me, I am thinking this operation would be like an inverted "Clip" in that I take the two layers, and instead of pulling out the clipped area, it would take everything not in the clipped area. I am using a Desktop Basic license.


I am preparing a math document, and would like to use the \bigtriangleup math operator from the package stmaryrd. However, calling the entire package is not an option as it overwrites several commands from mathabx which I am also using. Is there a way I can extract this operator (possibly using a different name, so that mathabx's \bigtriangleup binary operator isn't affected) without having to use the package?

Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way?


how can I add numbering to this equation and make it more elegent??  \[ \begin{bmatrix} [0] & [m] \\  [m] & [c]   \end{bmatrix} \begin{Bmatrix} \vec{\ddot x}  \\  \vec{\dot x}   \end{Bmatrix} + \begin{bmatrix} -[m] & [0] \\  [0] & [k]   \end{bmatrix} \begin{Bmatrix} \vec{\dot x}  \\  \vec{x}   \end{Bmatrix} = \begin{Bmatrix}  \vec{F}\\ 0 \end{Bmatrix} \]

I would like to put in a code that automatically assigns a number to the equations in my documents preferably aligned on the right hand side.   How can I go about this?   \documentclass[a4paper,11pt]{article} %\documentclass[a4paper,11pt]{scrartcl} \usepackage{amsmath}  \usepackage[utf8]{inputenc}  \begin{document}  $$\ddot{\underline{\mathbf{r}}} = \frac{d{^2}\underline{\mathbf{r}}}{dt^2}= 0$$.  \end{document}


I know about l (link) and d (directory) in the first column of the ls -la output. Very recently I have seen an p. What does it stand for? Example (I ommited some lines of the output as they have guid-like contents): user@user-ThinkPad-T440s:~/.zoom/data$ ls -latr [......] prw-r--r-- 1 user user      0 Mai  2  2020 com.zoom.ipc.assistantapp__res [......] drwx------ 2 user user   4096 Dez  7 19:49 ConfAvatar -rw------- 1 user user  35840 Dez  7 20:22 zoommeeting.enc.db prw-r--r-- 1 user user      0 Dez  7 20:23 com.zoom.ipc.confapp__req drwx------ 8 user user   4096 Dez  7 21:08 .. prw-r--r-- 1 user user      0 Dez  7 21:08 com.zoom.ipc.confapp__res -rw------- 1 user user 109568 Dez  7 21:08 zoomus.enc.db prw-r--r-- 1 user user      0 Dez  7 21:08 com.zoom.ipc.assistantapp__req drwxrwxr-x 4 user user  20480 Dez  7 21:08 . user@user-ThinkPad-T440s:~/.zoom/data$

I'm very familiar with linux file permissions, and special perms (sticky bit, suid, guid) But I don't know what the c stands for? Is it a permission, or something else? I've done some googling with and can't figure it out. Here's the device file that has it. steven@A215:~$ ls -l /dev/null crw-rw-rw- 1 root root 1, 3 Dec 29 20:58 /dev/null   Image Reference:


I have admin rights. Could there be a way to change back my pass. I dont even know whats my password is because I already set it to "none' now its very hard to install apps. Need help please ! Fast.

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


My girlfriend applied for a 1 year Italian visa because they had already given it to her before for some weeks so now they would give her the whole year.  What ended up happening is that life got in the way and we ended up not going to Italy, but going to several other European countries (specially Portugal, where I'm from).  She is very worried that she will have difficulties applying for European Visa again.  Should she be? What's the worst case scenario and how can it be remedied?

I am a non-EU national, permanent UK Resident. Recently, my work issued me with a multiple Schengen visa with Norway as the first (main) point of entry. Now I want to go on holidays to Greece - do I need to apply to Schengen visa again, as Greece is not Norway and I am not going there for work?


Beginner here so I'm not even sure if this issue is because of a setting I have, or if it's a bug. So when I change viewports, I noticed the that the last two options just give me a greyed out image. Even in older projects I have which used to render correctly, it would give a trippy image. Tried recording my issue hopefully it helps!  This happens in Evee, but I also noticed that even in cycles, it would render it like this:

I don't know why but now, when i go in material preview or rendered (in solid mode it works fine), my object is entirely gray, or invisible idk, because it has the same color of the background. I've been working for days on this project without having this issue, it suddenly showed up. I tried opening other old projects and suddenly they all do the same so i guess it is some blender program setting that applies for all the projects, but idk how it happened cuz i didn't change anything :/, anyone got any tips?


I write C# Windows form in Visual Studio.  In code of application I load image from local maschin using absolute path:  string path = "C:\imag.png"   Ater I load this in pictureBox.  Problem is that when I compile program and run on another computer I get errors, because there are not files, that should be loaded.  How can I use resources in VS or compress images in exe file?

How do I create a resource that I can reference and use in various parts of my program easily?  My specific problem is that I have a NotifyIcon that I want to change the icon of depending on the state of the program. A common problem, but one I've been struggling with for a long time.


I understand that every 10 feet of distance fallen is 1d6 bludgeoning damage at the bottom... but how do you determine when to start calculating that if a player intentionally jumps down from a ledge? At what point does "dropping down" become "falling"?  I don't think it's based on the jump range measurements provided by the PHB, because the vertical distance is almost always less than 10ft, and the jump distances seem to be just an allowance to bypass terrain obstacles during your move by jumping over them.  Ten feet isn't that high and, while it can certainly hurt, 20 feet didn't kill me or break any bones. I expect more physically capable people would be able to jump down from higher, but I wouldn't dare do it myself — 20 feet was scary enough.  Clarification: In the absence of magic. How high is "a great height"? When dropping down, the only distance restriction is how high off the ground you are. Another example of this could be an aarakocra who chooses to drop from the sky to his feet, rather than flying down and landing. It's controlled because they chose to jump, so does that mean they're immune go damage regardless if height? Just because they wanted it? By that reasoning, saying "I meant to do that" could save your life. Is it just 10ft or more automatically becomes a fall unless magic is helping you? That seems totally arbitrary and random.

I have a multiclass Monk / Druid (2 levels of monk).  He cast jump on himself, wild shaped into a brown bear, activated step of the wind, then took a high jump with a height of 42':  High Jump When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier  Strength mod is +4 from the brown bear, so 7 × 3 (jump spell) × 2 (step of the wind) = 42. Our group got into an argument over whether he would take 4d6 falling damage after his high jump, and the PHB doesn't seem to answer this.


show that for $a,b,c \geq 0$ if $a \leq b+c$ then $\frac{a}{1+a} \leq\frac{b}{1+b} + \frac{c}{1+c}$ I can not get a good start in this problem. a hint will be appreciate it thanks

Suppose that $a$, $b$ and $c$ are positive real numbers and that $a \leq b + c$. By cross multiplying or otherwise, show that  $$\frac{a}{1 + a} \leq \frac{b}{1 + b} + \frac{c}{1 + c}$$  Anyone able to get this to work out? I cross multiplied them but am unable to manipulate it into an expression that verifies the statement.


I'm from north Alabama and grew up with the phrase "scat old cat your tail's in the gravy".  This was used when someone would sneeze.  Just was curious as to it where this originated.  Thanks, Ronnie

I use the phrase "SCAT" when I sneeze, and sometimes when someone in my presence sneezes.   I have lived in different parts of the US and don't know where I picked up this expression. Has anyone heard of this practice before, or is it common anywhere?


What exactly is Ubuntu Core, and how does it relate to Ubuntu itself (i.e. the main desktop and server distribution)?   I've read  to , which says it's just a minimal install of Ubuntu, but it says nothing about the "snappy" transactional updates that Mark Shuttleworth mentioned in .

Exactly what does  consist of?  I know of a similar project called , which, while not an official Ubuntu project, is :    metapackage  casper lupin-casper   What does Ubuntu Core contain?  What are the differences between the purposes of these two projects?  I would like to make sure of this before I choose a starting point to build my own Ubuntu derivative.


Where $N(\alpha)$ is the norm of alpha. I have proved in a previous question that $N(\alpha\beta) = N(\alpha)N(\beta)$. and I have no trouble proving the $\Rightarrow$ but I don't know how to prove the other direction where we start by assuming $N(\alpha) = 1$.  The norm of an element alpha (= $a + b\sqrt{d}$) is: $N(a + b\sqrt{d}) = |{a^2 - db^2}|$.There is a similar question to mine but it only deals with the direction I have already proved.

Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$  Where $N$ is the norm function that maps $\gamma = a+b\sqrt{n} \mapsto \left | a^2-nb^2 \right |$  I have managed to prove $N(\gamma) = 1 \Rightarrow \gamma$ is a unit (i think), but cannot prove $\gamma$ is a unit $\Rightarrow N( \gamma ) = 1$  Any help would be appreciated, cheers


As part of my job as a web developer, I spend an amount of time doing UI prototypes to show the client. It's a pain in the behind but sometimes it has to be done.  I've seen Shuttleworth (and the design team) pump out images like this:    That's made by something called ... Something that balances on top of Adobe Air (yack!) and costs $79.  I've tried it but it kept falling over. I think it had something to do with Air not the app itself. My point is if I'm paying out for something, I want it to be native.

Are there any interface mockup design applications for Ubuntu? I need one in order to design programs or interfaces (internet sites and more).


I need to install a few packages from Debian contrib. (Specifically, ZFS-related packages.) However, I want to prevent myself from accidentally installing other packages from contrib without noticing. Therefore I would like to have a safelist of packages that can be freely installed from contrib, and block the rest.  I've searched the web and glanced over apt_preferences(5), apt.conf(5), and , but I didn't see anything that would let me fully specify the desired policy.  I'm currently on Debian stretch (oldstable as of this writing) but I have to upgrade to buster anyway, so I would happily take answers for that distribution too.

I want to block all packages from non-free, except for those that I  name explicitly. Currently, I have:  /etc/apt/sources.list :  deb http://ftp.us.debian.org/debian stable main contrib non-free   /etc/apt/preferences.d/non-free_policy :  Explanation: Disable packages from `non-free` tree by default Package: * Pin: release c=non-free Pin-Priority: -1   (The idea is, that I add an explicit stanza for every package I want from non-free.)  But it doesn't work:  root@silber:/etc/apt/preferences.d# apt-get -s install firmware-linux-nonfree Paketlisten werden gelesen... Fertig Abhängigkeitsbaum wird aufgebaut.        Statusinformationen werden eingelesen.... Fertig Die folgenden NEUEN Pakete werden installiert:   firmware-linux-nonfree 0 aktualisiert, 1 neu installiert, 0 zu entfernen und 0 nicht aktualisiert. Inst firmware-linux-nonfree (0.43 Debian:8.4/stable [all]) Conf firmware-linux-nonfree (0.43 Debian:8.4/stable [all])   What am I missing?


Why body of if() in 1st code Executes While the body of if() in 2nd code Doesn't Executes       Working          double num1 = 0.2; double num2 = 0.2; double num3 = num1 + num2; if (num3 == 0.4) {     MessageBox.Show("1st"); }      Not Working               double num1 = 0.1; double num2 = 0.2; double num3 = num1 + num2; if (num3 == 0.3) {     MessageBox.Show("2nd"); }

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I'm using Ubuntu 13.04 , it can't read Arabic letters and words properly. that what I get when I open files contains Arabic, please notice that same files are showed correctly on windows:  ÇáÞÇäæä íÌÈÑ ÇáíåæÏ Úáì ÇáÚíÔ ÈãäØÞÉ ãÚÒæáÉ ãä ÇáãÏíäÉ ÊÏÚì ÇáÌíÊæ

I have some files that Ubuntu can't read it ( ANSI encoding ) but Windows can read it well.  When I open it in gedit or notepad++ it seems like this :     Êã ÇáÊÍæíá áÜÜ   How can I make Ubuntu read ANSI encoded files well?


I was reading a text and it had the following listed as immediate:  $\int_{0}^{1}\int_{0}^{1-x_{1}}\cdots \int_{0}^{1-x_{1}-\cdots -x_{n-1}} dx_{n}\cdots dx_{1}=\frac{1}{n!}$  I haven't actually evaluated an integral and done calculus in a while so I'm sorry if this is apparent.  But why is this immediate?

Let $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$. I know $T_n$ is tetrahedron.  My question: How can I compute the volume of $T_n$ for every $n$?


I am an Indian Citizen, with a valid H1B visa and I am traveling to Europe for my vacation. I will be getting a Schengen Visa from the consulate of my destination. I wanted to ask if I have a stop at LHR (or any airport in UK for that matter), will I need a transit visa?   The layover will be on the same calendar day (about 10 hours or less), and I do not want to get out of the airport.  I did check online resources like:     And it says that I will not require it.   I checked at this link:  And it says I do need it:     You’ll need a visa to pass through the UK in transit (unless you’re exempt)      You should apply for a Direct Airside Transit visa if you arrive in the UK on a flight and leave again without passing through immigration control.   Exemptions      You don’t need a visa if you have one of the following:         a visa for Canada, New Zealand, Australia or the USA (this can be used for travel to any country)   a residence permit issued by Australia or New Zealand   a common format residence permit issued by an European Economic Area (EEA) country or Switzerland   a resident permit issued by Canada after 28 June 2002   a uniform format category D visa for entry into a country in the European Economic Area (EEA) or Switzerland   an Irish biometric visa (marked ‘BC’ or ‘BC BIVS’ in the ‘Remarks’ section)   a Schengen Approved Destination Scheme (ADS) group tourism visa where the holder is travelling to the Schengen country that issued the visa   a flight ticket from the Schengen area, if you can prove that you entered the Schengen area in the previous 30 days on the basis of a valid Schengen ADS visa   a valid USA I-551 Temporary Immigrant visa issued by the USA (a wet-ink stamp version will not be accepted)   a valid USA permanent residence card issued by the USA on or after 21 April 1998   an expired USA I-551 Permanent Residence card issued by the USA on or after 21 April 1998, with a valid I-797 letter authorising extension   a valid standalone US Immigration Form 155A/155B issued by the USA (attached to a sealed brown envelope)      I don't see any exemption criteria that qualifies a H1B Visa holder with a valid Schengen visa to transit without a transit-visa.  In case I do need it, how long does it usually take? I have about 30 days before I travel.  Note: Last year I had a stop in Toronto, and I found that I need a transit visa the hard way. The airline didn't warn me until I tried to check-in into the flight the day before, and as a result I had to do a last minute change which was very expensive. So this time I want to confirm/assure to avoid the last minute stress.

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


How can I store my connection passwords in putty?

Is there a way to configure a password for a stored session in ?  I know there is the capability to specify an "auto-login username" (under Connection/Data), but is there a way to do the same with the password?


For example 2 electrons repel each other because they experience electromagnetic force, matter particles attract each other because they exert gravitational force on each other, fusion is possible because of overcoming coulomb force etc, now my question is what force is pushing the electrons apart under immerse gravitational force such as white dwarf star? Pauli exclusion principle is not a force unless I'm mistaken.

You can have two electrons that experience each other's force by the exchange of photons (i.e. the electromagnetic force). Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pushing them apart to balance the force that pushes them towards each other. Instead, you get a a repulsive force as a consequence of the Pauli exclusion principle. As I have read so far, this seems like a "force" that is completely separate from the other well known forces like the strong, electroweak and gravitational interaction (even though the graviton hasn't been observed so far).   So my question is: is Pauli-repulsion a phenomenon that has also not yet been explained in terms of any of the three other forces that we know of?  Note: does this apply to degenerate pressure too (which was explained to me as $\Delta p$ increasing because $\Delta x$ became smaller because the particles are confined to a smaller space (Heisenberg u.p.), as is what happens when stars collapse)?


The user types the name of file. If he writes the wrong name of the file and python has an error like "FileNotFoundError: [Errno 2] No such file or directory: '5'". How can I write to user that he has typed the wrong name of the file? This code doesn't want to work:   try:      filename = input ("Your file name") except OSError as e:     print('We have an error: ', str(e))

How do I check whether a file exists or not, without using the  statement?


I have been ask to find the limit $\lim \limits_{n \to \infty} \cos^2(\pi\sqrt{n^2-n})$  However surely as $n$ gets larger the expression inside the $\cos$ function tends to infinity and the whole thing oscillates between $0$ and $1$?

Followed my  ,  I still don't understand why the answers that were given are right.  By simply intuition and using the continuity of cosine, we get that we need to compute  $\lim_{n\to \infty}\cos (\pi n\sqrt{1-\frac{1}{n}})$ and because of that, as I see that, there are two clear limits: 1 and -1, and therefore the limit does not exist  Can someone please explain me why am I wrong? two answers that claimed that the limit is 0 got 25 votes together, so I must be mistaken, But still the answers are not satisfying me.  By the way, Wolfarmalpha  it does not have a limit.  Thank you.


I need to remap the tab key to a function key, as the Tab is broken. I've looked at , but it doesn't work on Sierra

This is an attempt to write a canonical QA for this issue, as per the Meta post:   I expect it to be periodically edited with the goal of becoming a comprehensive information resource.  I have a MacBook Pro that has a key(Shift, Return,   Command, P, etc.) that doesn’t respond when pressed or is stuck in the down position.    It's possible that my favorite beverage was spilled (or some other liquid damage).  It's also possible that I have no idea what happened.  It was working yesterday and suddenly today it's no longer working.  Is there any way to bypass or remap the key?  Can I  have the system ignore it completely?  (This question can also apply to external USB keyboards or the Bluetooth keyboards)


Let $p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$ be a polynomial over a commutative ring $R$. Prove that (a) $p$ is unit in $R[x]$ iff $a_0$ is unit and $a_1,a_2,\ldots,a_n$ are nilpotent in $R$. (b) $p$ is nilpotent in $R[x]$ iff $a_0,a_1,\ldots,a_n$ are nilpotent in $R$.  I have got no lead in part (a) and in part (b) I have proved the if part. for the only if part can we use the fact that a polynomial is vanish everywhere iff all its coefficients are $0$?

Let A be a commutative ring with 1.   1) Prove that a sum of a nilpotent element and an invertible element is invertible.   2) Prove that if $f=a_0+a_1x+\dots+a_nx^n \in A[x]$  a) $\exists f^{-1}\in A[x] \Leftrightarrow a_0$ is invertible and the other coefficients are nilpotent.  b) f is nilpotent $\Leftrightarrow $ all its coefficients are nilpotent.  p.s. Those are the first two in a series of problems. The rest easily follow from each other. I'm only struggling with the first two.


I could not share wifi from my MacBook air. I could not find Wifi option? how can I add it?  Thank you

I am using internet via wifi connection. Now I want to share my internet with my iphone. In the preferences, I found the option Internet Sharing, but there is no "wifi" option under "To computers using:". "Only ZTE WCDMA Tech" and "Thunderbolt Bridge".  What to do?


Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying $$f\left(f(x)f(y)\right)+f(x+y)=f(xy)$$  The only thought i could get is clearly $f(x)=0$ satisfies. Also if $f(x)$ is an even function the functional equation is alsways true, but no clue for finding those functions.

Find all functions $f\colon \mathbb R\rightarrow \mathbb R$ such that for all reals $x$ and $y$:   $$f(f(x)f(y))+f(x+y)=f(xy).$$   It was six hours ago in IMO 2017 (problem 2).  I tried  the standard way: $x=0$, $x=y$, $x=1$,etc. but without any success.   Let $f(0)=a$. Hence, for all $x\in\mathbb R$ we have $f(a(f(x))+f(x)=a$. What is the rest?   Also we have $(x-1)(y-1)-1+x+y-1=xy-1$ and  $1-(1-x)(1-y)+1-x-y=1-xy$.


Ok, I'm dumb, I've read like dozens of topics and I still don't get it.   Your animal companion has abilities and game statistics determined in part by your level. Your companion uses your proficiency bonus rather than its own. In addition to the areas where it normally uses its proficiency bonus, an animal companion also adds its proficiency bonus to its AC and to its damage rolls. Your animal companion gains proficiency in two skills of your choice. It also becomes proficient with all saving throws.  Let's say I have Blood Hawk pet:        Armor Class: 12 +2 From MY PROF? = 14   Hit Points : 7(2d6)    STR 6(-2) DEX 14(+2) CON 10(0) INT 3(-4) WIS 14(+2) CHA 5(-3)    Proficiency Bonus +2 - the same as my PC   Skills: Perception +4 - what about this? is it just +2 wis and +2 prof bonus?   Senses: passive Perception 14 - is this 10 + Wis Mod +2 and Perception Prof +2?   Keen Sight.The hawk has advantage on Wisdom (Perception) checks that rely on sight. - so if PP is 14, PP that rely on sight is 19? OR it's 10+2(wis)+2(prof)+4(hawk skill)=18 + 5 adv =23? that's kinda... broken?   Pack Tactics. The hawk has advantage on an attack roll against a creature if at least one of the hawk's allies is within 5 feet of the creature and the ally isn't incapacitated.   Actions: Beak. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 4 (1d4 + 2 +2) piercing damage. - that +2 because of PC prof?       Your animal companion gains proficiency in two skills of your choice. so TWO extra beside Perception? You have an innate ability to communicate with beasts, and they recognize you as a kindred spirit. Through sounds and gestures, you can communicate simple ideas to a beast as an action, and can read its basic mood and intent. - So if I would send that Hawk for a recon it could "tell" me if there are enemies or traps?

I am having Some trouble getting my head around levelling the new .  If someone could break it down it would be really helpful.  If there are any simple step-by step-video's out there, I have not been able to fine one.


Noob question I apologize, but I have been struggling with this for way too long jQuery(".mutiple_form_navigation_link > div" ).on( "click", function() {         jQuery("#shipping_customer_details .validate-required").each(function(){             console.log(jQuery(this));                 if (jQuery(this).hasClass('wooccommerce-invalid')) {                     alert('invalid shipping');                 }         });  Looking at the raw html when clicking <p class="form-row form-row-last validate-required validate-Select woocommerce-invalid woocommerce-invalid-required-field showErrors" id="shipping_last_name_field" data-priority="">  It has the class woocommerce_invalid Looking at the console.log in my jquery it says p#shipping_last_name_field.form-row.form-row-last.validate-required.validate-Select.woocommerce-invalid.woocommerce-invalid-required-field.showErrors  Showing woocommerce-invalid is a class... yet hasClass is not triggering because apparently woocommerce-invalid was not there on DOM load, but rather after input validations? How do I modify my on("click") jQuery to detect the class in the DOM...?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


On my box (which got this error under 16.04 and it continues under 17.04...)  Update-initramfs looks for an uninstalled kernel it can't find. dpkg -l does not show this... anyone know how to fix this leftover reference somewhere?  update-initramfs: Generating /boot/initrd.img-3.13.0-62 WARNING: missing /lib/modules/3.13.0-62 Ensure all necessary drivers are built into the linux image! depmod: ERROR: could not open directory /lib/modules/3.13.0-62: No such file or directory depmod: FATAL: could not search modules: No such file or directory depmod: WARNING: could not open /var/tmp/mkinitramfs_TQSiag/lib/modules/3.13.0-62/modules.order: No such file or directory depmod: WARNING: could not open /var/tmp/mkinitramfs_TQSiag/lib/modules/3.13.0-62/modules.builtin: No such file or directory

I just upgraded linux-firmware package and after that I used $ sudo update-initramfs -u -k all but I got some errors:  $ sudo update-initramfs -u -k all [sudo] password for piotrek:  update-initramfs: Generating /boot/initrd.img-4.4.0-34-generic Warning: No support for locale: en_US.utf8 update-initramfs: Generating /boot/initrd.img-4.4.0-31-generic Warning: No support for locale: en_US.utf8 update-initramfs: Generating /boot/initrd.img-4.4.0-13-generic WARNING: missing /lib/modules/4.4.0-13-generic Ensure all necessary drivers are built into the linux image! depmod: ERROR: could not open directory /lib/modules/4.4.0-13-generic: No such file or directory depmod: FATAL: could not search modules: No such file or directory Warning: No support for locale: en_US.utf8 depmod: WARNING: could not open /var/tmp/mkinitramfs_LJbkti/lib/modules/4.4.0-13-generic/modules.order: No such file or directory depmod: WARNING: could not open /var/tmp/mkinitramfs_LJbkti/lib/modules/4.4.0-13-generic/modules.builtin: No such file or directory   I'm sure I don't have kernel 4.4.0-13. I might have had it some time ago but removed it:   $ apt list --installed | grep linux-  WARNING: apt does not have a stable CLI interface. Use with caution in scripts.  linux-base/xenial,xenial,now 4.0ubuntu1 all [installed,automatic] linux-firmware/now 1.159 all [installed,local] linux-headers-4.4.0-31/xenial-updates,xenial-updates,xenial-security,xenial-security,now 4.4.0-31.50 all [installed] linux-headers-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-headers-4.4.0-34/xenial-updates,xenial-updates,xenial-security,xenial-security,now 4.4.0-34.53 all [installed] linux-headers-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-image-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-image-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-image-extra-4.4.0-31-generic/xenial-updates,xenial-security,now 4.4.0-31.50 amd64 [installed] linux-image-extra-4.4.0-34-generic/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-libc-dev/xenial-updates,xenial-security,now 4.4.0-34.53 amd64 [installed] linux-sound-base/xenial,xenial,now 1.0.25+dfsg-0ubuntu5 all [installed] syslinux-common/xenial,xenial,now 3:6.03+dfsg-11ubuntu1 all [installed] syslinux-legacy/xenial,now 2:3.63+dfsg-2ubuntu8 amd64 [installed]   How to fix those update-initramfs errors?


I should like t travel by ship from Helsinki to Norway, but prefer cargo instead of cruise ships. In Norway, the Hurtiguten line runs ships along the western coadst of Norway, stopping at ports along the way. It used to be a cargo and mail ship but is now more of a cruise. Is there something like tht in Finland> Can one take a cargo ship from Helsinki to Stockholm and then to Oslo? From Oslo, I should like to continue to Iceland.  A friend told me that she has done it a few years ago, but she is unable to give me details.  Thanks for your help.

Planning a low budget and environment friendly trip to Iceland from Helsinki, Finland next summer for me and my friend. Haven't been able to find relevant information on possibility for cargo travel (from where - eg. Norway, Denmark? - timetables, prices etc). Expected departure from Helsinki around June 18th, return at latest on July 7th 2015. I'm very thankful for any related advice (and first time on stackexchange, so apologies if I didn't formulate my question in a best possible way)


Apart from specific mathematical uses, "linear" (from Latin linea "line") means "in the form of/having to do with a straight line". A linear equation is obviously called that because its graph is a straight line.  But why is a linear map, which is a different thing, called "linear"? What is it about a linear map that is "having to do with a straight line"?    Please note: I know that "linear function", and the word "linear" in general, can mean these two different things:   A function, such as $f(x)=ax+b$, that has a straight-line graph on the Cartesian plane, also called a "linear equation" A function obeying the constraints $f(\mathbf{a}+\mathbf{b})=f(\mathbf{a})+f(\mathbf{b})$ and $f(k\mathbf{a})=kf(\mathbf{a})$, also called a "linear map"   I am not asking for a definition of either of these things. Nor am I asking whether or not they're the same. I know they aren't.  I am trying to be clear about this because there seems to be confusion. There is a very similarly-worded question title already, "" That's marked as a duplicate of another question, "". And my question was closed as a duplicate too, but I'm positive that it's not. You see, both of those are actually about confusion between those two things, and the answers are "they're different, don't get them confused, they just use an ambiguous name".  My question is, why is the name "linear" applied to the second concept at all? What is "linear" about it? Why wasn't it called a "proportional", or "fandangled", or "dinglehopper" map instead? I want to know why it is that "linear" is an applicable term for this thing we call a "linear map".    Reasons that don't seem to suffice, but please correct me if I'm wrong on any of these:   Because its graph is a straight line. (Not good enough, because it's specifically a straight line through the origin, not a general straight line. Straight lines in general are affine maps, AKA linear equations in the other sense.) Because it preserves straight lines. (Unless I'm mistaken, so does an affine map.) Because it bears the property that we call "linearity". (Circular reasoning. Which came first, linearity or the linear map? Whichever it is, I want to know why that was called "linear".)

I always thought linear functions need to satisfy $$f(x+y)=f(x)+f(y).$$ I am a tad confused now, consider $f(x)=2x+3$. $f(1)=5$, $f(2)=7$, $f(1+2)=f(3)=9 \neq f(1)+f(2)$ which was what I thought linear functions should satisfy.  Could someone clarify?


"Big, white, mountain goat." "Fast, red, Japanese car"  Should there be a comma before "mountain" and before "Japanese"? Adjectives in a list are separated by commas in English, but somehow this last comma seems wrong to me. I've seen sentences with and without this comma. Can someone clarify this for me?  I apologize if my question is unclear, I'm not a native English speaker. I'd appreciate edits for clarity.

You can also contact me to customize your template, or create a new unique one.   Do I need to put a comma between the new and unique adjectives in this sentence?  In my native language (if I am not mistaken) we don't put a comma if the adjectives are of a different type. Not sure about English though, and if it's the case here anyway. Any help would be appreciated!


I have a table in MySQL with 3 columns a, b, c. Each has an index but none is primary key. When I run query SELECT * FROM table LIMIT 50;   I am trying to have the result sorted by column b ascending, however the result is sorted by column a ascending instead. I cannot make column b primary key because there are some duplicate values in column b. How do I do this without making column b primary key?

Suppose you have the following table and data:  create table t (     k int,     v int,     index k(k)     ) engine=memory;  insert into t (k, v) values (10, 1),        (10, 2),        (10, 3);   When issuing select * from t where k = 10 with no order by clause, how does MySQL sort the records by default?


Even in those days, this was incredibly rude! Giving the President of your country only seventeen days'' notice before making a speech, especially as he wasn’t top of the bill, would be unthinkable today! So, the day arrived, and Everett, well prepared, displayed his oratorical skills in a speech which lasted over two hours. Lincoln, on the other hand, spoke for just over two minutes.      I guess there is a mistake in the above context. It should be seventeen day's notice, not seventeen days notice, but I am not sure. Am I right or not?

Which one is correct?  1: Well, you canceled on Tuesday and our policy is 24 hours' notice for all cancellations. 2: Well, you canceled on Tuesday and our policy is 24 hours notice for all cancellations.  To me personally, the first one makes more sense grammatically. But I've also heard that the second version is how they typically write it on paper forms at hospitals (that's what native speakers say). Could you please clarify my confusion?


I'm making a PVP-style server for a group of my friends and I, and I wanted to make it so when a player was holding a "Dark Gnome's Shadow Wand" (a stick) in their hotbar or offhand, that it would trigger a command block to give them the blindness potion effect. I got the command to work before with scoreboards, but it would target everyone, which made it difficult to balance around...is there a way to target only one player with custom named items such as this?

I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,id:"minecraft:diamond_sword"}]}   but I can't get them together. The block should only look for an item in the active slot.


I have the below end points of line segments.  Line segment 1:  A = (X1, Y1) B = (X2, Y2)   Line segment 2:  C = (X3, Y3) D = (X4, Y4)   I want to get the point of intersection of these two line segments.  I tried like this:  def intersectionfn(l1,l2):      x1,y1 = l1.src.x, l1.src.y     x2,y2 = l1.dst.x, l1.dst.y     x3,y3 = l2.src.x, l2.src.y     x4,y4 = l2.dst.x, l2.dst.y      try:         xnum = float(((x1*y2-y1*x2)*(x3-x4))-((x1-x2)*(x3*y4-y3*x4)))         xden = float(((x1-x2)*(y3-y4))-((y1-y2)*(x3-x4)))         #print xnum, xden         xcoor = float(xnum)/xden         #print xcoor         ynum = float((x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4))         yden = float((x1-x2)*(y3-y4)-(y1-y2)*(x3-x4))         #print ynum, yden         ycoor = float(ynum)/yden         #print ycoor         return Point(xcoor,ycoor)     except:         print "No intersection.. 0/0 attempted"   But I am getting the output for infinitely long lines. I'm not aware of how to find it for line segments. If there is any algorithm/mathematical rule for it, please suggest it to me. I will implement it.

How do I determine whether or not two lines intersect, and if they do, at what x,y point?


Bonjour. I need help for this.     Let $a$, $b$, $a^\prime$, $b^\prime$, $a^{\prime\prime}$, and $b^{\prime\prime}$ be six non-zero positive numbers such that    $$\frac{a}{b}<\frac{a^\prime}{b^\prime}<\frac{a^{\prime\prime}}{b^{\prime\prime}}$$    We want to prove that this stuff holds:    $$\frac{a}{b}<\frac{ab+a^\prime b^\prime+a^{\prime\prime}b^{\prime\prime}}{b^2+{b^{\prime}}^2+{b^{\prime\prime}}^2}<\frac{a^{\prime\prime}}{b^{\prime\prime}}$$   Thanks.

Let $a_1,a_2,\dots,a_n$ and $b_1,b_2,\dots,b_n$ be two sets of reals such that $b_j>0$ for $1\leq j\leq n$. Let m and M be respectively the minimum and maximum of n fractions  $$\frac{a_1}{b_1},\frac{a_2}{b_2},\dots,\frac{a_n}{b_n}$$. Prove that  $$m\leq\frac{a_1+a_2+\dots+a_n}{b_1+b_2+\dots+b_n}\leq M$$.


How can I invert a mathematical operator about an imaginary vertical axis that runs through the symbol's center? Specifically, consider the symbol \prec, which resembles the less-than symbol <. I'd like to create an analogous version that is to the greater-than symbol > as \prec is to <. How can I do so?  I'm looking for an answer that I will be able to easily modify to various symbols other than \prec. In particular, besides \prec I'm currently interested in inverting the symbols \preceq as well as the following custom-made symbol:  \newcommand{\pprec}{\mathbin{{\prec}\mspace{-5mu}{\prec}}}   that is to \ll as \prec is to <.

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


I need to copy data values from one element to another, but jQuery's clone() method doesn't clone the data. And I can't iterate over the data either:  element.data().each   because data() is a function and not a jQuery object. It seems I have to keep a separate list of attribute names and reference those but that seems too hacky. So how can I do either of these:  a) Iterate over data items OR b) clone() an element with its data.

What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.


My application required to use some system command such as wm size and wm size reset to change the screen size so an application supposed be running on Portrait only mode will be displayed as portrait in a landscape screen.   I have gone through many of the answer in stack overflow but still can't get an idea of how to do it.  Somebody can give me a step by step guide how to achieve this thanks. I've tried the Andydroid emulator but still not work.  I know the emulator is rooted when using adb console but looks like if I test it with my program, it was not.

I'm using the official Android SDK with the Android Emulator to create a virtual Android 7.1.1 (x86). I need to test a number of things, amongst others, some applications require root access to the device.  Now I know that I can adb root and I have a root shell, but that doesn't allow the apps I install to have root access.  I've researched this topic now for a while and have seen various approaches. Most answer haven been posted rather long ago.  I think it's quite odd that there's no option to toggle root - this is after all an SDK.  How do I root an Android virtual device, running Android 7.1.1, effectively allowing installed apps root access?  edit: I'd rather not resort to paid emulators like Genymotion if possible.  edit2: This is solely for personal use.  edit3: Genymotion appears to be a viable solution, as an alternative emulator. How come Android SDK/Emulator does not offers such a feature?  edit4: The answer by  seems to work perfectly fine, however since Android Studio version 3.1 this doesn't seem to be a permanent rooting. Once the AVD is rebooted, root access is gone.


I have a simple question, how can I change name 'Develop' to some other name? You can see an example below:

After installing Windows 10 on my  it took my user name 'Jeremy' and created a user folder named C:\Users\jerem.  I want to rename the folder C:\Users\Jeremy.  does not work. There are a couple of reasons.   OneDrive is now a fully integrated part of the OS, and it completely breaks.  A find/replace in the registry seems to work, but it's hard to be confident in that approach. When the computer is rebooted, the TabletInputService writes a TextHarvester.dat file to the old user profile location (creating it if needed). This makes it impossible to keep the folder deleted. An old  doesn't work. This issue also causes an error message to pop up every time the computer boots.


Assume that $K$ be a number field and $L/K$, $L'/K$ are two separable extensions. Now let $\mathfrak{p}$ be a prime ideal of $\mathcal{O}_K$. Then if $\mathfrak{p}$ is totally split ind $L$ and $L'$, why is $\mathfrak{p}$ also a totally split in $LL'$?  My approach is to prove that every prime ideal $\mathfrak{P}$ of $L$ or $L'$ over $\mathfrak{p}$ is totally split in $LL'$, but I couldn't prove this either.

If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it?


I am maintaining a few Python packages, and on systems where dependencies are not fully satisfied, functions which may otherwise work, fail due to global scope imports:  import numpy as np  def lala(in):     out = max(in)     return out  def fufu(in):     out = np.mean(in)     return out   So for instance here I cannot use lala() if I do not have numpy, ven if lala does not use numpy. Of course, ideally dependencies would be managed correctly, still, it would make for a more robust package if functions failed only when they had to fail.  Is there any reason why imports are almost never done in function scope? Is this reason just reducing the number of lines?

I've discovered a new pattern.  Is this pattern well known or what is the opinion about it?  Basically, I have a hard time scrubbing up and down source files to figure out what module imports are available and so forth, so now, instead of  import foo from bar.baz import quux  def myFunction():     foo.this.that(quux)   I move all my imports into the function where they're actually used., like this:  def myFunction():     import foo     from bar.baz import quux      foo.this.that(quux)   This does a few things.  First, I rarely accidentally pollute my modules with the contents of other modules.  I could set the __all__ variable for the module, but then I'd have to update it as the module evolves, and that doesn't help the namespace pollution for code that actually lives in the module.  Second, I rarely end up with a litany of imports at the top of my modules, half or more of which I no longer need because I've refactored it.  Finally, I find this pattern MUCH easier to read, since every referenced name is right there in the function body.


Strange, but it seems the LWC Tree Grid component will only display fields on the object(s) queried, and not any values retrieved through a relationship (__r). I can't imagine why this would be - the values returned are parsed in JS anyway, and I don't see how they are any different from other fields. Anyone else discovered this? This makes it virtually impossible to use them with junction objects! <template>     <lightning-card title="Success Criteria with Adapters">          <div class="slds-m-bottom_small">             <lightning-button                 label="Expand All"                 onclick={clickToExpandAll}>             </lightning-button>             <lightning-button                 label="Collapse All"                 onclick={clickToCollapseAll}>             </lightning-button>         </div>                  <lightning-tree-grid              columns={gridColumns}              data={gridData}              key-field="Id"             hide-checkbox-column="true">         </lightning-tree-grid>              </lightning-card> </template>  JS import {LightningElement, wire, api} from 'lwc'; import getSCsWithAdapts from '@salesforce/apex/OppTrackTree.SCsWithAdapts';  export default class SCsWithAdapts extends LightningElement {          @api recordId;      gridData;     gridColumns = [{             type: 'text',             fieldName: 'Use_Case__c',             label: 'Use Case',                      },         {             type: 'text',             fieldName: 'Use_Case_Status__c',             label: 'Use Case Status',                      },         {             type: 'text',             fieldName: 'Sales_Engineer__r.Name',             label: 'Sales Engineer',         },         {             type: 'text',             fieldName: 'Use_Case_Category__r.Name',             label: 'Category',                      },         {             type: 'text',             fieldName: 'Adapter__r.Name',             label: 'Adapter',                      },     ];      clickToExpandAll(e) {         const grid =  this.template.querySelector('lightning-tree-grid');         grid.expandAll();     }      clickToCollapseAll(e) {         const grid =  this.template.querySelector('lightning-tree-grid');         grid.collapseAll();     }      @wire(getSCsWithAdapts, {OppID: '$recordId'})         SCsWithAdapts({data, error}) {             if (data) {                 let parseData = JSON.parse(JSON.stringify(data));                  for (let i = 0; i < parseData.length; i++) {                     parseData[i]._children = parseData[i]['POC_Success_Criteria_Adapters__r'];                     delete parseData[i]['POC_Success_Criteria_Adapters__r'];                 }                  this.gridData = parseData;              } else if (error) {                 console.log('error ====> ' + JSON.stringify(error));             }         } }  Apex public with sharing class OppTrackTree { @AuraEnabled(Cacheable=true) public static list<POC_Success_Criterion__c> SCsWithAdapts(String OppID){          String strSOQL = 'SELECT Use_Case__c, Use_Case_Status__c, Sales_Engineer__r.Name, Sales_Engineer__c, Use_Case_Category__r.Name, Use_Case_Category__c, (SELECT Adapter__r.Name, Adapter__c FROM POC_Success_Criteria_Adapters__r) FROM POC_Success_Criterion__c WHERE Opportunity__r.Id = \''+OppId+'\'';          return Database.query(strSOQL);   }  }

Working with a prototype of a lightning web component, I get that the datatable, just like its Aura brother, needs the columns to be manually specified.   That being said, I have the following specification for a datatable that receives pricebook entries:  const columns = [     { label: 'Name', fieldName: 'Product2.Name' } ]   The names do not display on the component, but if I use a forEach to list the data retrieved by the component, I get the products names, like in:  connectedCallback() {     getProducts({ pricebookId: this.pricebookId, countLimit: 4 })         .then(result => {             this.products = result             this.products.forEach(p => {                 console.log(p.Product2) // Proxy {} object is displayed                 console.log(p.Product2.Name) // The name is displayed             });             this.tableIsLoading = false         })         .catch(error => {             console.error(error)         }) }     If the datatable component does not support this, then the correct way of dealing with this is to work with the retrieved data, and build a new list with direct access to the data (no parent-child objects), or to edit the current data and include fields that I can access?   For example, should I iterate the result data and add a productName attribute to the elements, and then set 'productName' as the attribute on the column variable?  Edit: just noticed that you can't iterate the data list and create a new productName property. You end up with a TypeError: 'set' on proxy: trap returned falsish for property 'productName'.


I am trying to return a dictionary with key/value pairs, but this is what I got and it does not work. def lists_to_dict(keys, value):     for i in values:         value[i]=map(int, value[i])         return keys

Imagine that you have the following list. keys = ['name', 'age', 'food'] values = ['Monty', 42, 'spam']  What is the simplest way to produce the following dictionary? a_dict = {'name': 'Monty', 'age': 42, 'food': 'spam'}


I am leaving Jamaica to go to Austria, what should I write as my entry state of  first entry? I will be leaving to study for 4 months. Also, I am not sure what I need to write for member state (s) of destination. Should I write Austria since this is the main destination?

Travelling to France from UK with my family and while filling in the visa application form but there is a question that needs to be answered and I am not clear what to fill in:  Member State of first entry  - what should be filled in here?  Flight is from UK to France (CDG) but the flight operator is KLM and it is not direct. there is a 45 min break between two flights  UK(Leeds) — Netherlands(Amsterdam) — France (Paris)  Should the answer to this question be France (Paris) or Netherlands (Amsterdam).


I got my reputation back for the questions marked with green marker, but not for the questions marked with red color.  This is not a duplicate.  I saw that link before. I didn't get my reputation back.

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


Consider the sequence defined by $$ \begin{cases} r_0=1\\ r_1=3\\ r_n=6r_{n-1}-9r_{n-2} & \text{if }n\ge 2 \end{cases} .$$ Find a closed form for $r_n$.    The characteristic equation of the recurrence is $c^2-6c+9=0.$  But I don't know how to proceed.  Solutions are greatly appreciated.

Consider the sequence defined by $$ \begin{cases} a_0=1\\ a_1=2\\ a_n=3a_{n-1}+4a_{n-2} & \text{if }n\ge 2 \end{cases} .$$ Find a closed form for $a_n$.    I tried listing out examples, but I don't see any common pattern between them.  All solutions are greatly appreciated.


I have some code examples like this  ---------------------- First example -----------------  var rightFunction=function() {         if (options.currentPage < options.numberOfPages) {             options.currentPage += 1;             ajaxConnection();         }         return false;     };      $('#newsContainer #rightSlider').click(rightFunction);     $('#rightSliderHigh').click(rightFunction);   ---------------------- Second example-------------------   $('#rightSliderPagination').click(function(){         if (parseInt(_pagina_last_link.html()) >= options.numberOfPages) {             return false;         }         _first_page_num = parseInt(_pagina_first_link.html());         paginationGenerator(_first_page_num + options.centerNumber - 1);         $('#slider-inner').slider("option", "value", _first_page_num + options.centerNumber - 1);         return false;     });   ------------------------Third example ----------------------  $(".download").click(function(){         if($(this).attr('goToPage')=='true') {             var url=$(this).attr('href');             document.location.href=url;             return false;         }          var _this = $(this);         var thistext = $("#bg-download-box").html();         var _whattoshow = $(this).parent().find(".what-to-show").html();          if (_whattoshow){             $("#bg-download-box form").html(_whattoshow);         }          else{             $("#bg-download-box").html("

");         }           if ($(".reccomend-box").length != 0){         $("#rightColumn").css("z-index",99999);         }          $("#bg-download-box").show();         var whattocopy = $("#bg-download-box");         $(whattocopy).insertAfter(_this);         $("ul#songs-list").css("z-index","99999");           $("ul#songs-list li.b-a-r").removeClass("emph");          $(this).parent().parent().parent().addClass("emph");         return false;     });     Why is return false is used at end of these functions. Please, somebody could explain the purpose of return false.

Many times I've seen links like these in HTML pages:  Click here !   What's the effect of the return false in there?  Also, I don't usually see that in buttons.  Is this specified anywhere? In some spec in w3.org?


I have a C++ std::map that I'm using to store information about connected components. Here's the segment of code from my BaseStation class, it's very basic  //Constructor BaseStation(string name, int x, int y){     id = name;     xpos = x;     ypos = y; }  //Accessors string getName(){     return id; }   In my main code, I have a map declared as   map<BaseStation, vector<string> > connection_map;  The connection_map is updated in a while loop as follows, and then for my own debugging purposes I want to dump the contents of the map. I append a BaseStation object to the map (as the key) and as the value we have the list of links to the BaseStation object:  connection_map[BaseStation(station_name, x, y)] = list_of_links;  list_of_links.clear();  for(auto ptr = connection_map.begin(); ptr != connection_map.end(); ++ptr){     cout << ptr->first.getName() << " has the following list: ";     vector<string> list = ptr->second;     for(int i = 0; i < list.size(); i++){         cout << list[i] << " ";     }     cout << endl; }   This is the error I get in my main when I try to compile my code via clang++:  server.cpp:66:11: error: 'this' argument to member function 'getName' has type   'const BaseStation', but function is not marked const             cout << ptr->first.getName() << " has the following list: ";   and in VSCode, the tooltip highlight at the cout (cout << ptr->first.getName()) is the following:  the object has type qualifiers that are not compatible with the member  function "BaseStation::getName" -- object type is: const BaseStation   I don't understand what's going on, as the getName() function is most definitely not constant, and nowhere do I declare my BaseStation object as const either. If someone could help me out that would be great. Thanks!

The following code says that passing the map as const into the operator[] method discards qualifiers: #include <iostream> #include <map> #include <string>  using namespace std;  class MapWrapper { public:     const int &get_value(const int &key) const {         return _map[key];     }  private:     map<int, int> _map; };  int main() {     MapWrapper mw;     cout << mw.get_value(42) << endl;     return 0; }  Is this because of the possible allocation that occurs on the map access? Can no functions with map accesses be declared const? MapWrapper.cpp:10: error: passing const std::map<int, int, std::less<int>, std::allocator<std::pair<const int, int> > > as this argument of  _Tp& std::map<_Key, _Tp, _Compare, _Alloc>::operator[](const _Key&)  [with _Key = int, _Tp = int, _Compare = std::less<int>,  _Alloc = std::allocator<std::pair<const int, int> >] discards qualifiers


I am getting a value as 9999912499 from the database. I have separated it in two parts 99999 and 12499 using substring. Now I want to check whether if the 1st string is equal to 99999 then i do some processing otherwise something other processing. But controls never gets in to the if loop   Following is a snapshot:  String strPscId = Long.toString(pscID); String convPscID = strPscId.substring(5, strPscId.length()); String checkNine = strPscId.substring(0,5); BigDecimal jpaIdObj = jeuParam.getJpaIdObj(); Long mod_id  = modele.getModId();  log.info("outstrPscId == " +strPscId); log.info("outconvPscID == " +convPscID); log.info("outcheckNine == " +checkNine); log.info("outjpaIdObj == " +jpaIdObj); log.info("outmod_id == " +mod_id);  if(checkNine == "99999") { <method-call> } else { <another - method - call> }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


In  it is shown that when a pair of parabolas have perpendicular axes and intersect at four points, the four points are concyclic (belong to the same circle).  It's easy to show that this is true in general, if we have coordinate equations in the form   $ax^2+bxy+cy^2+dx+ey+f=0, a'x^2+b'xy+c'y^2+d'x+e'y+f'=0$  for each parabola, by taking a linear combination of the two equations you can make the quadratic component a multiple of $x^2+y^2$ (from the hypothesis you can render $a'=c, b'=-b, c'=a$).  But is there a way to prove the claim by purely geometric techniques?  It smells like something that would have a purely geometric proof, but I can't see exactly how.

Problem: Consider two parabolae such that their axes of symmetry form a right angle. Prove that all four points of intersection lie on a common circle (it is an assumption that there exist such four points). Could you help me obtain a non-algebraic solution? (The algebraic one I did is given below.)  Algebraic solution:  There is a very simple algebraic approach, just introduce a Cartesian coordinate system such that the parabolae are given by equations:  $$y = \alpha_1 x^2 + \beta_1 $$ $$x = \alpha_2 y^2 + \beta_2 $$  and by scaling, adding and simplifying we can get the following ordinary circle equation (the right-hand side is positive because parabolae intersect): $$ \left(x-\frac{1}{2\alpha_2}\right)^2 + \left(y - \frac{1}{2\alpha_1}\right)^2 = \frac{-\beta_1}{\alpha_1} + \frac{-\beta_2}{\alpha_2} + \left(\frac{1}{2\alpha_1}\right)^2 + \left(\frac{1}{2\alpha_2}\right)^2$$  Non-algebraic solution: ??


It doesn't matter what wagon you board; you will love the journey.   In  this sentence do I use what or should I say which?

Most of the time one or the other feels better, but every so often, "which" vs. "what" trips me up.   So, what's the exact difference and when should you use one or the other?