Find isomorphism between $F_2[x]/(x^3+x+1)$ and $F_2[x]/(x^3+x^2+1)$.    It is easy to construct an injection $f$ satisfying $f(a+b)=f(a)+f(b)$ and $f(ab)=f(a)f(b)$. However, I am stuck how to construct such a mapping that is bijective.  Thank you for help!

Suppose $K$ is a finite field, $K = \mathbb F_{p^s}$. If we take an irreducible polynomial $f$ of degree $d$ over $K$, then the splitting field $L$ of $f$ is $K(\alpha)$ where $f$ is the minimal polynomial of $\alpha$. But then $L = \mathbb F_{p^{sd}} $. Since $\mathbb F_{p^{sd}}$ is unique, we see that this is the splitting field of every irreducible polynomial of degree $d$ over $K$.   Take $K = \mathbb F_2$ and let $P(X) = X^3 + X + 1$, $Q(X) = X^3 + X^2 + 1$. Let $L$ be the splitting field of $P$ and $L'$ be the splitting field of $Q$. The above tells us that $L$ and $L'$ are isomorphic. I would like to construct an explicit isomorphism between $L$ and $L'$.   I know that $L \cong \mathbb F_2[X] /(X^3 +X + 1)$ and $L' \cong \mathbb F_2[X] / (X^3 + X^2 + 1)$. Intuitively, I want to find an isomorphism $\phi : \mathbb F_2[X] \to \mathbb F_2[X]$ such that $\phi((X^3 + X + 1)) = (X^3 + X^2 + 1)$. A little playing around gives me $\phi(X) = X+1$. It now feels like I'm falling at the last hurdle: how do I finish the construction of an isomorphism between $L$ and $L'$? I don't think $\phi$ makes sense as a map from $L$ to $L'$, yet it seems the map I want.


I'm reading Shreve's Stochastic Calculus for Finance. On page 35, he gives this example:  Example 1.6.4. Recall Example 1.2.4 in which $\Omega =  [0, 1]$, $\mathbb{P}$ is the uniform (i.e., Lebesgue) measure, and $$\widetilde{\mathbb{P}}[a, b] = \int_a^b 2\omega d\omega = b^2 - a^2, > 0 \leq a \leq b \leq 1.$$ We may use the fact that $\mathbb{P}(d\omega)=d\omega$ to rewrite the above as $$\widetilde{\mathbb{P}}[a, b] = \int_{[a, b]} 2\omega d\mathbb{P}(\omega)$$  I'm confused by "$\mathbb{P}(d\omega)=d\omega$". In my mind, $\mathbb{P}$ is a measure, $d\omega$ outside of an integral is meaningless, and $\mathbb{P}(d\omega)$ symbolically doesn't have any meaning. How do I interpret $\mathbb{P}(d\omega)$? How do I make sense of Shreve's substitution? Edit: What set is the equivalence relation $=$ in "$\mathbb{P}(d\omega)=d\omega$" defined over?

I am currently reading S. Shreve's book Stochastic Calculus II, and I have a question regarding Example 1.6.4 (p.35-36) which describes a change of measure, but I am puzzled by the notation.  $\Omega=[0,1], \mathbb{P}$ is the uniform measure and  $$\tilde{\mathbb{P}}[a,b]=\int_a^b 2\omega d\omega=b^2-a^2$$ for $0\le a\le b \le 1$.  The first step is:     We may use the fact that $\mathbb{P}(d\omega) = d\omega$ to rewrite the equation above as   $$\tilde{\mathbb{P}}[a,b]=\int_a^b 2\omega d\mathbb{P}(\omega).$$   I have several questions regarding this statement:   $\mathbb{P}$ is a probability measure from $\mathcal{F}\rightarrow\mathbb{R}$, I cannot find a clear definition in the book what $\mathbb{P}(d\omega)$ actually means. Is $d\omega$ actually an event? Why does this $\mathbb{P}(d\omega) = d\omega$ help in rewriting, shouldn't we need $d\mathbb{P}(\omega) = d\omega$? What does $\mathbb{P}(d\omega) = d\omega$ even mean, and why is this true?


For an arbitrary quadrilateral ABCD prove that Area(ABCD) ≤ (AB·CD+BC·AD)/2

Prove that the area of a quadrilateral is one half the product of the lengths of its diagonals and the sine of the angle between the diagonals.


my server copy it if you want! :)  how do i find my ipv4 using python? can i you try to keep it real short?  import socket  def Main():     host = '127.0.0.1'     port = 5000      s = socket.socket()     s.bind((host,port))      s.listen(1)     c1, addr1 = s.accept()     sending = "Connection:" + str(addr1)     connection = (sending)      print(connection)     s.listen(1)     c2, addr2 = s.accept()     sending = "Connection:" + str(addr2)     connection = (sending)     print(connection)     while True:         data1 = c1.recv(1024).decode('utf-8')         data2 = c2.recv(1024).decode('utf-8')         if not data1:                                         break         if not data2:             break         if data2:             c1.send(data2.encode('utf-8'))         if data1:             c2.send(data1.encode('utf-8'))     s.close()   if __name__== '__main__':     Main()    thx for the help i appreciate it!

How can I find local IP addresses (i.e. 192.168.x.x or 10.0.x.x) in Python platform independently and using only the standard library?


How can I align the small, large and user columns under every multicolumn. Alignment gets lost when using multicolumn. Code below:  \begin{table}[] \centering \resizebox{\columnwidth}{!}{ \begin{tabular}{l|c|c|c|c|cccccccccccccccccccccccc} \toprule \multirow{3}{*}{\color{red}{\textbf{SAD}}} & \multicolumn{4}{c}{} & \multicolumn{3}{c}{\textbf{Troll}} & \multicolumn{3}{c}{\textbf{Doll}} & \multicolumn{3}{c}{\textbf{Donkey}} & \multicolumn{3}{c}{\textbf{Elephant}} & \multicolumn{3}{c}{\textbf{Plant}} & \multicolumn{3}{c}{\textbf{Pineapple}} & \multicolumn{3}{c}{\textbf{Plastic bag}} & \multicolumn{3}{c}{\textbf{Net}} \\  & overall & avg. small & avg. large & avg. medium & \multicolumn{3}{c}{(Strongly Transparent)} & \multicolumn{3}{c}{(Strongly Transparent)} &      \multicolumn{3}{c}{(Medium Transparent)} & \multicolumn{3}{c}{(Medium Transparent)} & \multicolumn{3}{c}{(Little Transparent)} & \multicolumn{3}{c}{(Little Transparent)} & \multicolumn{3}{c}{(Highly Transparent)} & \multicolumn{3}{c}{(Highly Transparent)} \\  & rank & rank & rank & rank & small & large & user & small & large & user & small & large & user & small & large & user & small & large & user & small & large & user & small & large & user & small & large & user \\  \rowcolor{blue!10} GAN & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ & $1.0_{\color{blue}1}$ \\  \bottomrule \end{tabular} } \label{tab:my_label} \end{table}

I'm trying to typeset a table that would have a header in the first row (I'm not looking for a different/better solution to adding a header, but for a fix to this solution. Thanks). I want to achieve this by having a multicolumn cell spanning all the columns of the first row. The problem is that if the text is too long, the column widths are uneven, with the last column accumulating excess width. I would expect all of the columns to be of approximately the same width (although I cannot find a decent source that would say they should), given the fact that all the text in the second row is of approximately the same width.  I find this behaviour quite puzzling and have no idea what the cause could be. I know I could perhaps remedy this by manually setting the column widths, but am curious as to how to fix this without doing that (I do not need or indeed want the columns to be of the same width, but roughly proportional to the length of their content), preferably but not necessarily by using the tabular environment only (some other conflict with the document class I am using).   What is it that I'm doing or assuming wrong? And why?  MWE:  \documentclass{article} \begin{document}  \begin{tabular}{ccccc} \multicolumn{5}{c}{This is a piece of text. The longer it is, the longer the last column.} \\  1 & 2 & 3 & 4 & 5 \\ \hline \end{tabular}  \end{document}   Resulting table. Notice how the last column of the second row accumulates excess width.


We recently moved our 2016 sql server mirror into Azure, but it's on an underpowered machine.  Our main database server has 16 physical cores with hyper threading and 2 numa nodes.  We have set the maxdop to 16 for this machine. Edit: I had previously set it to 8 and saw the same issues. The mirror host has a much weaker cpu, so we had to set the maxdop to 4. When we are running an intense query on the principle database, we sometimes get an error: Unexpected job failure.: System.Data.SqlClient.SqlException (0x80131904): The query processor could not start the necessary thread resources for parallel query execution.  I am wondering if could be due to the underpowered mirror server running out of resources while it is trying to commit all the transactions that are being fed across to it from the principal server. I'm not a DBA, and we currently do not have one on staff (so I guess I am the DBA), so a lot of these settings and errors are foreign to me. Edit2:  This question is different from the one suggested because I originally followed the directions and scripts in that post to set my MAXDOP to appropriate values.

Today we experienced a degradation in performance on our production sql server.  Durring the time this occurred we logged several "The query processor could not start the necessary thread resources for parallel query execution" errors.  The reading that I've done suggests that this has to do with how many CPUs to use when executing a complex query.  However when I checked during the outage our CPU Utilization was only at 7%.  Is there something else this could be referring too that I haven't come across yet?  Is this a likely culprit of the performance degradation or am I chasing a red herring?  My sp_configure values for this are as follows:  name                                minimum maximum config_value run_value cost threshold for parallelism      0       32767   5            5


So, I had a windows laptop that I installed Linux onto. Fedora onto the storage drive, and Kubuntu on a separate NVMe drive. A lot of my data was on the Fedora drive, then I put the old Windows drive back into the laptop, and it apparently thought the Fedora drive was supposed to be an NTFS storage drive because now the drive is called DATA, all that's on it is: $RECYCLE.BIN     S-1-5-18         desktop.ini     S-1-5-21-4039987853-288116331-4186372247-1001         desktop.ini Recovery     Logs System Volume Information     AadRecoveryPasswordDelete     ClientRecoveryPasswordRotation     EDP         Recovery     IndexerVolumeGuid     tracking.log     WPSettings.dat  What's not there is my personal files or Fedora system files. If you could help me get my personal files back, that would be great.

Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file.


The following code just keeps on crashing when it reaches the part with _itoa, I've tried to implement that function instead and then it got even weirder, it just kept on crashing when I ran it without the debugger but worked fine while working with the debugger.  # include "HNum.h" # include <stdio.h> # include <stdlib.h> # include <string.h> # include <assert.h> # define  START_value 30   typedef enum {     HNUM_OUT_OF_MEMORY = -1,     HNUM_SUCCESS = 0, } HNumRetVal;  typedef struct _HNum{     size_t Size_Memory;      char* String; }HNum;  HNum *HNum_alloc(){     HNum* first = (HNum*)malloc(sizeof(HNum));     if(first==NULL){         return NULL;     }     first->String =(char*)malloc(sizeof(START_value));     if(first->String==NULL){         return NULL;     }     first->Size_Memory = START_value; // slash zero && and starting from zero index;     return first; }  HNumRetVal HNum_setFromInt(HNum *hnum, int nn){     itoa(nn,hnum->String,10); }  void main(){     HNum * nadav ;     int h = 13428637;     nadav = HNum_alloc();     nadav->String="1237823423423434";     HNum_setFromInt(nadav,h);     printf("nadav string : %s \n ",nadav->String);     //printf("w string %s\n",w->String);     //printf("nadav string %s\n",nadav->String);     HNum_free(nadav);  }   I've been trying to figure this out for hours and couldn't come up with anything... The IDE I'm using is Visual Studio 2012 express, the crash shows the following: "PROJECT C.exe has stopped working windows can check online for a solution to the program."

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.


If the power series $\sum_{n\in\mathbb N}a_n\frac{x^n}{n!}$ converges for all real $x$, then the answer is trivially yes.  If the power series above has radius of convergence $3r>0$, let $\psi_r\in C^\infty(\mathbb R)$ be supported in $[-r,r]$ with $\psi_r(0)=1$ and $\psi_r^{(n)}(0)=0$ for $n>0$, and observe that $$ h(x):=\begin{cases} \psi_r(x)\sum_{n\in\mathbb N}a_n\frac{x^n}{n!}&\text{if }x\in [-2r,2r],\\ 0&\text{otherwise} \end{cases} $$ does the job. (For the sake of completeness, I construct such a $\psi_r$ below.)  The case where $\sum_{n\in\mathbb N}a_n\frac{x^n}{n!}$ converges only at $x=0$ (e.g., if $\{a_n\}$ is something awful like $\{(n!)^2\}$) is the one I'm stuck on.    Here we construct the function $\psi_r$ used in the second case above: Define $$\begin{align} f(x)&=\begin{cases} e^{\frac {-1}{x}}&\text{if }x>0,\\ 0&\text{if }x\leq 0 \end{cases}\\ g(x)&=\frac {f(x)}{f(x)+f(1-x)} \end{align}$$ as in . Then $$\begin{align} \psi(x)&:=1-g(x)-g(-x) \end{align}$$ is a $C^\infty$ function with support $[-1,1]$ satisfying $\psi(0)=1$ and $\psi^{(n)}(0)=0$ for all $n>0$ (this much is clear from the list of properties of $g$ given in the linked article). Take $\psi_r(x)=\psi(x/r)$, and observe that $\psi_r$ does the job.

Do you have some reference to a proof of the so-called Borel theorem, i.e. every power series is the Taylor series of some $C^{\infty}$ function?


I wish to understand geometrically (not just algebraically) why the dimension of the Grassmanian $G(k,n)$ is $k(n-k)$ and the dimension of a flag manifold $F(k_{1},k_{2},...,k_{n},N)$ is $\sum_{i=1}^{n}k_{i}(k_{i-1}-k_{i})+Nk_{n}$ (in fact with understanding the Grassmanian case it would be enough because the flag are just "nested" Grassmanians).  I am thinking in a spatial way in the well known $G(2,5)$ but I am unable to see geometrically how the space of all $2$-planes in $\mathbb{P}^{5}$ can be $6$-dimensional...


I'm extremely new to oracle and I've been tasked to send the result of a certain SELECT query through email and have it regularly scheduled as well.  I've tried looking at other posts as well but I could not make sense of any of it. Can someone show me how to do it in a simple way?

I have couple stored procedures and a package.  Whenever this stored procedure and package goes invalid, I need to send an email.    How can I achieve this?  Can you please give me an idea how this can be done.


I want to add come mouseover and mouseout functions to a series classes. So I use JQ selectors with variables in a loop:  for(i=1;i<=2;i++){     cid='.Cid'+i;     ccid='.CCid'+i;     csid='.CSid'+i;          $(cid).mouseover(function(){     $(ccid).addClass("RelatedMainComment");     $(csid).addClass("RelatedMainComment");     });     $(cid).mouseout(function(){         $(ccid).removeClass("RelatedMainComment");         $(csid).removeClass("RelatedMainComment");     });     }   But it doesn't run correctly, It seems to add the last one class, which in the example it is the class "Cid2", the mouseover ande mouseout function. So I take an another experiment:  i=1;     cid='.Cid'+i;     ccid='.CCid'+i;     csid='.CSid'+i;          $(cid).mouseover(function(){     $(ccid).addClass("RelatedMainComment");     $(csid).addClass("RelatedMainComment");     });     $(cid).mouseout(function(){         $(ccid).removeClass("RelatedMainComment");         $(csid).removeClass("RelatedMainComment");     });     i=2;   it's result is same with the former one . besides,If the code is :          for(i=2;i>=1;i--){     cid='.Cid'+i;     ccid='.CCid'+i;     csid='.CSid'+i;          $(".Cid"+i).mouseover(function(){     $(".CCid"+i).addClass("RelatedMainComment");     $(".CSid"+i).addClass("RelatedMainComment");     });     $(".Cid"+i).mouseout(function(){         $(".CCid"+i).removeClass("RelatedMainComment");         $(".CSid"+i).removeClass("RelatedMainComment");     });     }   it can't work. Can you explain why?

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


I have table with the following structure:  id | sender_mail | recipient_mail | username | subject | message | created 1    aa@test.com    bb@test.com        aaa       xxxx     yyy       10 2    bb@test.com    aa@test.com        bbb       xxxx     yyy       11 3    cc@test.com    bb@test.com        ccc       xxxx     yyy       12 4    bb@test.com    cc@test.com        bbb       xxxx     yyy       13 5    dd@test.com    gg@test.com        ddd       xxxx     yyy       14 6    gg@test.com    bb@test.com        ggg       xxxx     yyy       15   What I want is to get all unique pairs between columns sender_mail and recipient_mail where one of those columns has a value of email I'm passing in to the query. For example, if i put in bb@test.com as argument, the desired output should be:  id | sender_mail | recipient_mail | username | subject | message | created 2    bb@test.com    aa@test.com        bbb       xxxx     yyy       11 4    bb@test.com    cc@test.com        bbb       xxxx     yyy       13 6    gg@test.com    bb@test.com        ggg       xxxx     yyy       15   I tried out this SQL query:  SELECT * FROM messages AS m WHERE     m.sender_mail = 'bb@test.com' OR     m.recipient_mail = 'bb@test.com'  GROUP BY m.sender_mail, m.recipient_mail   It seemed to work when I passed the query to database directly (sequel pro). But when I put this code in a Drupal controller, an error gets thrown out:     Drupal\Core\Database\DatabaseExceptionWrapper: SQLSTATE[42000]:    Syntax error or access violation: 1055 'drupal.m.username' isn't in   GROUP BY:  SELECT m.sender_mail, m.recipient_mail, m. username,   m.subject, m.message, m.created   After googling, I found out that Drupal 8 enforces ONLY_FULL_GROUP_BY for SQL.  What is the workaround for this? How do I need to alter my query?

In my custom Drupal 8 plug-in I perform such query:  $select = db_select('my_table', 'e'); $select->addField('e', 'field1');  $select->condition('field3', 'NULL', '!='); $select->condition('field4', array(11, 12, 31, 32, 33), 'IN');  $select->groupBy("e.field1"); $select->orderBy("e.field1"); $select->orderBy("e.field5"); $entries = $select->execute()->fetchAll(\PDO::FETCH_ASSOC);    And it works fine. It returns me all records grouped by field1 that meets the condition, orderered. But it returns only field1 column.  I wanted to get more columns, so I have added another $select->addField('e', 'field2'); just after first one:  $select = db_select('my_table', 'e'); $select->addField('e', 'field1'); $select->addField('e', 'field2');  $select->condition('field3', 'NULL', '!='); $select->condition('field4', array(11, 12, 31, 32, 33), 'IN');  $select->groupBy("e.field1"); $select->orderBy("e.field1"); $select->orderBy("e.field5"); $entries = $select->execute()->fetchAll(\PDO::FETCH_ASSOC);    This time I get error:     Drupal\Core\Database\DatabaseExceptionWrapper: SQLSTATE[42000]: Syntax error or access violation: 1055 Użyto 'my_database.e.field2' bez umieszczenia w group by:   Which means "my_database.e.field2 has been used without putting in into group by". But I don't want to group by every column I select.  Unfortunatelly Drupal 8 added ONLY_FULL_GROUP_BY :( Then, how can I use groupBy and select more then one column at the same time?


Searching for clear explanations of why FTL equals time travel I found this  Go at the bottom, when he draws the blue lines. He says that those are the lines of costant time and they are parallel to the space line of the relativistic ship. This imply that the time line is perpendicular to the space line. But before he had said that the time line of the ship was the one named "space ship time" that is skewed towards the space line. So it seems to me that there are two time lines for the ship: the "space ship time" line and the one perpendicular to the space line that isn't drawn.  To say it in other words: if we have a relativistic ship its space and time lines should both be skewed towards the light line, right ? Because light speed is costant for any observer. This means that the light line should always be at the same distance from both the time and the space line.  But when the blue lines are drawn the time line is said to be perpendicular to the space line. This means that the light line would be closer to the space line that the time line. Thus meaning that light would be faster for that observer.  The problem is that if we consider the "space ship time" line as the correct time line there is no time travel.  EDIT: I think I'm starting to understand. In other examples I found online they suggest to rotate the graph, so that the time line of the space ship is pointing towards high. That makes evident the FTL communications between Earth and AC are distorted from the point of view of the ship, with the ones sent from AC to Earth arriving before they are sent. If the ship can sent messages at near istantaneous speed those messages would be a line perpendicular to their time line, but these lines woldn't be perpendicular to the time lines of Earth and AC, arriving after or even before they are sent. So to avoid time paradoxes you have time lines of different reference frames to always make an acute angle. If they were to make a dull angle (by going FTL) that would mean they are going in the past of each other. In fact you could rotate the graph to make on of them your y axis and see that the other is going down (towards the past). Is this correct ?  EDIT 2: Graph I made  In the horrbible graph above we have Earth and AC time lines (black), the realtivistic ship time line (blue) and near istantaneous FTL communications (purple). The first message is sent from AC to Earth, from their point of view is istantaneous, but from the point of view of the ship is going back in the past. When they receive it they sent a message back to AC (purple line perpendicular to blue line). Again this message is istantaneous from their POV, but from AC POV it arrives before it is sent. So AC receive an answer to a message that they haven't sent yet. What did I do wrong ?

Is this statement true?     You can not travel back in time. If I travel fast enough the clock will start to go backwards, but that does not mean I am traveling back in time. It would only mean that the time reference is producing a negative count.


I know that this question has been asked before, but I have read the posts and tried everything and it still won't light. I have used 10 obsidian blocks to make a 4x5 portal, not touching any other obsidian. when I try to activate the portal it just sets the obsidian block on fire. any suggestions?

Where do I light my nether portal on Minecraft Pocket Edition 0.10.5?


I was watching a Mathologer video on a proof that $\pi$ is irrational that used continued fractions. At one point in the video, the person presenting the proof challenged the viewers to prove that $\frac{2}{3-\frac{2}{3-\frac{2}{3-...}}}=1$. I attempted this the following way: Let $x=3-\frac{2}{3-\frac{2}{3-...}}$.We can then see that $x=3-\frac{2}{x}$. We can then solve for $x$, arriving at $x^2-3x+2=0$, which we can solve with the quadratic formula, yielding $x=1$ or $x=2$. Now, $1-3+2=0$; $3-\frac{2}{1}=1$, and the coefficient of $x^2\neq0$, so $1$ should be a valid solution for $x$, however in that case $\frac{2}{x}=2\neq1$ (which we were trying to prove), which is a bizarre result, seeing as a continuing fraction should only have one result (or so I think...).  I'm still only a high school student, and my formal math education is around Algebra I and Geometry level, so it's possible I may be missing something obvious. Clearly, my reasoning is flawed. Can someone please help me see where I'm wrong here, and what I missed? Is my approach completely wrong?

I am preparing to teach an enrichment session to some 16 year olds, about Continued Fractions. I am confused about the following paradox.  1=2 via Continued Fractions This is true of course that $1=\frac{2}{3-1}.$ Now, let's substitute this very expression for $1$ in the denominator: $$1=\frac{2}{3-\frac{2}{3-1}}.$$ We can do that one more time: $$1=\frac{2}{3-\frac{2}{3-\frac{2}{3-1}}}.$$ And one more time to make sure there is no misunderstanding of the construction, $$1=\frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{2}{3-1}}}}.$$ At this point I am assuming that further steps could be performed by any reader who got this far. To indicate that possibility I'll use the ellipsis: $$1=\frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{2}{3-\ldots}}}}.$$ Well, we also know that $2=\frac{2}{3-2}.$ With this as a starting point, we follow in the footsteps of the previous example. Replacing $2$ in the denominator with that expression gives $$2=\frac{2}{3-\frac{2}{3-2}}.$$ To continue as before: $$2=\frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{2}{3-2}}}}.$$ And finally, $$2=\frac{2}{3-\frac{2}{3-\frac{2}{3-\frac{2}{3-\ldots}}}}.$$ But this is exatly the same continued fraction. By necessity we conclude that $1=2.$ — by 24.0.94.225 at 20110927 via   What is the hole in the argument? Presumably it has something to do with lack of convergence, but would anyone be able to explain it so that:  I could undersatnd it (I studied Maths at university)  16 year olds (with no formal knowledge of analysis or the language of convergence) would understand it?   Thank you.


I am a student of linguistics, not a mathematician. I am trying to account for some linguistic expressions with the set theoretical terminology and hence I am trying to learn the basic membership rules for sets. This is the problem with which I am struggling -  If $x$ is a member of set $y$, where $y$ is a set of cats $x$ is necessarily a cat.  $\therefore$ An expression like $a$ $cat$ will refer to a noun which is a member of set $C$ i.e. set of all cats.  Now what about an expression like $a$ $black$ $cat$? Obviously we know that black is an adjective here, but what is it's membership? If we say set $C$ has a subset $B$ which includes all the black cats, it will violate the first condition because we have defined set $C$ as a set of cats, but set $B$ is not a cat. How to account for $black$ in this model?

I had a task where I had to figure if the argument was true or not.  $A=\{ n ∈ ℤ \mid n^2 < 5 \}, \quad  B=\{ 7, 8, \{2\}, \{2, 7, 8\}, \{\{7\}\} \}$  The first one was $\{-1, 2\} ∈ A$ and the answer to this was not true  since the set is not an integer.  The second one was $\{-1, 2\} ⊂ A$ and the answer to this was true since  -1 and 2 are elements of $A$.  I just can't seem to understand the difference between ∈ and ⊂ in this task and why the first argument was not true. Also it confuses me that the answer to the first one was that not true because the set is not an integer but aren't -1 and 2 integers?  There is other parts of this task that also add more confusion:     {2, 7, 8} ∈ B Answer: True since {2, 7, 8} is an element of set B      {2, 7, 8} ⊂ B Answer: Not true, for example 2 is not an element in set   B


Is it true that $\mathbb C^*$  can be expressed as a direct product of two proper non-trivial subgroups ?

Let $\mathbb{C}^{\times}$ be the group of nonzero complex numbers under multiplication. Then $\mathbb{C}^{\times}$ is the direct product of the circle group $T$ of unit complex numbers and the group $\mathbb{R}^{+}$ of positive real numbers under multiplication.


Here's the command, formatted what I thoughtwas correctly...  /tellraw @p ["",{"text":"This map is based off of 1.9 features such as detecting when you pick up items,","color":"green"},{"text":" [HINT] ","color":"dark_green","bold":true,"clickEvent":{"action":"run_command","value":"/tellraw @p {{\"text\":\"[HINT]\",\"color\":\"dark_blue\"},{\"text\":\"This pickaxe cannot break lit glowstone lamps.\",\"color\":\"light_purple\"}}"},"hoverEvent":{"action":"show_text","value":{"text":"","extra":[{"text":"Click For Hint"}]}}},{"text":"so you may need to think outside of the box for some levels. good Luck!","color":"green"}]   However it's giving me Invalid json: malformed JSON at line 1 column 3 Please help!

I've been at this for almost two hours and no one seems to have the same problem as I and I doubt this will be solved but I'll try anyway.  this is the code  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}},{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   this part is fine  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}}   it's just when I add this  ,{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   Minecraft gives me the error:     Invalid JSON at line 1 column 203   I've tried to space it out and figure out what column 203 is but I can't, I don't know what I did. Anyone got any ideas?


I am fairly new to java, and I cannot figure out for the life of me why this piece of code is not working, I am trying to see if a word is an adverb, and hence if it ends in "ly" or not (they will always be lowercase). This is my code:      String str = "evenly";     int a = str.length()-2;     int b = str.length();     String res = (String)str.substring(str.length()-2,str.length());     System.out.println(res + " == ly -> " + (res == "ly"));   I am testing it here:  The output is: ly == ly -> false Which means that, res = "ly" but res == "ly" is false? Why is this happening?

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?


I don't like white wine. Me neither.  We're talking about subjects here, so naturally the pronoun should be "I". The use of "me" would only make sense to me if "neither" was a postposition. According to a dictionary it can be all kinds of things but not a preposition.  Why are we using "me" here? What part of speech is neither? Is this sentence a shortened version of something that explains the weird grammar?

I've heard that "me neither" is incorrect. Instead one should say "neither do I." People definitely say "me neither" conversationally, but is it technically incorrect?


How to build a regression model with a continuous response variable bounded from 0 to 1?   I think it is not logistic regression, where I am not predicting a binary response variable, Right?  Sorry for duplication if any, I tried to search but not find. (I feel this question must be asked many times.)

I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a > 0$ and $b > 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c?


I have a list with letters:  list1 = [abcdefghijk]   I have num = 3 and want to break list1 in parts of 3, i.e:  [[abc], [def], [ghi], [jk]]   My code is:  for i in range(0, len(list1), num):     chunks = [list1[i:i+num]]   I get wrong output:  chunks = ['k']   But I expect:  chunks = [[abc],[def],[ghi],[jk]]   I have gone through all the available solutions here. But they did not help. How should I fix this?

I have a list of arbitrary length, and I need to split it up into equal size chunks and operate on it. There are some obvious ways to do this, like keeping a counter and two lists, and when the second list fills up, add it to the first list and empty the second list for the next round of data, but this is potentially extremely expensive.  I was wondering if anyone had a good solution to this for lists of any length, e.g. using generators.  I was looking for something useful in itertools but I couldn't find anything obviously useful. Might've missed it, though.  Related question:


I have been proposed this enigma, but can't solve it. So here it is:  $$\begin{align} e^{2 \pi i n} &= 1 \quad \forall n \in \mathbb{N} && (\times e) \tag{0} \\ e^{2 \pi i n + 1} &= e &&(^{1 + 2 \pi i n})\ \text{(raising both sides to the $2\pi in+1$ power)} \tag{1} \\ e^{(2 \pi i n + 1)(2 \pi i n + 1)} &= e^{(2 \pi i n + 1)} = e &&(\text{because of (1)}) \tag{2} \\ e^{1 + 4 \pi i n - 4 \pi^2 n^2} &= e && (\div e) \tag{3} \\ e^{4 \pi i n - 4 \pi^2 n^2} &= 1 &&(n \rightarrow +\infty) \tag{4} \\ 0 &= 1 &&(?) \tag{5} \end{align}$$  So the question is: where is the error?

We have $$e^{2\pi i n}=1$$  So we have $$e^{2\pi in+1}=e$$  which implies $$(e^{2\pi in+1})^{2\pi in+1}=e^{2\pi in+1}=e$$ Thus we have $$e^{-4\pi^{2}n^{2}+4\pi in+1}=e$$  This implies $$e^{-4\pi^{2}n^{2}}=1$$  Taking the limit when $n\rightarrow \infty$ gives $0=1$.


I am prompted for a sudo password.   Since I am a user at a very basic level of knowledge, I am very shaky in getting to the terminal and/or using the commands. When I am told to take the step "enter sudo command", before which I am prompted for the "sudo password", what do I do?   I've never set a sudo password. I see from other questions that there is a facility called passwd; surely that has to be entered at the terminal... I'll try it.

What is the default password of the sudo? I visit some forums, it tells that the default password is password, but it doesn't work, how can I determine the password?


Suppose $X_1,X_2,\ldots,X_n$ are i.i.d variables having a two-parameter exponential distribution with common location and scale parameter $\theta$ :     $$f_{\theta}(x)=\frac{1}{\theta}e^{-(x-\theta)/\theta}\mathbf1_{x>\theta}\quad,\,\theta>0$$  I am wondering if it is possible to derive a maximum likelihood estimator (MLE) of $\theta$.  The likelihood function given the sample $x_1,\ldots,x_n$ is   $$L(\theta)=\frac{1}{\theta^n}e^{-n(\bar x-\theta)/\theta}\mathbf1_{x_{(1)}>\theta}\quad,\,\theta>0$$  , where $\bar x=\frac{1}{n}\sum\limits_{i=1}^n x_i$ and $x_{(1)}=\min\limits_{1\le i\le n} x_i$.  Since $L(\theta)$ is not differentiable at $\theta=x_{(1)}$, I cannot apply the second-derivative test here.   Even if I could say that $L(\theta)$ is increasing and/or decreasing in $\theta$ under the constraint $\theta<x_{(1)}$, I am not sure what choice of $\theta$ maximises $L(\theta)$. Differentiation is not valid as I understand. I think it is safe to assume $x_{(1)}<\bar x$, so the constraint is actually $\theta<x_{(1)}<\bar x$.  If MLE is unique, then it is likely to be a function of the sufficient statistic $(\overline X,X_{(1)})$. However I don't see how to derive it in this particular model. Any suggestion would be great.

Let $X_1,X_2,X_3....X_n$ be a random sample from a population having probability density function $$f(x)=\dfrac{1}{\theta} e^\frac{-(x-\theta)}{\theta} ;x\geq\theta$$  where $\theta\in(0,\infty)$. Find the MLE of $\theta$.  In this question when i followed normal method of finding MLE(taking log likelihood differentiating with respect to $\theta$)I found $\hat\theta =\bar x$.  But like in uniform distribution case we have here parameter dependent on $x$  . Now i am not sure if MLE is $\bar x$ or $x_{(1)}$.


It seems to me that if everyone is infected so that even a natural death would turn a human into a zombie, why is there concern over non-lethal zombie bites?  For example, the need to cut off Herschel's leg.  Does the bite itself, no matter how insignificant, cause death?

In  it is pointed out that everyone appears to be infected with the virus.  As we saw in the CDC center, death triggers the virus to reactivate portions of the brain.  Yet even a single bite from a Walker results in fever, eventual death (within days), and then reanimation.  If the Walkers are infected with the same virus that is already latent in the survivors, why do bites seems 100% fatal?


I was writing the Junit code below in eclipse kepler. I pressed the shortcut ctrl+shift+o to automatically import all the packages that are needed by this code. The shortcut only imported Test and gave me an error in assertEquals - The method assertEquals(int, int) is undefined for the type FootballTeamTest  import org.junit.Test;  public class FootballTeamTest {      @Test     public void constructorShouldSetGamesWon() {         FootballTeam team = new FootballTeam(3);         assertEquals(3, team.getGamesWon());      }  }   This was fixed by adding an import import static org.junit.Assert.*;. Why does eclipse not do this import automatically ?   Related post -  Go to the answer for Junit4 in that question. Amazing.

Is there anyway to get Eclipse to automatically look for static imports? For example, now that I've finally upgraded to Junit 4, I'd like to be able to write:  assertEquals(expectedValue, actualValue);   hit Ctrl + Shift + O and have Eclipse add:  import static org.junit.Assert.assertEquals;   Maybe I'm asking too much.


I was wondering what are the "creative limits" of LaTeX. I've seen many beautifully typeset documents, books, scientific papers, which are of the highest quality, both aesthetically and in respect to content. After all, LaTeX is the best typesetting system in my opinion — overwhelming amount of amazing works written in it is therefore no surprise. I've even seen it put to work when constructing facsimile of a medieval manuscript.  But I am convinced I haven't seen it all. Please link me some of the best works ('best' as in the best overall aesthetics, "cleaneness" of the final product) done with this superb piece of software. As an example of a brilliant scientific paper, I must link  paper — the amount of attention to detail and hard work that went into this article is astonishing (and further demonstrated the power of  package). Of course I accept literary works typeset with LaTeX with open arms as well. Thank you for your suggestions in advance.

If you were asked to show examples of beautifully typeset documents in TeX & friends, what would you suggest? Preferably documents available online (I'm aware I could go to a bookstore and find many such documents called 'books'). Extra bonus for documents whose LaTeX source is available.  This is not an idle question. Seeing great examples of any craft is both educational and inspiring, let alone explaining why we prefer TeX to Word or other text editors.  For instance, I like how Philipp Lehman's  looks. I don't know enough LaTeX to realize how much customization was done, but the ToC looks polished.  Your nominations, please ...


I installed a new pci card into my pc and it does not work.  It is a new version of old card so I think I need to update my drivers for this card.

I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily?


How can this be explained that I get a result that ends in 92 for the first two calculations, and 94 for the third one?       console.log(Number.MAX_SAFE_INTEGER + 1); //...92     console.log(Number.MAX_SAFE_INTEGER + 2); //...92     console.log(Number.MAX_SAFE_INTEGER + 3); //...94

Is this defined by the language? Is there a defined maximum? Is it different in different browsers?


Example:   So when was Mary actually baptized?   1744 or 1745 ?   Is there something I need to understand about why it would have been reported with two different dates?

What is a "double date"?  Why do I sometimes see dates written as January 13, 1718/1719?  See also:


This is my sentence:     The A & P’s regular customers are depicted as "scared little pigs in a chute."  Daily,  they live the same monotonous existence.    Microsoft word insists that there should be a comma after "depicted".  I don't think it makes sense.  What say you?

Sam developed an annual sweepstakes promotion entitled “The Free Gas Punt Return Game”.    Do I need a comma after entitled or not?


For example the \MakeLowercase is a command and takes an argument enclosed in {} like \MakeLowercase{UPPER} to generate upper. What I would like is to be able to define a declaration, such as MakeItlower so that {\MakeItlower UPPER} will generate upper. This is similar to the distinction between \textbf{Bold} and {\bfseries Bold}.

There are two forms of setting the type style: the declarative method e.g, \itshape and the command form, e.g, \textit. The command form takes an argument whereas the declarative form does not --- it just applies itself to whatever comes afterwards.  I would like to develop a declarative form, say \UppercaseIt, of the command form \MakeUppercase{<text>}. I have read, in source2e.pdf on CTAN the code for implementing \textit, \itshape and \MakeUppercase and can't claim that I understand any of them. I am after something like {\UppercaseIt some text} instead of \MakeUppercase{some text}.  I only have a code outline of what I'm after, since I don't know how to do it:  \documentclass{article}  \newcommand{\UppercaseIt}{%   %... magic }  \begin{document}  \MakeUppercase{some text}% Yields SOME TEXT  {\UppercaseIt some text}% Should yield SOME TEXT  \end{document}


I am getting an error on the following line of code  String appName = (String) packageManager.getApplicationLabel(applicationInfo);   However, the label is clearly defined and correct and the page was running perfectly before. Not sure why its throwing a null pointer exception? Can anyone help rather than just redirecting me to another question please?      Java.lang.NullPointerException: Attempt to invoke virtual method 'java.lang.CharSequence android.content.pm.ApplicationInfo.loadLabel(android.content.pm.PackageManager)' on a null object reference at android.app.ApplicationPackageManager.getApplicationLabel(ApplicationPackageManager.java:1550)   CODE:      @Override public int onStartCommand(Intent intent, int flags, int startId){     Context context = getApplicationContext();     ApplicationInfo applicationInfo = null;      HashSet<String> app = new HashSet<String>();       SharedPreferences setting = getSharedPreferences("Preferences", 0);      //Stores apps that are blocked//     HashSet<String> blockedApplications = (HashSet<String>) setting.getStringSet("HashSet", app);      String appsInForeground = printForegroundTask();       PackageManager packageManager = getPackageManager();       try {         applicationInfo = packageManager.getApplicationInfo(appsInForeground, 0);     } catch (PackageManager.NameNotFoundException e) {         e.printStackTrace();     }     String appName = (String) packageManager.getApplicationLabel(applicationInfo);      if (blockedApplications.contains(appName)) {         showHomeScreen();         //Show my dialog instead of just homescreen //         Intent dialogIntent = new Intent(this, MyDialog.class);         dialogIntent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);         startActivity(dialogIntent);     }else{         //Toast.makeText(this, "App in foreground: " + appsInForeground, Toast.LENGTH_LONG).show();     }     return Service.START_REDELIVER_INTENT;

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I want to write a program in which I want to initialize integer array of size 987654321 for storing values of 1 and 0 only, here is my program  #include <stdio.h> #include <stdlib.h>  int main(){     int x,y,z;     int limit = 987654321;     int arr[limit];     for (x = 0;x < limit;x++){         printf("%d \n",arr[x]);     }     return 0; }   but it gives segmentation fault

The following code is generating a stack overflow error for me  int main(int argc, char* argv[]) {     int sieve[2000000];     return 0; }   How do I get around this? I am using Turbo C++ but would like to keep my code in C  EDIT:  Thanks for the advice.  The code above was only for example, I actually declare the array in a function and not in sub main.  Also, I needed the array to be initialized to zeros, so when I googled malloc, I discovered that calloc was perfect for my purposes.  Malloc/calloc also has the advantage over allocating on the stack of allowing me to declare the size using a variable.


Class MyClass {     public int[] MyArray     {         get {return MyArray;}         set         {             if (value == null) { MyArray = new int[2] { 0, 0 }; return;}             else { MyArray = value; return;}         }     }     public MyClass()     {         this.MyArray = new int[2] { 0, 0 };     } }   In my class I have an int[] and I need to do things with value in set except when I try to make a new instance of MyClass I get a stack overflow.  When I put a breakpoint on the constructor and on set it reveals myArray = new int[2] {0, 0}; in the constructor calls the set method and once the set gets to line myArray = value it calls the set method again. This loops for some time, then it throws a stack overflow exception. I've tried putting a return; right after the assignment but it doesn't reach the return.  Any enlightenment on using the set method for an array would be wonderful.

I know java and would normally put in getter/setter methods. I am interested in doing it in C# with the following code, but it throws a StackOverflow exception. What am I doing wrong?  Calling Code  c.firstName = "a";   Property Code    public String firstName; {     get     {         return firstName;     }     set     {         firstName = value;     } }


I recently installed trisquel on my computer. When I decided to use the terminal and sudo I was prompted to use a password despite the fact that I set a blank one.  I want to know what I am supposed to type then.  I am open to going into grub and somehow replacing the password.  I have tried out pressing enter at the terminal to no avail.  I am the root user and cannot make changes without the password.

I want sudo to behave like this, for all users:   If the user currently has a non-empty password, prompt for the password. If the user currently has an empty password, either prompt for the password and accept the empty string, or don't prompt at all and permit.   Is this possible? Right now, I have (1) but this is what happens for a user with an empty password:  $ sudo echo Sorry, try again. Sorry, try again. Sorry, try again. sudo: 3 incorrect password attempts   Alternatively, I can switch off password checking per-user, but that's not what I want, because the user might set a password later, and then sudo should prompt for it.


I have wondered this on and off for years, and was prompted to find out the answer:  Any time I've seen capacitors, they're listed with milli- or pico-Farad ratings. I understand that, nowadays, we have special purpose supercapacitors that package "whole" Farads into single components.  But, why on earth did "they" use such a large base value that for "most" applications you'd need something in the milli- to pico- range? It just seems ... unnecessarily skewed.

Most capacitors are in the µF, nF and pF range. I know there are some special ones that go that high, but at the time faraday was around, and the unit was named after him, they didn't have such a thing. Why is the unit so large if we rarely use caps with that high of a value?


How do you add subscript text within a text string e.g. I would like my the output to have the max as subscript  \text{AC generator emf_max}

It's easy to make subscripts in math mode: $a_i$.   How do I make a subscript outside math environment, likethis?


My company has developed a search engine and handed over to the testing to test. I have no idea how to start. Its taking results from bing API

I had an interview question:     You were told that a search engine result by target query does not satisfy a requirement by its position. How would you test it?   How would you test it?  I had some thoughts though:   You need a list of input search queries You need a target position for each of the query You match each target position with actual   But it was not enough.


What is required from me in reviewing a post? There is a similar question on    I clicked on  and see many first time posts. I see I have 2 options:    I'm done  Not sure.    I'm done is grayed out. I don't understand why as this actually now forces the post to be edited or voted up when in many cases neither of these are applicable.   So, I guess by voting up is a good way to start - it rewards new posters for good questions and makes them feel welcome - and what happens -- I'm limited to X number of votes a day (up voting and down voting). Currently there are 2.1k posts on Super User which need reviewing and with these limitations I expect it will take some time (although I use Super User, it's applicable to all sites on SE).   I don't think writing a comment saying 'well done for a good post' is useful either for future visitors (IMO it also may impact SEO but we won't discuss that here) but it adds 'noise'.  Any thoughts on this, have I missed the point?

I'm happy to see the "first posts" facet arriving on the Beta Review system.  I like that it encourages reviewers to make a decisive move on a question or answer, but frankly, I think there should be a No vote, but okay option in addition to the I'm done and Not sure ones.  I think that there are some posts that are perfectly acceptable, but that show no demonstrable lack of effort or lack of clarity that might warrant a downvote.  I am a firm advocate for voting good quality posts up, I just think that forcing an option of voting or making the reviewer throw their work back into the pool untouched (assuming no edits or flags, etc. are needed) may be detrimental in the long term.


<?php class dbConnect{ public function __construct() {  global $pdo;   try{   $pdo = new PDO('mysql:host=localhost;dbname=quran','root','');   } catch(PDOException $e){    exit('Database error');   } } } class get_data{  function __construct(){ $connect = new dbConnect(); } public function get_sura_list() {   global $pdo;   $query = $pdo->prepare("SELECT * FROM sura ORDER BY sura_no");   $query->execute();   return $query->fetchALL(PDO::FETCH_ASSOC); } }  ?> <meta http-equiv="content-type" content="text/html; charset=utf-8"><?php $all_sura_list = new get_data();$sura_list = $all_sura_list-> get_sura_list(); foreach($sura_list as $sura){       echo $sura['sura_no'];    echo '-';    $sura_name = rawurldecode($sura['sura_name']);    echo $sura_name;    echo '-';    echo $sura['total_ayat'];    echo '
';   } ?>    Using This Script I'm trying to listing data from my database. non-English Charecters are showing Like this "???????".  I have some non-english charecter in my Database like this "ফাতিহা". Using this script they are showing like this '??????'.   I Used  This code in HTML Head but nothing happend.  How Can I show thoes non-english words properly?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


Let $a, b \in G$, where $G$ is a group, and $|a| = 12$ and $|b|=22$.  If $\langle a \rangle \cap \langle b \rangle \neq \{e\}$, prove that $a^6  = b^{11}$.

Let $a$ and $b$ be elements of a group $G$. If  $|a| = 12, |b| = 22$ and $\langle a \rangle \: \cap \: \langle b\rangle \ne e$, prove that $a^6 = b^{11}$.   Any ideas where to start would be helpful.  Thanks.


The following scenario: I have purchased multiple domains for a project:   domain.app domain.com domain.de   Originally it was planned to display a landing page on domain.app.   On domain.de the german version of the PWA. On domain.com the english version of the PWA.   Now it all seems a bit complicated and I would like to use the following structure:   domain.app as the main domain that recognizes the browser language. domain.de redirected to domain.app/de/ domain.com redirected to domain.app/en/

When I set up a site in multiple languages, how should I set up my URLs for search engines and usability?  Let's say my site is www.example.com, and I'm translating into French and Spanish. What is best for usability and SEO?  Directory option:  http://www.example.com/sample.html http://www.example.com/fr/sample.html http://www.example.com/es/sample.html   Subdomain option:  http://www.example.com/sample.html http://fr.example.com/sample.html http://es.example.com/sample.html   Filename option:  http://www.example.com/sample.html http://www.example.com/sample.fr.html http://www.example.com/sample.es.html   Accept-Language header:  Or should I simply parse the  header and generate content server-side to suit that header?  Is there another way to do this? If the different language versions don't have different urls, what do I do about the search engines?    UPDATE 2011-12-06  Google has new recommendations for meta tags for explicitly pointing to other language content: .  UPDATE 2012-05-25  Related but not precisely:   UPDATE 2013-06-12  includes discussion of several URL schemes directly relevant to the question.


I am exploring UARTs on the STM32F103RB on a nucleo board. The board is connected via USB to my laptop, and I can send/receive messages using the HAL_UART_Transmit_IT and HAL_UART_Receive_IT functions.  What I am actually failing to do, is send a message from UART2 to UART3. I wired as follows:   UART2 TX (PA2) => UART3 RX (PB11) UART2 RX (PA3) => UART3 TX (PB10)   Then I send a transmit an array of 2 bytes from UART2 to UART3, but the interrupt handler never fires.   So I thought to isolate the problem further, and just connect RX to RX and TX to TX, so that the signals to UART2 are "mirrored" to UART3.   Wiring as follows:   UART2 TX (PA2) => UART3 TX (PB10) UART2 RX (PA3) => UART3 RX (PB11)   From the pinout here that I identified the following pins:   PA2 and PA3   PB10 and PB11  In that setup, I again activate the callback on UART3, send a message from my laptop to UART2 (and thus 'also' to UART3 if my theory works in practice) and hoped to hit the breakpoint in the HAL_UART_RxCpltCallback. But it doesn't work.  The code for completeness:  In the main function:    // Activate the callback on receive UART3    HAL_UART_Receive_IT(&huart3, receive, 2);    __NOP();   while (1)   {       // Do nothing, all is done via callbacks   }   (the default setting up of UARTs and GPIO, generated with CubeMX, is left out for readability)  The UART receive callback:  void HAL_UART_RxCpltCallback(UART_HandleTypeDef *huart) {   /* Prevent unused argument(s) compilation warning */   UNUSED(huart);    if (huart->Instance == huart3.Instance)   {       __NOP();       HAL_UART_Receive_IT(&huart3, (uint8_t *)receive, 2);   } }   I am sending a few bytes using a tool (Hercules). It works fine when I change to huart2. So I am sure the code works as it supposed to.   Is it possible to "mirror" UART2 pins to UART3 pins like I did?  Or is there something else that comes to mind what I might be doing wrong?  Update  As already explained in the comments, this is not a duplicate of the linked question (otherwise I wouldn't have asked it, since both are mine...). The problem in the linked question was regarding transmitting from UART2 to UART3, the question now is to mirror receiving pins to drill down to the actual issue at hand.   Update 2  Justme was spot on. The problem that I can't mirror the pins is simply because no signal is receive on the PA3 pin. I need to solder a bridge to make that happen, as explained in the user manual:    The answer / comment of Justme is most likely the actual problem that solves my issue.

I thought to create a simple test to send and receive a buffer via UART. I succeeded in sending bytes from my PC to the nucleo bord and receiving them in blocking and non-blocking mode. But for some reason I can't succeed to send data from UART3 and receive the bytes on UART2.  I have a nucleo-f103rb and have the following pins setup:   UART2: tx=PA2;rx=PA3 UART3: tx=PB10;rx=PB11   And then the following code:    while (1)   {     /* USER CODE END WHILE */     /* USER CODE BEGIN 3 */     if (HAL_UART_Transmit(&huart3, send, 2, 1000) == HAL_OK)     {         if (HAL_UART_Receive(&huart2, receive, 2, 1000) == HAL_OK)         {             HAL_GPIO_TogglePin(GPIOA, LD2_Pin);         }     }   }   All the boiler plate is generated using cube mx. So the UART 2 and 3 are all default, same for the button pins.    I connected the transmit pin of uart3 to the receiving pin of uart2 I connected the receive pin of uart3 to the transmitting pin of uart2 (while not used in this trivial example though)   What am I missing here?  Update  As comments and answers suggested, I shouldn't be using the blocking mode approach. So I rewrote it slightly to rely more on interrupts.  I attached a callback to the nucleo blue button  void HAL_GPIO_EXTI_Callback(uint16_t GPIO_Pin) {     if (GPIO_Pin == B1_Pin)     {         HAL_UART_Transmit_IT(&huart3, (uint8_t *)send, 2);     } }   And I added a callback for receiving stuff over uart  void HAL_UART_RxCpltCallback(UART_HandleTypeDef *huart) {   /* Prevent unused argument(s) compilation warning */   UNUSED(huart);    /* NOTE : This function should not be modified, when the callback is needed,             the HAL_UART_RxCpltCallback can be implemented in the user file    */       // Toggle the pin to see some proof that I received something      HAL_GPIO_TogglePin(LD2_GPIO_Port, LD2_Pin);       // Resubscribe uart2      HAL_UART_Receive_IT(&huart2, (uint8_t *)receive, 2); }   In the main function I call the interrupt so that the callback is active.  while (HAL_UART_Receive_IT(&huart2, receive, 2) != HAL_OK);  __NOP(); while (1) { }   Again, when debugging through I do end up in the button released callback, but the callback on the uart receive isn't triggered. When I send stuff from the PC, it does. So it seems that sending stuff via uart3 isn't working. So I guess that must be the wiring.     But I really can't see what I am missing here, the pins are clearly defined in the pinout here: .  I hope the photo is clear enough, but this is how I connected them.


In C#, if an exception occurs inside a "using" block, does the Dispose method get called?

In the example below, is the connection going to close and disposed when an exception is thrown if it is within a using statement?  using (var conn = new SqlConnection("...")) {     conn.Open();     // stuff happens here and exception is thrown... }   I know this code below will make sure that it does, but I'm curious how using statement does it.  var conn; try {     conn = new SqlConnection("...");     conn.Open();     // stuff happens here and exception is thrown... } // catch it or let it bubble up finally {     conn.Dispose(); }   Related:


I have a statistical problem in connection to interaction effects and main effects in the social sciences.  I am doing a regression where I have two interaction terms with one common variable. The interaction terms are used in order to prove or falsify two hypotheses. If I include all main effects and interaction effects, all effects become insignificant.  My approach is to leave the main effects out. This will leave with only significant interaction effects. Is this a valid approach?

Is it ever valid to include a two-way interaction in a model without including the main effects?  What if your hypothesis is only about the interaction, do you still need to include the main effects?


As the title asks, the reason I'm asking is because I have a wordpress site which gets about 10K visitors per day on a dedicated server from iweb but in the evenings, around 8 to midnight the site crawls to a halt and page load time goes up to about 12 seconds or more compared to 2-3 during the day. Checking my google analytics its shows that traffic is pretty dispersed throughout the day so its not the case where the server is being hammered during those hours by visitors. The two server specs are:  ---------------------------------- 1 -------------------------------------  OS: Linux CentOS  CPU: Intel Core 2 Duo - 2.13 GHz  RAM: 2 GB  Storage: 2 x 300 GB hard drives  Bandwidth: 1,000 GB per month  ----------------------------------2 --------------------------------------  Core 2 Duo 2.4GHz (800MHz FSB)  4GB RAM  500GB SATA2  Enterprise Linux - CentOS - 64 bits  cPanel/WHM Internal  There's nothing weird in the logs for apache except Internal server error which happens a few times during those hours but not during the day and results in httpd and mysqld consuming 100% cpu for long periods of time. Load average on the server is usually about 15,15.x,15.x during those hours then in the day its 0.x,0.x,0.x

This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application?


How do I open an extra window to display a reference image? How do I import the reference image into the window?

How do I put a backdrop behind the model that I am creating so that I can compare the picture to the model while editing?


if we do the double slit experiment but we shoot metal balls in a closed box so we don't observe. what pattern comes then on the board? if i understand correctly there will be no interference pattern because for bigger objects the wavelengths are too small. but do we see as a result then evenly divided points all over the wall or do we see a particle pattern in two places?

I read an interesting question here in the forum () and came up with the following doubt: even though its diffraction angle is too small to be detected, if we had the possibility to detect it, what would the diffraction of a soccer ball through a pair of posts look like? I mean, in the case of electrons, there is a screen in which the diffraction pattern can be appreciated. But what about this case? Would we see lots of soccer balls in different places or what?


I came across the following statement:     If $A$ and $B$ commute and $B$ and $C$, do $A$ and $C$ necessarily commute. Prove or disprove.   I think it's generally untrue. Consider $A = X$, $B = P_y$ and $C = Ly$, where $X$ is the position operator, $P_y$ is the momentum operator in the $y$ direction and $L_y$ is the angular momentum operator in the $y$ direction.  If the statement is generally untrue, by virtue of the counterexample, I have the following question:  Don't we implicitly use the argument in the statement to assert for instance, adding an operator to a list of operators to complete a set of commuting observables. For example, assume $H$ is a rotationally invariant scalar operator (Hamiltonian). We know that it commutes with $L_z$. We also know that $L_z$ commutes with $L^2$ and we then assert that $H$ and $L^2$ must also commute as well and we then looking for the simultaneous eigenbasis of th two angular operator momentum operators to get the spherical harmonics.  Am I missing out on something here?

I noticed the following:  $$[L_{+},L^2]=0,\qquad [L_{+},L_3]\neq 0,\qquad  [L^2,L_3]=0.$$  This would suggest, that $L^2,L_+$ have a common system of eigenfunctions, and so do $L^2,L_3$, but $L_+,L_3$ don't. How is that possible?


I am trying to load data from a table which looks like below and use the 'label' column for xticklabels.  idx,label,value 1,20040101_20050108.rotation.summary, 19.470949839091155 2,20040101_20050115.rotation.summary, 3.2633743485078925 3,20040101_20050122.rotation.summary, 2.6505513476912275 4,20040101_20050129.rotation.summary, 1.8865512077042033 5,20040101_20050205.rotation.summary, 2.2793107344143277   I have around 600 rows and when I used xtick=data with xticklabels from table={\mydata}{1} I am getting a plot like below.     So I tried to use xticklabel customization like below with \pgfplotstablegetelem.  \begin{tikzpicture}   \begin{axis}[     xmax=573,     xticklabel={$\pgfplotstablegetelem{\tick}{1}\of{\mydata}$},     xticklabel style={rotate=90, anchor=east}]       \addplot[mark=none] table [         x index={0},         y index={2}] {\mydata};  \end{axis} \end{tikzpicture}   But what I got was following:    Please let me know if anyone has any ideas to fix this.  Update 1  I figured out that I should use \pgfplotsretval to get the element value and updated my plot to reflect that like below  ... xticklabel={$\pgfplotstablegetelem{\tick}{label}\of{\mydata}\pgfplotsretval$}, ...   But the label still has prefix added to the beginning of each label like .000000002004010120061209.rotation.summary.  Update 2  I found the solution. xticklabel should be something like below.  {   \pgfmathparse{int(round(\tick))}   \pgfplotstablegetelem{\pgfmathresult}{[index]1}\of{\stresscculogerr}\pgfplotsretval }

I have monthly data, and I want to show ticks for, say, each quarter. Thus, instead of showing 12 ticks per year, I want to show 4. There is a very similar post , but the solution is to write the coordinates manually. That is not helpful for me, since my dataset is long. I have tried using the xtick={0,4,...,100} option, but that doesn't skip dates (see plot below).   My MWE is:  \documentclass[12pt]{article} \usepackage{graphicx} \usepackage{pgfplots,tikz} \RequirePackage{filecontents}  \begin{filecontents}{Data1.csv} Period,spot jun 15,1.93 jul 15,2.12 aug 15,2.23 sep 15,1.81 oct 15,1.76 nov 15,1.18 dec 15,1.12 jan 16,1.05 feb 16,1 mar 16,0.9 apr 16,0.75 may 16,1 jun 16,1.15  \end{filecontents}  \begin{document}  \begin{figure}     \centering     \pgfplotsset{table/col sep = comma}     \begin{tikzpicture}         \begin{axis}[             xticklabels from table={Data1.csv}{Period},             xtick={0,2,...,12},             enlarge x limits=0.02,             width=16cm,             height=8cm,             xticklabel style={rotate=45},             ]             \addplot+[smooth] table [x expr=\coordindex, y=spot, col sep = comma] {Data1.csv};         \end{axis}     \end{tikzpicture} \end{figure}  \end{document}


The eardrum is pretty thin.Therefore it should be very sensitive to movement.So, why don't we hear the air that is constantly moving.My guess is that the force of air pressure is not enough.Maybe I am right, but I want to make sure.

In other words, given a magical room with walls that produce no vibration and transmit zero vibration from the outside, and nothing on the inside except room temperature air, what would be the noise level in dB SPL () from the  of the air itself?  (Similar to the  of electronics being determined by  in the conductors.)  What is the quietest possible anechoic chamber?  What is the noise floor of air?  For reference: Sound pressure is defined as the root-mean-square value of the instantaneous pressure, measured in pascal = N/m².  SPL is the same number, but expressed in decibels relative to 20 µPa.  (I assume that it has a white spectrum, but I could be wrong.  Thermal noise in electronics is white, but other types of electronic noise are pink, and blackbody thermal radiation has a bandpass spectrum.)   in the context of underwater acoustics.  Not sure how this applies to air:     Mellen (1952) developed a theoretical model for thermal noise based on classical statistical mechanics, reasoning that the average energy per degree of freedom is kT (where k is Boltzmann’s constant and T is absolute temperature). The number of degrees of freedom is equal to the number of compressional modes, yielding an expression for the plane-wave pressure owing to thermal noise in water. For non-directional hydrophones and typical ocean temperatures, the background level due to thermal noise is given by:      NL = −15 + 20 log f (in dB re 1 µPa)      where f is given in kHz with f >> 1, and NL is the noise level in a 1 Hz band. Note that thermal noise . There are few measurements in the high-frequency band to suggest deviations from the predicted levels.    Citation is R. H. Mellen, The Thermal-Noise Limit in the Detection of Underwater Acoustic Signals, J. Acoust. Soc. Am. 24, 478-480 (1952).


I recently Installed Ubuntu 18.10 and downloaded gnome-tweaks to customise. I used it for a while and had disabled the icons on the desktop with this tool, but when I wanted to activate them again, I did not see the desktop options in tweaks.  So I could no longer retrieve my Icons on the desktop. Could someone help me recover them? I use Gnome 3.30

After using ElementaryOS I am back on Ubuntu. In eOS one of the features are "no desktop icons" and "no right-click option on desktop" and i prefer that setting, its simple and lightweight and I don't use the desktop anymore, only for wallpapers.  How can I completely deactivate the desktop in Ubuntu 14.10 (like eOS)?


I run my daily work load in Windows 7 inside a VMware Workstation 11.1 VM, with 3 monitors(VM using all 3 monitors in full screen mode). The graphics performance inside VM is not so fast, and quite oftenly(every hour) Windows 7 force the desktop theme to be "Basic", with a prompt of "Windows has detected that your computer's performance is slow". Actually the Basic theme does not improve VM graphics speed a bit, and I have to manually turn the theme back to Aero (because Basic theme is just ugly).    So my question is, is there a way(maybe tweak) to disable the stupid behavior of "force turning off Aero theme"?  There has been someone asking rougly , but unfortunately no satisfying answer yet.    As magicandre1981 suggests, 10~20 seconds after the switching-to-Basic-theme happens, I capture GPU graph info with Process Explorer v16.01, but still seems no clue.   ========== UPDATE 1 =========  Although I cannot find a way to suppress Windows' Aero-turning-off behavior, I managed to find a way to avoid it. Thanks to the first comment pointing out observing GPU info inside the VM, and I managed to increase the dedicated GPU memory to 800MB and the turning-off-Aero symptom does not appear any more, at least for recent two days.  The workaround is simple: Simply downgrade virtual machine hardware version from v11 to v10. Now I see GPU info as below:    Now my Dedicated GPU Memory is 851968K, and the "current" value goes from 110MB(initial boot up) to near 250MB(run for two days).  Although VMware Workstatoin 11.1 provides a setting to increase Graphics memory to 2GB (), I found it no help. It just increase the so called "System GPU Memory", and as you can see, my original setting for the VM was 1GB, and procexp reports only 64MB consumed. So it would be stupid to further increase it to 2GB.  So, I'm afraid VMware Workstatoin 11.1.0 has done a lame job regarding its virtual graphics hardware, maybe a very subtle problem.  Note: No manual tuning of .vmx content involved.

Every time I attend a Webex meeting, after only a few minutes in, Windows determines that my performance is too low and disables Aero. This is not an issue with Webex. It's an issue with Windows determining that I do not have enough resources.  I have plenty of resources: 8GB of RAM and my CPU usage never rises above 30%. I'm less concerned about how Windows determines whether I have enough resources and more concerned about how to stop Windows from doing that. If I determine that my machine doesn't have enough resources, I will disable Aero.  Is there a way to prevent Windows from disabling Aero based on available resources? I know that Aero gets disabled when an Aero-incompatible program runs, but that's not the issue in this case. I've checked Power Options, but none of those settings apply. Thanks.  Update  Joe Internet makes a good point about GPU resources. I have 512MB of dedicated video memory, which is well beyond the .


This is my opening a new question after having one of my questions marked as a duplicate (). If you came from my previous question, after reading everything at this link:  :my question is still unanswered. I don't need a command line script, I think. The chosen answer at that link isn't suited for my problem, nor did I find anything pertaining to my problem in the other answers. The other answers contained information I would find useful if I were trying to enable unicode characters on the command line on my own computer.  I am trying to learn as much about coding as I possibly can. So I wrote a few small programs, and wanted to allow my mother to use them on her computer, which does not have Python, of course. So in order to do that, I have been using the cx_Freeze module to make it to where these little programs of mine will work on her computer, with her having nothing to do but extract a .rar and move the shortcut to her desktop.  This is what the programs look like when the .exe's are run.    This is the loop I am using containing the instructions for what to do if help is asked for.  valid_help_string_list = ['\'help\'',                           '\'HELP\'',                             'help',                             'HELP',                            '"help"',                            '"HELP"'] while True:     weight_entry = input('Please enter your weight or type \'help\' for the pictogram legend.\nPlease round decimal numbers to the nearest tenth: ')     if weight_entry in valid_help_string_list:         print('\nLegend:\n□ = 10 lbs\n▪ =  5 lbs\n▫ =  1 lb\n∙ = .1 lbs\n')     else:         weight_entry = validate_entry(weight_entry)         if weight_entry:             break   This is what it should look like when anything in the help list is input.    This is what I am getting. Whenever anything in valid_help_string_list is typed, the program crashes because of the unicode characters.    Is there any actual Python code that can handle something like this? I want to be able to make this happen on other people's computers locally during runtime (the change to the encoding of the command line, if that's what needs to happen).

When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016).


I'm Brazilian, and my wife is Chinese; we just got married in China a few days ago.  The problem is, her visa expired just as we got to China for the wedding, and we don't have time to apply for a new one before our flight to Brazil.   Can she use her  (which is valid) to come to Brazil instead of needing a visa?

I am married to a Brazilian citizen and I was recently given an RNE (Registro Nacional de Estrangeiro or National Alien Registration card). Last year, I visited Brazil with a tourist visa and this time I have the RNE.   Will my RNE be accepted to board a flight to Brazil, or will I be asked for a visa.  I checked with local my Brazilian Consulate and they informed me that a visa is not required. Still, I want to confirm the with someone who has already travelled with just the RNE.


This is Ahlfors q. 1, p. 227. Prove that in any region the family of analytic functions with positive real part is normal. Under what added condition is it locally bounded? Hint: Consider $e^{-f}$. Well I proved that $e^{-f}$ is normal, but I don't know what to do next, moreover If I am right normality implies locally boundeness in the analytic case,I'm trying to figure out why asked that question...

I'm having difficulty with the following exercise in Ahlfors' text, on page 227.     Prove that in any region $\Omega$ the family of analytic functions with positive real part is normal. Under what added condition is it locally bounded? Hint: Consider the functions $e^{-f}$.   Here is what I've tried:  I will start with a remark:  Apparently, Ahlfors wants us to show that the family is "normal in the classical sense". That is, every sequence of functions in the family has a subsequence which converges uniformly on compact subsets or tends uniformly to $\infty$ on compact subsets. In order to see why this is the right definition, consider the sequence $f_n(z)=n$. It is contained in the family but has no appropriate subsequence (in the sense of definition 2 in the text with $S=\mathbb C$).  Now, to the attempt itself:  Let $\Omega \subset \mathbb C$ be a fixed region, and consider the family $$\mathfrak F=\{f: \Omega \to \mathbb C | f \text{ is analytic and } \Re(f) >0 \}. $$ We would like to show that $\mathfrak F$ is normal in the classical sense. Following the hint, we examine the family $$ \mathfrak G=\{e^{-f}:f \in \mathfrak F \}.$$  $\mathfrak G$ is locally bounded (since $|e^{-f}|=e^{- \Re (f)}<1$ for every $f \in \mathfrak F$), thus it is normal with respect to $\mathbb C$ (theorem 15), and obviously, it is normal in the classical sense as well.  Let $\{ f_n \}$ be a sequence in $\mathfrak F$, and consider the sequence $\{ g_n \}=\{e^{-f_n} \}$ in $\mathfrak G$. According to normality it has a convergent subsequence $\{ g_{n_k} \}=\{e^{-f_{n_k}} \}$ which converges uniformly on compact subsets of $\Omega$ to some function $g$ (which is analytic by Weierstrass' theorem).  Since each $\{ g_{n_k} \}$ is nonvanishing, the limit function $g$ is either identically zero, or non vanishing as well (Hurwitz's theorem). In the former case it is easy to show that the subsequence $\{ f_{n_k} \}$, obtained by the same indices, tends to $\infty$ uniformly on compact sets. Hence, we will assume from now that $g(z) \neq 0$ for all $z \in \Omega$.  Up until now, I was trying to show that the subsequence $\{ f_{n_k} \}$ works in all cases, but sadly, this is not the case. Consider the sequence $f_n(z) \equiv 1+2 \pi i (-1)^n \in \mathfrak F$. In that case $g_n(z)=e^{-1}$, and an admissible subsequence is $g_{n_k}=g_k=e^{-1}$. However, $f_{n_k}=1+2 \pi i (-1)^k$ diverges everywhere.  Can anyone please help me finish this proof? Or maybe give me some hints?  Thanks!


I'm trying to gain intuition for matrix norms. I'd like to know why if $A\in\mathbb{R}^{n\times n}$ that $||A||$ is equal to both $\max _{x\in\mathbb{R}^n}\frac{||Ax||}{||x||}$ and $\max_{||x||=1}||Ax||$. Why are these two definitions equivalent?

How do you prove that these four definitions of the operator norm are equivalent? $$\begin{align*} \lVert A\rVert_{\mathrm{op}} &= \inf\{ c\;\colon\; \lVert Av\rVert\leq c\lVert v\rVert \text{ for all }v\in V\}\\ &=\sup\{ \lVert Av\rVert\;\colon\; v\in V\text{ with }\lVert v\rVert\leq 1\}\\ &=\sup\{\lVert Av\rVert\;\colon\; v\in V\text{ with }\lVert v\rVert = 1 \}\\ &=\sup\left\{ \frac{\lVert Av\rVert}{\lVert v\rVert}\;\colon\; v\in V\text{ with }v\neq 0\right\}. \end{align*}$$


i am running ubuntu 20.04, i tried to install codeblocks for c programming while installing i have entered these follwing commands: sudo apt install gcc g++ gpp   To extract: tar -xf codeblocks Then installed extracted deb-packages  by: sudo dpkg -i *20.03*.deb  after which i faced an error: dpkg: error: unable to create new file '/var/lib/dpkg/info/format-new': No such file or directory E: Sub-process dpkg --set-selections returned an error code (2) E: Couldn't record the approved state changes as dpkg selection states  after this error i tried to solve it by entering these commands: sudo dpkg --configure -a  sudo apt-get install -f sudo apt-get auto remove  sudo apt update   but then also i m stuck in that same problem that my codeblocks ide is not starting ,also my software update is not able to update my applications cause of that error how to rectify this error?

I installed Dev C++ using Wine on Ubuntu 18.04 and the program is compiling but it not showing any output screen.


I just did a fresh installation of Ubuntu 14.04. To not break anything, I created the default user during install, but I neither need nor want it. I added my usual users (UIDs > 10000), which work great.  Now I want to remove the user that I created during the installation from the greeter.   Using gdm I would usually put  [greeter] Exclude = dummy   into /etc/gdm/custom.conf as . When using lightdm, I would use its minimum-uid setting in /etc/lightdm/users.conf like this:  [UserAccounts] minimum-uid=1001 #1100 10000 11000  <-- other attempts   as  and reading the comments in users.conf this is also very intuitive.   However, it would seem gdm and lightdm couldn't care less about my configuration settings. The users set up on this system will change so I would rather use the facilities to exclude certain users, rather than keeping the display manager configurations up to date.  How can I make Ubuntu care for my display manager settings? Do I need to enable this somewhere?  I even went tried the Windows way of rebooting a few times ...  As a next step I will delete this default user, but I don't know if this has some side effects on the Ubuntu installation.

I have recently added several new users, that I need for qmail. Now they appear in the box in the login screen and clutter it, and I have to scroll to find my user. How can I hide those users from the login box?


i just bought and build a BLB classic frameset. size 53 and im using 700x28c wheelset. but after that, my toe clip touching the front wheelset especially when i want to turn right or left. please help me to solve this prob.

My girlfriend got a new city bike today and she touches the front wheel every time she has to make a hard turn.  Is there anyway to avoid this besides replacing the whole bike?  LATER EDIT: I think I found my answer .


A mother spends much time with her children in comparison to the father.  A mother spends much time with her children in comparison with the father.    I don't have an idea which preposition to chose. I thought that I would get help online, but could not get what I wanted. However there is one blog post of Oxford English Living Dictionaries site under the title of ; the title contains the words "compare to" rather than comparison, thus is not akin to what I am asking here.

Is only one of them correct? Are they used in different situations? Or are they interchangeable?


How do I say that my mouth is feeling very hot from the spicy food that I ate?  What word should I say?

I've read the discussion here about .  I've also read this one: .  But I did not find any word or phrase that describes the reaction someone has when eating a too spicy-hot food. You know, they tend to sweat, catch their breath, and even sometimes shed tears; due to the spiciness of the food.  So my questions:        What do you say to describe the reaction someone has when being excitedly "suffered" by a very spicy-hot food? In Indonesian, we would call it kepedasan.   What do you say when you get that thing [the answer to question 1] with you, other than the list I enclose below:                Oh, spicy!     My God, it's spicy-hot!                      Is that it?


Let $(X, A)$ and $(Y,B)$ be two measurable space. Let $f \geq 0$ be measurable w.r.t $A \times B$ (product $\sigma$ -algebra). Let $g(x)=\sup_{y \in Y} f(x,y)$ and suppose $g(x)< \infty$ for each $x$. Is g necessarily measurable w.r.t $A$?   I am not sure whether the answer is no or yes. But, I haven't been able to produce a proof. Thanks in advance for any help!

Let $f:X\times Y \mapsto R$ be a measurable function on product space $X\times Y$, where $X$ and $Y$ both are some metric spaces. Define $g(x) := \sup_{y\in Y} f(x,y)$.   [Q.] Is $g$ a measurable function on $X$? If not, what is the sufficient condition to be measurable?


I am having difficulty troubleshooting this error message:    I don't get any indication any details about the failed connection attempt.   How can I diagnose such timeouts and resolve the connection issue?  I am aware of and have tried methods like rest your airport, reset the computer, delete profiles, down to install new operating system and , I'd like to know how to pick apart the connection process to know where the problem lies.  When I successfully connect, system information has excellent details:    However, without changing anything, at a later time, I will time out again when joining. Can I see the details of the process for the connection and find what is making it fail? What would it take to create or access a log file of the wifi connection process?

I'm having issues with my macbook pro OS X 10.7.5.  It used to connect to the wifi router (D-Link N300, DIR=615) no problems.  But for the past several weeks, I haven't been able to at all.  What pops up when I select my wifi network from the list:   "Failed to join "network" A connection timeout occured".   What happens when I try to enter my password manually:   "Connection timeout"   What I've tried to do as solutions:   Google Restart router by pressing reset & refresh button Delete System & User (Login) Keychain access Network > Gear symbol by the + and - bottom left of the screen > Set Service Order > Drag Wifi to the top


How can i download wine on a unity desktop environment? I've been trying to do so by using commands i found online but nothing helps. I found it easy to download it in xfce4, but now im using unity.

Can someone please explain how I can install  in the following ways?   By using the package manager? By downloading and installing a pre-built package?


Let $G$ be a group and $H$ is subgroup of $G$.Prove that there not exists subgroup $S$ of $G$ such that $S$ not equal with $G$ and $G-H \subseteq S$ I try to prove with contradiction and $(G-H)⋃ H\subseteq (S⋃H)$, so $G \subseteq (S⋃H)$ and $G$ is a group, but I'm more concerned with how I can derive

$H$ is subgroup of $G$ with $H$ not equal $G$.  Be $S=G-H$. I am being asked to prove that $\langle S \rangle=G$.  Some tip to solve this? I think in $S_3$ is possible but I can´t prove.


My dough is not proving because the room temperature is too cold in my house. Is there another method to make my dough rise without over-proving it?

It is winter down here in Australia and I find it challenging to find a warm spot to raise my bread dough. What I have been doing is placing the dough in the oven (not switched on) with a pot of hot water, replacing it once or twice. The oven becomes a warm and moist environment for the yeast to do its magic.   What other alternative spots are there to raise the dough in cold seasons?


I am writing in Latex. I am new with it and need some help. I need to add figures. I can do it with the following code:  \begin{figure}[h]     \includegraphics[width = 15cm]{figures/mlpStrSingle}     \caption{MLP neural network for one single output node}     \label{fig:mlp} \end{figure}   However, if I use this the figure goes to the next page. I need it right after the text, then the next text should start. How can I do that?

Is there any package or a method to force LaTeX to keep floating environments like table and figure closer to where they are declared?


If you cast Polymorph on yourself to turn into a creature with low intelligence, can you/it continue to concentrate and thus remain in the polymorphed state for the duration of the spell? Or would the spell fail almost instantly because the new creature wouldn't be able to concentrate?   The question arose from one of our players wanting to cast Polymorph on himself to turn himself into a Black Pudding (MM p.241). We all looked into the distance pensively.   The spell says it can transform to be a beast, so the "Black Pudding" would be out of the question, but some beasts have an Intelligence of 1, like the Black Pudding, for instance: a Lizard.     This spell transforms a creature that you can see within range into a new form. [...] The transformation lasts for the duration, or until the target drops to 0 hit points or dies. The new form can be any beast whose challenge rating is equal to or less than the target’s (or the target’s level, if it doesn't have a challenge rating). The target’s game statistics, including mental ability scores, are replaced by the statistics o f the chosen beast. It retains its alignment and personality. [...] The creature is limited in the actions it can perform by the nature of its new form, and it can’t speak, cast spells, or take any other action that requires hands or speech.      (PHB p.266)

The level 4 spell Polymorph requires concentration to maintain.  The subject retains their personality and alignment, but they have the mental statistics of the new form, which must be a beast and cannot speak or cast spells.  If a caster targets themselves with this spell, can they concentrate to maintain it, or does this depend on the mental statistics of the beast form they choose?  This situation certainly occurs in practice, since Wizards reaching level 10 in the School of Transmutation gain the Shapechanger feature.  This allows them to cast Polymorph, but only upon themselves and only to change into a beast of CR 1 or lower.  Beasts with CR 1 or less range in Intelligence from the Giant Eagle (Int 8) to the Frog (Int 1).


I've been working through Chapter 2 questions and have thought about Exercise 2.18 for a while, but couldn't come up with an answer.     Is there a nonempty perfect set in R which contains no rational number?   I had a look  but I think this is wrong because obviously the Cantor set is not a subset of the rationals * (See below). Another thing that the above "solution" states is that the Cantor set only has endpoints but this is not true, e.g. 1/4 is a member of the Cantor set but is not an endpoint (See ).  Other solutions to this question based on a quick google search also give the same - seemingly incorrect - answer.  I have thought about sets like {x: Only 4 and 7 are in the decimal expansion of x, and the decimal expansion of x is non-repeating}, but this set doesn't work because 4/9 is a limit point of this set but is not a member of this set and so it is not a perfect set.  Other ideas I have come up with include starting with the irrational numbers in [0,1] and taking away lots of irrational numbers systematically, but I couldn't make this work.  The denseness of Q has something to do with it but I can't figure it out...  Any ideas?  *I say "obviously" but I should really explain myself here. The Cantor set is a perfect set, and every perfect set is uncountable, but any subset of rationals is countable.

Give an example of a perfect set in $\mathbb R^n$ that does not contain any of the rationals.  (Or prove that it does not exist).


I would like to set a variable (x=100) in the brackets such as   x=100     for i in {0.."$x"..50} ;do echo $i  done   the desire output for i should be   0 50 100   although I get as an output  {0..100..50}

I have a program that generates a variable number of pictures, ordered like that: 1.jpg, 2.jpg [...] 10.jpg..etc  I can't use *.jpg as input because the 10 will be processed before 2, 3, etc. so I want to use:  convert page_{1..$N}.jpg out.pdf   but does not work. How should the command be?


As in the header, I remember very little about this book or series   Some guy who is a key leader, either Earth Government or a corporation or a power bloc. There was a space trading element but I really can't remember anything about that. I don't think this person was the main character.  The key point I remember is, from the moment he wakes up, there's a little device or implant at one of his ears. All day long he gets updated on stock market and political info and military dispersals. A continuous low murmur.

I read it as a paperback book somewhere in the mid-90s, I think. The protagonist lived in an apartment building. He's out on the balcony when a birdlike (but humanoid) alien swooped down and attacked him. The presence of the aliens was commonly known and was a known danger. He kills it with his watering can and is rewarded by either the aliens or the humans for it with money. Other than that, all I remember was that the chapters were started with an internet-like news report which I think chronicled things getting worse and more violent. One of the updates involved the bombing of a bridge with the casualties raised by having two slow-moving trucks moving side by side obstructing traffic and ensuring a full bridge.  The internet system was pretty ubiquitous as I recall. I think that he looked up his watering can shortly after the incident with the aliens, but decided to keep this one, even if it leaks a bit. I want to say that it was by Piers Anthony, but none of the book titles look familiar. I think the cover I had showed the man being attacked by the bird-man, which looked kind of like the illustrations on the cover of The Stand.


15.04 - Unity -   This morning, all my icons, as well as the top bar, went missing.   I've tried everything I've found here (commands for re-installing unity, etc) but nothing has helped.  I HAVE noticed that the GUEST profile works just fine. Everything displays great. So this would SEEM to indicate a problem with the configuration of my primary account, right?  Is there a way to locate and reset my main accounts Unity configuration using the Guest account? If not, I CAN log into my main account, and use CTRL-ALT-F1 to get to a login screen, where I can log in as my main account.  To be clear, the only thing that appears when I log in as my main user is the desktop background, and the mouse cursor. Nothing else.   This seems to be a common problem, but none of the fixes out there are working so far.  The system is an old HP Mini netbook. No fancy GPUs.  Help!

When I login, nothing happens.   I am presented with my desktop wallpaper.    No Dash, no Launcher, nothing.


I recently reviewed the  for low quality, but when reviewing it have no radio option to select, see the below screenshot. Note I think I already flagged that post, but I'm not sure about the reason(probably "unclear what you are asking"). Like this situation what should I do ? or Is this bug?        Later: (Since it have no option I clicked the Looks good button)

I saw this bug mentioned in image below, where in I was about to mark the question as duplicate..    Has you can see there is no radio buttons to select and go further.. And I am stuck..  Is this a KNOWN bug..  I am using Mozilla Firefox Browser..  Edit:-  As guided by @AzizShaikh, This kind of behaviour is observed when you have already flagged a post. In my opinion, I think the page as I mentioned above should not have come in first place, I mean don't allow the user to enter it doesn't belong here, or it is a duplicate section if his vote has been posted successfully for that section rather than showing go nowhere Im lost Screen ..  Can we do something about this...??


. Assuming that two wizards cast  on the same chest and then go in different directions could they use this chest to exchange items over vast distances? To clarify a bit.  1- Wizard A and Wizard B cast Leomund's secret chest on the same chest.    Wizard A leaves to venture into a dungeon while Wizard B stays at the city. Wizard A finds a huge hoard of gold but cannot carry it. Using sending to reach Wizard B he asks Wizard B to summon their chest every five minutes and dump it's contents. Wizard A summons the chest    and fills the empty chest with gold. Sends it to Ethereal Plane Wizard B summons the chest and empties the content before sending it to Ethereal Plane Rinse and repeat till the entire hoard is taken back to the city within the span of an hour.

In my game, in which I play a wizard, I have met an NPC wizard who is willing to let me learn  from her spellbook. This got me wondering what would happen if I learned the spell and cast it on the same large chest that she had already cast it on (using my own separate tiny replica). Would this enable us to effectively teleport objects back and forth by alternately summoning the chest and placing things in it, then letting the other person summon it and remove the items? Or would something else happen? How would the chest work if 2 different wizards cast Secret Chest on it?


I'm using Leaflet map + GeoServer to display a map. I have a TIFF file and a DTED level 2 file.  I created a GeoTIFF store and layer that i'm showing in Leaflet, And I created a DTED store and layer in GeoServer.  I want now to display the altitude of each point from the DEM Layer, like so:  Latitude: 32.123 ,longitude: 12.112, Altitude: 12312 m   How do I get the altitude data from the store I created?  I tried using WCS protocol but I only get images.

I have a GeoTIFF published by Geoserver 2.2 and being used by Leaflet via WMS. How can I get Geoserver to return the raster value at a lat/long point?   I'm guessing it has to do with using WCS, but no examples seem to exist for doing this!  This will be similar to querying PostGIS with ST_Value(raster, ST_SetSRID(ST_Point(lon,lat),4326)). I dont really want to import the same raster into PostGIS just to find the raster value at a point. Or is this the recommended solution?