What is the difference between the studentized and non-studentized Breusch-Pagan test?
What is the difference between these two Breusch-Pagan Tests?
Find duplicate files Is it possible to find duplicate files on my disk which are bit to bit identical but have different file-names? I'm trying to convert some strings that are in French Canadian and basically, I'd like to be able to take out the French accent marks in the letters while keeping the letter. (E.g. convert é to e, so crème brûlée would become creme brulee)  What is the best method for achieving this? SVD: How to find the columnvector of U corresponding to a singular value equal to zero I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated. What's the fastest connection speed / shortest elapsed time using Migration Assistant? Is it possible to add images to comments? I was wondering if it is possible to post a comment with an image.  Recently, during a question about data-visualization in Cross Validated, there was a controversy about using one type of chart for another.   I had posted a question about pie-charts, after reading some references I decided to build an example and clarify the point of using waffle-chart vs pie-chart. In a way, my example was not an answer it was more properly a comment on waffle-charts. But it seems to be impossible to post a comment with an image (Maybe, there is a way but I can't figure out how).  I don't know if it is relevant to post images in comments in other SO sites. So, if there is no way to post images in comments... why not making it possible? And if there is a way to post an image with a comment, how I can do it? I don't know if this is a well-known fact, but I have observed that every number, no matter how large, that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there is $1$ digit. A quick example of what I mean:  $9*99 = 891$ $8+9+1 = 18$ $1+8 = 9$  This works even with really long numbers like $4376331$ Why is that? This doesn't work with any other number. Similarly for $11$ and alternating digits sums. Do I need Transit Visa to visit London for 4-5 hours during layover? Includepdf causes an error message from pgfplots externalization I have a file test.pdf which I include in a document containing also an externalized pgfplots picture.  When I compile the following code, I get the error message Sorry, the system call pdflatex ... did NOT result in a usable file.  In order to make my code work, I first need to remove the includepdf statement, compile (to create the externalized figures) and then compile again with the includepdf statement.  I suppose that it is a bug, or is there any possibility to solve it ?  Of course, the file test.pdf is totally independent from the externalized pictures from pgfplots.  \documentclass{scrbook}   \usepackage{pgfplots}  \pgfplotsset{compat=1.8}  \usepgfplotslibrary[external]  \tikzexternalize[shell escape=-enable-write18]  \usepackage{pdfpages}   \begin{document} \includepdf{report_test-figure44}   \begin{tikzpicture}  \begin{axis}[  xlabel=Cost, ylabel=Error]  \addplot[color=red,mark=x] coordinates {  (2,-2.8559703) (3,-3.5301677) }; \end{axis}  \end{tikzpicture}   \end{document} Finding the n-th lexicographic permutation of a string I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a way without brute-forcing the task.  So my thinking was like this:  For 10 variable symbol positions, we have 10! permutations, obviously. Now we want to find the first symbol.  If we fix the first symbol, then the remaining 9 symbols can have 9! combinations.  That means that 0 or 1 cannot be the first symbol, because the highest possible position is 2*9! = 725,760, which is lower than 1,000,000.  The lowest position for a leading 3 is 3*9! + 1 = 1,088,641, so it can't be 3 or higher, either.  Therefore, the first number must be 2. 2*9! is the largest multiple of 9! no greater than 1,000,000, so I need the 2nd symbol (zero-based) from the current set.  So now the question becomes, of the remaining S := S \{2}, which permutation of these symbols is at lexicographic position (1,000,000 - 2*9!) = 274,240?  6*8! = 241,920 is the largest multiple of 8! which is smaller than 274,240, so I need the 6th-smallest symbol of the remaining set, which is 7. So the prefix should be 27 by now.  That way, I keep going and finally arrive at: 1,000,000 = 2*9! + 6*8! + 6*7! + 2*6! + 5*5! + 1*4! + 2*3! + 2*2! + 0*1! + 0*0!  which results in "2783905614" as my solution.  However, according to the , (free reg. req.) that is incorrect.  Where did I go wrong in thinking or applying? Let $X$ be any distribution with defined mean, $\mu$, and standard deviation, $\sigma$.  The central limit theorem says that  $$ \sqrt{n}\frac{\bar{X} - \mu}{\sigma}  $$ converges in distribution to a standard normal distribution.  If we replace $\sigma$ by the sample standard deviation $S$, is there a theorem stating that  $$ \sqrt{n}\frac{\bar{X} - \mu}{S}  $$ converges in distribution to a t-distribution?  Since for large $n$ a t-distribution approaches a normal, the theorem, if it exists, may state that the limit is a standard normal distribution.  Hence, it would seem to me that t-distributions are not very useful - that they are useful only when $X$ is roughly a normal.  Is this the case?    If it is possible, would you indicate references that containing a proof of this CLT when $\sigma$ is replace by $S$?  Such a reference could preferably use measure theory concepts.  But anything would be great to me at this point. Find the default application for a certain extension Given xdg-open and an extension, is there a way to get the application which xdg-open is set to for that particular extension?  For example given xdg-open and .jpg the result is eog. I've just installed ubuntu server 17.10. During installation, it suggested me to connect to the network through wifi, and so i did. After installation was finished and system was rebooted, computer connected to the wifi automatically (which means, it saved the connection creds somewhere). But in /etc/network/interfaces i found nothing. I need my computer connect to wifi network with static ip, so I've put configuration into the /etc/network/interfaces:  # /etc/network/interfaces -- configuration file for ifup(8), ifdown(8) # Generated by debian-installer.  # The loopback interface auto lo iface lo inet loopback   iface wlp2s0b1 inet static         wpa-driver wext         address 192.168.0.12         netmask 255.255.255.0         gateway 192.168.0.1         wpa-ssid *****         wpa-psk **********         dns-nameservers 8.8.8.8 192.168.0.1 auto wlp2s0b1   When system starts, it doesn't connect using my configuration. It does only after  sudo ifdown wlp2s0b1 &amp;&amp; sudo ifup -v wlp2s0b1  and after this command, system getting a SECOND IP! Server is still available by the ip it gets from DHCP, and in the same time, it is available by the static ip! $\exp(A)$ is orthogonal iff $A$ is skew symmetric Let $A \in M_n(\mathbb R)$ and $\exp(A)=\sum_{i=0}^{\infty}\frac{A^i}{i!}$. How to prove $\exp(A)$ is an orthogonal matrix iff $A^t=-A$?  I can get that $\exp(A)$ is an orthogonal matrix iff $\exp(A^t)=\exp(-A)$, but how to get $A^t=-A$ from it?  What's more, is $\exp(A)$ injective or not? Mathematician learning theoretical physics How to fix apt: Signature by key uses weak digest algorithm (SHA1)? I started setting up by adding repositories and then went to run a sudo apt-get update again before I started installing other software, and I get the Signature key lines and it stops. So it essentially won't let me update any packages now.  d@EliteBook:~/Downloads$ sudo apt-get update Ign:1 http://dl.google.com/linux/chrome/deb stable InRelease Hit:2 http://dl.google.com/linux/chrome/deb stable Release                      Hit:4 http://security.ubuntu.com/ubuntu xenial-security InRelease               Get:5 http://ca.archive.ubuntu.com/ubuntu xenial InRelease [247 kB] Hit:6 http://ca.archive.ubuntu.com/ubuntu xenial-updates InRelease Hit:7 http://ca.archive.ubuntu.com/ubuntu xenial-backports InRelease Fetched 247 kB in 0s (256 kB/s)                    Reading package lists... Done W: http://dl.google.com/linux/chrome/deb/dists/stable/Release.gpg: Signature by  key 4CCA1EAF950CEE4AB83976DCA040830F7FAC5991 uses weak digest algorithm (SHA1) d@EliteBook:~/Downloads$   I've never seen this before whenever I setup and start installing things in Ubuntu. Is there something else I can do? WARNING: Setting property 'source' to 'org.eclipse.jst.jee.server:appname' did not find a matching property I've been going through  and have a question on the inductive proof for the . Recurrent relation:  $J(1) = 1$ $J(2n) = 2J(n) - 1$ $J(2n+1) = 2J(n) + 1$  Closed form hypothesis:  $J(2^m + l) = 2l + 1$, for $m \ge 0$ and $0\le l&lt;2^m$  Inductive Proof (for the even case):  $J(1)=1$ $J(2^m+l)= 2J(2^{m-1}+l/2)-1=2(2l/2+1)-1=2l+1$  How do the authors get from $2J(2^{m-1}+l/2)-1$ to $2(2l/2+1)-1$? Concept of Linearity I hear so many terms involving the word "linear". Linear function, linear equation, linear system, linear operator, linear transformation, linear mapping, linear space, linear algebra, linear electrical circuits, linear filters, linear electrical elements, linear approximation, linear optimization.  I'm getting crazy trying to understand the application of the "linear concept" to all this aspects (function, equation, mapping, system, operator, transformation, algebra, etc.) and I wish to know the one essence that is to be linear. What something has to be to be linear? If I say something is linear, what do I know for sure about that something (no matter what the something is)?       I heard a definition of linearity is by homogeinity (scaling the input results in a scaled output) and addition (summing the inputs results in summing the outputs). Can I apply this simple definition to all the branches (operator, mapping, system, transformation, algebra, ...) I mentioned ? Do they all behave like a line ?  y = ax + b, for example, is a line but doesn't behave like a line because y is not linear. How do I get jQuery to select elements with a . (period) in their ID? Given the following classes and controller action method:  public School {   public Int32 ID { get; set; }   publig String Name { get; set; }   public Address Address { get; set; } }  public class Address {   public string Street1 { get; set; }   public string City { get; set; }   public String ZipCode { get; set; }   public String State { get; set; }   public String Country { get; set; } }  [Authorize(Roles = "SchoolEditor")] [AcceptVerbs(HttpVerbs.Post)] public SchoolResponse Edit(Int32 id, FormCollection form) {   School school = GetSchoolFromRepository(id);    UpdateModel(school, form);    return new SchoolResponse() { School = school }; }   And the following form:  &lt;form method="post"&gt;   School: &lt;%= Html.TextBox("Name") %&gt;&lt;br /&gt;   Street: &lt;%= Html.TextBox("Address.Street") %&gt;&lt;br /&gt;   City:  &lt;%= Html.TextBox("Address.City") %&gt;&lt;br /&gt;   Zip Code: &lt;%= Html.TextBox("Address.ZipCode") %&gt;&lt;br /&gt;   Sate: &lt;select id="Address.State"&gt;&lt;/select&gt;&lt;br /&gt;   Country: &lt;select id="Address.Country"&gt;&lt;/select&gt;&lt;br /&gt; &lt;/form&gt;   I am able to update both the School instance and the Address member of the school.  This is quite nice!  Thank you ASP.NET MVC team!  However, how do I use jQuery to select the drop down list so that I can pre-fill it?  I realize that I could do this server side but there will be other dynamic elements on the page that affect the list.  The following is what I have so far, and it does not work as the selectors don't seem to match the IDs:  $(function() {   $.getJSON("/Location/GetCountryList", null, function(data) {     $("#Address.Country").fillSelect(data);   });   $("#Address.Country").change(function() {     $.getJSON("/Location/GetRegionsForCountry", { country: $(this).val() }, function(data) {       $("#Address.State").fillSelect(data);     });   }); });