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How did Draco apparate within Hogwarts? Prove that $(x^2 + x+2)$ ideal is a maximal ideal in $F_3[x]$ ring.  I know the theorem about factor rings and fields     B ideal from A ring is maximal iff A/B factor-ring is a field   How can I use the theorem here? Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice? I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used? Remote Linux server to remote linux server dir copy. How? What is the best way to copy a directory (with sub-dirs and files) from one remote Linux server to another remote Linux server? I have connected to both using SSH client (like Putty). I have root access to both. Suppose $A$ and $B$ are similar matrices. Show that $A$ and $B$ have the same eigenvalues with the same geometric multiplicities.      Similar matrices: Suppose $A$ and $B$ are $n\times n$ matrices over $\mathbb R$ or $\mathbb C$. We say $A$ and $B$ are similar, or that $A$ is similar to $B$, if there exists a matrix $P$ such that $B = P^{-1}AP$. How can I override the OnBeforeUnload dialog and replace it with my own? How do I set up a folder so that anything created in it inherits permissions? how to install the DDE to the ubuntu 20.04? I have installed the Ubuntu 20.04, and want now I want to install Deepin Desktop Environment (dde)  My steps are:   add the ppa and install using apt  sudo add-apt-repository ppa:leaeasy/dde sudo apt-get update sudo apt install dde    But during the command sudo add-apt-repository ppa:leaeasy/dde I get the following error:  $ sudo add-apt-repository ppa:leaeasy/dde  You can install deepin desktop environment by run  sudo add-apt-repository ppa:leaeasy/dde sudo apt-get update apt-get install dde ------ Ubuntu Bionic: https://drive.google.com/file/d/1xkQPb4tWocknuYeY-t41W--kz-9SSL0V/view?usp=sharing ------ Important Issue: Q: Can dde on Ubuntu 16.04? A: Sorry, the dde depends on qt version above than 5.6.      If you want to install dde, please upgrade to 17.04 or above.  More info: https://launchpad.net/~leaeasy/+archive/ubuntu/dde Press [ENTER] to continue or Ctrl-c to cancel adding it.  Hit:1 http://in.archive.ubuntu.com/ubuntu focal InRelease Hit:2 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease                                      Hit:3 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease                                    Ign:4 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal InRelease                                      Hit:5 http://security.ubuntu.com/ubuntu focal-security InRelease            Err:6 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release             404  Not Found [IP: 91.189.95.83 80] Reading package lists... Done E: The repository 'http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   I get the similar error with sudo apt-get update :  $ sudo apt-get update Hit:1 http://in.archive.ubuntu.com/ubuntu focal InRelease Hit:2 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease                                       Hit:3 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease                                     Ign:4 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal InRelease            Hit:5 http://security.ubuntu.com/ubuntu focal-security InRelease Err:6 http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release   404  Not Found [IP: 91.189.95.83 80] Reading package lists... Done E: The repository 'http://ppa.launchpad.net/leaeasy/dde/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   How can I install dde ? Equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$ Find the equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$. will it also be an ellipse? Screen brightness control not working on Lenovo T530 Is it possible to have test error lower than training error?  I have a classification problem with 2000 samples, 500 of which are positives, 1500 are negatives. I split my data into 70% training data, 30% test data.  Run random forest with 200 estimators and cv=10. I did this several times and compared the recall and precision score and notice the scores for my test set is significantly better. Is this possible? At one point, I decided to make friends with the low-lying spectrum of QCD. By this I do not mean the symmetry numbers (the "quark content"), but the actual dynamics, some insight.  The pions are the sloshing of the up-down condensate, and the other pseudoscalars by extending to strangeness. Their couplings are by soft-particle theorems. The eta-prime is their frustrated friend, weighed down by the instanton fluid. The rho and omega are the gauge fields for flavor SU(2), and A1(1260) gauges the axial SU(2), and they have KaluzaKlein-like echoes at higher energies, these can decay into the appropriate "charged" hadrons with couplings that depend on the flavor symmetry multiplet. The proton and the neutron are the topological defects. That accounts for everything up to 1300 but a few scalars and the b1.  There are scalars starting at around 1300 MeV which are probably some combination of glue-condensate sloshing around and quark-condensate sloshing around, some kind of sound in the vacuum glue. Their mass is large, their lifetime is not that big, they have sharp decay properties.  On the other hand, there is nothing in AdS/QCD which should correspond to the sigma/f0(600), or (what seems to be) its strange counterpart f0(980). While looking around, I found this discussion: . The literature that it pointed to suggests that the sigma is a very unstable bound state of pions (or, if you like, tetraquarks).   gives strong evidence for an actual pole;  gives a more cursory review. The location of the pole is far away from the real axis, the width is larger than the mass by 20% or so, and the mass is about 400MeV. The authors though are confident that it is real because they tell me that the interpolation the interactions of pions is safe in this region because their goldstone properties dominate the interactions. I want to believe it, but how can you be sure?  I know this particle was controversial. I want to understand what kind of picture this is giving. The dispersion subtraction process is hard for me to visualize in terms of effective fields, and the result is saying that there is an unstable bound state.  Is there a physical picture of the sigma which is more field theoretical, perhaps even just an effective potential for pions? Did anyone who convinced himself of the reality of the sigma have a way of understanding the bound state properties? Is there an analog unstable bound state for other goldstone bosons? Any insight would be welcome. Git error: large files "detected", even though no large files exist Faithful representation of the Heisenberg group I have been trying to solve a problem concerning the Heisenberg Lie group $H$. Show that there does not exist a faithful representation $\rho:H\to\text{GL}(2,\mathbb{R})$.  Any ideas about how to solve it would be very appreciated. I have a CSV file which has postcode data in a field, but it is non-spatial e.g. no Easting and Northing.   I have a shapefile with postcode in a field and some additional data.  I want to join the CSV with the shapefile based on attributes (postcode fields). I know I can do this in ArcMap, but how can I achieve the same thing in QGIS? Many C++ books contain example code like this...  std::cout &lt;&lt; "Test line" &lt;&lt; std::endl;   ...so I've always done that too. But I've seen a lot of code from working developers like this instead:  std::cout &lt;&lt; "Test line\n";   Is there a technical reason to prefer one over the other, or is it just a matter of coding style? Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$ Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$. It is the distance of a point in a triangle from its vertexes which gives the minimum when $(x,y)$ is on the Fermat's point.  But now I am stuck in finding the location of Fermat's point.  $(1) \quad 4$ $(2) \quad 5$ $(3) \quad \sqrt{3}+2\sqrt{5}$ $(4) \quad 4\sqrt{2}$ How to make a domain receiving email behind cloudflare? What is the easiest way to find and replace text in 20 text files in a directory? I have 20 text files with various extensions in a directory.  I want to replace "nnn" with "ooo" in all files.  I could import them into a project in Eclipse or Visual Studio to replace them all but that is overkill and would add other meta files etc.  What is a simple way to do this, I'm thinking: select all files, right click, choose some tool called (e.g. "QuickReplacer") and fill in find and replace, click and done.  Does anyone know of a tool like this?