Does a lecturer have the right to prevent students from making their notes public?
Is it okay to publish my personal notes from a lecture?
Please excuse the selfishness of the following question:     Let $G$ be a group and $H \le G$ such that $|G:H|=2$. Show that $H$ is normal.   Proof:  Because $|G:H|=2$, $G = H \cup aH$ for some $a \in G \setminus H$.   Let $x\in G$. Then $x \in H$ or $x \in aH$.  Suppose $x \in H$. Then $xhx^{-1} \in H$ because $H$ is a group.  Suppose $x \in aH$. Then $ahH(ah)^{-1} = ahHh^{-1}a^{-1} = a(hHh^{-1})a^{-1}$ ***1  ***1: Can I say now that $x \in H$, based on the that $hHh^{-1} \in H$ and that $aa^{-1} = e$ ?  Thank you for the time you spent reading my doubts. How to print original variable's name in Python after it was returned from a function? How do I tell what gauge wire I need? I've been working on providing power for high current applications for my project. I'm working on a project with high current (or at least compared to what I'm used to...)  What a lot of people point to online is tables that you can look up the resistance for AWG per foot, and then you can calculate the current drop of your wire. However, with that current drop, how much of  a voltage drop will make my wire "too hot" and risk a fire? Am I looking at this the wrong way? How do I calculate the temperature of the wire and decide when it'll be too hot, and I should use a thicker wire? We all know that _spPageContextInfo is a very useful thing in Client side development. I need something equivalent of _spPageContextInfo in SPFX. Currently I am unable to use it directly from typescript. It gives error like     Can not find '_spPageContextInfo'   Finally, I have gone through the API documentation of  and  found . PageContext has dependence with . My qestion is: How to use PageContext? I need to use it my BaseService class. constructor of my class is:  constructor(private $http: ng.IHttpService, private $q: ng.IQService, serviceScope: ServiceScope) {     serviceScope.whenFinished(() =&gt; {       this.pageContext = new PageContext(serviceScope);       console.log(this.pageContext);     });   }   Inside the constructor serviceScope is undefined. I know the reason: As I am not injecting/initialising serviceScope anywhere like other angular services. So what is the approach of injecting/initialising serviceScope in angular service class? How to set up passwordless SSH access for root user I need to configure a machine so software installation can be automated remotely via SSH. Following , I was able to setup SSH keys so my user can access the machine without a password, but I still need to manually enter my password when I use sudo, which obviously an automated process shouldn't have to do.  Although my /etc/ssh/sshd_config has PermitRootLogin yes, I can't seem to be able to log in as root, presumably because it's not a "real" account with a separate password.  How do I configure SSH keys, so a process can remotely log in as root on Ubuntu? If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $ How does Python evaluate the expression 1+++2?  How many ever + I put in between, it is printing 3 as the answer. Please can anyone explain this behavior  And for 1--2 it is printing 3 and for 1---2 it is printing -1 I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this? For example:  $ sudo apt-get install curl Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: bsh : Depends: libjline-java but it is not going to be installed groovy : Depends: libjline-java but it is not going to be installed rhino : Depends: libjline-java but it is not going to be installed E: Unmet dependencies.   Try 'apt-get -f install' with no packages (or specify a solution).   I get the same or similar errors when I attempt to install clojure1.3, leiningen, and several other packages.   When I try the suggestion made in the error message, this is what happens:  $ sudo apt-get -f install  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages were automatically installed and are no longer required:   diffstat linux-headers-3.2.0-26-generic linux-headers-3.2.0-26 dh-apparmor dkms html2text libmail-sendmail-perl libsys-hostname-long-perl Use 'apt-get autoremove' to remove them. The following extra packages will be installed:   libjline-java Suggested packages:   libjline-java-doc The following NEW packages will be installed:   libjline-java 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. 23 not fully installed or removed. Need to get 0 B/72.0 kB of archives. After this operation, 129 kB of additional disk space will be used. Do you want to continue [Y/n]? Y (Reading database ... 226243 files and directories currently installed.) Unpacking libjline-java (from .../libjline-java_1.0-1_all.deb) ... dpkg: error processing /var/cache/apt/archives/libjline-java_1.0-1_all.deb (--unpack):  trying to overwrite '/usr/share/java/jline.jar', which is also in package scala 2.9.2-400 Errors were encountered while processing:  /var/cache/apt/archives/libjline-java_1.0-1_all.deb E: Sub-process /usr/bin/dpkg returned an error code (1)  $ sudo apt-get upgrade Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies:  bsh : Depends: libjline-java but it is not installed  groovy : Depends: libjline-java but it is not installed  rhino : Depends: libjline-java but it is not installed E: Unmet dependencies. Try using -f. Why are the IV (constant) values fixed for HMAC/SHA? Why do HMAC/SHA IV's have a fixed value? I refer to the arbitrary H constants which are included in the algorithm prior to any data being fed in.  Why aren't they exposed to the user, so one can decide on an IV and modify it accordingly (for example, in java they are provided at hash function specification, instead of being supplied by the user at init)?  How does modifying these IVs affect the algorithm? We have added JSON-LD structured data to our website, so Google knows information about our company (company name, url, logo, address, etc.). We worked from the template on Google's .  One thing I couldn't find an answer to is where exactly should this JSON-LD snippet be included on our website? Right now, I only have it on our home page. I didn't know if it would look bad to search engines to have the Organization markup on every single page. But is there any recommendation?  Should Organization markup about our company be included on every page or only on certain pages? How do I delete a folder that's in use? Sometimes when I'm working in Windows I'll get this prompt when I try to delete a directory:    Folder In Use The action can't be completed because the folder is open in another program Close the folder and try again.   However, the folder isn't "in use" at all, and I don't have it open. So how can I delete it short of rebooting? I am trying to make a floor plan for my office, have managed to make all of the rectangular components (e.g. the rooms) however some of the desk layouts are circular and I haven't been able to work out how to make exact and measured circles. They need to have a radius of 1.45m. What is the correct (most efficient) way to define the main() function in C and C++ — int main() or void main() — and why? And how about the arguments? If int main() then return 1 or return 0?  There are numerous duplicates of this question, including:       — For C++, with a very good answer indeed.     Related: Name for the center amplitude of a sine wave I am trying to find the name for the value at the center of a sine wave $$ y(t) = A\sin (kx \pm \omega t+\varphi) + D $$ i.e. the offset $D$ of the wave in the $y$-direction.  calls it Center Amplitude, but further googling this name is difficult and does not provide any further sources. I also found the expression , but I'm not sure that it refers to the same thing. Is there a commonly used name for the $y$-direction-offset of a sine wave? For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$ I have only recently been exposed to sets. According to , as seen on the first bullet mark of the link, $ \forall A: \emptyset \subseteq A$  Does this mean that $\emptyset$ is an element of all sets? (This is False, thank you those that answered)  Is the empty set also a set itself?  Assuming these statements are true, then the empty set therefore an element of the empty set. This does not sound right, please clarify for me. Thank you. Dropping one of the columns when using one-hot encoding I want to put four figures in a single row. The code I am trying to use is taken from .  This puts three figures in a row. When I add a fourth one, I get three images in row and the last one appears in the second row. But I want all of them in one row. Here is my code.  \documentclass[12pt,twoside]{report}% Use this line for the print version of the thesis   \usepackage{graphicx} \usepackage{caption} \usepackage{subcaption} \begin{document}  \begin{figure}         \centering         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull}                 \label{fig:gull}         \end{subfigure}%           \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{gull}                 \caption{A gull2}                 \label{fig:gull2}         \end{subfigure}%          ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{tiger}                 \caption{A tiger}                 \label{fig:tiger}         \end{subfigure}         ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc.           %(or a blank line to force the subfigure onto a new line)         \begin{subfigure}[b]{0.3\textwidth}                 \centering                 \includegraphics[width=\textwidth]{mouse}                 \caption{A mouse}                 \label{fig:mouse}         \end{subfigure}         \caption{Pictures of animals}\label{fig:animals} \end{figure} \end{document}   As I have mentioned above, it works for three figures.  But I can not use it for four figures. What should I change?   What does  width=\textwidth mean?   I changed    \begin{subfigure}[b]{0.3\textwidth}   to  \begin{subfigure}[b]{0.2\textwidth}   but it didn't help.  Then, I changed     \includegraphics[width=\textwidth]{mouse}   to  \includegraphics[width=0.5\textwidth]{mouse}   Still no solution. Javascript multiple replace I have read the first five Dune novels and after the first I do not recall any further mention of Imperial conditioning. In the novels written since Frank Herbert's death, were any further references or details given about what this process actually involved and why it was considered virtually impossible to remove?