Django manytomany signals?
django manytomanyfield .add() method
If you have an $m \times n$ matrix and the rows are linearly independent, are the columns linearly independent too?  I know that it's the case for $n \times n$ matrices. I've yet tried to think about it, and I think the answer is yes, for example the matrix: $\begin{bmatrix} 1 &amp; 2 &amp; 3 \\ a &amp; 2a &amp; 3c \end{bmatrix}$ has linearly dependent rows and columns, but I'm not sure that it works for every $m \times n$ matrix. Prevent people from downloading / copying / making a copy of data in Google doc Show that holomorphic $f_1, . . . , f_n $ are constant if $\sum_{k=1}^n \left| f_k(z) \right|$ is constant. While studying for an exam in complex analysis, I came across this problem. Unfortunately I was not able to solve it. Any help would be greatly appreciated.  Let $U ⊂ \mathbb{C}$ be a domain and $f_1, . . . , f_n : U \rightarrow \mathbb{C}$ holomorphic functions, such that $\sum_{k=1}^n \left| f_k(z) \right|$ is constant on $U$. Show that $f_1, . . . , f_n$ are constant. How to set tick label precision While trying some problems along with my friends we had difficulty in this question.   True or False: The value of the infinite product $$\prod\limits_{n=2}^{\infty} \biggl(1-\frac{1}{n^{2}}\biggr)$$ is $1$.   I couldn't do it and my friend justified it by saying that since the terms in the product have values less than $1$, so the value of the product can never be $1$. I don't know whether this justification is correct or not. But i referred to Tom Apostol's Mathematical Analysis book and found a theorem which states, that    The infinite product $\prod(1-a_{n})$ converges if the series $\sum a_{n}$ converges.   This assures that the above product converges. Could anyone help me in finding out where it converges to? And,   Does there exist a function $f$ in $\mathbb{N}$ ( like $n^{2}$, $n^{3}$) such that $\displaystyle \prod\limits_{n=1}^{\infty} \Bigl(1-\frac{1}{f(n)}\Bigr)$ has the value $1$? Syntax highlighting in app differs from normal web view I am unable to find the link for downloading Ubuntu 16.04 onto my   desktop/laptop. I am able to see the link only for 18.04, but I need 16.04. Game State 'Stack'? I was thinking about how to implement game states into my game. The main things I want for it are:   Semi-transparent top states-being able to see through a pause menu to the game behind Something OO-I find this easier to use and understand the theory behind, as well as keeping orgranised and adding more to.    I was planning on using a linked list, and treat it as a stack. This means I could access the state below for the semi-transparency.  Plan: Have the state stack be a linked list of pointers to IGameStates. The top state handles its own update and input commands, and then has a member isTransparent to decide whether the state underneath should be drawn.  Then I could do:  states.push_back(new MainMenuState()); states.push_back(new OptionsMenuState()); states.pop_front();   To represent the player loading, then going to options, and then main menu.  Is this a good idea, or...? Should I look at something else?   Thanks. How can I simplify the use of flags with Views Bulk Operations? I have an administrative display (made with views) that lists content that is pending approval.  In the case of my site, approval means flagging with the approval_for_pub flag (which triggers a custom rule).   allows nodes to be flagged/unflagged all at once by clicking a handy button:    However, upon clicking this button, by default it shows all possible flags and the flag/unflag option:    This is a problem on my site because some of the people responsible for approval get confused by the names of the flags and select the wrong option.  So, what I would like to do is create a VBO option that, when the button is pressed, automatically flags all applicable content with the approval_for_pub flag.  How can I approach this?  It seems like a small detail, but this step happens several times a day, so the chance of making a mistake is quite high. I used to have an icon on the Windows Vista taskbar showing the battery amount remaining (laptop). It has mysteriously vanished.  How can I get it back?  I followed the Windows  (see How can I hide the battery icon in the notification area? - hoping to reverse the instructions) but the Power checkbox on the Notification Area tab was greyed out and could not be checked or unchecked (it is currently unchecked). Gmail filters/labels: Force email to stay in Inbox? just wondering if anyone has ever tried embedding and actually integrating any js engine into the .net environment. I could find and actually use (after a LOT of pain and effort, since it's pretty outdated and not quite finished) spidermonkey-dotnet project. Anyone with experience in this area? Engines like SquirrelFish, V8..   Not that I'm not satisfied with Mozilla's Spidermonkey (using it for Rails-like miniframework for custom components inside the core ASP.NET application), but I'd still love to explore a bit further with the options. The command-line solutions are not what I'd need, I cannot rely on anything else than CLR, I need to call methods from/to JavaScript/C# objects.  // c# class public class A {     public string Hello(string msg)     {         return msg + " whatewer";     } }  // js snippet var a = new A(); console.log(a.Hello('Call me')); // i have a console.log implemented, don't worry, it's not a client-side code :)   Just to clarify - I'm not trying to actually program the application itself in server-side javascript. It's used solely for writing custom user subapplications (can be seen as some sort of DSL). It's much easier (and safer) to allow normal people programming in js than C#. So I did a fresh install of Ubuntu 20.04 on a computer with the new RTL8125B Realtek network card and I cannot get the network to work. I was very suprised since this is supposed to be the new feature of the 5.4 kernel (I have 5.4.0-26-generic installed). Does anyone have any idea on how to get it working? Thank you. $ lspci -knn | grep Eth -A3 06:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8125 2.5GbE Controller [10ec:8125] (rev 04) Subsystem: ASUSTeK Computer Inc. RTL8125 2.5GbE Controller [1043:87d7] Kernel modules: r8169 07:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] Ellesmere [Radeon RX 470/480/570/570X/580/580X/590] [1002:67df] (rev e7)  $ dmesg | grep -i r8169 [    0.911236] r8169 0000:06:00.0: unknown chip XID 641 Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)&gt;c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?  There are a number of equivalent definitions for the measurability of a function and the most obvious one would be to show that $\{x\in E : f(x)&gt;c\}$ is measurable for all $c\in\mathbb{R}$.  Thus my strategy has been to consider an arbitrary irrational $y$ and use the density of the rationals in the reals to show that there exists some open set $O$ such that $m^*(O-\{x\in E : f(x)&gt;y\})&lt; \varepsilon$.  I would do this by choosing some rational $q&lt;y$, close enough to $y$, such that the set of values in $E$ which get sent under $f$ to values strictly greater than $q$ and less than or equal to $y$ is small enough.  But that doesn't in general seem possible since I could keep sending intervals of some fixed positive length to smaller and smaller regions just beneath $y$.  However conversely, such a function would not be enough for a counter example, since finding such a function only rules out this strategy, but doesn't necessarily entail non-measurability.  Is there a better definition of the measurability of a set I should use? or does the statement actually not imply measurability?  Thanks. Easiest way to prove that $2^{\aleph_0} = c$ $\aleph_0$ is the cardinality of the set of natural numbers, $\aleph_0 = |N|$. $c$ is the cardinality of the continuum, i.e. the set of real numbers $c = |R|$.  I know that $|P(A)| = 2^{|A|}$. This means that the cardinality of the power set of a set is 2 raised to the power of the cardinality of that set.  This basically means that to prove  $2^{\aleph_0} = c$, I need to prove $c = |P(N)|$. I've seen the Cantor diagonal argument, although I have no idea on how to use it to prove this.   Could anyone suggest ideas of the simplest way to prove that $2^{\aleph_0} = c$? The Complete Rate-Limiting Guide I noticed that I can only perform certain actions such as commenting a finite number of times in a given period of time. Obviously, rate limiting is in place to prevent accidental misuse or intentional abuse of certain features.  Where else is rate limiting applied on Stack Exchange sites, and what are the limits? "Dark L" is "L" at the end of the word or after a vowel sound. Example: ball, pull.  "Light L" is "L" at the beginning or before a vowel sound. Example: light, love.  There are 4 explanations of how to pronounce "dark L":   1st explanation: the tongue tip must contact the ridge right behind the upper teeth. 2nd explanation: before the tongue tip must contact the ridge right behind the upper teeth, you must curl the tongue and make sound like /r/ before make the /l/ as in the 1st explanation. 3rd explanation: just put the tongue between upper and lower teeth is enough to make the dark L 4th explanation: the tongue tip must contact the ridge right behind the upper teeth &amp; the back of the tongue raises up (a British teacher teaches that).   see this vid:  and  for more info  So what is the correct way to make the "dark L"? what is wrong with this??? please,can anyone help?  \begin{equation} \label{probabilityy} P^{t}({E_{0})=P_{0}+(1-P_{0})P_{1}+ (1-P_{0})(1-P_{1})P_{2}+.......+P_{n}\Pi_{k_{0}}^{n-1}(1-P_{k}) \end{equation} Windows 10 puts my first and last name to lock screen. How to avoid this? After upgrading to Windows 10, I see my LastName and FirstName on the lock screen. Is there a way to change this? On Windows 8.1 there was just my nickname and email address (maybe there were my first name and last name, but not displayed so large as they are now).  I mean the name and surname parameters specified in my Microsoft account.  Another question: I prefer the format FirstName LastName, not vice versa.  Is there any way to change this as well?   Apart from Lock Screen I see it on the Start Menu. How to Pass an Object Method as a Parameter in Delphi, and then Call It? I fear this is probably a bit of a dummy question, but it has me pretty stumped.  I'm looking for the simplest way possible to pass a method of an object into a procedure, so that the procedure can call the object's method (e.g. after a timeout, or maybe in a different thread).  So basically I want to:   Capture a reference to an object's method. Pass that reference to a procedure. Using that reference, call the object's method from the procedure.   I figure I could achieve the same effect using interfaces, but I thought there was another way, since this "procedure of object" type declaration exists.  The following doesn't work, but might it help explain where I'm confused...?  interface    TCallbackMethod = procedure of object;    TCallbackObject = class     procedure CallbackMethodImpl;     procedure SetupCallback;   end;  implementation  procedure CallbackTheCallback(const callbackMethod: TCallbackMethod); begin   callbackMethod(); end;  procedure TCallbackObject.CallbackMethodImpl; begin   // Do whatever. end;  procedure TCallbackObject.SetupCallback; begin   // following line doesn't compile - it fails with "E2036 Variable required"   CallbackTheCallback(@self.CallbackMethodImpl); end;   (Once the question is answered I'll remove the above code unless it aids the explanation somehow.)