Is there any software to map button 4 and 5 of mouse in macos catalina to a keyboard stroke?
Make Launchpad Appear on screen with mouse
Undefined reference to static class member Can anyone explain why following code won't compile? At least on g++ 4.2.4.  And more interesting, why it will compile when I cast MEMBER to int?  #include &lt;vector&gt;  class Foo {   public:       static const int MEMBER = 1;   };  int main(){       vector&lt;int&gt; v;       v.push_back( Foo::MEMBER );       // undefined reference to `Foo::MEMBER'     v.push_back( (int) Foo::MEMBER ); // OK       return 0; } To my knowledge there are three types of acceleration when a body (e.g. a rod) is moving in a circle about an axis. These are:   Angular acceleration : this is the rate of change of angular velocity. Tangential acceleration : this is the linear acceleration of the system in a tangential direction to the circle and equals the radius times the angular acceleration. Radial/centripetal acceleration : this is the linear acceleration of the system that is directed inwards towards the center of the circle.   I also think there are two types of velocity:   Linear velocity: this is its velocity in the tangential direction and is constantly changing Angular velocity or angular frequency: this is the rate of change of angle.   Is the above correct? And have I missed anything? Increase close vote weight for gold tag badge holders In order to increase the efficiency with which poor quality questions are closed, it could make sense to have weighted close votes for a small subset of qualified users.   A very good way to measure the qualified users would be to leverage the tag badges. However, it needs to be rationally limited to a set of users that are knowledgeable with the subject. A very good way to measure the top users in a tag would be to look at those who have a gold badge in the tag.  If two users who have a gold tag badge pertinent to a question issue a close vote, the question should probably be closed (or probably will be very soon under the current system). I think it would make sense to allow users with a gold tag badge to have a 3x weight for close votes in those tags.  Please keep in mind, this isn't suggesting full moderator one click closure. It only adds weight to the vote. A single user could not do it on their own. These singular users cast close votes all the time, so that aspect would not change. Some will vote to close, some wont, but the ones who do should have a stronger weight to their vote. Even with 3x it will require 2 of said votes to accomplish, or still 2 other users (meaning 3 agreed it should be closed - which is the same amount of high rep users it takes to delete a question and that has a much greater impact than closure).  tldr;  Allow gold tag badge users to have a weighted close vote in their tag Remove entire row in a file if first column is repeated I have a file containing two columns and 10 million rows. The first column contains many repeated values, but there is a distinct value in column 2. I want to remove the repeated rows and want to keep only one using awk. Note: the file is sorted with values in column 1. For example:    1.123 -4.0 2.234 -3.5 2.234 -3.1 2.234 -2.0 4.432 0.0 5.123 +0.2 8.654 +0.5 8.654 +0.8 8.654 +0.9 . . . .   Expected output  1.123 -4.0 2.234 -3.5 4.432 0.0 5.123 +0.2 8.654 +0.5 . . . . NSString instance reports its class as NSCFString My objective here is really simple -- I'm trying to set an NSString to some test data, then return the class, which should be NSString. Here's my code:  NSString* stringer = [NSString stringWithFormat: @"Test"]; NSLog(@"%@", [stringer class]);   The log says that the class is NSCFString, not NSString. What's going on here? Show that conguence $\bmod m\,$ is an equivalence relation Are recommendation questions an acceptable kind of list-type question or should they be closed? Recommendations are a recurring topic on multiple Stack Exchange (SE) sites. Some sites allow recommendations (ex: ), some do not (ex: ). There are many reasons for that and I can still remember animated discussions on this subject on the Gaming meta. Then there is that existential problem with Sci-Fi SE, &quot;What problems does answering a question on this site solve?&quot;  The only common problem I can think of is What to read/watch next?, which obviously led to a big number of recommendation questions, later slightly disguised as list question. And the main trouble with these questions isn't objectivity at all, some of them aren't even subjective. It's the fact that they don't have an answer - they are open ended. -  Those questions are monstrously popular because:  There's an actual problem to be solved,  or  This problem is quite common.  In view of the  blog post, a recommendation question fails the &quot;real questions have answers, not items or ideas or opinions.&quot; criteria. But it's still a &quot;practical, answerable questions based on actual problems that you face. &quot; and it requires expertise to answer. The problem is that there are multiple acceptable answers, and the asker is not the best person to evaluate the best answer because he doesn't know which one is the best compared to the others, and he cannot test it in short term. Even the need to accept an answer is questionable. So, is a recommendation question an acceptable kind of list-type question or should it be closed just like any other list-type questions? Floating point arithmetic not producing exact results How many square meters "twenty feet square" is? One would assume it to be about 2 square meters, but this is obviously not the case. In fact, I'm reading Illium by Dan Simmons. A quote follows:     Much like the room they had faxed into, this space was windowless and about twenty feet square. But unlike the other room, this one was warm, lighted, and free of snow or ice. And unlike the other room, this one was almost filled with an oval metal machine about fifteen feet long.   By this description, "twenty feet square" seems to mean 20x20 feet aka 400 square feet or 40 square meters. Given that Dan Simmons is a renowned American writer, it's not likely that he just can't speak English correctly. So, who's right and who's wrong here? I am just a high school student, and I haven't seen much in mathematics (calculus and abstract algebra).  Mathematics is a system of axioms which you choose yourself for a set of undefined entities, such that those entities satisfy certain basic rules you laid down in the first place on your own.  Now using these laid-down rules and a set of other rules for a subject called logic which was established similarly, you define certain quantities and name them using the undefined entities and then go on to prove certain statements called theorems.  Now what is a proof exactly? Suppose in an exam, I am asked to prove Pythagoras' theorem. Then I prove it using only one certain system of axioms and logic. It isn't proved in all the axiom-systems in which it could possibly hold true, and what stops me from making another set of axioms that have Pythagoras' theorem as an axiom, and then just state in my system/exam "this is an axiom, hence can't be proven".  EDIT : How is the term "wrong" defined in mathematics then ? You can say that proving fermat's last theorem using the number-theory axioms was a difficult task but then it can be taken as an axiom in another set of axioms .  Is mathematics as rigorous and as thought-through as it is believed and expected to be ? It seems to me that there many loopholes in problems as well as the subject in-itself, but there is a false backbone of rigour that seems true until you start questioning the very fundamentals . $2+2 = 5$? error in proof $$\begin{align} 2+2 &amp;= 4 - \frac92 +\frac92\\ &amp;= \sqrt{\left(4-\frac92\right)^2} +\frac92\\ &amp;= \sqrt{16 -2\times4\times\frac92 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{16 -36 + \left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {-20 +\left(\frac92\right)^2} + \frac92\\ &amp;= \sqrt{25-45 +\left(\frac92\right)^2} +\frac92\\ &amp;= \sqrt {5^2 -2\times5\times\frac92 + \left(\frac92\right) ^2} + \frac92\\ &amp;= \sqrt {\left(5-\frac92\right)^2} +\frac92\\ &amp;= 5 + \frac92 - \frac92 \\ &amp;= 5\end{align}$$  Where did I go wrong Black screen on boot after AMDGPU-Pro install (16.04) I have been having some screen freezing issues on my new Ubuntu 16.04 system, and have been in the troubleshooting process for this issue. I thought it was a graphics driver problem, as I am running an AMD R9 380x card which was supposed to be fully supported by the open-source AMDGPU driver preinstalled with 16.04, but after looking around online, many people seem to have issues with. I thought the answer would be to install the recently released AMDGPU-Pro driver , following the instructions from . However, when I reboot I am getting a black screen. Is there an easy way to revert my changes back? My machine was semi-functional with the freezing issue but now with no video at all is useless to me. How to proceed? Cannot suggest retag-only edit because "edits must be at least 6 characters" I was trying to suggest a retag of  on Seasoned Advice, but the system won't let me; I get the familiar message     Edits must be at least 6 characters; is there something else to improve in this post?   In general, that's not true for retagging; if you don't change the question body at all, it should work. I suspect the logic checking the edit is thrown off guard because of the title warning:     The question you're asking appears subjective and is likely to be closed       I found , but I cannot find any evidence (in SEDE) for invisible characters being present in the question's source. Also, that's supposed to be . Does it make sense to combine PCA and LDA? Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via dimensionality reduction techniques such as Principal Component Analysis (PCA) and/or Linear Discriminant Analysis (LDA).  Both techniques are projecting the data onto a smaller feature subspace: with PCA, I would find the directions (components) that maximize the variance in the dataset (without considering the class labels), and with LDA I would have the components that maximize the between-class separation.  Now, I am wondering if, how, and why these techniques can be combined and if it makes sense.  For example:   transforming the dataset via PCA and projecting it onto a new 2D subspace transforming (the already PCA-transformed) dataset via LDA for max. in-class separation   or    skipping the PCA step and using the top 2 components from a LDA.   or any other combination that makes sense. Converse of Schur's Lemma in finite dimensional vector spaces I am trying to prove (or disprove) the converse of Schur's Lemma in finite dimensional vector spaces. I am not sure if it holds in this case, but I have tried to apply the idea that proves it in representation theory (see for example Theorem 4.3  that uses Maschke's theorem or in questions  and ).  The converse of Schur's Lemma in finite dimensional vector spaces is:     Let $V$ be a finite dimensional vector space over the complex numbers. Let $S$ be a set of endomorphisms of $V$ and assume that every endomorphism $A$ of $V$ such that $$AB=BA\text{ for all }B\in S$$ is of the form $\lambda I, \ \lambda\in\mathbb{C}$. Then $V$ is a simple $S$-space.   (*an endomorphism of $V$ is a linear operator from $V$ to $V$  *$V$ is a simple $S$-space if the only $S$-invariant subspaces of $V$ are $V$ itself and the zero subspace)  What I've tried so far:  Assume to the contrary that $V$ is not a simple $S-$space. Then, there exists a subspace $W$ of $V$ such that $W\not =\{0\}$, $W\not= V$ and $W$ is $S$-invariant. Let $W'=V\setminus W$. Then, since $V$ is finite, we can easily prove that $V=W\oplus W'$ (this is my attempt to translate Maschke's theorem in vector spaces). Consequently, for every $v\in V$, there exists unique $w\in W$ and $w'\in W'$, such that $v=w+w'$. Define the projection $P:V\rightarrow V$ by $Pv=w$ for every $v\in V$.   What is left to prove is that $PB=BP$ for all $B\in S$. Then $P$ is clearly not a scalar and thus we have the contradiction we are looking for.  There is a difficulty in showing that $PB=BP$ for all $B\in S$, because $W'$ might be $S$-invariant or not. More precisely:   Let $v\in V=W\oplus W'$ and $v\not =0_V$.  If $v\in W$ then $Bv\in W$ because $W$ is $S$-invariant, therefore: $PBv=Bv$ and $BPv=Bv$.  If $v\in W'$ then $Pv=0$, hence $BPv=B\cdot 0=0$, and  (i) if $Bv\in W'$ then $PBv=0$.  (ii) if $Bv\in W$ then $PBv=Bv$ and this is where the problem occurs.  Any hints, ideas or counterexamples would be very helpful. I want to make a generic class that accepts only serializable classes, can it be done with the where constraint?  The concept I'm looking for is this:  public class MyClass&lt;T&gt; where T : //[is serializable/has the serializable attribute] Is it possible to use NBT tags in commands in Minecraft: Bedrock Edition? How can I best describe "making a new discovery"? proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem I have build a website for a finance company.  The Cognito Form is on the website as an application form.  I would like the information sent automatically to the finance company's email address (as soon as the form is submitted) without having to log into Cognito Forms. The finance company needs to know the exact moment the application for finance comes in. The finance company can not possibly log in to Cognito Forms 24/7 to check if there are any finance applications.