Should I use the singular or plural verb form with "one or more"?
Which is correct: "one or more is" or "one or more are"?
Intuition behind the definition of a measurable set How to show path-connectedness of $GL(n,\mathbb{C})$ Well, I am not getting any hint how to show $GL_n(\mathbb{C})$ is path connected. So far I have thought that let $A$ be any invertible complex matrix and $I$ be the idenity matrix, I was trying to show a path from $A$ to $I$ then define $f(t)=At+(1-t)I$  for $t\in[0,1]$ which is possible continous except where the $\operatorname{det}{f(t)}=0$ i.e. which has $n$ roots and I can choose a path in $\mathbb{C}\setminus\{t_1,\dots,t_n\}$ where $t_1,\dots,t_n$ are roots of $\operatorname{det}{f(t)}=0$, is my thinking was correct? Could anyone tell me the solution? I changed both the desktop and login screen background photos. However,only desktop photo is changed. The one on the login screen is still the purple Ubuntu one. Is this a bug? canonical-livepatch, Doesn't seem to patch anything I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$.  One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th edi, p442) is as following: $$ \langle x|[x,p]|y \rangle = \langle x|xp-px|y \rangle = (x-y) \langle x|p|y \rangle. $$ On the other hand,  $ \langle x|[x,p]|y \rangle = i \langle x|y \rangle = i \delta (x-y)$. Thus $$ (x-y) \langle x|p|y \rangle = i \delta(x-y). \tag{1} $$  We use $(x-y) \delta(x-y) = 0$. Take the derivative with respect to $x$; we have $\delta(x-y) + (x-y) \delta'(x-y) = 0$. Thus $$ (x-y) \delta'(x-y) = - \delta(x-y). \tag{2} $$  Comparing Eqs. (1) and (2), we identify $$ \langle x|p|y \rangle = -i \delta'(x-y). \tag{3} $$  In addition, we can add $\alpha \delta(x-y)$ on the right-hand side of Eq. (3), i.e. $$ \langle x|p|y \rangle = -i \delta'(x-y)  + \alpha \delta(x-y), $$ and $[x,p] = i$ is still satisfied. We can also add $$ \frac{\beta}{\sqrt{|x-y|}}\delta(x-y)$$ on the RHS of Eq. (3).  Here $\alpha$ and $\beta$ are two real numbers.  My question is, what is the most general expression of $\langle x|p|y \rangle$? Can we always absorb the additional term into a phase factor like Dirac's quantum mechanics book did?  Thank you very much in advance. Abelianization of free group is the free abelian group SharePoint People.aspx Page is Visible for All Users The SharePoint People.aspx page is visible for all users by default. Is there any way to restrict this page from certain readers? Give each site a parallel site for polling, recommendations and subjective-ish stuff Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com. 'Country have' vs 'country has' 1) Australia has won the World Cup Cricket.      2) Australia have won the World Cup Cricket.   Which sentence is correct? Also, I would like to know more contexts where 'country has' and 'country have' are used. This question aims to create an &quot;&quot;  of numerous questions that ask about determinants of specific matrices (I may have missed a few):              The general question of this type is  Let $A$ be a square matrix of rank$~1$, let $I$ the identity matrix of the same size, and $\lambda$ a scalar. What is the determinant of $A+\lambda I$?  A clearly very closely related question is  What is the characteristic polynomial of a matrix $A$ of rank$~1$? Why do neural networks need so many training examples to perform? A human child at age 2 needs around 5 instances of a car to be able to identify it with reasonable accuracy regardless of color, make, etc. When my son was 2, he was able to identify trams and trains, even though he had seen just a few. Since he was usually confusing one with each other, apparently his neural network was not trained enough, but still.  What is it that artificial neural networks are missing that prevent them from being able to learn way quicker? Is transfer learning an answer? How to remove all files in a directory except hidden ones? Update help center on syntax highlighting to point to an actual list of options Reading the help center article on syntax highlighting, one of the paragraphs within it reads:     You can use either , like lang-cpp or lang-sql, or you can specify a tag, and the syntax highlighting language associated with this tag will be used:   Note the link in there, which goes to .  Problem is, a long time ago we removed the list of options from several questions/answers across meta Stack Exchange because it was a pain trying to keep all of them updated. It makes a lot more sense to just have one list that we keep updated, and the most logical place for that list was in the , which is where it now resides.  Can the link in the help center be updated to point directly to the list, rather than to a post that explains that the list has been moved? I used a website called Seeking Arrangements and met a  sugar daddy. He asked for my email login, online banking login, routing, account number, Facebook, as well as my  address which is the only thing I gave him since it’s a PO. I’ve been extremely vague just to see if this is real.   I don’t plan to give him anything because I have only been talking to him for a few months and  I feel conflicted. I doubt that he is trying to scam me but I suspect that he has some kind of master plan. With things such as Venmo, Zelle, and Cashapp, what is the need for “put me on his payroll?”   He claims that he is in another country on a business trip.  He said that  he tried to send me a gift but he lost access to his card. He is now asking to deposit more than 10k into my account and have me wire it. Is this a l classic way of scamming people? If so, is it common that they spend months creating a relationship with you  to catfish you? Frequentism and priors Robby McKilliam says in a comment to  post:     It should be pointed out that, from the frequentists point of view, there is no reason that you can't incorporate the prior knowledge into the model. In this sense, the frequentist view is simpler, you only have a model and some data. There is no need to separate the prior information from the model   Also, , @jbowman says that frequentists use regularization by a cost/penalty function, while bayesians can make this a prior:     Frequentists realized that regularization was good, and use it quite commonly these days - and Bayesian priors can be easily interpreted as regularization.   So, my question is, can frequentists in general incorporate into their models what Bayesians specify as priors? Taking the regularization as an example, is the cost/penalty function really integrated into the model, or is this a purely artificial means of adjusting the solution (as well as making it unique)? How to make pipes work with Runtime.exec()? Function to determine if two numbers are nearly equal when rounded to n significant decimal digits I have been asked to test a library provided by a 3rd party. The library is known to be accurate to n significant figures. Any less-significant errors can safely be ignored. I want to write a function to help me compare the results:  def nearlyequal( a, b, sigfig=5 ):   The purpose of this function is to determine if two floating-point numbers (a and b) are approximately equal. The function will return True if a==b (exact match) or if a and b have the same value when rounded to sigfig significant-figures when written in decimal.   Can anybody suggest a good implementation? I've written a mini unit-test. Unless you can see a bug in my tests then a good implementation should pass the following:  assert nearlyequal(1, 1, 5)  assert nearlyequal(1.0, 1.0, 5)  assert nearlyequal(1.0, 1.0, 5)  assert nearlyequal(-1e-9, 1e-9, 5)  assert nearlyequal(1e9, 1e9 + 1 , 5)  assert not nearlyequal( 1e4, 1e4 + 1, 5)  assert nearlyequal( 0.0, 1e-15, 5 )  assert not nearlyequal( 0.0, 1e-4, 6 )    Additional notes:   Values a and b might be of type int, float or numpy.float64. Values a and b will always be of the same type. It's vital that conversion does not introduce additional error into the function. Lets keep this numerical, so functions that convert to strings or use non-mathematical tricks are not ideal. This program will be audited by somebody who is a mathematician who will want to be able to prove that the function does what it is supposed to do. Speed... I've got to compare a lot of numbers so the faster the better. I've got numpy, scipy and the standard-library. Anything else will be hard for me to get, especially for such a small part of the project. How do I Enqueue styles/scripts on Certain /wp-admin Pages? I have two simple functions that load stuff using  and , something like these:  function admin_custom_css() { wp_enqueue_style( 'stylesheet_name', 'stylesheet.css') };   function admin_custom_js  { wp_enqueue_script( 'javascript_file', 'script.js') };   ... and a few admin pages, created with  and   function my_menu() {    add_menu_page('Page 1', 'bar', 'something', 'else', 'foo');    add_submenu_page( 'theme_menu', 'Subpage 1', 'Subpage', 'something', 'else', 'foo');  } add_action('admin_menu', 'my_menu');    How do I load my two functions only on these pages?  Right now I'm using:  add_action('admin_init', 'admin_custom_css' );  add_action('admin_init', 'admin_custom_js' );     But it loads my files on every admin page, which is not nice at all.  Can I do this via one simple line in functions.php or have to enqueue them within my pages separately (I prefer the first option strongly, since I'd have to edit a lot of admin-page-creating-functions).  Thanks! What is some good free software for doing physics calculations?  I'm mainly interested in symbolic computation (something like Mathematica, but free). X,Y are independent exponentially distributed then what is the distribution of X/(X+Y) Been crushing my head with this exercise. I know how to get the distribution of a ratio of exponential variables and of the sum of them, but i can't piece everything together.  The exercise goes as this:  If X,Y are independent exponentially distributed with beta = 1 (parameter of the exponential distribution = 1) then what is the distribution of X/(X+Y)  Any ideas?  Thanks a lot.