I sent a mod message to myself before sending it to the user to check the formatting and such, and noticed missing links in the plain text version:  HTML version:   Plain text version:   As you can see, the first three links don't show up at all in the text/plain version of the email.  I pasted the links as-is:  http://vi.stackexchange.com/... some text  http://vi.stackexchange.com/... Some text   Looks like this only happens if there is a text description for the link ([..](http://..)), as the fourth link as well as a  link to a post's revisions did survive intact.    By the way, also note how it doesn't add the &gt; markers, and just adds that as plain-text.  The input field is in Markdown – why not just use that as-is as the text/plain part of the email?
I just signed up, a day or two ago, and I've received a notification that there's something in my inbox.  Unfortunately, my email client isn't able to show me a link to my Inbox, or the message, because of the format of the email.  I normally use the email address that I gave when I signed up, just with MailWasher, which is intended to safely preview emails, as plain text, to decide whether or not to open them in a normal HTML email client.  I would be nice if that email contained a link to my inbox, which could be shown in MailWasher.  In order to collect that email in a normal email client, I'd also have to collect or delete all the other emails sent to that address.  I'm not entirely clear what's been done in that email to stop MailWasher seeing the link.  I can see a link to leave feedback, and one to unsubscribe, but not one to check my inbox.  Sure, I can live without one, but those emails would be a lot more useful to me if I could just click a link to go to my Inbox.
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$ Evaluate the summation of: $$ \sum_{k=1}^n {n \choose k-1} {n \choose k} $$ I have been trying to solve this problem by translating C(n, k-1) into C(n, k), because I know that: $$ \sum_{k=1}^n {n \choose k}^2={2n \choose n} $$ However, I haven't been having any luck. Am I on the right track? What am I doing wrong? Space which is connected but not path-connected If I have the following state:  $$ \left| \varphi \right&gt;=\frac{1}{\sqrt{2}}\left(\left(\frac{1+i}{\sqrt{2}} \right)\left| 0 \right&gt; + \left| 1\right&gt;\right) $$  How can I find the $\theta$ and $\phi$ values of this qubit on the Bloch sphere? My wife is an Indian national with an Indian passport. She holds an indefinite leave to remain in the UK (permanent residence card). Does she need to apply for a Schengen visa before travelling to France or any other Schengen countries? I am looking for a driver for the TP-Link AC600 Archer T2U Nano, on Kubuntu 18.04 (kernel version 4.15.0-51-generic).   I already tried different drivers, none of them worked. I notice that the space between each column of a table in LaTeX is not quite wide (at least for me). Is there any way to set this? I found the \hspace, but I don't get how to use this in the table. I'm using NetBeans, trying to change the familiar Java coffee cup icon to a png file that I have saved in a resources directory in the jar file.  I've found many different web pages that claim they have a solution, but so far none of them work.  Here's what I have at the moment (leaving out the try-catch block):  URL url = new URL("com/xyz/resources/camera.png"); Toolkit kit = Toolkit.getDefaultToolkit(); Image img = kit.createImage(url); getFrame().setIconImage(img);   The class that contains this code is in the com.xyz package, if that makes any difference.  That class also extends JFrame.  This code is throwing a MalformedUrlException on the first line.  Anyone have a solution that works? Simulate a uniform distribution on a disc I was attempting to simulate injection of random points within a circle, such that any part of the circle has the same probability of having a defect.  I expected the count per area of the resulting distribution to follow a Poisson distribution if I break up the circle into equal area rectangles.    Since it requires only placing points within a circular area, I injected two uniform random distributions in polar coordinates: $R$ (radius) and $\theta$ (polar angle).  But after doing this injection, I clearly get more points in the center of the circle compared to the edge.     What would be the correct way to perform this injection across the circle such that the points are randomly distributed across the cirlce? Excluding empty(Null) fields when using EntityFieldQuery query condition Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem. In terms of purely set theory, the axiom of choice says that for any set $A$, its power set (with empty set removed) has a choice function, i.e. there exists a function $f\colon \mathcal{P}^*(A)\rightarrow A$ such that for any subset $S$ of $A$, $f(S)\in S.$ Is this correct?  My question then is about proving this fact, so that we do not need to put it as an axiom. Now as per the research done on this single object- Axiom of Choice, I believe here that there should be some falsity in my argument. I do not find the mistake.  For any $S\in \mathcal{P}^*(A)$, since $S\neq \emptyset$, $\exists s\in S$. Define $f(S)=s$. Then $f$ is a choice function.  This was showing me that the axiom of choice is proved, but then why it had been put as an axiom? For example, in  book, the author asserts that      It is a metatheorem of mathematical logic that it is impossible to specify the function that assigns to each non-empty subset of $\mathbb{R}$, an element of itself.     There are several notes and books on axiom of choice, but here I am trying to understand through doing some argument for some problem, where problem actually arises. I've been trying to prove   $$\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$$  I've tried perturbation and inversion but still nothing. I've even tried expanding the sum to try and find some pattern that could relate this to the harmonic series but this just seems surreal. I can't find any logical reasoning behind this identity. I don't understand . Is there any proof that doesn't require the integral transform? When is the union of a family of subspaces of a vector space also a subspace? It is not difficult to prove that the union of a chain (or, more generally, a directed family) of subspaces of a vector space $V$ is a subspace of $V$.   Given a family $\mathcal{F}$ of subspaces of a vector space $V$ such that the union of $\mathcal{F}$ is a subspace of $V$, is it true that $\mathcal{F}$ is a directed family?  If not, is there a "nice" characterization of families of subspaces whose union is a subspace? Cooking away alcohol When you cook with wine or spirits, when does the alcohol cook away? Obviously high temperatures will do it, but how low of temperatures will work? Also, does it vary by the type of alcohol? 1.  Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an explanation that I need some help with: that the de Broglie wavelength and the wavelength of an elastic wave do not show similar properties under a Galilean transformation. He basically says that both are equivalent under a gauge transform and also, separately by Lorentz transforms. This, accompanied with the observation that $\psi$ is not observable, so there is no "reason for it being real". Can someone give me an intuitive prelude by what is a gauge transform and why does it give the same result as a Lorentz tranformation in a non-relativistic setting? And eventually how in this "grand scheme" the complex nature of the wave function becomes evident.. in a way that a dummy like me can understand.  2.   A wavefunction can be thought of as a scalar field (has a scalar value in every point ($r,t$) given by $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{C}$ and also as a ray in Hilbert space (a vector). How are these two perspectives the same (this is possibly something elementary that I am missing out, or getting confused by definitions and terminology, if that is the case I am desperate for help ;)   3.   One way I have thought about the above question is that the wave function can be equivalently written in $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{R}^2 $ i.e, Since a wave function is complex, the Schroedinger equation could in principle be written equivalently as coupled differential equations in two real functions which staisfy the Cauchy-Riemann conditions. ie, if $$\psi(x,t) = u(x,t) + i v(x,t)$$ and $u_x=v_t$ ; $u_t = -v_x$ and we get $$\hbar \partial_t u  = -\frac{\hbar^2}{2m} \partial_x^2v + V v$$ $$\hbar \partial_t v  = \frac{\hbar^2}{2m} \partial_x^2u - V u$$ (..in 1-D) If this is correct what are the interpretations of the $u,v$.. and why isn't it useful. (I am assuming that physical problems always have an analytic $\psi(r,t)$). Will Ubuntu get patched against Meltdown and Spectre? The following is a canonical post that attempts to cover a broad number of Meltdown and Spectre questions.  It is being maintained by Thomas Ward who is in contact with the Security and Kernel teams on this matter for other reasons as well.   I recently read about the  vulnerabilities.  I was wondering, will Ubuntu be patching against the vulnerabilities?  And is there an ETA on a fix? Where can I download Ubuntu 16.04? 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. Is there an idiom for people who boast too much? Allow new users to comment for X times in a day While reviewing "First Posts" on Stack Overflow, I often come across new users posting comments as answers. It seems (at least to me) they are not doing this because they are unaware of how Stack Overflow works but because they can't comment on any question they are forced to put it as answer.  I have found duplicate questions for my request like:   ,  and    but the best explanation I have found is an  to .     I think the main reason this isn't supported is there's no way to   downvote comments, which would make them attractive to spammers. If   somebody comments on the top answer in a question the only way to get   rid of it is for six people to flag it. Comment flags don't show up on   10k tools, so it needs to be six people that happen to stumble across   the spam comment, or a moderator that checks the list manually. People   can comment every 15 seconds, so that can get out of hand pretty   quickly. Comments also aren't listed on the user's profile page, so   it's hard to see at a glance if a user has been spamming   So I am suggesting allowing new users (with less than 50 reputation points) to comment only 5 times every day or only 25 times times until they reach 50 reputation points or any other variation of it. Where such a term would reference the location/time of an object, almost like it was of a property of the object. That is to say, if a duck is red, blue, yellow etc, we describe it has having a certain colour. If it's a nanometre, or 10km big, then it's property of size.  Now I know that where/when an object exists an object isn't a property of an object, but it is something unique to that object, so I think it would be useful to have a shorthand for 'geographical location', and 'time of existence'.  There are terms describing both time and location, such an event, or rendezvous (which I think is used to describe the when and where of a meeting between two humans) but I wan't a term that just describes one of each. How do I delete a Git branch locally and remotely?