It's easy to click "Visit the site now!" on the Area 51 page, but how can I go back without using the search engine on Area 51 or using the back button on my browser?
I'm participating in the  and wanted to refer to the on- and off-topic questions on the  proposal.  However, I couldn't find a link to it anywhere in the SE site.  If I'm not missing the obvious, could we have one?
If $u$ is harmonic and bounded in $0 < |z| < \rho$, show that the origin is a removable singularity This is a reworking of a previous question  which was marked as a duplicate. Some nice folks have referred me to solutions to similar problems. I still have a couple of questions, since one of the solutions used the Poisson kernel, which is not the desired solution in the text, because the Poisson kernel has not been introduced yet. The other solutions were for problems that were similar, but whose solutions were only partially applicable, as I understand them.  I'm working on a problem from p. 166 of Lars Ahlfors' Complex Analysis:     If $u$ is harmonic and bounded in $0 &lt; |z| &lt; \rho$, show that the origin is a removable singularity in the sense that $u$ becomes harmonic in $|z|&lt;\rho$ when $u(0)$ is properly defined.   My Solution So Far:   Here's what I've got for a non-Poisson kernel solution: We want to find a harmonic conjugate for $u$ in the punctured disk, and then we can apply big Picard to show that $0$ is a removable singularity. The problem is that the punctured disc is not simply connected.   If we take $\sigma = (u \circ \exp)(z): L \to \mathbb{C}$, where $L$ is the left half-plane, now we have $\sigma$ harmonic, and defined in a simply connected set $L$, so it has a harmonic conjugate $\tau$. Now we wish to take $v = (\tau \circ \log):\{0 &lt; |z| &lt; \rho\}\to \mathbb{C}$, but in order to do so we need $\tau$ to be $2\pi i$-periodic. This is where my proof breaks down.  One of the similar problems which readers referred me to used the following strategy: note that since $\sigma$ is $2\pi i$-periodic, and $\sigma, \tau$ satisfy the Cauchy-Riemann equations, we have that $\nabla\tau(z) = \nabla\tau(z + 2 \pi i)$ for all $z\in L$, or in other words, $\tau(z) - \tau(z+2\pi i)$ is a constant function, say, equal to $\alpha \in \mathbb{R}$. Then, the solution suggests, we can set $$g(z) = u + iv - \frac{c}{2\pi}z,$$  in order to make $g$ $2\pi i$-periodic, and then we can use $(g\circ \log)$ on $\{0 &lt; |z| &lt; \rho\}$. But the reason why this won't work for my purposes is: now we have changed $u$! On the other hand, we can't simply subtract $\frac{c}{2\pi}\Im{(z)}$, and try to leave $u$ untouched, because now $g$ is not analytic. How can we get around this?  Another strategy entirely might be to try to use the mean-value property. Ahlfors discusses that a lot in the preceding section, and his main example is the punctured disc. Since $u$ is harmonic, we know that the average over circles centered at zero is a constant... Let's say that there is a question asked in a bad manner, in a way that the question is missing. For example the user shows the code and doesn't explain very well which is the problem.    Usually someone starts digging in the OP mind posting comments and asking him for details. It may happen that the question gets edited and the OP edits it to a valid question.    Do you usually give the OP time to edit the question or you immediately vote to close it? How can I accept the Microsoft EULA agreement for ttf-mscorefonts-installer? After a recent update, ttf-mscorefonts-installer prompted me to accept its license agreement.     ┌─────────────────┤ Configuring ttf-mscorefonts-installer ├─────────────────┐  │                                                                           │   │ TrueType core fonts for the Web EULA                                          │                                                                               │ END-USER LICENSE AGREEMENT FOR MICROSOFT SOFTWARE                             │                                                                               │ IMPORTANT-READ CAREFULLY: This Microsoft End-User License Agreement           │ ("EULA") is a legal agreement between you (either an individual or a          │ single entity) and Microsoft Corporation for the Microsoft software           │ accompanying this EULA, which includes computer software and may include      │ associated media, printed materials, and "on-line" or electronic              │ documentation ("SOFTWARE PRODUCT" or "SOFTWARE"). By exercising your          │ rights to make and use copies of the SOFTWARE PRODUCT, you agree to be        │ bound by the terms of this EULA. If you do not agree to the terms of          │ this EULA, you may not use the SOFTWARE PRODUCT.                              │                                                                               │                                  &lt;Ok&gt;                                         │                                                                           │   └───────────────────────────────────────────────────────────────────────────┘    Screenshot:   For some reason my terminal will not allow me to accept, or for some reason I am pressing the wrong hotkey...  I've tried every letter on the keyboard and Enter among others...  I'm sure there is a very simple and obvious solution to this.  I've also just tried to remove the package completely however the terminal states that due to the package not being correctly installed, I should reinstall the package before removing it.  Very frustrating!  Essentially, because I cannot successfully install this package, I can't really ever upgrade my system because I always have to end up terminating the terminal with the license agreement (thus the upgrade fails). I just finished taking my first year of calculus in college and I passed with an A.  I don't think, however, that I ever really understood the entire $\frac{dy}{dx}$ notation (so I just focused on using $u'$), and now that I'm going to be starting calculus 2 and learning newer integration techniques, I feel that understanding the differential in an integral is important. Take this problem for an example: $$ \int 2x (x^2+4)^{100}dx $$ So solving this... $$u = x^2 + 4 \implies du = 2x dx \longleftarrow \text{why $dx$ here?}$$ And so now I'd have: $\displaystyle \int (u)^{100}du$ which is $\displaystyle \frac{u^{101}}{101} + C$ and then I'd just substitute back in my $u$. I'm so confused by all of this.  I know how to do it from practice, but I don't understand what is really happening here.  What happens to the $du$ between rewriting the integral and taking the anti-derivative?  Why is writing the $dx$ so important?  How should I be viewing this in when seeing an integral? Conjunction Puzzle: Is this clause dependent or independent? Third grade teacher here. I plan to teach students to distinguish between simple, compound and complex sentences — but only if I can demonstrate a clear and meaningful difference between the latter two!  Complex or Compound? Each sentence in the following pairs is similar to its partner.   All dogs are mammals, so huskies are mammals. All dogs are mammals, therefore huskies are mammals. I come bearing soup, for Kate is sick. I come bearing soup, because Kate is sick.   Are the sentences above complex or compound?   First, we need to decide whether each italicized clause is independent or dependent. To me, they all look dependent. If that is the case, there's not much need to teach about compound sentences. Is there a meaningful difference between the sentences in each pair that I am missing? (Are the FANBOYS as special as they'd like to think?) This is a Q&amp;A so I answer it myself. I searched for an answer to this question for ages and didn't find anything so I'll add this here if anybody else struggles with the same issue.  So, how can I merge two edge loops to one? I do not want to connect them (I have seen many answers that suggest to just bridge the edge loops), nor do I want to merge each vertex by hand. I just want each vertex to be merged with the closest opposing vertex.  Also, I find it highly unpractical and in most situations useless to remove doubles after moving the vertices to overlap each other by scaling and moving the edge loops. This is another common suggested answer. Ring and Subring with different Identities I think that  is pretty good prima-facia evidence that  is just facilitating the deposition of crap. Usually, in Star Trek, when there's a timeline change, the indication is that the original timeline is gone and replaced with the new one.  In City on the Edge of Forever, Kirk makes a comment that if they don't get the timeline straight, that millions of people who never died before will die.  Much of the time travel in Trek created suspense by declaring a need to restore the original timeline.  It's already been discussed in other questions about how, in the new movie (simply titled Star Trek with no subtitle or series number) they were unable to restore the original timeline.  While some of this is open to interpretation, it seemed like in this instance, for the first time, in Trek, there was an alternate timeline that was seen as an alternate possibility - no reference was made to it replacing the original timeline.  In this movie, was there any reference to the original timeline still existing?  In this movie, was the original timeline still considered to be intact? Ubuntu 16.04 Jan 3 2018 update causing screen/access issues Yesterday (Jan. 3, 2018), I installed an OS update (Ubuntu 16.04), using the Software Center. My system isn't working correctly now. When my mouse rolls over the Launch bar, it disappears, then any open window disappears, leaving me with only the desktop screensaver showing. I can't even shut the computer off using the settings button on the top.  I went into the Terminal and attempted to fix it using the following commands:  sudo apt-get dist-upgrade sudo apt-get autoremove   But I'm still having the same problem.  I have reinstalled Ubuntu 16.04 and when I accepted the update on install had the same problem.  I have reinstalled it a second time but have not done an OS update and everything seems to be working fine.    Found another user with the same problem:    Is it possible that the Meltdown security update is at fault?  I've read the update has been issued for 64-bit x86 architecture ();  I'm running a 32 bit i386 architecture.  Could that be an issue and is there a way to correct it? "Reality" of length contraction in SR I was in argument with someone who claims that length contraction is not &quot;real&quot; but only &quot;apparent&quot;, that the measurement of a solid rod in its rest reference frame is the &quot;real length&quot; of the rod and all other measurements are somehow just &quot;artificial&quot; and &quot;apparent&quot;. Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick &amp; Halliday) At the same time, the  insists that length contraction and time dilation are &quot;real&quot;, with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is &quot;real&quot; and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick &amp; Halliday use the word &quot;apparent&quot;? Pages: How to put a word between horizontal rules How can I make something that looks like this?  --------   Text   ---------  where the horizontal rules extend to the margin on either side? Are there any official specifications regarding the torque for camera mounts? I've been wondering why I've never seen any official specifications of the maximum allowed torque that can be exerted upon lens mounts. It seems to me like a very useful specification, but I can't seem to find it from any manufacturer.  indicates that there might be no specifications for Nikon mounts. Are there really no manufacturer that publish these specification of their mounts? How to delete Windows.old in Windows 8 It seems to be a common thing that a Windows Update creates a Windows.old folder under C:\Windows.old My question is now, can it be deleted with Windows 8 and how can I do that?  If I try to manually delete it in Windows Explorer it does not let me, a permissions issue. When should I publish in interdisciplinary versus subject-specific scientific journals? Most science research is published in subject-specific journals, of which there are many. However, there are a relatively small number of interdisciplinary journals, some of which are the most highly cited of all journals (Nature, Science); others have impact factors comparable to subject-specific journals (e.g., PLOS ONE, J. R. Soc. Interface, etc.).  If we discount arguments around open science and similar business model arguments (which could favor journals like PLOS ONE), and assume that the purpose of publishing is simply to get your research read (and cited) by the largest "relevant audience", when should one publish in an interdisciplinary journal versus a subject-specific journal (assuming they have comparable impact factors)? (Are there any papers out there that compare the fate of publications [or their authors!] in the two different types of journal?)  Thanks in advance. My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect? How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$? I can see that this works for any integer $n$, but I can't figure out why this works, or why the number $42$ has this property. I recently installed Ubuntu 12.10 and it requires a passphrase to boot up (I installed it with an encrypted file system).  Do I have to reinstall to change to a standard unencrypted file system? What are the benefits of running chef-server instead of chef-solo? I am looking at automated deployment solutions for my team and have been playing with Chef for the past few days. I've been able to get a simple web app up an running from a base Red Hat VM using chef-solo.  Our end goal is to use Chef (or another system) to automatically deploy application topologies to the cloud as we run builds. Our process would basically run like this:   Our web app code, dependencies, and chef cookbooks are stored in SCM A build is executed and creates a single package for images to acquire and test against The build engine then deploys new cloud images that run a chef client to get packages installed. The images acquire the cookbooks from SCM or the Chef server and install everything to get up and running   What are the benefits and/or use cases for getting a Chef Server running?  Are there any major benefits to have a Chef Server hold and acquire the cookbooks from SCM vs. using chef-solo and having a script that will pull the cookbooks from SCM? Prove $r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$ for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, exradii $r_1$, $r_2$, $r_3$