Batch frequency of point groups to single table in ArcGIS Desktop?
How to count occurrences of one field grouped by values of another?
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$? This is inspired by some discussions in .  In the Harry Potter universe, how are Dementors born?  Or are they artificially created by some magical means? 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... I have been editing an answer on , with some considerable amount of effort, and when I hit on Save Edits, the edit gets rejected with the following error. I got to know the meaning of this from .     The edit queue is full at the moment - try again in a few minutes!     I tried in a few mins, and still it didn't work. I believe that some edits might be valuable and this resists the users from doing so.   Main Question: Is there a way to show the queue limit at the beginning of the editing process? (So that we won't spend time on doing the edit, knowing it will fail) Almost surely convergence of the sequence Let ${X_n}$ be a sequence of independent and identically distributed, square integrable random variables.   Write $ u = E(X_n)$. Study the almost sure convergence, as $n \rightarrow \infty$, $$S_n = (X_1X_2 + X_2X_3 + ... + X_{n-1}X_{n})/n$$   Since $X_iX_{i+1}$ are not independent, it seems we cannot directly use law of large number for that, so anyone can give me some idea? When should I use the subjunctive mood? Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$ Question: Let $F_n$ the sequence of Fibonacci numbers, given by $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$. Show for $n, m \in \mathbb{N}$: $$F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$$   My (very limited) attempt so far: after creating a small list of the values $F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_{10}=55$ i can see that yes it does seem to work for instance $F_{6+3}=F_5 F_3 +F_6 F_4 = 10 +24 = 34 = F_9$. However, I really don't know where to begin as showing that this must hold in general terms. Should I be looking to use limits? Or perhaps induction? What is the best way to solve this? Where to securely store API keys and passwords in WordPress? I'm looking to use a few APIs and many come with keys, secret keys and passwords required to work. Where in WordPress can you store that information? Assuming anyone can hack your DB is there anyway for WordPress to make saving that information more secure? Also, consider the ability to change these keys ever so often so I would need to update the keys on an options page.  UPDATE If the universe is expanding, what is it expanding into? When the big bang happened where did it occur?  When the big bang happened how did it occur?  Where did the energy come from? Energy can not be created or destroyed does that mean, energy has existed before the universe was here? How to parse a string to an int in C++? What's the C++ way of parsing a string (given as char *) into an int? Robust and clear error handling is a plus (instead of ). has played the role of Wolverine as a major character in various X-Men films since 2000 and contributed highly to the brand of the X-Men movie series. But is he playing the Wolverine character for the last time in Logan?  I am getting to know from my friends that  is the last movie in which he is playing Wolverine and they all say that this is his last contracted film.  Are these rumors true? Is there any official information that confirms that this is Hugh Jackman's last movie as Wolverine? Can I watch the progress of a `sync` operation? I've copied a large file to a USB disk mounted on a Linux system with async. This returns to a command prompt relatively quickly, but when I type sync, of course, it all has to go to disk, and that takes a long time.  I understand that it's going to be slow, but is there somewhere where I can watch a counter go down to zero? Watching buffers in top doesn't help. Why Does Software Updater Say No updates Available, but apt-get upgrade Shows updates available? "Eat" is to "feed" as "drink" is to what? I can say "I feed someone". Am I forced to say "I give someone a drink", or is there a single word for this (as in "I [verb] someone")?  Unfortunately my thesaurus can't really help me. Reviewed suggested edit view for title-only edits takes body of last revision? Yesterday I was pointed at some rejected suggested edits. Some of the corrections were valid, so I edited the posts accordingly, while making several further edits. Looking at the suggested edits now however, it seems that for those posts where only changes to the title were originally suggested, the post mortem suggested edit view now incorporates the body of the latest revision. (Or at least it appears like that to me)  Take for example . If you take a look at  of that post, you will see my later edits. The edited body seems to have been incorporated in the suggested edit view. For edits where originally changes to the body were suggested, there is no such confusion.   Why does this matter? In the case of some post mortem discussions or explanations it might help to see the actual situation as it was when the edit was suggested. Especially in the case of edits that might be considered too minor.   So have I stumbled upon a bug here? Are black hole regarded as baryonic matter in cosmology? How do I convert materials from Blender Internal to Cycles? I know this may be a tough or confusing question, but I have numerous existing materials I created and reuse for a project, which were all prepared for Blender Internal.  Now, I want to start the transition to Cycles, but I've hit a roadblock. How can I transition my materials without completely starting over? Or should I just forget it and start with fresh materials? “situation where” vs. “situation in which” I don't understand this and I'm now worried as I have donated to a lot of servers and I don't want to lose this account. On the launcher it says my new username but when I log on it says "Account not Authenticated with minecraft.net" and "Non-Valid Username".  How can I regain the ability to use my account online? Can airlines deny boarding if my port of entry is different than the country which issued the Schengen visa? Few days back I did a Europe tour from India. As stated by many (I haven't confirmed official documents), I can apply for a visa from the country which is either my first port of entry in this case Paris or the longest stay which in this case was Italy.  Now following is what happened with me.   My flight was New Delhi to Paris via Istanbul with Turkish Airlines I Traveled from New Delhi to Istanbul (no problem here). When I was boarding to flight Istanbul to Paris, zhe airlines officials (the ones who checks the boarding pass before boarding the flight) told me that I could not board the flight because my visa was issued by Italy and I need to go to Italy First. They were denying the longest stay option of the visa. Moreover NONE of the staff of Istanbul airport were able to understand English so I had to go to a lot of problems before I managed to get tickets to Venice. I somehow managed to fly to Venice from Istanbul after almost 24 hours of struggle at Istanbul airport (without food and water).   So, my question is do the airlines staff have a right to deny flight boarding in this case?