Why did the Nazgûl not try to reclaim their rings from a weakened Sauron together?
How did Sauron remain in control of the Nazgûl?
Cropping Shapefiles in QGIS? Running Yosemite 10.0 with a clean erase and install, when I reboot, all my launchpad apps are totally disorganised, folders and un-official apps disappears...  After reorganizing the layout twice, I don't want to keep sorting my launchpad every time I restart my Mac. TikZ rectangular node with different rounded corners Difference between "try to do" and "try and do" What is the difference between try to do and try and do?  To me (non-native speaker), asking someone try and do this seems a bit rude. It's like saying you can try all you want but this must be done: try and fail is not an option. However, asking someone try to do this means I am asking you to try: success is bonus, failure is OK. Using a comma before "but" I keep hearing about tandem breakers, and how they won't work with 240V loads and how they should never be used for a multi-wire branch circuit.  Aside from those issues...  What is a tandem breaker?     (note: they can be thrown independently). set session - custom variable to store user id I want to store user id in custom session variable and use it (read) in trigger procedures to authorize user actions. I found something like this:  set session "myapp.user" = '12345'; ... SELECT current_setting('myapp.user');   and it seems to work - I thought that "myapp.user" should be declared in .conf file but it seems that I can create session variables on the fly (I didn't change .conf file at all).  Is there any disadvantage of doing like this? How to make a GIS inventory? My office will be seeing a big change in its GIS section. This section has been operational since the 1980's and has a huge collection of GIS data (i.e., shapefiles, raster files, data, etc) but never been through any inventory. Now it will happen.   Is there any automated way to extract all the information about the GIS data (i.e., shapefile, arc-info coverage, layer file, *.mxd, gdb, raster file, and more) from a PC to an Excel file? The information may include date of creation, date last edited, folder or container name, etc. Equivalence Relation problem Let $S$ be the relation on $\mathbb{N} \times \mathbb{N}$ defined by $(a,b)S(c,d)$ if and only if $ad=bc$. Prove this is an equivalence relation on $\mathbb{N} \times \mathbb{N}$.  I think I've found this to be reflexive and symmetric, but I'm stuck on transitivity. Can someone check my work so far and assist with testing transitivity?  Reflexive: Let $(x,y)S(x,y)$. Then $xy = yx$. So $S$ is reflexive. Symmetric: Suppose $(a,b)S(c,d)$. Then, $ad = bc$. Therefore, $da = cb$ and $cb = da$. Therefore, $(c,d)S(a,b)$. Thus, $S$ is symmetric.  Transitive: Suppose $(a,b)S(b,c)$. Then $ac = bb$.   This is where I'm stuck. Any ideas? Redirecting cout to a console in windows I have an application which is a relatively old. Through some minor changes, it builds nearly perfectly with Visual C++ 2008. One thing that I've noticed is that my "debug console" isn't quite working right. Basically in the past, I've use AllocConsole() to create a console for my debug output to go to. Then I would use freopen to redirect stdout to it. This worked perfectly with both C and C++ style IO.  Now, it seems that it will only work with C style IO. What is the proper way to redirect things like cout to a console allocated with AllocConsole()?  Here's the code which used to work:  if(AllocConsole()) {     freopen("CONOUT$", "wt", stdout);     SetConsoleTitle("Debug Console");     SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_GREEN | FOREGROUND_BLUE | FOREGROUND_RED); }   EDIT: one thing which occurred to me is that I could make a custom streambuf whose overflow method writes using C style IO and replace std::cout's default stream buffer with it. But that seems like a cop-out. Is there a proper way to do this in 2008? Or is this perhaps something that MS overlooked?  EDIT2: OK, so I've made an implementaiton of the idea I spelled out above. Basically it looks like this:  class outbuf : public std::streambuf { public:     outbuf() {         setp(0, 0);     }      virtual int_type overflow(int_type c = traits_type::eof()) {         return fputc(c, stdout) == EOF ? traits_type::eof() : c;     } };  int APIENTRY WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPTSTR lpCmdLine, int nCmdShow) {     // create the console     if(AllocConsole()) {         freopen("CONOUT$", "w", stdout);         SetConsoleTitle("Debug Console");         SetConsoleTextAttribute(GetStdHandle(STD_OUTPUT_HANDLE), FOREGROUND_GREEN | FOREGROUND_BLUE | FOREGROUND_RED);       }      // set std::cout to use my custom streambuf     outbuf ob;     std::streambuf *sb = std::cout.rdbuf(&amp;ob);      // do some work here      // make sure to restore the original so we don't get a crash on close!     std::cout.rdbuf(sb);     return 0; }   Anyone have a better/cleaner solution than just forcing std::cout to be a glorified fputc? How to print colored text to the terminal? How can I output colored text to the terminal in Python? iPhone stuck on Connect to iTunes My iPhone is stuck on Connect to iTunes Screen (support.apple.com/iphone/restore iTunes logo and up arrow with lightning cable) I have Tried :-   Connecting it to iTunes and Updating, It updates Successfully.But on the same screen again   Restoring, It restores successfully.But on the same screen again  Tried Recovery Mode Screen Method and DFU method Tried Closing and Restarting iTunes Tried Deleting 'iPhone Software Update' folder in iTunes and Re-Downloding Updates    Nothing Works... Any Help will be appreciated I have a directory where daily subdirectories are created, literally named according to $date. How can I delete folders and their contents that are older than 7 days according to the YYYYMMDD in the file name and not the metadata date? Say I have (skipped some for brevity):  20170817 20170823 20170828 20170901   I would end up with the following folders (which those should keep):  20170828 20170901   I created a variable that holds the date 7 days ago: dt_prev=$(date -d "`date`-7days" +%Y%m%d)  My thought was to ls -l a list of these folder names and compare row by row, but this involves cleaning that list, etc., and I figure there has to be an easier way. What packages do you use and recommend for creating graphics in your LaTeX documents?     As this is a community wiki post, please add your package to the accepted answer (or add a comment, and someone with >100 rep will add it to the CW answer), and include a brief description of what differentiates it from others and how it can be used (GUI drawing tool which generates code, type in raw text, or generates image for inclusion in document).   We'll eventually sort these answers under headings. The replier's From email address is modified when Marketing Cloud RMM forwards an email to the routing address We've set up RMM to forward replies to routing address and SFMC adds our subdomain to the replier's From email address (i.e. replier@gmail.com becomes replier.gmail.com@oursubdomain.com). However, their reply-to address remains the same.  It seems like DMARC Forward Reply Rewrite is enabled, but we were advised not to touch it as that may affect email deliverability.  Is there any workaround to this? And what will happen if we disable this feature? How to calculate $\lim_{x\to 1^+} \log (x)^{\log(x)}$? How to calculate $\lim_{x\to 1^+} \log (x)^{\log(x)}$ ? i know that its "1", but why? How can i calculate this?  Thank you very very much =) Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$ I have some questions with string theory:   Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR? How to show that $C=C[0,1]$ is a Banach space Let $C=C[0,1]$ be the space of all continuous functions on $[0,1]$. Define $\|f \|=\max \ |f(x)|$. I want to show that $C$ is a Banach space.     Below is my attempt and I was wondering if it's ok.    I know I have to show that $C$ is a complete normed space. Clearly, $\|f\| \geqslant 0$ and $\|f\|=0 \Leftrightarrow f=0$. $\|cf \|=\max~|cf(x)|=|c|\max |f(x)|=|c| \cdot \|f\|$. $\|f+g\|=\max~|f(x)+g(x)|\leq \max~|f(x)|+\max~|g(x)|=\|f\|+ \|g\|$. So $C$ is a normed space.   Next, I show that every Cauchy sequence in $C$ is convergent. Let $\{f_n\}$ be a Cauchy sequence in $C$. Let $\varepsilon \gt 0.$ Then $\exists$ an $N_1$ such that $$ \max~|f_n(x)-f_m(x)| \lt \frac{\varepsilon}{2}$$ for $n, m \gt N_1$ and $x\in[0,1]$.  But there is a subsequence $f_{k_n} $, which converges to $f$. So $\exists$ an $N_2$ such that $$ \max~\left|f_{k_n} - f\right|\lt \frac{\varepsilon}{2}$$ for each $n\gt N_2$.  Now Let $N = \max\{N_1, N_2\}$, if $n \gt N$ then $k_n \geqslant n\gt N$. So we have $$ \max~\left|f_n(x) - f(x)\right| \leqslant \max~\left|f_n - f_{k_n}\right| + \max~\left| f_{k_n} - f\right| \lt\frac{\varepsilon}{2} + \frac{\varepsilon}{2} = \varepsilon.$$  Thus, $\|f_n-f\| \to 0$ as $n\to \infty$. $\quad \square$  Thanks. Scoring when two triple word squares are covered in one play The word QUAGMIRE is on the board vertically, with the Q on the top row, second column. The next player creates SQUEEZED horizontally, landing the S on the triple word square in the top row, first column, and remaining UEEZED landing to the right of the existing Q, ending with the D on the triple word square in the eighth column. Since two triple word squares are covered in this one placement, how would it be scored?  Letters:   S: 1 Q: 10 U: 1 E: 1 x 2 (double letter) E: 1 Z: 10 E: 1 D: 1   27 Total for letters. Do you then multiply by 3 for the first triple word square, and then multiply that result by 3?  27 X 3 = 81, 81 X 3 = 243  Bonus for all 7 tiles placed:  243 + 50 = 293