blessed be the mystery of love
What is the grammar behind "Thanks be to God"?
Calculate $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ After I just learned there are ways to cancel out $0$s in the divisor of fractions onto limits I looked back at a task where I gave up when I got the result $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ so I tried to find a way to get the $0$ out here, as well. Am I just not seeing the solution or is there no way to do it? Why do modern mountain bike forks no longer use boots on fork stanchions? Why do modern mountain bike forks no longer use boots on fork stanchions? Older mountain bikes used to have them on the forks, and lefty and headshocks still do. Why have these fallen out of fashion and would putting aftermarket fork boots on your stanchions be productive or not? How do you use a variable in a regular expression? I would like to create a String.replaceAll() method in JavaScript and I'm thinking that using a regex would be most terse way to do it.  However, I can't figure out how to pass a variable in to a regex.  I can do this already which will replace all the instances of "B" with "A".  "ABABAB".replace(/B/g, "A");   But I want to do something like this:  String.prototype.replaceAll = function(replaceThis, withThis) {     this.replace(/replaceThis/g, withThis); };   But obviously this will only replace the text "replaceThis"...so how do I pass this variable in to my regex string? What is the difference between a neural network and a deep neural network, and why do the deep ones work better? I haven't seen the question stated precisely in these terms, and this is why I make a new question.  What I am interested in knowing is not the definition of a neural network, but understanding the actual difference with a deep neural network.  For more context: I know what a neural network is and how backpropagation works. I know that a DNN must have multiple hidden layers. However, 10 years ago in class I learned that having several layers or one layer (not counting the input and output layers) was equivalent in terms of the functions a neural network is able to represent (see Cybenko's ), and that having more layers made it more complex to analyse without gain in performance. Obviously, that is not the case anymore.  I suppose, maybe wrongly, that the differences are in terms of training algorithm and properties rather than structure, and therefore I would really appreciate if the answer could underline the reasons that made the move to DNN possible (e.g. mathematical proof or randomly playing with networks?) and desirable (e.g. speed of convergence?) Stern-Brocot tree where each node has two fathers Is it possible to dynamically set Views' pager settings? Say for instance, you have a view that displays when viewing a certain node type, but you want the pager settings to be different for each individual node. I was thinking of making a CCK field like "pager setting" and then give it an integer option of x-y. But I don't know if it's possible to somehow dynamically plug that field into the Views' settings. Or is there another way to do this maybe? I am trying to align some text to left/center/right in the same line. For example, I want to put my phone number on the left, my name in the center, and my email on the right, how do I do that? Is there a way to get the red artifact in Undertale? My brother has been trying different ways of getting the artifact without the Annoying Dog consuming it, but has been unsuccessful. I'm kind of curious as well. The artifact is obviously a throwing ball, but I kind of want to know the description for the artifact itself, and if you need to cheat to get it... If it even is an item in the code, too. How do I run a GUI app via SSH? Isn't the const modifier here unnecessary? Edit Mail rules manually Safety of installing Ubuntu alongside Windows Is it really safe to choose the "Install Ubuntu alongside Windows" option from the Ubuntu installation program?  I never used that option, instead I used other tools such as partition magic or windows 7's disk tool to resize my partitions.  Since I'm going to install Ubuntu across a lot windows (XP, Vista and 7) machines. It would not be nice to damage those Windows partitions.  What is your experience? Can I use this feature without concerns? Cosmological constant doubts Implementing INotifyPropertyChanged - does a better way exist? When is 6 a square in Zp To find when $6$ is a square I divided $6$ in to $2$ and $3$ by The Legendre symbol.  $$\frac{6}{p} = \frac{2}{p} \times \frac{3}{p}$$  I know that we can multiply the cases of when $2$ and $$ are squares because then it is (1)(1) by Legendre.   $2$ is a square when $p \equiv 1 \pmod{8}$   $3$ is a square when $p \equiv 1 \pmod{12}$  so $6$ is a square when $p \equiv 1 \pmod {24}$ ($96$, but the $lcm(8,12)= 24$)   but how do I find the cases when $2$ and $3$ are both NOT squares? because then $6$ would be a square then as well, $(-1)(-1) = 1$ by Legendre. Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$ I am interested in good integer approximation from below and from above for binary Log(N!).  and  provides only a general idea but not exact values. In other words I need integers A and B so that  A &lt;= Log(N!) &lt;= B In the new header could we please move the chat link back to where it was? (One click away)  As a daily frequent to the JavaScript room that's the one link I'd love to have visible 100% of the time.  Aside from that, I actually love the new header. (Maybe take it a step further an add a customizable header with (X) link spots for your most used links?)  Just my thoughts How do I resize my current ubuntu partition? Extracting a regex matched with 'sed' without printing the surrounding characters To all the 'sed' doctors out there:  How can you get 'sed' to extract a regular expression it has matched in a  line?   In other words words, I want just the string corresponding to the regular  expression with all the non-matching characters from the containing line stripped away.  I tried using the back-reference feature like below  regular expression to be isolated           gets `inserted`                here                     |                v    sed -n 's/.*\( \).*/\1/p    this works for some expressions like   sed -n 's/.*\(CONFIG_[a-zA-Z0-9_]*\).*/\1/p    which neatly extracts all macro names starting with 'CONFIG_ ....' ( found in some '*.h' file ) and prints them all out line by line             CONFIG_AT91_GPIO           CONFIG_DRIVER_AT91EMAC                    .                    .              CONFIG_USB_ATMEL           CONFIG_USB_OHCI_NEW                    .                  e.t.c.    BUT the above breaks down for something like    sed -n 's/.*\([0-9][0-9]*\).*/\1/p    this always returns single digits like                    7                  9                  .                  .                    6   rather than extracting a contiguous number field such as.                 8908078               89670890                    .                  .                    .                23019                     .                e.t.c.     P.S.: I would be grateful to feedback on how this is achieved in 'sed'.        I know how to do this with 'grep' and 'awk'       I would like to find out if my - albeit limited - understanding of        'sed' has holes in it and if there is way to do this in 'sed' which I       have simply overlooked.