How to force counting page numbers from a particular page
Start TOC from chapter 1 and also page numbering
How prove :         $$ {31}^{11}&lt;{17}^{14} $$       help please! How to check if current thread is not main thread This is a  about IPv6 Subnetting.      Related:               I know a lot about , and as I prepare to (deploy|work on) an IPv6 network I need to know how much of this knowledge is transferable and what I still need to learn. IPv6 seems at first glance to be much more complex than IPv4. So I would like to know:   IPv6 is 128 bits, so why is /64 the smallest recommended subnet for hosts? Related to this:   Why is it recommended to use /127 for point to point links between routers, and why was it recommended against in the past? Should I change existing router links to use /127? Why would virtual machines be provisioned with less than a /64 worth of addresses? Are there other situations in which I would use a subnet smaller than /64?  Can I map directly from IPv4 subnets to IPv6 subnets? For instance, does an IPv4 /24 correspond directly to an IPv6 /56 or /120? My interfaces have several IPv6 addresses. Must the subnet be the same for all of them? Why do I sometimes see a % rather than a / in an IPv6 address and what does it mean? Am I wasting too many subnets? Aren't we just going to run out again? In what other major ways is IPv6 subnetting different from IPv4 subnetting? Collapsing a stream of multiple lines into one line I have a file containing a a large number of lines, each of which contains a bunch of numbers which are separated by spaces. I process this data in a pipe in some way, and then I want to collapse the multiple lines into a single line of all the numbers separated by spaces.  Is there a standard command-line utility I can use to do this? It seems like most line-by-line utilities won't mess with the newlines... Comprehensive book on group theory for physicists? I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated? Given the key, the plain text and the cipher text can I calculate the IV used in CBC mode? If I have the plain text, the ciphertext and the key for an AES-128 CBC operation, can I determine the IV, even if I don't know the padding (assuming the padding follows one of the more common formats)?  I believe it should be possible since my understanding is that the IV is only used as an initial XOR of the plain text in encryption, and should, therefore, be able to be available like this:  AESDecrypt(key, ciphertext) =&gt; (PlainText XOR IV); IV = ((Plaintext XOR IV) XOR (Plaintext))   Is this correct? How to check if a column exists in a SQL Server table? I need to add a specific column if it does not exist. I have something like the following, but it always returns false:  IF EXISTS(SELECT *           FROM   INFORMATION_SCHEMA.COLUMNS           WHERE  TABLE_NAME = 'myTableName'                  AND COLUMN_NAME = 'myColumnName')    How can I check if a column exists in a table of the SQL Server database? I could install with an error message "unknown media /ALL". It could not run WPS Office. How to get file extension from string in C++ Given a string "filename.conf", how to I verify the extension part?  I need a cross platform solution. I would very much like that the the appendix sections of the Table of Contents doesn't have a section numbers, dots, and page numbers. If I do the following  \documentclass{article} \usepackage{tocloft} \addtocontents{toc}{\cftpagenumbersoff{section}} \renewcommand{\cftdot}{} \begin{document} \tableofcontents \newpage \section{Appendix} \section*{Another Letter} \addcontentsline{toc}{section}{Another Letter} \end{document}   then the section "Another Letter" is left aligned, so it doesn't look like the  others.  Question  Is it possible to have "Another Letter" styled the same way as normal TOC entries, but just without section number, dots, and page number? Entropy increases when two substances mix with each other.  For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$  But, the entropy doesn't increase when the two gases mixing are same.  This is pointed by Daniel V Schroeder:     It's important to note that this result applies only if the two gases are different like helium and argon. If you start with the same gas on both sides, the entropy doesn't increase at all when you remove the partition.   Now, why is this so? Both the gases, though the same, increase their individual entropies when they expand, don't they?  So, why did Schroeder say there is no entropy of mixing? What actually happens such that there is no change in entropy when the gases are the same? A game called  is making rounds on social media. I am trying to determine the maximum score attainable for this game.  Let's assume WLOG that only 2s are returned (if 4s are possible the max score is doubled).  First, I'll relax some of the rules to create a game, $\mathcal{G}$, that can achieve a score at least as high as the original, 2048 game.  A run $R$  of $\mathcal{G}_n$ consists of a sequence of moves $m_1,\ldots,m_k$ which manipulate a multiset, $\mathcal{S}$ of maximum size n.  Each $m_i$ is either:   a put $p$, which inserts a 2 into $\mathcal{S}$, or a merge, $\alpha_i$, which replaces two $2^i$ elements from $\mathcal{S}$ with a single $2^{i+1}$ elt.   I allow sequential moves of the same type because 2048 allows multiple merges or no-merge turns.  The score of a position is the sum of $\mathcal{S}$.  What is the maximum score possible on a game of order n?  Note: The final position must have only unique values, else a merge and put would be possible in increase score.  I claim it is $\sum_{i=1}^{n} 2^i$, but couldn't come up with any good induction arguments.  It's pretty easy to prove that an element $2^k$ is producible in a game $\mathcal{G}_k$, but proving an upper bound for production got a bit hairy, and also doesn't cover the full space. Can you explain this word to me?   Can I rephrase it as     Can you explain me this word? Why do two bodies of different masses fall at the same rate (in the absence of air resistance)? I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.  According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.  BUT Newton's second law states that $a = F/m$, with $a$ the acceleration of a particle, $m$ its mass and $F$ the sum of forces applied to it.  I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don't comprehend why the mass, which is seemingly affecting the acceleration, does not affect the "time of impact".  Can someone explain this to me? I feel pretty dumb right now :) Say I have a Zombie token, , and  on the battlefield. Can I sacrifice the Zombie token to activate both the Altar's and Seer's abilities?  Similarly, if I have one card in hand, and  and  on the battlefield can I discard the one card to both of their abilities?  If I have a  with 3 charge counters can I activate both of its abilities by tapping it to add a counter, and tapping it to remove 3 counters and destroy a permanent without untapping it in between? Disable chat migration notification if one of the users has insufficient rep? Does walking fast prevent eggs hatching? I have a couple of eggs that I've picked up from some Pokestops (I'm lucky enough to live above one).   I walk a lot. I get to work through a 2 mile walk / train journey every day, so I should be picking up loads of steps for the eggs I have. However, because I'm normally always running late... for everything, I have to rush everywhere, so I walk at an above average pace.   Today I've walked around 5 miles, but the game has registered 100 metres. Is this because I walk too fast, or because of something else?  It's worth pointing out that I have the app open when walking... mostly because I have to catch them all. (This made me miss a train this morning... luckily I was early :D) I have the following code:  if ($_POST['submit'] == "Next") {     foreach($_POST['info'] as $key =&gt; $value) {         echo $value;     } }   How do I get the foreach function to start from the 2nd key in the array? Word for someone who is driven by morality I'm looking for a word to describe someone who is very driven by morality, constantly trying to do what they believe is morally right.  This word would be used in a sentence like "I really admire her; she truly is a (...) person." How does a magnet work?