Equivalent definition operator norm
Operator norm. Alternative definition
Are all integers fractions? What is the function of the RNA primer in DNA replication? Root filesystem check fails after power failure during installation During the "install" phase of the upgrade there was a power failure. After when starting up again the following errors are reported:  init: udevtrigger main process (420) terminated with status 1 init: udevtrigger post-stop process (428) terminated with status 1 init: udevmonitor main process (419) killed by TERM signal The disk drive for / is not ready yet or not present Continue to wait; or press S to skip mounting or M for manual recovery   Pressing M gives me the following message:  Root filesystem check failed. A maintenance shell will now be started. CONTROL-D will terminate this shell and reboot the system. Best way to parse command line arguments in C#? When building console applications that take parameters, you can use the arguments passed to Main(string[] args).   In the past I've simply indexed/looped that array and done a few regular expressions to extract the values. However, when the commands get more complicated, the parsing can get pretty ugly.    So I'm interested in:   Libraries that you use Patterns that you use   Assume the commands always adhere to common standards such as . How could Thranduil have met a dragon? I'm trying to prove that any group $G$ of infinite order has an infinite number of subgroups.  I think that if the group has an element of infinite order, then it's easy because I can take the groups generated by the powers of this element.  What if it doesn't? Every element generates a cyclic subgroup. Every element belongs to at least one cyclic subgroup (that generated by itself). So the group is the union of its cyclic subgroups. If all these are finite, we would have to have an infinite collection of subgroups anyway.  Is that correct? Is the trio's Polyjuice escapade in Chamber of Secrets ever discovered? What caused the apocalypse in the Hunger Games? So the stories of the Hunger Games are set in , a post-apocalyptic society situated in North America. Is there anything to explain what caused the Apocalypse? Whether from the main books, any extra material or interviews? (No fanfic please.)  As well as the cause, is there any indication of when the apocalypse happened? And how long after the apocalypse are the events of the Hunger Games? Convert file contents to lower case I have temp file with some lower-case and upper-case contents.  Input  Contents of my temp file:  hi Jigar GANDHI jiga   I want to convert all upper to lower.  Command  I tried the following command:  sed -e "s/[A-Z]/[a-z]/g" temp   but got wrong output.  Output  I want it as:  hi jigar gandhi jiga   What needs to be in the substitute part of argument for sed? Where did the world go? I was playing on my main world when my laptop ran out of power.  I found a charger and woke it up, but Minecraft had crashed.  Now, it doesn't appear in the world selection screen!  I have verified that it still exists in the Minecraft folder, and the directory contents look to be in order.  Does Minecraft save an internal flag somewhere when it crashes hard?  If so, how do I reset it? I have being using Skype for a long time on my Ubuntu 14.04 LTS. From this morning on, Skype simple cannot connect to my account anymore.  That is my Skype version:     Skype 4.3.0.37   © 2014 Skype and/or Microsoft   My Ubuntu system:  LSB Version:    core-2.0-amd64:core-2.0-noarch:core-3.0-amd64:core-3.0-noarch:core-3.1-amd64:core-3.1-noarch:core-3.2-amd64:core-3.2-noarch:core-4.0-amd64:core-4.0-noarch:core-4.1-amd64:core-4.1-noarch:cxx-3.0-amd64:cxx-3.0-noarch:cxx-3.1-amd64:cxx-3.1-noarch:cxx-3.2-amd64:cxx-3.2-noarch:cxx-4.0-amd64:cxx-4.0-noarch:cxx-4.1-amd64:cxx-4.1-noarch:desktop-3.1-amd64:desktop-3.1-noarch:desktop-3.2-amd64:desktop-3.2-noarch:desktop-4.0-amd64:desktop-4.0-noarch:desktop-4.1-amd64:desktop-4.1-noarch:graphics-2.0-amd64:graphics-2.0-noarch:graphics-3.0-amd64:graphics-3.0-noarch:graphics-3.1-amd64:graphics-3.1-noarch:graphics-3.2-amd64:graphics-3.2-noarch:graphics-4.0-amd64:graphics-4.0-noarch:graphics-4.1-amd64:graphics-4.1-noarch:languages-3.2-amd64:languages-3.2-noarch:languages-4.0-amd64:languages-4.0-noarch:languages-4.1-amd64:languages-4.1-noarch:multimedia-3.2-amd64:multimedia-3.2-noarch:multimedia-4.0-amd64:multimedia-4.0-noarch:multimedia-4.1-amd64:multimedia-4.1-noarch:printing-3.2-amd64:printing-3.2-noarch:printing-4.0-amd64:printing-4.0-noarch:printing-4.1-amd64:printing-4.1-noarch:qt4-3.1-amd64:qt4-3.1-noarch:security-4.0-amd64:security-4.0-noarch:security-4.1-amd64:security-4.1-noarch Distributor ID: Ubuntu Description:    Ubuntu 14.04.3 LTS Release:    14.04 Codename:   trusty   Any suggestion why or how to fix it?  Thanks in advance. How did "When" become the customary answer to "say when"? When a waiter at a restaurant comes by with pepper or Parmesan cheese, he says, "say when" and starts putting it on your food.  Many people will say "OK" or "that's enough," but it seems that the customary answer is "when".  How did this become the customary answer?  Did everyone decide to make the exact same joke, until it became commonplace.  I thought it was funny when I was a kid, but even now as an adult, I still say it.  For evidence that this is indeed commonplace, see .  The answer "when" is used and is external to the joke of the strip. But even so, I'm curious as to just how commonplace this really is.  I see it a lot in the US.  Is it used elsewhere in the world?  (by the way, I'm new to asking questions on this site, and I have no idea what tags to put on this question) What's the weight of the earth? What's the weight of the earth?  That is, what's the weight of the earth in the gravitational field of the sun? I imagine it's either   $0$, because there's no net fall toward the sun, so the downward component of acceleration is $0$ and $F=ma=0$, or $Gm_1m_2/r^2\approx7\cdot10^{-11}\cdot6\cdot10^{24}\cdot2\cdot10^{30}/(1.5\cdot10^{11})^2\approx4\cdot10^{22}$ Newtons,   but which, and why? where do I use Database. Methods? I m trying to understand where we use following Database.Methods. I know if we want to insert a record to an object we use DML Statement. What i want to know is why/where we use Database. methods. It might be silly question. Database.saveResults Database.insert Database.query Database.Query Database.error   really appreciate the inputs. Thanks a ton in advance. Directory index forbidden by Options directive Does $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely? Per the title, does $\displaystyle\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely?   I'm stuck on this question, not sure how to approach it.  Thank you! I opened terminal windows and I got a message   your screen size %d%d is bogus. Expect trouble   I closed the terminal and the next time I opened terminal, the message didn't show up.   What is this message and why did I receive it? Was or is? Confusion $a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$ So far I have that $a|b$ implies $b=ax$ for some x in the integers and $c|d$ implies that $d=cy$ for some y in the integers.  From here I can see that $gcd(a,c)|gcd(b,d)$ is logically equivalent to $gcd(a,c)|gcd(ax,cy)$ but I am not sure where to go from there. How does HOTP keep in sync? My understanding of  is that each password is unique and based on a counter.    $$PASSWORD = HOTP_1(K,C)$$  Where $C$ is an incremental counter.  What I wish to know, is how you keep the client and server in sync?  Looking at current systems (google authenticator), there appears to be no indication if the actual 'counter' number, but you can generate successive passwords at will.  What happens if, for example, the password you have generated uses $C = 5$, but the server is expecting $C = 3$?  Also, what is the 'integrity check' for?  Google cant seem to come up with a solution.