regex for mobile number validation in java
How to validate phone numbers using regex
vertical spacing in nested fraction I have complicated math expression:    Vertical spacing between text and fraction line is too small. I tried to define new \frac command (with amsmath package) with adjustable vertical spaces. As you can see, the result is not satisfying:    \documentclass[a4paper,fleqn,leqno]{article} \usepackage{polyglossia} \usepackage{color,pifont,fontspec} \usepackage[top=2.54cm,bottom=2.54cm,left=2.54cm,right=2.54cm]{geometry} \usepackage{tikz,tikz-3dplot,graphicx} \usepackage{mathtools,breqn,amsmath} \usepackage[fontsize=12]{scrextend} \usepackage{array,multirow} \usepackage{pgfplots} \DeclareMathSizes{12}{14}{14}{10} \newcommand{\myfrac}[3][0pt]{\genfrac{}{}{}{}{\raisebox{#1}{$#2$}}{\raisebox{-#1}{$#3$}}} \begin{document} \begin{dmath*}[breakdepth={0},style={\mathindent=0pt},spread={10pt}] {n=\myfrac[3pt]{\myfrac[3pt]{0,0625N+0,0215}{2}-0,043}{\myfrac[3pt]{\myfrac[3pt]{\scriptstyle 0,0625N+0,0215}{\scriptstyle 2}-0,043}{\myfrac[3pt]{\scriptstyle N}{\scriptstyle 2}-1}+0,0215}} \end{dmath*} \end{document}   How can I enlarge verticall spacing in whole fraction? Do I need to change my ESTA address when visiting the US? Cartoon with a young unicorn and a demon Is there anything to do during an 8 hour after-midnight layover in Dubai? We are planning a trip with an 8 hour layover in Dubai spanning from 1am-9am. I am thinking about going to see the city, but is it worth it to do it given the very late night hours? Will at least the outside attractions accessible?   Will Burj Khalifa be visible in the middle of the night?  Will at least some of the malls be open?  Will there be anything to do at night?  I have seen other questions about layovers in Dubai (), but none of them is asking about a night-only stay. Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$ I've encountered the following problem in complex analysis:  Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$.  I've decomposed $f$ to it's real and imaginary parts and got that it's enough to prove that:  $(\int_0^{2\pi}cos(\theta)g(\theta)d\theta)^2 +(\int_0^{2\pi}sin(\theta)g(\theta)d\theta)^2 \le 16$   Where $g(\theta)=f(e^{i\theta})$.   But now I'm stuck. Any ideas?  Thanks How are Dementors created/born? 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? $e^{i\theta}=\cos\theta + i\sin \theta$  $e^{i\sin^{-1}x}=\cos(\sin^{-1}x)+i\sin(\sin^{-1}x)$  $i\sin^{-1}x=\ln|\sqrt{1-x^2} + ix|$  $\sin^{-1}x=-i\ln|\sqrt{1-x^2} + ix|$  Now from here I'm kind of lost, since it seems like this should be the definition, but when I look it up, the definition of inverse hyperbolic sine is:  $\sinh^{-1}x=\ln(\sqrt{1+x^2} + x)$  So although they're very similar, I guess I just don't know how to handle the logarithm and anything to the ith power or drop off the absolute value. What is the difference between ANSI/ISO C++ and C++/CLI? How do I configure a new Ubuntu installation to accept ssh connections? Please revisit the CAPTCHA & China issue Back in 2012 when China first blocked all Google services, thereby preventing non-VPN users from proving their non-roboticness, someone quickly opened this thread on Meta:    The consensus at the time was "we can't think of a better way of doing things".  Well, 3 years have passed and China is showing no signs of unbanning Google. Meanwhile, CAPTCHA technology has evolved. Can the SE admins please revisit this situation? People in China without a VPN are completely unable to prove they are not bots. I couldn't even search for the phrase "pgp" on Security.SE without hitting the human verification barrier. Blocking questions is one thing, but searches also? I think that's too strict.  (yes, I wrote this with my VPN) Is there a word for when an action has an effect opposite to the one intended? Is there a word or phrase to express the concept of an action having the opposite effect of the expected outcome?  For example, a drug taken to cure headaches that actually causes headaches, or an advertising campaign designed to deter smoking that leads to an increase in smoking. Negative integer division surprising result I was just wondering since i have the 12.04 lts ubuntu edition if it's possible to upgrade it to 13.04 or even 14.04 after it gets released without losing any of my files and installed apps?  That's actually the main reason i chose the LTS version because i didn't know if i had to re-install all my apps every time a new ubuntu version gets released. Using Fingerprint reader in 16.04 I have a Dell laptop with fingerprint reader inbuilt. I just ran lsusb on terminal and got the following result:   Bus 002 Device 003: ID 138a:0011 Validity Sensors, Inc. VFS5011 Fingerprint Reader Bus 002 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 003 Device 002: ID 046d:c077 Logitech, Inc. M105 Optical Mouse Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 001 Device 004: ID 05ca:1820 Ricoh Co., Ltd Integrated Webcam Bus 001 Device 003: ID 0a5c:21bc Broadcom Corp. BCM2070 Bluetooth 2.1 + EDR Bus 001 Device 002: ID 8087:0024 Intel Corp. Integrated Rate Matching Hub Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub   Is it possible to use fingerprint scanning instead of traditional login with 16.04 and Unity ? Thanks. Footnotes in tables? If I use  two different router in the same network while both are running in the default router mode then we can access the setup page or setup interface from browser just by IP address of corresponding router. But when I use one of the router as repeater then I can only enter the setup page of the router which is running in router mode. Why router's setup page cannot be accessed when using the router as repeater? Now how can I change the settings of the router in repeater mode? The only way is to reset router with the hardware key then setup again. I'm using listings and I want to extend a language with additional keywords for highlightning. I know there is an option morekeywords available, but that only works for a particular lstset declaration and I don't want to have to copy-paste all keywords into all listings. I've tried declaring the keywords as part of a command but that doesn't work (probably because the command is not expanded and I don't know how to fix that).  So is there any way of declaring a new language by copying an existing one and just adding more keywords? Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$ For invertible $A_{n\times n}$ find $\min(\operatorname{trace}(AA^T))$  (a) $0$ (b) $1$ (c) $n$ (d) $n^2$  Clearly for $A=I$, it is $n$, and I am unable to get any lower values, but how do I prove it. What is wrong with the following "proof" that $e=1$? Let's analyze this expression   $\lim_\limits{n\rightarrow\infty} (1+\frac{1}{n})^n$  It's the definition of $e$ which, as we know is not equal to $1$. So what is wrong with the following "logic":  As $\lim_\limits{n\rightarrow\infty}(a_{n}b_{n}) = \lim_\limits{n\rightarrow\infty}(a_{n})\times\lim_\limits{n\rightarrow\infty}(b_{n}) $ and $\lim_\limits{n\rightarrow\infty}(1+\frac{1}{n}) = 1$, we can say that $\lim_\limits{n\rightarrow\infty} (1+\frac{1}{n})^n=1^n$, which is equal to $1$.  I know something's wrong there, but the question is - what? I've somehow lost my id_rsa.pub file. I still have my id_rsa file. How do I recover the public key from the private key?  (This question came up after ssh-copy-id was reporting "ERROR: No identities found" while ssh-keygen reported "/root/.ssh/id_rsa already exists". ls ~/.ssh pointed out the problem was having id_rsa but not id_rsa.pub. I found the solution, but it was buried at the bottom of a long post on an Ubuntu support forum.)