travelling to uk as a family from ireland
How should a family with young children apply for UK visas?
How to print every Nth character of a string? This line of code does exactly this except I want it to start at the first character not the 7th. $ echo 1234567890abcdefghijklmnopqrstuvwxy | sed 's/.\{1,7\}\(.\{0,1\}\)/\1/g'  What I'm looking for is 19gow Trigger a button click with JavaScript on the Enter key in a text box If the order of all nontrivial elements in a group is 2, then the group is Abelian. I know of a proof that is just from calculations (see below). I'm wondering if there is any theory or motivation behind this fact. Perhaps to do with commutators?    Proof: $a \cdot b = (b \cdot b)  \cdot (a \cdot b) \cdot (a \cdot a) = b \cdot (b \cdot a) \cdot (b\cdot a) \cdot a = b \cdot a$. Quick directory navigation in the bash shell I would like to frequently switch between directories that are in totally unrelated paths, for example /Project/Warnest/docs/ and ~/Dropbox/Projects/ds/test/.  But I don't want to type cd /[full-path]/ all the time. Are there any shortcut commands to switch to previously worked directories?  One solution I could think of is to add environment variables to my bash .profile for the frequently used directories and cd to them using those variables.  But is there any other solution to this? I have two cameras, a 6mpix Panasonic FZ8, and 14mpix Canon A2200.  When I compare shots from two cameras, one of differences I notice is dpi number that camera reports in JPG info:   FZ8 reports dpi=72 A2200 reports dpi=180   What physical meaning can these numbers have? I am at loss for guesses.    I am fairly familiar with notion of dpi in scanning and printing. I can calculate density of pixels on the sensor of the camera. But then, the linear density of pixels on the sensor will be hundreds times larger than number above. So what, if anything, does it mean? Filling HTML  dropdown list in JSP with values fetched from database in Servlet Best word wrap algorithm? Word wrap is one of the must-have features in a modern text editor.  How word wrap be handled? What is the best algorithm for word-wrap?  If text is several million lines, how can I make word-wrap very fast?  Why do I need the solution? Because my projects must draw text with various zoom level and simultaneously beautiful appearance.  The running environment is Windows Mobile devices. The maximum 600&nbsp;MHz speed with very small memory size.  How should I handle line information? Let's assume original data has three lines.  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Afterwards, the break text will be shown like this:  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Should I allocate three lines more? Or any other suggestions? ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ Evaluating $\zeta(0)$ using the functional equation of Riemann-Zeta function. $$\zeta(it)=2it\pi it−1\sin(i\pi t/2)\Gamma(1−it)\zeta(1−it).$$ Everything on the RHS is never zero,  Does that means LHS has no zeros, since $\sin(s)$ has a simple zero at $s=0$ while $\zeta(1−s)$ has a simple pole at $s=0$  (the Laurent expansion), so the product $\sin(i\pi t/2)\zeta(1−it)$ is finite and nonzero at $t=0$.  My question is that from functional equation one can't get direct answer $\zeta(0)=−1/2$ unless using alternate infinite series ! Show that $\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment functions Let $X\sim N(\mu,\sigma^2)$. Show that $Z=\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment generating functions. \begin{align*} M_Z(t)&amp;=M_{\frac{X-\mu}{\sigma}}(t)\\ &amp;=M_{X-\mu}\left(\frac t\sigma\right)\\ &amp;=e^{-\mu t}M_X\left(\frac t\sigma\right)\\ &amp;=e^{-\mu t}\cdot e^{\frac{t\mu}{\sigma}+\frac{t^2}{2}}\\ &amp;=e^{-\mu t+\frac{t\mu}{\sigma}+\frac{t^2}{2}} \end{align*} I'm not sure how to conclude that $Z\sim N(0,1)$. I have seen the options such as a4paper, a5paper, letterpaper, etc... to go in the square brackets after \documentclass, but what I want is 8.25 inches width by 10.75 inches height for one document and 6 inches width by 9 inches height for another one. How is this done? How to test for equality of means for proportions? And two-sided or one-sided? I have the following problem: two groups A and B.  The proportions of married and single are ($p_1$) and ($p_2$) respectively, and the standard deviations ($s_1$) and ($s_2$). The sample consists of  ($n_1$) A and  ($n_2$) B observations.  Now I want to test whether the proportions are equal. I use the following formula to compute the z-statistic:  z = $abs(p_1 - p_2) / \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2} }$  and test the hypothesis: h0: $p_1 \neq p_2$  An alternative approach I tried is to estimate the t-value based on the standard deviations (hence just comparing means), that is by the formula (assuming unequal variances):  t = $abs(p_1-p_2)/\sqrt{ s_1^2/n_1 + s_2^2/n_2 }$  My question are:    do you agree with my approach or; should it be two-sided or one-sided?   Thank you. Sheet Specific Scripts I'm currently using the below script to timestamp when an edit is made to column 7 on a sheet named "Sheet 1".  function onEdit(e) {    if ([7].indexOf(e.range.columnStart) != -1) {    e.range.offset(0, 7).setValue(new Date()).setNumberFormat("dd.MM.yyyy at HH:mm");    }   }     I have a second sheet "Sheet 2" which I need to run the same script on but against column 5.  function onEdit(e) {    if ([5].indexOf(e.range.columnStart) != -1) {    e.range.offset(0, 7).setValue(new Date()).setNumberFormat("dd.MM.yyyy at HH:mm");    }   }     I've tried .getSheetByName("Sheet1") but just cant seem to get it working correctly. Tsunami dampening mechanisms Joined pipelines Considering a routine such as this one:  alpha() { echo a b c |tr ' ' '\n'; }   which outputs a stream, I would like to take the output stream, transform it, and paste it with the original output stream.  If I take use upcasing as a sample transformation, I can achieve what I want with:  $ mkfifo p1 p2 $ alpha | tee p1 &gt;( tr a-z A-Z &gt; p2) &gt;/dev/null &amp; $ paste p1 p2 a       A b       B c       C   My question is, is there a better way to do this, preferably one not involving named pipes? Let $X\sim B(n,p_h)$ and $Y\sim B(n,p_\ell)$ be two random variables following a respective binomial distribution, where $p_h&gt;p_\ell$. I want to show that  $$P(X\ge\alpha)\ge P(Y\ge\alpha),$$ for any $\alpha\in\{0,1,\dots,n\}$. In other words, I want to show  $$P(X\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge P(Y\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  The statement to be proven is obviously true, but proving it is extremely difficult (at least for me). Can anyone give me some guidance on proving it?  It would be nice if someone can give an algebraic proof too, that is, show that  $$\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge \sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  Thank you very much! Stop iPhone alerting me when I'm in a phone call When I'm in a phone call, I still get alerts for emails and texts. The noise will play and, if the phone is on Speaker, it will vibrate -- often leading the person I'm talking to wonder what that weird noise was.  Surely there must be a way to silence the phone while you're talking on it. It's very distracting to have beepings going off right next to your ear! What's that ship in the opening credits of 'Star Trek: Enterprise'? ARMA/GARCH estimation in sequence I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with the auto.arima model in the forecast package in R and a GARCH model on the residuals of the ARIMA model.   Is the procedure of sequentially estimating ARIMA and GARCH model correct or would it have been better to jointly model the mean and the variance of the series? If this were correct, is there a (possibly R) function to do it? Typically Apt packages are served over bare HTTP and the downloaded contents are verified with GPG signatures. This makes it easy for  to proxy the HTTP connections and add the downloaded packages to its cache. apt-cacher-ng is unable to directly MITM an HTTPS connection created by Apt. It is possible to  apt-cacher-ng, but then the contents are not cached--they are re-downloaded from the remote server every time. This quickly gets annoying when rebuilding Docker containers that install many packages from Apt repositories served over HTTPS. Is there a way to get apt-cacher-ng to cache packages downloaded from HTTPS repositories? I am looking for a convenient way to set the background of tabular cells. I'd like to do two things:  (1) Set the background shaded in a color (2) Set the background hatched  I learned that the TikZ package provides means to do this but I am unable to come up with a solution that does not use matrices (such as here: ) but instead uses the tabular package.  Here's what I'd like to do:  \documentclass{article} \begin{document} \begin{tabular}{|l|l|l|} \hline   1 &amp; \setBGGray 2 &amp; 3 \\\hline   4 &amp; 5 &amp; 6 \\\hline   7 &amp; \setBGHatched 8 &amp; 9 \\\hline \end{tabular} \end{document}   The output should look like this:    Can someone please help me achieving this using tabular (or tabularx) and TikZ?