could I ask you please about Sommerfeld radiation condition (for example link:  )? What does mean derivative with respect to Euclidean norm? For example if I had function $A(\bf X)$ where $\bf X$ is vector of dimension. So the expression with derivative with respect to Euclidean norm will be: $\frac{\partial A(\bf X)}{\partial|\bf X|}$. What does it mean derivative with respect to Euclidean norm? And how I can it derivative? Thank you for your time and answears!
Given $f = f(u(t), t)$, is it possible to find the following derivative? ($f$,$u \in \mathbb{R}^n$, $t \in \mathbb{R}$)  $$ \frac{\partial f}{\partial||u||^2_2} $$  I am aware of the following derivatives:  $$ \frac{\partial||x||^2_2}{\partial x} = \frac{\partial ||x^Tx||_2}{\partial x} = 2x $$  So I can invert it to give me (elementwise division in the RHS)  $$ \frac{\partial x}{\partial||x||^2_2} = \frac{1}{2x} $$  This step does feel like abuse of notation I find it hard to convince myself of its validity.  If it's right though, I could just apply the chain rule to find  $$ \frac{\partial f}{\partial u} \frac{\partial u}{\partial||u||^2_2} $$  However, knowing that both $f$ and $u$ are a function of $t$, I am somehow doubting my own reasoning. Or does that just mean that the derivative will still be a function of $t$ and I have nothing to worry about? Can anyone shed some light?  UPDATE: I'm now doubting the existence of  $$ \frac{\partial u}{\partial ||u||^2_2} $$  because $u = u(||u||_2^2)$ is not injective. Is the inversion step I did above legitimate? Is there another possible approach?
How to place an image at the right top of a document? I've been learning LaTeX and this community has been very helpful. Currently, I'm trying to set up corporate letters but as a newbie I'm encountering a  of , so I'm posting them one by one instead of putting it in the comments... maybe this helps others as well.  Anyway, I am trying to implement this  that indicates that I can use vbox to float an image to the right of my header. I almost have this working, but I now try to adjust this to get my logo to stick to the top of the page. So I want to have this at the right top of my document. This is quite difficult! When I place the vbox, it creates unwanted spacing, for some odd reason. So I can not get the logo to be at the right top, even though I 'reset' every possible margin to 0 (in my opinion). Here is my distilled code:  \documentclass[a4paper]{article} \usepackage{graphicx} \graphicspath{{./img/}} \usepackage{color} \usepackage{xcolor} \definecolor{orange}{HTML}{DD4616} \definecolor{white}{HTML}{FFFFFF} \usepackage{fullpage} \usepackage[margin=0cm, paperwidth=215.9mm, paperheight=30mm,top=0cm]{geometry} \parindent=0pt  \begin{document} \fboxsep0pt  \pagecolor{orange}   \fbox{\vbox to 0pt{\hfill\fbox{\includegraphics[height=3cm]{logo}}}}  \end{document}   I've used a full black logo for illustrative purposes. Here you can see this:    The black line is the vbox border. For some reason, it jumps down. The only way to get rid of this that I found out about is this:    Which means that I need to add:  \edef\theprevdepth{\the\prevdepth}\nointerlineskip \vbox to 0pt{...}\prevdepth=\theprevdepth   But there are two problems with this:   I get an error with I try this (Improper \prevdepth.) More importantly, I really want to understand my code at this point, and get to master the basics of positioning elements. This feels overcomplicated and I do not understand it at all.    Is there any easy way to position an image at the right top of a document? Truncated 200GB table but disk space not released I'm looking for a high current DC switch (able to switch something like 5V@30A) and I've encountered several DPDT that might do what I need, however they are only rated for AC applications (3A@250VAC or 6A@125VAC). Are these rating convertible to DC? or is that something that only the facturarer would know? Sum of digits of repunits I was setting up up android-studio referring to . While installing oracle-java7-installer, this error is displayed:  sudo apt-get install oracle-java7-installer [sudo] password for cyan:  Reading package lists... Done Building dependency tree        Reading state information... Done oracle-java7-installer is already the newest version (7u80+7u60arm-0~webupd8~1). The following package was automatically installed and is no longer required:   snap-confine Use 'sudo apt autoremove' to remove it. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue? [Y/n] y Setting up oracle-java7-installer (7u80+7u60arm-0~webupd8~1) ... Downloading Oracle Java 7... --2017-11-27 08:40:47--  http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz Resolving download.oracle.com (download.oracle.com)... 223.223.158.138, 223.223.158.136 Connecting to download.oracle.com (download.oracle.com)|223.223.158.138|:80... connected. HTTP request sent, awaiting response... 302 Moved Temporarily Location: https://edelivery.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz [following] --2017-11-27 08:40:47--  https://edelivery.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz Resolving edelivery.oracle.com (edelivery.oracle.com)... 23.58.58.93, 2600:140f:7:18e::2d3e, 2600:140f:7:18d::2d3e Connecting to edelivery.oracle.com (edelivery.oracle.com)|23.58.58.93|:443... connected. HTTP request sent, awaiting response... 302 Moved Temporarily Location: http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz?AuthParam=1511752368_824528560c20825821ecbcac8f4e9be9 [following] --2017-11-27 08:40:48--  http://download.oracle.com/otn-pub/java/jdk/7u80-b15/jdk-7u80-linux-x64.tar.gz?AuthParam=1511752368_824528560c20825821ecbcac8f4e9be9 Connecting to download.oracle.com (download.oracle.com)|223.223.158.138|:80... connected. HTTP request sent, awaiting response... 404 Not Found 2017-11-27 08:40:50 ERROR 404: Not Found.  download failed Oracle JDK 7 is NOT installed. dpkg: error processing package oracle-java7-installer (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  oracle-java7-installer E: Sub-process /usr/bin/dpkg returned an error code (1)   How do I fix this error? I did a fresh installation of Ubuntu 16.04. How to completely disable Siri on Sierra? I have a rechargeable vacuum cleaner with NiMH batteries, 1800mAh and 14.4 volts, 12 cells. The charger is 18v 200mA. The batteries have now died.  Can I replace the batteries with 4 cell Li-ion in series?   That will be 14.4 volts, if considered 3.7v each. Of course, I know it will be roughly 4 volts when fully charged.  Li-ion batteries in my mind: 18650, 2500mAh.  Also, can I charge them with the same charger? When moving large directories using mv, is there a way to view the progress (%)? The cp command on gentoo had a -g switch that showed the progress. Feeling a tingling sensation by touching stuff, Is this safe? I'm putting on my desktop computer on steel rack as usual. A while ago, when I touch the steel rack for seconds, practically I feel a tingling sensation, sort of electrical shock in my finders. After that I measured how voltage the steel rack has, the multi-tester meter indicated almost 50V by AC mode. Is this safe to touch or keep the PC on the position, or I should get away the PC somewhere electricity-safe? I'm not sure this site is suit for asking this kind of question, but I'm very worrying whether this is safe or not since this experience is my very first time. Thank you. My table is:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   3 10 03/03/2009 john 300   4 11 03/03/2009 juliet 200   6 12 03/03/2009 borat 500   7 13 24/12/2008 borat 600   8 13 01/01/2009 borat 700     I need to select each distinct home holding the maximum value of datetime. Result would be:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   8 13 01/01/2009 borat 700     I have tried: -- 1 ..by the MySQL manual:   SELECT DISTINCT   home,   id,   datetime AS dt,   player,   resource FROM topten t1 WHERE datetime = (SELECT   MAX(t2.datetime) FROM topten t2 GROUP BY home) GROUP BY datetime ORDER BY datetime DESC  Doesn't work. Result-set has 130 rows although database holds 187. Result includes some duplicates of home. -- 2 ..join  SELECT   s1.id,   s1.home,   s1.datetime,   s1.player,   s1.resource FROM topten s1 JOIN (SELECT   id,   MAX(datetime) AS dt FROM topten GROUP BY id) AS s2   ON s1.id = s2.id ORDER BY datetime   Nope. Gives all the records. -- 3 ..something exotic:   With various results. Random number generation and probability When looking for the path to an executable or checking what would happen if you enter a command name in a Unix shell, there's a plethora of different utilities (which, type, command, whence, where, whereis, whatis, hash, etc).  We often hear that which should be avoided. Why? What should we use instead? Adding tags to files in OS X: How to use, where are tags stored, and will they work on a network? I've heard it is possible to add tags to a file's meta data in OS X, and have Spotlight search through such tags.   In a nutshell, how would one access this feature in Finder &ndash; not Spotlight (Command+Space) &ndash; but the adding of tags themselves? Where are these tags stored?  Do they go in .DS_Store (I tend to delete those!) or elsewhere in the filesystem? Does this tagging mechanism work on removable drives?  What are the requirements? Does this tagging mechanism work over a network share?  I have some Windows SMB network shares at home that I frequently store files on.  Would it work on those or is another configuration required? Aside from Spotlight, are there any command-line tools for searching through or accessing the tag data for files?   Thank you! How to run a server on port 80 as a normal user on Linux? I have Googled about a solution for quite some time, but couldn't find an answer.   I am on Ubuntu Linux and want to run a server on port 80, but due to security mechanism of Ubuntu, I get the following error:      java.net.BindException: Permission denied:80   I think it should be simple enough to either disable this security mechanism so that port 80 is available to all users or to assign required privileges to the current user to access port 80. I recently traveled from India to USA. I am on H1B. I entered USA on 29th December 2016. As my Visa extension is due in August 2017, I was gathering documents for Visa Extension. It was required to provide a scanned copy of passport page with all entry and exit stamps.  Myself and my wife both travelled back from India. My wife's passport has a entry stamp with date as 29th December 2016. But the same is missing from my passport. I guess the officer missed putting the entry stamp on my passport. My I 94 reflects the correct date of entry as 29th December. Somehow I still have my boarding pass from this trip (usually I throw them once trip is complete).   Want to know what could be implications of missing entry stamp when I travel to India next time (somewhere towards early next year)? Does this impact my H1B Visa extension ? Also what can I do to correct this information on my passport? Can we implement a dead time on answers for high reputation user Summary: High reputation users on SO come swooping in the second a simple question is posted, and get the first answer in before I've even opened my Python interpreter to test my idea out.  This actually is a problem because it prevents use lower users who aren't as good  at programming from getting any answers in.  This makes it very hard to build up reputation.  Thus, I propose a short dead time for high reputation users where their answers do not appear.  The Problem: This isn't just reputation.  By answering questions and having discussions with OP, we all get better at our language.  Teaching is one of the best ways of learning, and a more well versed population is absolutely good for SO.  (If anyone wants to argue that, go home)  While its nice to have folks who can quickly answer nearly all questions in a jiffy, its a little frustrating for those of use who simply aren't as fast, but still want to contribute.  The result is that many people do not answer questions because they feel like they just can't get an edge in.  SO should aim to incentivize as many answers by as many users as possible.  The most answers from the most users is the most beneficial situation for the site and the community. Once we accept this idea, it is clear that something needs to be done to address the issue at hand    The Solution: Luckily, this is an easy problem to solve; we use a dead time.  High reputation users can post answers whenever they like, but they won't appear until after the dead time is completed.  The trick is balance, a dead time which is too long will harm the OP as the question will remain unanswered, however, a dead time which is too short won't actually fix the problem.  There definitely needs to be a discussion about what "high reputation" means and what dead time to use, but it should be independent of whether y'all agree that this is a problem.  So, what do you think?  EDIT: Wow, -18, I leave for lunch for 30 minutes and this is what happens!  I guess y'all think this is a bad idea, but let me try to clarify a few things on which I was unclear earlier.  This is not about reputation.  This is not about getting the first answer just for the sake of getting to say "in before..."  This is about learning.  By getting a shot at answering questions before the high reputation users, people learn. Think of it as doing an example problem in class before the teacher does it. You get a chance to try it yourself, test your knowledge, and if you fail, then the teacher is right behind you to show the correct solution.  This is what I'm trying to accomplish. However, seeing the solution, and then trying to answer the question, is not very helpful. This is how I view the status quo.    In response to Mr. Pieters' answer and comments: You're absolutely right, this is not about quantity, its about quality.  The fastest answer isn't always the best.  But asking the high reputation users to take a step back for a few minutes is a means of getting there.    Hopefully this clears things up a bit. If a linear operator has an adjoint operator, it is bounded I would like to replace the usual \hat in maths with a larger one, but I do not want it to stretch. The size I want is "the smallest \widehat" (as in $\widehat{.}$). Is there a way to put that one above a wide character like M ($\widehat{M}$ would stretch and give be an even wider hat).  I guess I have a lack of understanding for the mechanism behind accents that extend, so feel free to explain. After some gorgeous updates I witness this: Prove that the point of intersection of the diagonals of the trapezium lies on the line passing through the mid-points of the parallel sides Prove,by vector method,that the point of intersection of the diagonals of the trapezium lies on the line passing through the mid-points of the parallel sides.    My Attempt: Let the trapezium be $OABC$ and that the O is a origin and the position vectors of $A,B,C$ be $\vec{a},\vec{b},\vec{c}$.Then the equation of $OB$ diagonal is $\vec{r}=\vec{0}+\lambda \vec{b}................(1)$ And equation of $AC$ diagonal is $\vec{r}=\vec{a}+\mu(\vec{c}-\vec{a}).......(2)$ And the equation of the line joining the mid points of $OA$ i.e.$\frac{\vec{a}}{2}$ and $BC$ i.e. $\frac{\vec{b}+\vec{c}}{2}$ is $\vec{r}=\frac{\vec{a}}{2}+t(\frac{\vec{b}+\vec{c}}{2}-\frac{\vec{a}}{2}).........(3)$. Here $\lambda,\mu,t$ are scalars. I do not know how to solve $(1)$ and $(2)$ and put into $(3)$ to prove the desired result. Please help me.Thanks.