given the 2 PDE  $$ \Delta u-au_{tt}+u_{t}=0$$  and $$ \Delta u + Du*Df=0 $$  here $ \Delta u $ is the Laplacian $ Du= grau$ and * means scalar product $u_{t} = \frac{\partial u}{\partial t}$  my doubt is what term should i include to get the linear part of the equations $ u_{t} $ and $Du*Df $ from the Euler Lagrange equations in $ R^{n} $ thanks
given the 2 PDE  $$ \Delta u-au_{tt}+u_{t}=0$$  and $$ \Delta u + Du*Df=0 $$  here $ \Delta u $ is the Laplacian $ Du= grad(u) $ is the gradient and * means scalar product $u_{t} = \frac{\partial u}{\partial t}$  my doubt is what term should i include to get the linear part of the equations $ u_{t} $ and $Du*Df $ from the Euler Lagrange equations in $ R^{n} $ thanks
System App Permissions I have an application that needs root permissions to run.  No biggie, all of my personal devices are rooted, so I am very comfortable with the process. The problem is that this application is to be used on company owned devices issued to certain employees and I don't want them to be able to uninstall the application nor do I want them having root access to the device.  I was thinking that the following process would accomplish my goals:   Root the device Install my app as a system app Launch the application and grant su rights to it Unroot the device   Since it would be a system app, and the device wouldn't be rooted, users would be prevented from removing the app.  What I am unsure of is whether or not that application would retain its root privileges once the device is unrooted?   Any feedback or insight would be greatly appreciated! Any idea what kind of tool should I but to fix the loose left crank on my bike? I found this  but not sure if it's gonna suit. Or is it enough to buy only nut driver? Profile Gravatar get change Do not know whether someone else observe it or not but today I found my profile Gravatar changed. It is now different than earlier I have. Is it because today I have updated my profile information?        My previous gravatar looks like: How can I prevent inline math formulas from overflowing into the margin? When I compile my document in LaTeX, some formulas in the document in math mode, between $ $, go into the right margin area beyond all the text.  Is there a way to fix this aesthetic problem? How to share files through the local network? I have a desktop (Ubuntu 13.04 &amp; Win 7 Home Premium) and a Laptop (Ubuntu 12.04), both having WiFi adapters. I also have a WiFi router connected to internet which both my computers can access.  I want to share files between my desktop and my laptop using WiFi (similar to Homegroup on Windows 7 but without using Ethernet cables).  How do I set-up that?  I want to share files using both OSs, if anyone have have information about sharing files with any of the OS please answer! Suggested edit review should show custom rejection reasons Somewhat similar to , but rather more limited: when Rejecting an edit, not only the count of custom rejection reasons but the actual text of the reasons should be shown, IMO. Just now I  on SO that tidied some code in a trivially correct and substantially superior way because it looked perfectly legitimate and I couldn't understand why anyone would bother with a custom rejection reason. As it turned out, it was code in a question, of course.  In this case, the rejection reason correctly identified the problem, and had I seen it, I would have been reminded of that aspect I had neglected to check. How can I pad an integer with zeros on the left? How do you left pad an int with zeros when converting to a String in java?  I'm basically looking to pad out integers up to 9999 with leading zeros (e.g. 1 = 0001). If a product of relatively prime integers is an $n$th power, then each is an $n$th power So what does Cyanogen Inc shutting down mean for CyanogenMod and similar ROMs? So Cyanogen Inc (cyngn), known for their support for their support for CyanogenMod and their efforts to integrate Cyanogen OS into devices such as the OnePlus One, Alcatel POP Mirage, and . Cyanogen Inc just recently .  What does this mean for CyanogenMod, Cyanogen OS, and the devices which originally shipped with Cyanogen OS? Will they no longer receive OTA updates? Find $ \lim\limits_{ x\to 100 } \dfrac { 10-\sqrt { x } }{ x-100 }$  (without using a calculator and other machines...?) How is Google Scholar compared to other academic search engines and catalogues such as ScienceDirect, Scopus, and universities' own online catalogues--in terms of the following?   comprehensiveness of search (i.e. can fetch all the ever published relevant titles, whether the user have access to full-texts or not) accuracy and precision of results advanced search features usability  Are there good reasons for (or against) using Google Scholar as the only literature search tool for PhD research? Does the answer of (2) depend on the research discipline? Posting images in chat using drag and drop I think it will be a good idea if there is a drag and drop image posting in chat. User needs to follow many steps to upload an image using upload button. Let $D \subset \mathbb{C}$ be an open, connected set and let $\{ u_n \}$ be a sequence of harmonic functions with $u_n: D \longrightarrow (0, \infty)$. Show that if $u_n(z_0) \rightarrow 0$ for some $z_0 \in D$, then $u_n \rightarrow 0$ uniformly on compact subsets of $D$.  If you could offer a hint or a helpful question to get me started I'd appreciate it.   Progress: I now see why showing it for the unit disk suffices (any compact subset in $D$ can be covered by finitely many disks each which is contained in $D$). Does being denied entry to a country affect future travel to other countries? I was denied entry to India due to a visa technicality. I was advised by organisation I was travelling with to get tourist visa when I actually needed miscellaneous visa. Will this affect future travel to other countries if I have been refused once by a country, or if I want to re-enter India? HTML table headers always visible at top of window when viewing a large table Make \cite{my reference} show name and year I am trying to figure out how to make author's name and year show up every time I make a reference.  For example:  my_bibtex.bib has this entry:  @article{Franklin1999,  author = {Franklin Allen and Risto Karjalainen}, title = {Using genetic algorithms to find technical trading rules}, year = {1999}, volume = {51}, pages = {245-271}, journal = {Journal of Financial Economics}  }   If in my_paper.tex I use this line:  Important result has been found by \cite{Franklin1999}   My output looks like:  Important result has been found by [1]   But I want it too look like:  Important result has been found by Franklin 1999   I there a way to do it?  My bibliographystyle is set to plain  \bibliographystyle{plain}  \bibliography{my_bibtex} I can't open google-related sites I'm  getting timeout errors on google-related sites. If I try to open google.com, gmail.com, etc, it will keep displaying the "waiting reply" on the browser bottom, and the page won't open. If I am browsing another site that includes, say, www.google-analytics.com, ajax.googleapis.com, google fonts, etc, then it start loading, displaying a "connecting to [google-related site]" on the browser bottom, and stall at that point for a long time.  I can browse other sites fine and they load quickly. I can ping the domains with 0% loss and &lt;100ms times. I can ping 8.8.8.8, I am not behind a proxy, there is nothing on my hosts file, I am not at work or in a networked environment: it is a home network behind a router. I connect using wifi (I am too distant to use wired).   Other users on the same network don't have the issue. I can both ping and browse the sites. I have pinged ajax.googleapis.com from my android and my other laptop, and they return the same IP than on this laptop. They also share the same external IP address, according to   The issue happens on ubuntu 12.04, and as it is cyclic but not frequent enough to make sure, I don't honestly remember if it happens on Windows 7 as well (it is a dual-boot machine). Rebooting the router won't help. Rebooting the computer fixes the problem, until it happens again.  It's been happening for a few months now. The last time it happened (earlier today) I performed a ping before and after the reboot. Here's the results:  before  $ping ajax.googleapis.com PING googleapis.l.google.com (74.125.21.95) 56(84) bytes of data. 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=1 ttl=47 time=157 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=2 ttl=47 time=163 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=3 ttl=47 time=156 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=4 ttl=47 time=165 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=5 ttl=47 time=157 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=6 ttl=47 time=155 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=7 ttl=47 time=159 ms 64 bytes from yv-in-f95.1e100.net (74.125.21.95): icmp_req=8 ttl=47 time=157 ms   after  $ping ajax.googleapis.com PING googleapis.l.google.com (74.125.134.95) 56(84) bytes of data. 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=1 ttl=47 time=207 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=2 ttl=47 time=154 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=3 ttl=47 time=154 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=4 ttl=47 time=152 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=5 ttl=47 time=157 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=6 ttl=47 time=160 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=7 ttl=47 time=154 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=8 ttl=47 time=157 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=10 ttl=47 time=154 ms 64 bytes from gg-in-f95.1e100.net (74.125.134.95): icmp_req=11 ttl=47 time=152 ms   The issue happens on different browsers, I installed epiphany and it shows the same behaviour.  I have inspected the network tab on firefox and it shows a single, unreplied GET request:   I installed wireshark and listened for HTTP GET requests; on other sites it pops up on the report, but on ajax.googleapis it shows nothing. I listened then for DNS requests, there are some differences:     If connect via telnet to the port 80 of a random site and perform a GET it works, but I can't telnet to ajax.googleapis.com (or it's IP), the connection never completes. Zooming / Focusing certain parts of a chart in latex I am using pgfplot to draw graphs in latex. Now this is the problem I am facing:  \begin{tikzpicture}[scale=1] \begin{axis}[ybar,grid=major,bar width=2pt,width=8cm, height=8cm,xmin=1,xmax=540,ymin=1,ymax=240] \addplot [draw=black,fill=green]  table [x=size, y=cluster, col sep=comma] {sim-0.4-0.6.csv}; \end{axis} \end{tikzpicture}   It generates the following graph:    Since, I have values mainly between 0-50 on x-axis, I want to zoom there. After that, values comes around 500. S0, there are no graph points between 50 - 450. How should I do that? Let $a,b,c\in \mathbb{Z}$. If $ac&gt;bc$ and $c&gt;0$, then $a&gt;b$   I think I would use contrapositive to prove this. But I am not sure proper contrapositive statement.   Is it If $a&lt;b$, then $ac&lt;bc$, and $c&lt;0$.? If so, contrapositive is not a good choice, isn't it? Frequent Write to Non-volatile Memory I am designing a device that automatically adjusts it's physical position as temperature changes. If the device it shut off or power is disconnected the device needs to remember it's last temperature and position. I have the ability to store these values in EEPROM but the problem is the position and temperature could be changing very rapidly. If I were to write the temp and pos to EEPROM after every time they changed that would (1) slow down the firmware a bit, and (2) likely kill the EEPROM after a year or two. So as I see it my options are as follows...  1) use a capacitor/battery to keep the device powered for a short time after power is lost so that I can write the values to EEPROM at that time only. I don't like this because the board is kinda power hungry and this would require a big cap. And I don't have a ton of free space. And I don't want the added cost of a battery and battery holder / or a big cap.  2) use F-RAM instead of EEPROM so that I can write to it trillions of times without wearing it out. I don't like this option because FRAM is quite a bit more expensive than EEPROM and this is for a production product (not just one).  3) Only write the position and temperature every 5 minutes or so. That way I always have a fairly recent position/temp recorded but I am not writing every second so my program is not slowed down and the EEPROM won't die as fast. This seems like my best option.  Does anyone else have any suggestions that I'm not thinking of?