My question is related to the mollifier properties in the appendix of Evans' PDE.  In proving that $f^{\varepsilon}$ is smooth, he constructs the difference quotient, with the original integral over $U.$ He then goes to the effort of writing the exact same line but changing the region of integration to V where V is some open set compactly contained within U.   I am wondering why he does this.   I'm sure it has something to do with the next line when he mentions uniform convergence of the mollifier's difference quotient to the partial derivative on V. Obviously I am a little lost and don't have a clear understanding of everything that's going on here.   Also, after he concludes the partial derivative of $f^{\varepsilon}$ exists, he writes it as an integral over U again. If someone is able to clear up my misunderstandings it would be greatly appreciated!
I'm currently reading Evans' PDE book. In it he claims that for $f \in C^2_c(\mathbb{R}^n)$ $$\frac{f(x + he_i) - f(x)}{h} \to \frac{\partial}{\partial x_i}f(x)$$ and $$\frac{\frac{\partial}{\partial x_i}f(x + he_j) - \frac{\partial}{\partial x_i}f(x)}{h} \to \frac{\partial^2}{\partial x_jx_i}f(x)$$ uniformly as $h \to 0$.  My question is why must the convergence be uniform?  Thanks in advance.
DC Motor as a Generator Voltage and Current This is almost surely an Arzela-Ascoli question, since it comes from an old exam of which such problems are quite common. Unfortunately, I can't seem to get it though.  $\{ f_n \}$ is a sequence of functions $[0,1] \to \mathbb{R}$ satisfying $|f_n'(x)| \leq \frac{1 + |\ln (x)|}{\sqrt{x}}$ and $-10 \leq \int_0^1 f_n(x) dx \leq 10$ for every $n$. The question is to show the existence of a uniformly convergent subsequence.  In these kinds of situations, the bounds given usually turn into something nice  to force uniform boundedness. Maybe I could hope to establish equicontinuity using the integral somehow, but I'm not told that the $f_n$ are always positive, so the absolute values would probably screw things up anyway.  Is it an easy problem I'm missing or is this totally the wrong track? If so, what's the right track? Update to latest version of java after ppa is discontinued I have been trying to install the latest version of java-8. However, I found out that the  due to changes in the java licence.  How should I update my java to 8.0_201 or 8.0_211 now?  Thanks! I'm trying to write a shell script that, when run, will set some environment variables that will stay set in the caller's shell.  setenv FOO foo   in csh/tcsh, or  export FOO=foo   in sh/bash only set it during the script's execution.  I already know that   source myscript   will run the commands of the script rather than launching a new shell, and that can result in setting the "caller's" environment.  But here's the rub:  I want this script to be callable from either bash or csh.  In other words, I want users of either shell to be able to run my script and have their shell's environment changed.  So 'source' won't work for me, since a user running csh can't source a bash script, and a user running bash can't source a csh script.  Is there any reasonable solution that doesn't involve having to write and maintain TWO versions on the script? What is a lambda (function)? For a person without a comp-sci background, what is a lambda in the world of Computer Science? Biblatex: URL-breaking not working in DVI-mode I'm preparing my bibliography and noticed that biblatex-printbibliography produces Overfull \hbox several times.  Examples (gray lines indicates text margins, red line is the physical page margin):        Why is hyperref line-breaking not working as expected using pdflatex or even latex -&gt; dvipdfm BUT not using latex -&gt; dvips -&gt; ps2pdf?  Also it would be great if someone could point out how I can raise the indentation of the second (and following) lines, as this might look better.  edit: Customized question, as the answer given by lockstep solved the third problem. The second problem seems to be identical to the first.  \documentclass[12pt]{scrbook} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[ps2pdf]{hyperref} %\usepackage[ps2pdf,breaklinks=true]{hyperref} %This doesn't change anything. %\usepackage{breakurl} %That makes no difference either.  \usepackage[a4paper,twoside,showframe]{geometry} %show text margins  \usepackage[style=alphabetic,backend=biber,maxnames=4,minnames=3,maxbibnames=99]{biblatex} \bibliography{biblatex-issue}  \begin{document} \nocite{*}  \printbibliography[heading=subbibliography,type=article,prefixnumbers={A-}] \printbibliography[heading=subbibliography,type=book,prefixnumbers={B-}] \printbibliography[heading=subbibliography,type=online]  \end{document}   And the bib-file:  @online{GLS:datasheet,     title         = "GLS Datasheet",     organization  = "Optoelectronics Research Centre",     howpublished ="Website",     date = "2004-09",     urldate="2013-07-01",     url ="http://www.southampton.XXXX",     address       = "Southampton, United Kingdom" } @book {Lifante:Fundamentals,     title = "Integrated Photonics: Fundamentals",     author = "Lifante, Ginés",     publisher = "J.Wiley",     address = "Chichester",     year = "2003",     type = "text",     isbn = "9780470848685" } @article{Labadie:First_fringes,     author = {Labadie, L. and Mart\'{\i}n, G. and Anheier, N. C. and Arezki, B. and Qiao, H. A. and Bernacki, B. and Kern, P.},     title = {First fringes with an integrated-optics beam combiner at 10},     DOI= "10.1051/0004-6361/201116727",     journal = {A\&amp;A},     year = 2011,     volume = 531,     pages = "A48" }     P.S.: I noticed that the visiting-date of the GLS-datasheet is wrong ;-) My Ubuntu is running fsck on every bootup On every bootup it's the same:  /dev/sda1: clean, 908443/38690816 files, 44176803/154733312 blocks   Is it some kind of option Ubuntu uses to ensure filesystem consistency or is there something wrong with my HDD? fsck takes up to 30s while booting and so about triples the time needed otherwise.  Full output (partly in German):  Begin: Loading essential drivers ... done. Begin: Running /scripts/init-premount ... done. Begin: Mounting root file system ... Begin: Running /scripts/local-top ... done. Begin: Running /scripts/local-premount ... done. Begin: Running /scripts/local-bottom ... done. done. Begin: Running /scripts/init-bottom ... done. fsck von util-linux 2.20.1 /dev/sda1: sauber, 908443/38690816 Dateien, 44176803/154733312 Blöcke udevd[623]: unknown key 'SYSFS{idVendor}' in /lib/udev/rules.d/45-libticables.rules:6  udevd[623]: invalid rule '/lib/udev/rules.d/45-libticables.rules:6'   * Starting mDNS/DNS-SD daemon                                                 [ OK ]  * Starting Reload cups, upon starting avahi-daemon to make sure remote queues are populated                                                                   [ OK ]  * Starting configure network device security                                  [ OK ]  * Starting bluetooth daemon                                                   [ OK ]  ####* Starting all other stuff Force as gradient of scalar potential energy My text book reads      If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $.   I was just wondering what may be the criteria for force to be expressed as negative gradient of scalar potential energy and HOW DO WE PROVE IT? Finn knows nothing about his family because he was taken while he was very little.   But a black main character makes me think (not being racist guys). And when he used the lightsaber I thought that he had a Jedi parent. Master Windu is the only black Jedi we know so is there any canon explanation to that? Is it right? Sum data based on cell color in Google Spreadsheets I have seen  and altough I face the same problem, the answer to that question is not helpful to my case.   I have large spreadsheets which are changed frequently. So, according to the solution accepted to that question, it is hard to duplicate all populated columns and it is cumbersome to edit one more cell everytime I wish to make a change on cells background colors.  Isn't there a way to sum data based on a condition regarding cell background color in Google Spreadsheets? How do I write a correct micro-benchmark in Java? Mapping Russia - Int'l dateline splitting polygon I am having the issue where the International Dateline is splitting a polygon I am working with.  I have a layer of the "Federal Districts" of Russia, and the eastern most federal district is being "cut" by the international dateline.   I currently have the data frame's coordinate system set to Asia Lambert Conformal Conic and this places the two "cut" polygons next to each other (how they should be).  I really need the polygon to not be cut and show as a continuous polygon.   I've researched up and down, tried changing the projection/coordinate system, but with no luck.  I've attached a screenshot of the one multi-part polygon that is being split by the international dateline.  I would like it so that there is no cutting of the polygon, and therefore no boundary line going through the polygon.  I've even tried transforming this multi-part polygon into separate, single-part polygons, then merge them back together, but anytime any part of any polygon crosses this line, it gets cut.  Layout View:    Data View: I am typing to get a sale amount (by input) to be multiplied by a defined sales tax (0.08) and then have it print the total amount (sales tax times sale amount).  I run into this error. Anyone know what could be wrong or have any suggestions?   salesAmount = raw_input (["Insert sale amount here \n"]) ['Insert sale amount here \n']20.99 &gt;&gt;&gt; salesTax = 0.08 &gt;&gt;&gt; totalAmount = salesAmount * salesTax  Traceback (most recent call last):   File "&lt;pyshell#57&gt;", line 1, in &lt;module&gt;     totalAmount = salesAmount * salesTax TypeError: can't multiply sequence by non-int of type 'float' Help me understand Support Vector Machines I understand the basics of what a Support Vector Machines' aim is in terms of classifying an input set into several different classes, but what I don't understand is some of the nitty-gritty details. For starters, I'm a bit confused by the use of Slack Variables. What is their purpose?  I'm doing a classification problem where I've captured pressure readings from sensors I've placed on the insole of a shoe. A subject will sit, stand, and walk for a couple of minutes while pressure data is recorded. I want to train a classifier to be able to determine whether a person is sitting, standing or walking and be able to do that for any future test data. What classifier type do I need to try? What is the best way for me to train a classifier from the data I've captured? I have 1000 entries for sitting, standing and walking (3x1000=3000 total), and they all have the following feature vector form. (pressurefromsensor1, pressurefromsensor2, pressurefromsensor3, pressurefromsensor4) I've been trying to solve the following problem:  Suppose that $f$ and $f&#39;$ are continuous functions on $\mathbb{R}$, and that $\displaystyle\lim_{x\to\infty}f(x)$ and $\displaystyle\lim_{x\to\infty}f&#39;(x)$ exist. Show that $\displaystyle\lim_{x\to\infty}f&#39;(x) = 0$.  I'm not entirely sure what to do. Since there's not a lot of information given, I guess there isn't very much one can do. I tried using the definition of the derivative and showing that it went to $0$ as $x$ went to $\infty$ but that didn't really work out. Now I'm thinking I should assume $\displaystyle\lim_{x\to\infty}f&#39;(x) = L \neq 0$ and try to get a contradiction, but I'm not sure where the contradiction would come from.   Could somebody point me in the right direction (e.g. a certain theorem or property I have to use?) Thanks Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words? Why is the voltage across a capacitor and the current across an inductor continuous? Why is the voltage across a capacitor (as a function of time) continuous? Why is the current across an inductor (as a function of time) continuous? Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ by defining a bijection $f:A^{B \cup C} \rightarrow A^B \times A^C$.  Any hints on this one?  Thank you! gedit "cannot open display" , on remote computer , using ssh - Ubuntu 12.04 Should we have a tag for significant points in time?