If $f\in L^p(\mathbb{R^n})$ $1\leq p &lt; \infty$ then prove $\displaystyle\lim_{|h|\to 0} \|f(x + h) - f(x)\|_p = 0$.  I had tried to prove the continuity a.e. of $\|f(x + h) - f(x)\|_p$, then could pass the $\lim$. This way is good or there is other more simple?
I am having a hard time with the following real analysis qual problem.  Any help would be awesome.  Suppose that $f \in L^p(\mathbb{R})$, where $1\leq p&lt; + \infty$. Let $T_r(f)(t)=f(t−r)$. Show that $\lim_{r \to 0} \|T_rf−f\|_{L_p} =0$, that is $$ \lim_{r\to 0} \left( \int_{\mathbb R} |f(t-r) - f(t)|^p \mathrm d t\right)^{1/p} =0.$$
I have Canon lenses and would like to purchase an adapter to use them on the D3200? Is there one available? If so name and model would be appericated. I understand that I will have to shoot on manual mode. I've just started to play with pgfplot. I'm trying to prepare a plot like to following   \begin{figure}[h] \centering \begin{tikzpicture} \begin{axis}[minor tick num=1,  axis x line=middle, axis y line=middle, xlabel=$k$, ylabel=$\omega$, ymin=0,xmin=-2,ymax=60] \addplot[blue,domain=0:5, line width=1.5pt] {x^2+25}; \addplot[orange,domain=0:5,line width=1pt]{3*x+22.75}; \addplot[cyan,domain=0:1.5, line width=1pt,dashed]{18.166*x}; \node[coordinate,pin=right:{$v_{\phi}=\frac{\omega}{k}$}]     at (axis cs:1,17) {}; \node[coordinate,pin=right:{$v_{g}=\frac{d\omega}{dk}$}]     at (axis cs:2.5,30) {}; \node[coordinate,pin=left:{dispersion relation}]     at (axis cs:4.5,47) {}; \end{axis} \end{tikzpicture} \caption{Wave dispersion relation with phase and group velocity} \label{fig:2} \end{figure}   What I would like to do is dropping the x-y tick labels so that we just maintaing the x-y title. How can I obtain it? Is it worth self-funding a PhD to attend a top 10 university? What should I opt for?   Option A) very well paid PhD, around €3000 per month at a respectable university or;  Option B) a non-paid PhD, where I have to pay €2000 per year at one of the top 10 universities of the world?  EDIT: Actually they are both UK universities, Option B  is ranked between the top 10 in the world in engineering and tech, and I do get a scholarship that pays 18000 pounds which covers the difference between international student tuition and EU tuition. In Option A, I will be doing research in a good university and will be working alongside giants in the industry. Prove $\frac{1}{2}\sum_p \frac{1}{p^2}+\frac{1}{3}\sum_p \frac{1}{p^3}+\cdots$ converges I have file1.txt    this is the original text   line2   line3   line4   happy hacking !     and file2.txt    this is the original text   line2   line4   happy hacking !   GNU is not UNIX     if I do: diff file1.txt file2.txt I get:    3d2   &lt; line3   5a5   &gt; GNU is not UNIX     How is the output generally interpreted? I think that &lt; means removed but what do 3d2 or 5a5 mean?  If I do:    $ diff -u file1.txt file2.txt   --- file1.txt        2013-07-06 17:44:59.180000000 +0200   +++ file2.txt        2013-07-06 17:39:53.433000000 +0200   @@ -1,5 +1,5 @@    this is the original text    line2   -line3    line4    happy hacking !   +GNU is not UNIX     The results are clearer but what does @@ -1,5 +1,5 @@ mean? When should I use a struct rather than a class in C#? How do I manage (add/remove) all the startup applications in Ubuntu 11.10 and up?  Startup Applications doesn't show all the applications which are started during boot. Adobe Illustrator: Lines with stroke < 2.0pt doesn't change color I created lines using the line segment tool in Adobe Illustrator (latest Adobe Cloud version) and I can't change the color of the stroke (through the Appearance panel) if the stroke weight is less than 2.0pt.   If the stroke is 2pt or more, then the color around the line changes but not the line itself.    The whole behavior is odd for me as I've never faced in Illustrator before.  Edit: added screen below with the line selected. How do I make a user's browser blink/flash/highlight in the task bar using JavaScript? For example, if I make an AJAX request every 10 seconds to see if the user has any new messages on the server, I want the user to know it right away, even if he is using another application at the time.  Edit: These users do want to be distracted when a new message arrives. I've been trying to play with a rigid body simulations.  I prepared a project of a building made of domino tails. I've placed all objects very tight, but as soon as I start animation it looks like there was some tiny gap between objects, so they all fall down a little bit. For a high building it leads to a construction disaster as the whole building colapses.  Here is an example:  (I'd suggest to use 0.25x speed).  How can I fix it? How does the Java 'for each' loop work? Consider:  List&lt;String&gt; someList = new ArrayList&lt;String&gt;(); // add "monkey", "donkey", "skeleton key" to someList     for (String item : someList) {     System.out.println(item); }   What would the equivalent for loop look like without using the for each syntax? How could I write my name, for example, to look like the \LaTeX logo? How could I write my name, for example, in a \LaTeX style? It is just interesting, as in Google all other things pop up when I try to search for an answer! New database server hardware and software inserts slower than old setup I'd like to know if the following problem of elementary linear algebra is already solved / solvable.  For two (singular) $n\times n$ matrices $P$ and $Q$, if $\det(\lambda P+\mu Q)=0$ for any $\lambda,\mu\in\mathbb{R}$, what are conditions on $P$ and $Q$? Can it be assumed a evaluation order of the function parameters when calling it in C ? According to the following program, it seems that there is not a particular order when I executed it.   #include &lt;stdio.h&gt;  int main() {    int a[] = {1, 2, 3};    int * pa;      pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa), *(pa++),*(++pa));    /* Result: a[0] = 3  a[1] = 2    a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(pa),*(++pa));    /* Result: a[0] = 2  a[1] = 2     a[2] = 2 */     pa = &amp;a[0];    printf("a[0] = %d\ta[1] = %d\ta[2] = %d\n",*(pa++),*(++pa), *(pa));    /* a[0] = 2  a[1] = 2 a[2] = 1 */  } If in a UFD every maximal ideal is principal then it is a PID Specify CSS class names on SVG paths using Illustrator Is there a way to edit SVG files in Illustrator where you can specify a CSS class for each path?  I already know in Illustrator that if you give the layer name an actual name, Illustrator will use that name as the path's ID, which is fine if you don't plan on reusing the icon more than once on the same page.  My current workaround is to just use the IDs method, but then later convert the IDs to classes in my code editor, but it's pretty annoying to have to do every time I generate my SVG sprite.  If that's currently not possible in Illustrator, are there any other apps that will allow you to specify that? Or maybe a Grunt or Gulp package?  It looks like you might be able to do it with Inkscape with a , so I might look at that if there's no other good solutions out there. First of all, I think this question is not duplicated, because I have tried all other solutions I found here, but nothing solved my problem.  I use Ubuntu 14.04 64 bit.  I have tried until now: sudo apt-get install skype -> It didn't work. The error was:   The following packages have unmet dependencies: skype : Depends: skype-bin E: Unable to correct problems, you have held broken packages.   I have tried sudo dpkg add-architecture &amp;&amp; sudo dpkg -i skype-ubuntu-precise_4.3.0.37-1_i386.deb but it didn't work either. The error was:  dpkg: dependency problems prevent configuration of skype: skype depends on libqt4-dbus (&gt;= 4:4.5.3); however: Package libqt4-dbus is not installed. skype depends on libqt4-network (&gt;= 4:4.8.0); however: Package libqt4-network:i386 is not installed. skype depends on libqt4-xml (&gt;= 4:4.5.3); however: Package libqt4-xml:i386 is not installed. skype depends on libqtcore4 (&gt;= 4:4.7.0~beta1); however: Package libqtcore4:i386 is not installed. skype depends on libqtgui4 (&gt;= 4:4.8.0); however: Package libqtgui4:i386 is not installed. skype depends on libqtwebkit4 (&gt;= 2.2~2011week36); however: skype depends on libstdc++6 (&gt;= 4.2.1); however: Package libstdc++6:i386 is not installed. skype depends on libx11-6; however: Package libx11-6:i386 is not installed. skype depends on libxext6; however: Package libxext6:i386 is not installed. skype depends on libxss1; however: Package libxss1:i386 is not installed. skype depends on libxv1; however: Package libxv1:i386 is not installed. skype depends on dpkg: error processing package skype (--install): dependency problems - leaving unconfigured Processing triggers for hicolor-icon-theme (0.13-1) ... Processing triggers for gnome-menus (3.10.1-0ubuntu2) ... Processing triggers for desktop-file-utils (0.22-1ubuntu1) ... Processing triggers for bamfdaemon (0.5.1+14.04.20140409-0ubuntu1) ... Rebuilding /usr/share/applications/bamf-2.index... Processing triggers for mime-support (3.54ubuntu1) ... Errors were encountered while processing: skype   I have tried to use after sudo apt-get -f install but it didn't solve the issue.  I have tried to install by using Gdebi. The error was:  Cannot install 'libqtwebkit4:i386'   I have tried to install using Ubuntu Software Center. The error was:  Cannot install 'libqtwebkit4:i386'   I have tried changing the server in "Software and Updates". I have tried to use "Main Server" and "Servers for United States". But it couldn't solve my problem.  Anyone has any idea how to solve that?  SOLVED  Well, I formatted my pc and I installed Skype first of all. Probably another installation that I had done before the Skype installation was the problem, i guess.  Thanks people! Opening website external links in new window -- published usability tests why this code can run ? double a[3]; a[1,1]=1;