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Update to latest version of java after ppa is discontinued
Am I too old for academia after a PhD? Multivariate differentiability verification I have tried an attempt on the following:  Let $F:U\in \Bbb{R}^n\to \Bbb{R}$ and $f:\Bbb{R}\to \Bbb{R}$ where $f$ is an even function. Now $F(\mathbf{x})=f(|\mathbf{x}|)$, where $|\ . |$ is the Euclidean norm. Given $f$ is $C^r$, I have to show that $F$ is $C^r$.  My attempt was to argument by induction. I showed that $F$ is $C^1$, basically using univariate chain rule on $\frac{\partial f\left(\sqrt{x_1^2+\dots+x_n^2}\right)}{\partial x_1}$ and arguing that it would be continuous using the fact that $f$ is $C^r$. Since the argument works for all $x_i$, it establishes first-differntiability for $F$ and continuity of the operator $DF(\mathbf{x})$. Then I moved on to show $F$ is $C^r$ assuming $F$ is $C^{r-1}$ and $f$ is $C^r$. Now what I did was partially differentiate:  $$ {\partial \over \partial x_2} \left[\frac{\partial ^{k-1}f}{\partial x_1^{k-1}}\right] = \underbrace{{\partial \over \partial |\mathbf{x}|} \left[\frac{\partial ^{k-1}f}{\partial x_1^{k-1}}\right]}_{(1)} . \underbrace{{\partial |\mathbf{x}| \over \partial x_2}}_{(2)} $$  My argument runs as follows: this partial derivative is continuous since $f$ is $C^r$ and hence $(1)$ is continuous. Continuity of $(2)$ is establishd in a similar manner, since $\sqrt{\mathbf{x}}$ is $C^r$ if $\mathbf{x} \neq \mathbf{0}$. Then the product would be continuous. I am uneasy on multivariate arguments and dont know if my approach is completely off track. I didnt use the even function property, so I am sure I might me missing something. Any hints and references would be welcome. Thanks! Differentiable functions satisfying $f'(f(x))=f(f'(x))$ timestamp, modification time, and created time of a file Steam not opening in Ubuntu 16.04 LTS I have never used Ubuntu or any other Linux OS before last Friday. For all I know, I might have installed Ubuntu wrong and be missing a component. I would prefer if you use simplest terminology possible, but I'm OK with doing a bit of googling if need be. I just installed Steam for Ubuntu 16.04 but it won't open when I click on it in the launcher. The icon flashes for a few seconds, stops and then nothing happens. I looked in the system monitor and steam shows up there but ending the process and trying again does nothing. I heard trying to open apps that aren't working through the terminal tells you what the error is so I tried that and I got this:  Running Steam on ubuntu 16.04 64-bit STEAM_RUNTIME is enabled automatically Installing breakpad exception handler for appid(steam)/version(0) libGL error: unable to load driver: radeonsi_dri.so libGL error: driver pointer missing libGL error: failed to load driver: radeonsi libGL error: unable to load driver: swrast_dri.so libGL error: failed to load driver: swrast   Please help I just want to play CS:GO again. in bash I have some jobs running, in background. They are always producing random irrelevant error messages that pollute the terminal. I am not always so prompt to start them with the 2&gt;&amp;1 &gt; /dev/null redirect. How can I redirect the output when they are already running? Relation between intensity of light and refractive index Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$ Prove $\sin(x)\tan(x) &gt; x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$  So I did the following: Let $f(x) = \sin(x)\tan(x) - x^2$.  Then of course $f(0) = 0$ and I want to show that for $x \in ( \,0, \frac{\pi}{2}) \,$ $f'(x) &gt; 0$ but I don't really know where to go from here as I can't get anything reasonable done with the derivative.  I was thinking of approximating it using the following inequality $\sin(x) &lt; x &lt; \tan(x)$.   Is that a good direction? using underscore's “difference” method on arrays of objects I have few methods that returns different Generic Lists.   Exists in .net any class static method or whatever to convert any list into a datatable? The only thing that i can imagine is use Reflection to do this.  IF i have this:  List&lt;Whatever&gt; whatever = new List&lt;Whatever&gt;();   (This next code doesn't work of course, but i would like to have the possibility of:  DataTable dt = (DataTable) whatever; Simulating a Brownian Excursion using a Brownian Bridge? Homemade coconut milk separates into different layers after a day in the fridge Is there any way to recover deleted files which may have since been overwritten? I deleted lots of files &amp; folders on my laptop and then I put a new files in the same folders. I need to recover the deleted files. I tried a lot of recovery software and I couldn't recover my old files.   I read that if you refill the folders with new files after deleting old ones then I can't recover them again. Is that true?   What should I do? How to call a parent class function from derived class function? How do I call the parent function from a derived class using C++? For example, I have a class called parent, and a class called child which is derived from parent. Within  each class there is a print function.  In the definition of the child's print function I would like to make a call to the parents print function.  How would I go about doing this? Regular cast vs. static_cast vs. dynamic_cast I've been writing C and C++ code for almost twenty years, but there's one aspect of these languages that I've never really understood. I've obviously used regular casts i.e.  MyClass *m = (MyClass *)ptr;   all over the place, but there seem to be two other types of casts, and I don't know the difference. What's the difference between the following lines of code?  MyClass *m = (MyClass *)ptr; MyClass *m = static_cast&lt;MyClass *&gt;(ptr); MyClass *m = dynamic_cast&lt;MyClass *&gt;(ptr); I would like to get all descendant text nodes of an element, as a jQuery collection. What is the best way to do that? Calculate the area on a sphere of the intersection of two spherical caps Complicated FOR loop nesting. Having trouble cleaning up legacy code What is the relationship between size of object with distance? How does the size/length of an object vary with distance?   Is it a logarithmic relationship? exponential? linear?   I plotted a curve of the size/length of an object for different distances from the camera, and the curve looked exponential/logarithmic. I was trying to understand the reasoning behind that. Ubuntu16.04 boots into initramfs