Intel HD Graphics 530 in Ubuntu 18.04
How do I install the Nvidia drivers?
Prove by induction $\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{n}\ge\frac{2}{3}n\sqrt{n}$ for all positive integers Assumption: $\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}\ge\frac{2}{3}k\sqrt{k}$   Prove true for $n=k+1$ $$\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}+\sqrt{k+1}\ge\frac{2}{3}(k+1)\sqrt{k+1}$$  I'm upto :$$\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}+\sqrt{k+1}\ge\frac{2}{3}k\sqrt{k}+\sqrt{k+1}$$after which I'm stuck. Move the period outside the quotes on the site-analytics page If you don’t have 25k reputation, the  contains a stub text:        As you can see on the image, the dot should be moved outside the quotes. Also, on ruSO we need to  from “” to «», but this is not possible via Transifex, because there is no full sentence available to translate. Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$ For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly? My google news page has burst forth the news that metallic hydrogen has been produced in a laboratory using a diamond anvil cell. Only  mentions (at this particular moment) that it has been called into question at - at least - premature. That can be read about in Nature:   Here I only want to ask about the evidence. Is it only the sudden change in visual appearance change as recorded in a camera on top of the microscope, at a specific temperature and pressure? That it "looks shiny?" Or is there actually more direct data than that?  note: I am not asking if the data is sufficient or not, nor if it is convincing, or metallic or not. Just a narrowly defined question about the extent of the observations that have lead to the proposal that a metallic state was achieved.     above: potentially three states of hydrogen as viewed in a diamond anvil cell, from . My understanding is that when using a Bayesian approach to estimate parameter values:   The posterior distribution is the combination of the prior distribution and the likelihood distribution. We simulate this by generating a sample from the posterior distribution (e.g., using a Metropolis-Hasting algorithm to generate values, and accept them if they are above a certain threshold of probability to belong to the posterior distribution). Once we have generated this sample, we use it to approximate the posterior distribution, and things like its mean.   But, I feel like I must be misunderstanding something. It sounds like we have a posterior distribution and then sample from it, and then use that sample as an approximation of the posterior distribution. But if we have the posterior distribution to begin with why do we need to sample from it to approximate it? I'd like to use a sequence of boxes to show how TeX works. I read some time ago that everything (or almost) in TeX are boxes.  So, how to show only the TeX boxes that surround each character, each line, each paragraph?  I'd like something similar to the image below, not fbox which contains blank space around it. Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, until they look at them (measure). If the observer A looks at his ball he will see its color, which is white, so he immediately knows the color of the second ball. Lets call this “classical entanglement”.  My question is: What is the difference between this “classical entanglement” and the quantum entanglement, for example, of two entangled electrons with opposite spins states? Can this analogy be used to explain the quantum entanglement? Full Name Requirement of Commit Phase The Commitment form on Area 51 requires your full name to be provided. Is this publicly viewable? Why not just use the existing usernames? Reading the extension of files in a directory with Java? Properties of p-adic valuations Let $n$ be a integer not equal to zero, $p$ a prime and $$|n|_p = p^{-\operatorname{ord}_p(n)}; |0|_p=0$$  Proposition: $|xy|_p=|x|_p|y|_p$  We want to show: $\operatorname{ord}_p(ab)=\operatorname{ord}_{p}(a)+\operatorname{ord}_p(b)$ So if we suppose there is a largest integral $v$ such that $p^{v}|(ab)$, then we can split up v such that $p^{v_1}|a,p^{v_2}|b$. If we suppose that there exist $v_1,v_2$ with them both being the largest integers such that $p^{v_1}|a, p^{v_2}|b$,  with $v_1+v_2= : v $ then $p^v|ab$. (I don't believe this to be a formal proof but rather my best own "idea" I can come up with...)  The script also mentions that the padic valuations' sums are bounded: $|x+y|_p\le \sup\{|x|_p,|y|_p\}$, how to show this?   Edit:   According to Robert Israel and Bill Dubuques answers, the first proposition is proven, if I understood correctly:   Given $ord(a)= v$ and $ord(b) = u$ which is the same as $a:= p^{v}m, b:= p^{u}n$ with $gcd(m,p)=gcd(n,p)=1$, because $ab=p^{u+v}mn$ with $gcd(mn,p)=1$ it follows that $ord(ab)=ord(a)+ord(b)$ and so $|xy|_{p}=p^{-ord(xy)}=p^{-(ord(x)+ord(y))}=|x|_{p}|y|_{p}$  Now to show: $|x+y|_{p}\le sup\{|x|_{p},|y|_{p} \}$  and the second can be tackled like this: set $a:=p^{v}m. b:=p^{u}n$, then checking two cases $1:(u=v)$ and $2:(v&lt;u)$: $(a+b)=p^{v}m+p^{u}n= p^{v}(m+p^{u-v}n)$ so in case of (u=v) it follows that  $ord(a+b)= u = sup\{ord(a),ord(b)\}$  and in case of $(v&lt;u)$ because the biggest v is $v:= u-1$: $ord(a+b)\le p^{u-1}(m+pn) \le p^{u}(m+n)= sup\{ord(a),ord(b)\}$  It seems that I did something wrong in both cases... Modular Arithmetic - Find the Square Root Using LINQ to concatenate strings What is the most efficient way to write the old-school:  StringBuilder sb = new StringBuilder(); if (strings.Count &gt; 0) {     foreach (string s in strings)     {         sb.Append(s + ", ");     }     sb.Remove(sb.Length - 2, 2); } return sb.ToString();   ...in LINQ? Disable commandButton after first click to prevent double submission I have an apex:commandButton on a visualforce page that invokes a method on the controller. There is currently no rerender value set for the button. Instead the controller method returns a PageReference to redirect the user as required.  E.g.  Visualforce:  &lt;apex:commandButton value="Save" action="{!save}"/&gt;   Controller:  public PageReference save() {     // save body ...      // return the user the a parent opportunity     return new PageReference('/' + opp.Id); }   Users are currently able to click on the resulting save button multiple times before the controller completes and returns the PageReference to redirect the browser to an opportunity.  How can I disable the commandButton after the first click?    I tried wrapping the commandButton in an actionStatus and facet, but the need to define the rerender property prevented the resulting PageReference redirect.  E.g.  This will render nicely in the browser and prevent multiple clicks, but doesn't redirect to the Opportunity on completion.  &lt;apex:actionStatus id="saveStatus"&gt;     &lt;apex:facet name="stop"&gt;         &lt;apex:commandButton value="Save" action="{!save}" status="saveStatus" rerender="saveParentBlock" /&gt;     &lt;/apex:facet&gt;     &lt;apex:facet name="start"&gt;         &lt;apex:commandButton value="Saving..." disabled="true" status="saveStatus"/&gt;     &lt;/apex:facet&gt; &lt;/apex:actionStatus&gt;     There is a similar question . I need to support an existing PageReference redirect, which slightly alters the requirements.  Force.com Discussion Boards:   Ideas: Opening Ubuntu 20.04 Desktop on WSL2 I installed Ubuntu 20.04 (server/terminal) from the Windows 10 app store, and then after launching the Ubuntu Terminal via WSL2 (Windows Subsystems for Linux) , I installed Ubuntu Desktop and did several steps to try and get a desktop instance of Ubuntu 20.04 launched.  In short, the steps involved editing the .bashrc file, installing Xming, and then attempting to open the Ubuntu desktop in Xming with the &quot;startxfce4&quot; command.  However, &quot;startxfce4&quot; just doesn't open the desktop for me.  I can get programs to open with &quot;grun&quot; and the file explorer to open with &quot;gopen&quot; though, so it is working partially. Does anyone have any alternative suggestions to how I might get the terminal to open up the full Ubuntu Desktop?  Obviously, this wasn't what Windows had in mind with WSL2 so this is kind of a reach, but any input would be helpful.  Could I somehow do this from the file explorer or with a program that could opened from &quot;grun&quot; or &quot;gopen&quot;? Regex for splitting a string using space when not surrounded by single or double quotes What is a virtual terminal for? I'm looking for an elegant way to show that, among non-negative numbers, $$ \max \{a_1 + b_1, \dots, a_n + b_n\} \leq \max \{a_1, \dots, a_n\} + \max \{b_1, \dots, b_n\} $$  I can show that $\max \{a+b, c+d\} \leq \max \{a,c\} + \max \{b,d\}$ by exhaustively checking all possibilities of orderings among $a,c$ and $b,d$.  But, I feel like there should be a more intuitive/efficient way to show this property for arbitrary sums like the one above. states:  Imports are always put at the top of the file, just after any module comments and docstrings, and before module globals and constants.  However if the class/method/function that I am importing is only used in rare cases, surely it is more efficient to do the import when it is needed? Isn't this: class SomeClass(object):      def not_often_called(self)         from datetime import datetime         self.datetime = datetime.now()  more efficient than this? from datetime import datetime  class SomeClass(object):      def not_often_called(self)         self.datetime = datetime.now() How do I set Windows to boot as the default in the boot loader? Asked again to review a paper, when the authors don't wish to modify it I have received a manuscript to review for a journal. The interesting thing is, I had already reviewed this article (exact same title, abstract and author list, almost exact same content) for another journal a few weeks ago where I recommended that it be published, but only after major revisions of both form and content. When I first reviewed it, I wrote a two-page review, listing some questions and several “actionable” comments, ranging from some concerns about exactness of the text (some conclusions didn't seem fully backed by the results) all the way down to trivial stuff (grammar, a few typos, graphic issues with the figures, etc.).  Now, the manuscript has come to me for review again, but it is almost unchanged from the first version. None of the serious stuff has been addressed, and even most of the trivial stuff was not fixed (there's at least one remaining typo, and the figures still aren't fully legible). However, I think this behavior from the authors is clearly a bad signal, which should be somehow conveyed to the editor: they're not willing to amend their work, and would rather do some journal-shopping.  What would you suggest me to do? Should I just re-send my earlier review? Add a note to the editor about my knowledge of the “history” of the paper? Or maybe even include it in my review, so the authors are aware that people know of their behavior, and maybe feel bad enough to change their ways?    PS: I wrote it in the present tense, but it's actually a story from my past. I'm not sure I did the right thing at the time, and I think it's better to actually formulate it as an open question…