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Formal proof for $q \land \neg q \vdash r \land \neg r$ Why my DCIM folder is empty seen in the computer but not empty in the phone I am using HuaWeiNova device, and I tried to access it with aft-mtp-cli. $ aft-mtp-cli $ ls DCIM/  I got folders listed here: |-photos |-Camera ....  When I tried to list or download my photos in the Camera/ folder, I got nothing. Only the empty folders are listed and the folders that contains files are not shown at all. I am quite sure my photos are stored in the Camera folder in my cell phone. How come I could not access my photos with my computer ? How do you parse and process HTML/XML in PHP? The recent discovery by the LIGO made me wonder about this.  We know that there exists a CMBR, Cosmic Microwave Background Radiation, a blanket of electromagnetic energy covering the universe, made by the Big Bang.  But, the big bang was an explosive event. The huge "shockwave" made by it sent ripples in space time. (Primordial gravitational waves)  Wouldn't these ripples flood the universe creating sort of a Cosmic Gravitational Background Radiation (not exactly radiation)?  If such waves do flood the universe, couldn't a much more sensetive version of LIGO be able to detect this and use it as a contrast to create "gravitational telescopes"? What is the appropriate statistical test when calculating the busiest day of the week? We have 10 years of data and Monday is the busiest (most visits to the hospital) on average. If we wanted to assess whether that is true and report a p-value, what is the appropriate statistic?   We believe the answer is chi-square as we found a peer-reviewed medical article from the Annals of Emergency Medicine (highest circulating journal for that specialty) that used chi-square for this very calculation.   If chi-square is appropriate, what values do we use for observed and expected values for chi-square? One approach would be to list all the values for Monday as observed values, or all the means for Mondays averaged across a month, or all the means for Mondays averaged across a year.  If there were no busiest or least busy days, we would assume that the visits would be the same every day of the week. That means our "expected values" for Chi-Square would be the mean of the visits for any given week. Which configuration of armor enchantments gives maximum protection? Proving the sum of two independent Cauchy Random Variables is Cauchy Normality of dependent variable = normality of residuals? PHP Session data not being saved I have one of those "I swear I didn't touch the server" situations. I honestly didn't touch any of the php scripts. The problem I am having is that php data is not being saved across different pages or page refreshes. I know a new session is being created correctly because I can set a session variable (e.g. $_SESSION['foo'] = "foo" and print it back out on the same page just fine. But when I try to use that same variable on another page it is not set! Is there any php functions or information I can use on my hosts server to see what is going on?  Here is an example script that does not work on my hosts' server as of right now:  &lt;?php session_start(); if(isset($_SESSION['views']))     $_SESSION['views'] = $_SESSION['views']+ 1; else     $_SESSION['views'] = 1;  echo "views = ". $_SESSION['views']; echo '&lt;p&gt;&lt;a href="page1.php"&gt;Refresh&lt;/a&gt;&lt;/p&gt;'; ?&gt;   The 'views' variable never gets incremented after doing a page refresh. I'm thinking this is a  problem on their side, but I wanted to make sure I'm not a complete idiot first.  Here is the phpinfo() for my hosts' server (PHP Version 4.4.7): How to add an image to a JPanel? I have a  to which I'd like to add JPEG and PNG images that I generate on the fly.  All the examples I've seen so far in the , specially in the  use ImageIcons.  I'm generating these images as byte arrays, and they are usually larger than the common icon they use in the examples, at 640x480.   Is there any (performance or other) problem in using the ImageIcon class to display an image that size in a JPanel? What's the usual way of doing it? How to add an image to a JPanel without using the ImageIcon class?   Edit: A more careful examination of the tutorials and the API shows that you cannot add an ImageIcon directly to a JPanel. Instead, they achieve the same effect by setting the image as an icon of a JLabel. This just doesn't feel right... Is there anybody who can help me show the following?      $$ \sum_{x=0}^{n-1} \cos\left(k +x{2\pi\over n}\right) =0  \qquad\hbox{and}\qquad  \sum_{x=0}^{n-1} \sin\left(k +x{2\pi\over n}\right) =0 $$   I can only prove this claim for the sine expression when $k=0$, by grouping the output values such that they all cancel out (for both $n$ even and odd). I have thought about using complex numbers in exponential form to prove it, but I can't do it ... :P   I would really appreciate an algerbraic proof. Prove a differentiable function between banach spaces is continuous I really don't know where to start with this problem. It intuitively makes sense from basic calculus knowledge but I have absolutely no clue how to show it. , When can I make opportunity attacks? Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$ I want to prove this equation, $$ \binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a} $$ I thought of proving this equation by prove that you are using different ways to count the same set of balls and get the same result. But I'm stuck. Help me please.   (Presumptive) Source: Theoretical Exercise 1.14(a), P19, A First Course in Pr, 8th Ed, by S Ross. How do you keep user.config settings across different assembly versions in .net? Signed to unsigned conversion in C - is it always safe? How do I place a bootable ISO on a USB drive? How do I use the conditional (ternary) operator? How can I install applications like Google Chrome on Ubuntu?  Are there any commands to install an application?    Index of answers: I have some troble understanding the Kernel density estimation.  If a consider the next example:  s&lt;-0 z&lt;-density(rnorm(25)) f&lt;-function(i)approx(z$x,z$y,xout=i)$y for(i in seq(min(z$x),max(z$x),length.out = 10000)) s&lt;-s+f(i) s   I expected getting that s is approximately equals to one since I am considering an approximation for the integral of the Kernel density function (that I suppose is also a density). However, I don't get the expected result. Why it doesn's sum one?  The idea behind this is that I wanted to use the Kernel as the density of my data points. I was interpolating to get my explicit function and use with other x values. Or do you know another way to get a density function estimated by fitting?