Find the value of expression
Find the value of $a^2-b^2+c^2$
Can I check iPhone, iPad, Watch battery on Mac? My goal is to have battery status of other Apple device on my Mac (preferably on menubar). I'd like to have a glimpse of the battery status of my iPhone, iPad, Watch, and Airpods.  I'm a user of Bitbar and iStat menu, but I haven't found any widgets can wirelessly check other Apple device's battery status.  What I know is that I can click the Wi-Fi icon on menu bar and it will show my iPhone battery status. To show the percentage, I have to option + click the Wi-Fi icon and hover over my mouse on the iPhone hot spot section. It's pretty clunky, but I guess at least the API is there.  I am also open to third party apps which can let me see battery status across devices. How to calculate square root or cube root? I was reading Richard Feynman biography when I read that one time he was able to calculate the  cube root of large number in his brain by just using simple facts of everyday life. So my question is there a way to calculate square root or cube root by using just a pen a paper, I mean a systematic way not by trial and error. Escape a string for a sed replace pattern Possible Duplicate:          Can anyone offer me advice on how to clean my camera's sensor?   Should I do this myself, or take the camera to a professional? Is it precarious, or easy with the right amount of care?   I have a Nikon D3000 that has a small dot off-center of the sensor. I believe it is dirt, and I would like to remove it. I'm tempted to use a cotton-bud, but I'm afraid that I might damage the sensor.  The dot appeared after a trip to a tropical area where the camera became wet. I took the lens off and a lot of moisture, and possibly some dirt, went into the camera. The lens became fogged-up.  When I returned from my trip I ran a hair dryer for (air only, without heat) 10 minutes through the battery compartment, believing this would circulate around and dry the camera. Consequently, I noticed many speckled dots around the sensor. I also believe there's a subtle but persistent haze when I look through the lens, but I could be wrong.  It's worth noting that the photos are fine, with no evidence of distortion or blurring. The camera is now dry and it's been months since this happened. But the dot on the sensor has been there since, like an itch I can't rub. If I attempt to change my password to nothing by opening "User Accounts", the "Change" button remains greyed out:    How do I change my password to be empty? I know you can set Ubuntu to automatically log you in, but I want my password to be empty, I never want to type in a password to authenticate myself as that user.  I know that there are reasons why this might not be a good idea, but I want to know if it is even possible. I'm using Ubuntu 12.10. Filesystem shows /dev/nvme0n1p1 instead of /dev/sda I installed a dual boot of Ubuntu 16.04 (Windows being my other OS) two months ago to try it out. I want to allot more space to it on my hard drive. I was looking up tutorials, and I noticed that my filesystem names don't look anything like those in the tutorials. For example:  df -h   outputs:    How would I allot more space to Ubuntu (in layman's terms)? Cannot start XAMPP on Ubuntu 11.10 Can a package overwrite the original commands in Latex? An example:  Without the amsmath package:   The equation environment numbers the equation automatically. The align environment cannot be executed.   With the amsmath package:   align and equation work seamlessly in numbering equations: I can use equation to write my first two equations, and align to write my third equation, and Latex will still number them correctly.   My questions are:   Is the code for the command equation after loading the amsmath package still the same as it was before loading the package? Moreover, if this is the case, then, in general, can loading different packages cause conflicts? And how do we avoid it? SF Short Story about resetting the world every day Trying to identify a short story. I recall it was quite short, shorter than a novella. I read it within the last few years, but my impression is that it's from the second half of the twentieth century, maybe the sixties. I can't recall if I read it online, in an anthology, or collection. Set in America, a middle-aged man stumbles on a team (maybe like dwarves or gnomes) whose job it is to set up the world for the next day by removing all the previous day's &quot;stuff&quot;, like street furniture? (I know that makes no sense). He disrupts this process and somehow prevents progressing to the next day. I also remember the story was quite lighthearted with the team behaving in a very grumpy way like interrupted workmen. I thought the title was something like &quot;What happened to Tuesday&quot; or similar. For some reason, I thought it was by Keith Laumer, but a search doesn't reveal anything. The trope was similar to &quot;The Tunnel Under the World&quot; by Pohl, and &quot;The Adjustment Team&quot; by Dick, in that reality was constantly changed and controlled by an organisation of some kind. Consider the subset $B=\{(x,y):x^2+y^2\leq 1\}\ \subseteq \mathbb{R}^2$. Show that $\vert B \vert = \vert \mathbb{R}^2 \vert$.  It is easy to see tht $f:B\rightarrow\mathbb{R}^2$ defined as $f(x,y)=(x,y)$ is injective.   However, in the book I'm working out of (Book of Proof by Richard Hammack), the other injection noted is  $g:\mathbb{R}^2\rightarrow B$ defined as  $$g(x,y)=\left(\frac{x^2+y^2}{x^2+y^2+1}x,\frac{x^2+y^2}{x^2+y^2+1}y\right).$$  In the book I'm asked to verify this is indeed an injective function.  My approach was to assume $g(x,y)=g(m,n)$ and through basic algebra I was able to deduce  $x(m^2+n^2+1)(x^2+y^2)=m(x^2+y^2+1)(m^2+n^2)$  and  $y(m^2+n^2+1)(x^2+y^2)=n(x^2+y^2+1)(m^2+n^2)$  but how does this show $(x,y)=(m,n)$? Or is this the wrong approach? Is there any way to find out what happened to a post card sent from other country? How to get the current time in Python What is the module/method used to get the current time? I try to clean my mid-2015 Macbook Pro with Retina display by wiping the screen with a damp cloth and then immediately drying.  However, there seems to be left some residue/streak marks, which look very oily. Sometimes these disappear after a few minutes, but they are still very unsightly, and a bit worrying (is there something wrong with my screen?)  I'm wondering if there are other cleaning techniques which avoid this issue, or whether this is completely normal behaviour.  Thank you! I want to show that for $S,T\in B(H)$ bounded operators on Hilbertspace with $S\geq 0,T\geq 0$ and $ST=TS$,  we have $S+T\geq 0$, and $ST\geq 0$.  $T\geq 0$ means $(Tx,x)\geq 0$.    To me it seems that $((S+T)x,x) = (Sx,x)+(Tx,x)\geq 0$. But for $ST$ i like some help.   There is a theorem in Rudin (12.32) that says that for every $T\in B(H)$ we have an equivalence:   $T$ is positive $\Leftrightarrow$ $T$ is self adjoint, i.e. $T=T^*$ and $\sigma(T)\subset [0,\infty)$.   Since $S, T$ are self adjoint we know that $ST=TS = S^*T^* = T^*S^*$ ($ST$ is selfadjoint since $S,T$ commute). Also I read somewhere that if $S,T $ commute then $\sigma(ST)\subset \sigma(S)\sigma(T)$, but I am not sure if this is true. Clearly I cant prove it, but if it were true by this ''Theorem'' it would follow that $ST \geq 0$.   Is there a more straightforward way? How to remove the Mail icon indicator applet? After using gdalwarp to project and align-to-grid (via -tap) a number of rasters I noticed that the output rasters were significantly larger than the original rasters. A fairly thorough web search turned up :  Frank Warmerdam explained the reason: &quot;On careful review, the difference in the file in question is because gdal_translate uses the TIFFWriteScanline() interface to write the output file from within GTiffDataset::CreateCopy?(), and this only writes as much of the final 'strip' of the file as is required to complete image area. But gdalwarp goes through the blockio interface which writes the complete final strip, even the portion that falls off the end of the file.&quot;  This Trac issue is ~7 years old, however, and I know some changes to the GDAL utilities, including gdalwarp have been made since. I'd like to know if the above reasoning still holds and if the file size inflation I'm seeing is &quot;normal.&quot; The word &quot;normal&quot; here might be taken to mean unsurprising or expected but, more importantly: is there anything that can be done to mitigate the effects i.e. reduce the output raster file size? Below is a table of the file size inflation I'm experiencing. Input File Size (bytes)     Output File Size (bytes)    Inflation 1437380431                  1698334217                   18% 1428001178                  1698334433                   19%   41683165                   137036637                  228%  The input TIFF files were created in ArcGIS and thus have external Worldfiles, XML and DBF files but these do not make up the difference in file size. Here is a sample gdalwarp call as I've used it in all of these cases; the actual execution was handled by a Python subprocess (subprocess.Popen): $ gdalwarp -tap -tr 30 30 -t_srs &quot;+proj=aea +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs&quot; -co &quot;COMPRESS=LZW&quot; input_file.tif output_file.tif  I understand that in rare cases compression makes a larger file, but the effect is the same without the LZW compression. The ratios in the table are with LZW compression. What's the easiest way to play a sound file (.wav) in Python? By easiest I mean both most platform independent and requiring the least dependencies. pygame is certainly an option, but it seems overkill for just sound. Seeing strange things in light I have noticed that if you look directly at tubelight (I have only white ones in my home) and close your eyes little, you see little random shaped colourless things sometimes with slow speed and sometimes with falling down.   They are shaped like circles with something in between and in chains of random length.   My father has also seen them. So, I am sure I am not imagining things. What the hell are they? Proof that the relation $5 \mid (a + 4b)$ is symmetric and transitive Take the relation $R$ to be defined on the set of integers:  $$aRb \iff 5 \mid (a + 4b)$$  As part of a larger proof, I have to show that $R$ is both symmetric and transitive. I'm lost.  I see the first steps, but I can't find how to progress further. Here's what I have at this point:    Proof of Symmetry  We have to prove that if $5 \mid (a + 4b)$, then $5 \mid (b + 4a)$. Clearly, this is true if $a = b$, but apart from that, it's unclear in my mind.  Proof of Transitivity  We have to prove that if $5 \mid (a + 4x)$ and $5 \mid (x + 4b)$, then $5 \mid (a + 4b)$.    I've fiddled around with sample values, but I still don't see it. I'm pretty lost here. Thoughts? I'm running tests of a variable-size-and-contents test set. Data files are added and removed frequently. I'm looking for an automated way of gathering a file list.  All files are in subdirectories of D; I need the full directory and name added to a text file. However, I only need those files that have a "paired" file, which has the same filename but a different extension (so... different filename, but in a structured way). So, if there is a MyFileName.A and MyFileName.B, then I want D/.../MyFileName added to the file list.  There are .A files without .B files, but no .B files without .A files. If a .A has a .B file, then both files are in the same directory.   Any advice?