Lines inside matrices
Sarrus Rule with LaTeX
"If I would have lost you" vs "If I had lost you" I watched a (Hollywood?) film the other day where a character visiting his just-hospitalised wife (who it seems will actually survive) says "If I would have lost you [I don't know what I'd do]".  I'd always thought this was an error made by non-native speakers (I myself would only expect "If I had lost you"), but there was nothing to suggest that in the movie. Is it a regionalism?  EDIT: Actually, that wasn't true about only expecting "If I had lost you". I'd have been perfectly happy with "If I'd have lost you", so long as I didn't think too hard about what was being elided. I'd usually elide "have" there to just a schwa (neutral vowel) anyway, and think no more about it. If $R$ is a local ring and $M$ and $N$ are finitely generated $R$-modules such that $M\otimes N=0$ then how does it follow from Nakayama's lemma that either $M=0$ or $N=0$?    This is an exercise in Atiyah and Macdonald. The part I could not show in the hints is $({M{\otimes}_R N)}_{k}=0$ implies $M_{k}{\otimes }_{k} N_{k}=0$, where $k=R/\mathfrak m$ and $\mathfrak m$ is the maximal ideal of $R$. Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$. Entity Query field condition for Webform submissions I'm trying to query webform submissions based on a field value. The field is called "ticket_for". Somethings I tried and do not work:      -&gt;condition('ticket_for',$adnummer)     -&gt;condition('webform_submission_data:ticket_for',$adnummer,'CONTAINS') ...   What kind of condition should I be using in a query like this?  $query = \Drupal::entityQuery('webform_submission') -&gt;condition('webform_id', 'ticket') -&gt;condition('entity_id', $eventID) -&gt;condition('webform_submission_data:ticket_for',$adnummer,'CONTAINS'); What are best practices for blocking UI when application is busy I'm writing a web app using Twitter Bootstrap with PHP on server side. My app makes regular ajax requests via jQuery and i want to disable certain parts of the UI until the server completes processing and hands back the control to Client-Side.  I wonder what would be best practices for the same? MTMFS consuming an entire CPU core and fans running full bore with Lion You may be aware that Lion introduced MTMFS, the Mobile Time Machine File System.  I've had a couple of instances now where MTMFS has been chewing up an entire core of my dual-core (mid 2009) MacBook Pro for hours on end with no evidence that it's actually doing anything constructive.  As a consequence, CPU temperature rises and the cooling fans run fast and noisy.  Restarting the machine quietened things down again, but I'm expecting it to start again.  Does anyone understand MTMFS well enough to suggest why it's keeping itself busy (or is it most likely, simply a bug), or if there's currently any solution? I fear I may have gone deaf or been scalded to death before Apple release an update... Is "forte" pronounced "fort" or "for-tay"? I've always heard people say something like     "Pronunciation is not my [for-tay]"   ... but I feel that I've heard that the correct pronunciation is     "Confusing people is my [fort]"   What is the proper way to pronounce this word? Can't execute .out files, getting permission denied I have written a C++ program and complied it to produce a.out file. However, whenever I try to run it, I get Permission Denied. I read that we can use sudo, but I can't quite get it to work. I use something like, sudo "./a.out" but that too doesn't work.  Edit:  Here is the message I get when I try "./a.out".  bash: ./a.out: Permission denied Is it true that $||a|^p - |b|^p| \le C_p|a - b|^p$ for $1 < p < \infty$? If $a, b \in \mathbb{C}$, then we have the standard triangle inequality for the difference:  $$||a| - |b|| \le |a - b|.$$  I am wondering if this inequality generalizes to exponents greater that one.     My question is, for $1 &lt; p &lt; \infty$, does there exists a constant $C_p$ such that $||a|^p - |b|^p| \le C_p|a - b|^p$ for all $a, b \in \mathbb{C}$?   I am aware of the "standard" triangle inequality for $p &gt; 1$:  $$|a +b|^p \le 2^{p}(|a|^p + |b|^p),$$  and that $2^p$ may not be sharpest constant possible. If I try to use this estimate to prove, say, that $|a|^p - |b|^p \le C_p |a - b|^p$, I get stuck with an extra term that I'm not sure what to do with.  $$|a|^p - |b|^p \le 2^p|a -b|^p + (2^p -1)|b|^p.$$  A resolution on this matter is greatly appreciated. On my fully updated Ubuntu 18.04.3 system, audio doesn't work unless I switch between outputs. When I boot my PC, the right output (stereo speakers) is already selected by default, but there is no audio from Chromium, Firefox, VLC or any other program. However, the GNOME speakers test works. I can hear "front left" and "front right" from there, but no audio from other programs. In order to fix that, I can simply switch to another audio output (e.g. HDMI out) and then switch back to the stereo speakers, and the audio will magically work. Any idea why? It's not a big deal because it takes a couple of seconds to switch between outputs, but it's kind of annoying to do that after every reboot. All beta sites (e.g. ) are appearing with 0 Q/D and 0 avid users.  is unaffected.  In the Q&amp;A spirit, my question is: Who borked the stats? What should I focus on when converting photos to black and white? When I look at the black and white photographs from professional photographers, I notice that they have a special look. Not a specific style—obviously each photographer has her own style—but a look which make them different from similar color photos, a special feeling, which makes them shine specifically as black and white and makes color irrelevant.  When I convert my own photos to black and white in Lightroom, they don't have any special look. They just look like any other of my photos, simply converted to black and white. I imagine that there are two reasons for that:   Some scenes are better for black and white. Talented and/or experienced photographers know which scenes would be beautiful in black and white, and shoot specifically those scenes. Moreover, they know how to adapt the scene itself and the lighting to black and white (for instance by not relying on the color contrast itself).  In my case, I don't think much about shooting for black and white. It comes only in post-processing, when I either think that the photo will look great in black and white (and very often, it doesn't), or I find the colors to be poor and turn the photo to black and white (which actually doesn't make the photo any better). Post-processing is much more complex than clicking on black and white button in an app. It involves not only adjusting black and white mix (i.e. raising or lowering the lightness of specific colors), but doing lots of other adjustments.  In my case, I do black and white mix, but other adjustments I do are similar to what I would do for a color photo: actually, I may even do them on a color photo, and only then turn it to black and white.   So, what should I take in account if I want to have decent black and white photographs? Are there specific techniques, tips, tricks or warnings for someone who usually shots in color and wants to start black and white photography?  Let me show some examples. Are those scenes not great for black and white photos in the first place? Or can they be salvaged through proper post-processing?  1.  First, a poorly done photo from Scotland with dubious composition and very poor colors that I was unable to correct in Lightroom.  The same image in black and white isn't much better. The difference between the trees and the grass on the hill is barely visible. Houses on the hill fade with the sky much more than in the original version.      2.  Here's a photo of a cute pet.  In black and white, the gap between the mouse's ear and the background is barely visible. There is absolutely no benefit compared to the original.      3.  Finally, an example of a much more contrasty picture. The black and white version is weird, since the lack of color makes it difficult to understand whether the soil is the actual sand or something else. I find the sky to be weird as well, and making the blue channel darker or lighter in Lightroom haven't changed that. How do I remove the proprietary ATI drivers? I've installed 11.10 and the proprietary ATI drivers using "additional drivers" The performance of my system is absolutely awful and it shouldn't be. I tried to remove the proprietary drivers using the Additional Drivers tool and it appears to remove them. However after I reboot I cant get back into my desktop properly (the panel and launcher go missing). This doesn't seem to be an isolated problem in 11.XX.  covers how to restore the desktop (panel and launcher), but the guide doesn't fix my problem though.   Whenever I do sudo unity --reset it runs through its normal processes until it hangs at setting update "run_key" and never gets past that. I must reinstall the proprietary drivers using jockey-text or jockey-gtk in order to get back to my proper desktop.   Interestingly enough the system performance seems improved while it is in its "broken" state (missing panel and launcher).  I think restoring the default drivers may solve my problems but I cant figure out how to do it. NORMAL label in top right of some applications I'm an idiot, I was writing an image to a USB drive using dd when instead of typing /dev/sdb I typed /dev/sdd and wrote the 135mb image to my 750gb External Hardrive full of files. Is there ANY possibility of recovering the files or did dd completely zero out the drive? Please help, as this is one of the lowest points of my life EVER.  dd finished writing the 135mb image in 5 seconds, so I didn't have a chance to stop it. By the time I knew what happened to was too late. The command was as follows:   sudo dd if=generic.img of=/dev/sdd bs=1M   EDIT2: The External Harddrive's filesystem was FAT32(I've had the drive for awhile and FAT32 was the most Universal FS at the time). I also have a 2TB drive I just got which I was planning on moving most of the files to from the 750gb, If needed I can use it to transfer the Recovered files to. What are these fuse-looking cartridge case components on small, battery operated RF tranceivers? I have recently opened up 3 dead, battery-operated RF transceivers lying around, both wearable and key-chains. I've noticed that all three had components that looked like fuses (cartridge case), soldered down, that are quite large compared to the size of the circuit. See the pictures below. I'm not posting full circuit pictures because I don't know if I should, I can update if they are necessary.  Device 1:    Device 2:    Device 3:    I can't see why such a device will require a fuse, and I couldn't find any other common components manufactured in cartridge cases, maybe I'm not using the correct name. I don't see them on any applications notes or reference designs for the ICs used either.  I've tried to figure out how they are connected to the circuit, I don't have schematics and PCBs are more than 2 layers so they may not be complete, but see the schematics I've figured below.  Device 1:    Device 2:    Device 3:    Also, when I do a continuity test between the terminals of the components with a multimeter, resistance starts in ~50 Ohms range and goes down to short as I keep the probes on its terminals so my best guess is something for ESD protection, maybe Varistors or Thermistors?   Does anyone know what these components are and why they are there? Why can't I travel onwards if my bag wasn't going to make the flight? I was flying KLM from the UK to the USA with a short layover in Amsterdam.  Because of delays in the UK, I almost missed my flight.  The flight attendant told me my bag wasn't going to make it, but if I walk fast, my gate is just two over.  When I got to the gate, they had already closed the doors, but the counter was opened - I mentioned that my bag was not going to make it, but that's okay.  She said, "hold on," got onto her walkie-talkie, and said,  "Yep, that's what I thought: you can't fly if your bag's not going."  I originally thought that it might be a security concern, but that doesn't really make any sense.  Why can't I travel if my luggage doesn't make the connection?  EDIT: I should clarify that I have no beef with KLM - they treated my overnight in Amsterdam professionally and helpfully; I'm just curious what the reason would be. i install ubuntu and followed a guide to put 20gb in '/' and the rest (150gb) in '/home'. Now i just found out that a lot of the things installed in ubuntu usually goes to '/' instead of '/home'. I have a lot more things to install.  So what is the point of '/home' ? How do I fix this ? Should I transfer 150gb from '/home' to / ?  Filesystem      Size  Used Avail Use% Mounted on udev            7.8G     0  7.8G   0% /dev tmpfs           1.6G  9.5M  1.6G   1% /run /dev/sda6        19G   16G  1.8G  91% / tmpfs           7.8G  676K  7.8G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           7.8G     0  7.8G   0% /sys/fs/cgroup /dev/sda2        96M   29M   68M  31% /boot/efi /dev/sda8       159G  1.1G  150G   1% /home tmpfs           1.6G   56K  1.6G   1% /run/user/1000   what is /boot ? Its not '/' or '/home' When to use ' (or quote) in Lisp? After making it through the major parts of an introductory Lisp book, I still couldn't understand what the special operator (quote) (or equivalent ') function does, yet this has been all over Lisp code that I've seen.    What does it do? What is the best way to restore the state of ViewController