More Complex ORDER BY (alpha first, then treat number as a whole number)
Natural Sort in MySQL
Isometries of the sphere $\mathbb{S}^{n}$ Got this as homework and I don't know how to tackle this. Help please!  Prove that the isometries of $\mathbb{S}^{n} \subset \mathbb{R}^{n+1}$, with the induced metric, are restrictions to $\mathbb{S}^{n}$ of the linear orthogonal transformations. How does Java Garbage Collection work with Circular References? Cause of black artifacts in render? I was following  on creating a watch and noticed that when I rendered the watch, some pieces were messed up.  I'm new to 3D modeling and I've just learned Blender, I can't explain it well, so here's a picture:    Other examples:     I don't know if it's a problem with my World texture, the object, or the object's texture/material, so I can't even guess how to fix it. What causes this? Is it possible to fix it? Value of $\frac{x^n -a^n}{ x-a}$? Does the Sun produce audible sound? Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound. When you earn one tag badge, and then don't click "Track the next one" in the tag badge progress tracking box for a while, and then earn a second tag badge, that box continues to show "Congratulations, you earned [the same badge as before]", rather than updating to show that you've actually earned another tag badge since then.  For instance, right now  looks like this:    Even though I  a few weeks ago and then  yesterday, my profile hasn't updated to show the new achievement.  I also didn't get the "cipher" tag badge until after the 3am watershed, even though tag badges usually appear as soon as I visit my profile after earning them (for instance, I earned the "tags" tag badge on meta.SFF.SE today the very instant I clicked on my own profile there after having become eligible for the badge). Even when I went to look at the list of my progress towards different tag badges on Puzzling, which I thought would jog the system into realising I'd actually earned the badge, "cipher" still showed up as 99/100 score even after I'd gone well past 100, until last night when the badge was finally awarded and "cipher" disappeared from my list of badges to track.  TL;DR: if I don't click "Track the next one", my tag badges update slower than they should.  It's a very unimportant bug, but there must be more people than just me who like to see the "Congratulations" thing there for a while and rest on their laurels before moving on to track their progress towards the next milestone. "To do this" or "For doing this" to start explaining something? Many questions have been asked and answered about "to + bare infinitive" vs "for + gerund" in the middle of a sentence.  However, when one wants to start explaining something, what is better? For instance:  "Now, let us focus on baking the bread.   To do this, start by turning the oven on.", or For doing this, start by turning the oven on."?   Are there even better expressions? I have not found anything concerning this situation, and I feel that the answers about the same problem but in the middle of a sentence do not apply here. After upgrading to Ubuntu 17.10 I noticed some of my screencasting applications are not working, for example screencasting tools like SimpleScreenRecorder and vokoscreen. ()  Also I noticed features like screenshot from GIMP is not working properly, producing blank screenshots (). Shutter too is producing glitchy screenshots ().  Screen-sharing option on Skype is also not working ().  The issue occurs sometimes on later Ubuntu releases too.  Why is this happening and how do I fix this? Coloring a black and white PDF graphic My question is about $CFT_1$. Page 18 of  says that $$L={\frac{\overset{.}{Q}^2}{2} - \frac{g}{2Q^2}}\tag{1.11}$$ is the most general Lagrangian that preserves time translation and scale invariance in $CFT_1$. How does one prove that? Using Mosfet with seperate Logic Converter and Arduino I am trying to use an IRLB3034 with an Arduino even though it is not a logic level MOSFET. I am planning on using an LM2937 12v regulator like the schematic below:    The connection going off the page goes to an Arduino digital pin pulled down with a 10k resistor. I assumed this would work but wanted to check. As a side note, if anyone could recommend a similar MOSFET that could handle 200a and 40v (in TH) that would be great. (Only if such thing excists or is readily available)  EDIT: I have not made it clear what I am planning on using this for so I will now. It is to drive an airsoft motor and I want to use the LM2937 because I didn't think I could turn the mosfet on and off with the arduinos 5v - because the IRLB3034 isn't a logic level mosfet - so that is the reason I added the 12v regulator.  EDIT (Sorry for the previous incorrect name)  EDIT: Unfortunately, I have made a mistake, the current is not 200 amps, it is infact 30-40 amps. I don't know how I made this mistake but I think it will be helpful for people trying to follow along. I am currently trying to use busbars/6awg copper wire to carry the high-ish current around. (Only 40 amps now though)  EDIT: This question is different because it is asking how to convert 5v to 12v to run a mosfet rather then how to use a mosfet with an arduino in the best way like the other post. The accepted answer on this post also answers the other question though. What solutions does the equation 4x≡2mod10 have? (Hint, it will have more that one.) What about solutions to an equation ax≡dmodn, where d=gcd(a,n)? What solutions does the equation $4x\equiv2\mod10$ have? (Hint, it will have more that one.) What about solutions to an equation $ax\equiv d\mod n$, where $d=\gcd(a,n)$?  This is the question that appeared in our universities last year paper. But it seems very difficult for me like for first part I am able to solve by simplifications I got $x=5\cdot Z +3$ as solution which makes sense and seems fair but for the second one, I have no idea how can I approach that. Can you please help me out with that one. I tried to simplify that by using Euclidean algorithm but still, I didn't get any idea that what actually the solution will be. My final exam is on 2nd of next month and because of covid I am unable to contact in person for any help. So any help from this site will be appreciated. Thank you for looking at this question! out file with multiple criteria in python? There have been a number of cases where I would like to thank someone for providing me with a thorough response and give them feedback beyond the vote up. Often I wish people would tell me why they voted me up. Not that the thank you part is necessary but it sets it apart from the other comments related to answering the question itself.  In this type of situation is a "Thank you" acceptable in a comment?     For more information, see  in the . Using relative paths for Windows shortcuts Over the weekend Sprint and T-Mobile announced again that they would try to merge.  Assuming the powers that be in the US don't have any issue with this deal and it moves forward as proposed, what does it mean for me as a shareholder?  I have 2,000 Sprint shares, and as part of the deal it looks like one Sprint share will be worth ~10% of a T-Mobile share as of the price on Friday.  So does that mean that, if this goes through in early 2019, my 2,000 Sprint shares would turn into 200 T-Mobile shares? What if the price of Sprint stock goes up from here? What if it craters? Is this price/ratio set in stone?  If my stock does get converted, does that happen automatically? Will Fidelity all of a sudden show that I own TMUS stock instead of S? A story about a guy who helped humanity by being held in a prison I remember a story I have read buy could not remember the author the name or anything apart from the basic plot. The story is about some future where humanity has to fight with some aliens (not 100% sure). The story tells about a guy who was some kind of activist and who was in a prison two or more times and somehow helped humanity by being held in a prison (can't remember details). I think the story starts by saying that there is a statue in his honor that is not very well known but he did more to help humanity than famous politicians.   The story is most likely written by some famous English-speaking author, though I read it in a translation. The feeling of always wanting newer possessions? I am looking for a word that describes the emotion or feeling of an intrinsic want of a new and better possession. Covetous or envious seem a bit too focused on the other other person's possession of the desired object whereas I am looking for something that is defined by the internal thoughts we have when seeing an advertisement for the latest iPhone or life-changing new service.    but I am wondering if there is a word with less emphasis on the second entity? Otherwise, would I covet new things from Amazon or Apple? Can I be envious of corporations?  For example, I just bought a new car and now, looking at my slightly out of date television, I feel the need to upgrade my T.V. with a newer, shiny one from Amazon. Would I be coveting that T.V. which Amazon sells?     I saw the ad for the latest iPhone, the iPhone 3000, and feel that my current phone is inadequate. I am a(n) ______ person, since I always desire something better than what I currently possess. If I was a caveman with a sharpened stick, I'd want your sharper, pointier stick.   I feel like there is probably some niche German word for exactly this, but I'm unsure it exists in English. Thanks! Javascript and PHP functions User is able to edit a file using vim I have a file named file.txt with some contents located in /home/myuser directory and I change the permissions of that file to root.root and 644.   -rw-r--r-- 1 root root 1.4K Jan 15 07:09 file.txt   Then I switched to myuser and opened it with vim(without sudo) and tried to edit and save it :wq! and I got output like:  "file.txt" E949: File changed while writing Press ENTER or type command to continue   Then I hit enter and then again :wq! and the output was :  WARNING: The file has been changed since reading it!!! Do you really want to write to it (y/n)?   I hit y, the file got saved and exit from vim.  The question is why a file with ROOT privileges and read-only access for a user changed by the way?  PS: 1. myuser is a sudo user.   The user permissions after saving the file changed to myuser.myuser as well.  -rw-r--r-- 1 myuser myuser 1.4K Jun 27 18:57 file.txt