We all know that speed of light is $3\times 10^8$ $\text{ }\mathrm{ms^{-1}}$. The speed of electron inside the atom is $2.7\times 10^8$ $\text{ }\mathrm{ms^{-1}}$, which is close to speed of light. So there is a machine that can accelerate the particle. Then when the particle move very fast, the resultant velocity of electron inside the particle should exceed the speed of light right?
Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$ I've encountered the following problem in complex analysis:  Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$.  I've decomposed $f$ to it's real and imaginary parts and got that it's enough to prove that:  $(\int_0^{2\pi}cos(\theta)g(\theta)d\theta)^2 +(\int_0^{2\pi}sin(\theta)g(\theta)d\theta)^2 \le 16$   Where $g(\theta)=f(e^{i\theta})$.   But now I'm stuck. Any ideas?  Thanks Buster Blader the DDS did not affect Destiny Hero - Decider effect; why so? How come  with  set to dragons didn't stop 's effect from being activated? How can I check which songs or videos that I purchased from the iTunes Store have DRM restrictions?  All of the mobile OSes are very impressive to me at the moment, and I'm thinking about trying a non-iOS device again. I want to know now the impact it has on my Apple-sourced music collection though.  Is there a date cut-off for purchases when items went DRM free? I've always managed my iPhone/iPad/iPod Manually, I recently updated to iTunes 11 and now I can see no way to get my music onto my device.  I used to be able to just drag songs from my library to my device, now there is seemingly no way to do this.  I can view the music on my device by clicking on it on the top right corner of iTunes, but I can't seem to get to a state where I can drag music from my computer onto my device.  I'm using iTunes 11.0.1.12 for Windows if that makes a difference. I have a WinXP installation that is used to only connect to another PC with RDP.   A dummy user account gets logged in automatically, then the user must click a link to start the RDP connection with predefined parameters.  Is there a way to run the RDP client without Windows Explorer being accessible? What is the purpose of Microsoft.SharePoint.Runtime.dll in CSOM? I know we need to use Microsoft.SharePoint.Client and Microsoft.SharePoint.Client.Runtime dll's reference in .NET managed CSOM application development. But can someone help me understand why we have to use Microsoft.SharePoint.Client.Runtime and whats it's purpose, in detail. or point me to a reference please. Thank you in advance How do I find out which DOM element has the focus? I would like to find out, in JavaScript, which element currently has focus. I've been looking through the DOM and haven't found what I need, yet. Is there a way to do this, and how?  The reason I was looking for this:  I'm trying to make keys like the arrows and enter navigate through a table of input elements. Tab works now, but enter, and arrows do not by default it seems. I've got the key handling part set up but now I need to figure out how to move the focus over in the event handling functions. Photoshop CS6 Resize Rectangle with Rounded Corners This question is about Photoshop CS6. Hopefully the feature was added in this version. Before posting I looked up Google and  and  but didn't find an answer for CS6.  So the question is: Is there a feature within CS6 or a script that allows to resize a vector element with rounded corners without using the Direct Selection Tool (white arrow tool) and not changing the border radius? What would be great would be something like simply using the transform tool or something like a grid resize tool. How do I prevent new villager trades from spawning? When making a custom adventure map, usually you only want the trades you programmed into a villager to show up. By default, however, the game will try to spawn new trades when the last one is made. The classic way I'm seeing in tutorials to prevent new trades is to make the last trade untradeable; however, with the release of 1.7, a lot of the old item IDs that were unobtainable have been removed from the game altogether, and following the tutorial I have crashes the game when the trade interface is scrolled to the last trade.   So there's two parts to this question:   Is there a better way to prevent new trades with the 1.7 mechanics? Or with the snapshots of 1.8 mechanics? If not, what is a safe data ID to use to prevent the last trade from being a real trade as of 1.7? Is there a law that you can add or multiply to both sides of an equation? How do you search for questions filtered by a particular user? I want to do a search on StackOverflow for a few terms, but also by user, since I know which user referenced the item I'm looking for. What ability should be used when resisting Intimidation? During our last play session (it was our second session, so everyone is first level) my fighter dwarf had a conflict with another player's human fighter. My dwarf became annoyed at the human's dismissive reaction to a roar outside the village that sounded like ogres (my dwarf has a bad history with ogres).   So, in order to emphasize the seriousness of this situation, my dwarf grabbed the human by shirtfront and pulled him closer (done with a successful roll). Still bent double, the human drew his sword and pointed it at my dwarf's belly (dwarf wearing chainmail). At this point the DM made the other player roll an Intimidation (Charisma) check, and me a Wisdom check to resist. I lost and my dwarf, chastened, let the human go.  That was pretty funny situation, but one thing is bothering me. By using a Wisdom check against Intimidation (Charisma), my dwarf (who has &minus;1 Wisdom modifier) was at a disadvantage (literally, not in the D&amp;D disadvantage mechanic sense) against the threats. Although he is a strong and capable warrior, he is not that wise.  But I have to wonder: is willpower really represented by Wisdom in 5e? I think that many not-so-wise creatures/characters can stand bravely against threats.  What ability/skill should be used in a contest to resist intimidation? Nonabelian semidirect products of order $pq$? What should I do when I have lenses with different filter thread sizes? Base64 Encode String in VBScript I have a web service load driver that's a Windows Script File (WSF), that includes some VBScript and JavaScript files. My web service requires that the incoming message is base64 encoded. I currently have a VBScript function that does this, but it's very inefficient (memory intensive, mostly due to VBScripts awful string concatenation)  [Aside; Yes, I've seen . The concatenation is happening in a loop across messages that are 1,000's to 10,000's bytes in size.]  I've tried using some custom string concatenation routines; one using an array and one using ADODB.Stream. These help, a little, but I think it would help more if I had some other way of encoding the message rather than via my own VBS function.  Is there some other way of encoding my message, preferebly using native Windows methods? build argument lists containing whitespace In bash one can escape arguments that contain whitespace.  foo "a string"   This also works for arguments to a command or function:  bar() {     foo "$@" }  bar "a string"   So far so good, but what if I want to manipulate the arguments before calling foo?  This does not work:  bar() {     for arg in "$@"     do         args="$args \"prefix $arg\""     done      # Everything looks good ...     echo $args      # ... but it isn't.     foo $args      # foo "$args" would just be silly }  bar a b c   So how do you build argument lists when the arguments contain whitespace? Security of GCM if Implemented with Stream Cipher instead of Block Cipher When will my phone get the Android 2.3 update (Gingerbread)? I have to give low and high bounds for the following:  $$ \sum_{n=1}^\infty \frac{1}{2^n - 3^n } $$  How do I determine an upper bound? How can I show this sum exists?  edit: removed erroneous conclusion. Is there a way to take a mesh, cut it with seams or sharp edges and flatten it, so that the faces stay the same shape and size?  Making paper models is one aspect, where you could use that technique.  No, I'm afraid SZ0Return is not going to do it properly.  And misusing the UV-unwrap is only a last option.    Note, while it's an option to revert to Blender 2.49 which had a script to do this, I'd like a solution that I can use inside the current workspace.