Why do we use 3.3 V in circuits? Why not 3 V? Is there a specific standard? Or do we use it because it was 3.3 V from the beginning? I am just curious to know.
Integrated circuits seem to have standard voltages of 5 V, 3.3 V, 2.5 V, 1.8 V, etc.  Who decides these voltages? Why do smaller devices require lower voltages?
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$ Can't quantum teleportation be superluminal some percentage of times? I apologize if this is a really silly question.   In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical information to Bob, she is about to send one of the following values: 00,01,10,11.   What if Bob doesn't want to wait and simply takes a guess? Wouldn't there then be superluminal communication 25% of the time? "Unable to locate package" while trying to install packages with APT When I try to install any package through the command line, I get an error.   $ sudo apt-get install &lt;package&gt; Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package &lt;package&gt;   Can anyone help me on this? What is the importance of the Diophantine inequality $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} > 1$? In Humphreys' book  Introduction to Lie algebras and Representation Theory(3rd printing, p.62), the Diophantine inequality $$\frac{1}{p} + \frac{1}{q} + \frac{1}{r} &gt; 1$$ appeared while classifying all Coxeter graphs of irreducible root systems. Under the assumption $p \geq q \geq r \geq 2 $, the possible triples turn out to be $(p,2,2), (3,3,2),(4,3,2),(5,3,2)$, which correspond to the Coxeter graph $\text{D}_{p+2}, \text{E}_6, \text{E}_7, \text{E}_8$, respectively.  It seems quite straightforward to solve the inequality in positive integers, but Humphreys said that      This inequality, by the way, has a long mathematical history.   without further comment. So I want to know if this Diophantine inequality has any important significance, or if it has appeared in other context (maybe relevant history) before. Why are light rays able to cross each other? See the image first:   Why are light rays able to cross each other? Air isn't able to. Star rating in AJAX with Ruby On Rails Determine all of the accumulation points of the following sets in $\mathbb{R}^1$ and decide whether the sets are open or closed or neither.  The set $X$ of all numbers of the form $2^{-n} + 5^{-m}$ where $m,n = 1,2,\ldots$.   Claim: The set of accumulation points is the following: $$\left\{\frac{1}{2^n}: n \in \mathbb{N} \right\} \cup \left\{\frac{1}{5^n}: n \in \mathbb{N}\right\} \cup \{0\}.$$ Let $n \in \Bbb{N}$ and $r&gt;0$, and consider the open neighbourhood $B\left(\frac{1}{2^n},r\right) = \left(\frac{1}{2^n} - r,\frac{1}{2^n} + r\right)$. For the given $r$ we can find $m$ large enough such that $5^{-m} &lt; r \implies \frac{1}{2^n} + \frac{1}{5^m} &lt; \frac{1}{2^n} + r$, and $\frac{1}{2^n} - \frac{1}{5^m} &gt; \frac{1}{2^n} - r$; therefore $5^{-m} + 2^{-n} \in B\left(\frac{1}{2^n},r\right)$. A similar argument shows that each element of $\{5^{-m}: m \in \mathbb{N}\} \cup \{0\}$ is an accumulation point of $X$. Now consider $y \in X$. $B(y,r)$ isn't a subset of $X$ since for all $r &gt; 0$, $B(y,r) \subset (\mathbb{R} - \mathbb{Q}) \not\subset \Bbb{Q}$, hence $B(y,r) \not\subset X$. A lot of my scripts stopped working after installing Ubuntu 15.10 and I have trouble remembering this new name as I was used to ethx and wlanx for years. Is there a reason for this change? Do I have to get used to this or can I just rename it and go back to good old eth0?  $ ifconfig  enp0s25   Link encap:Ethernet  HWaddr 77:5a:5e:a6:86:d5         inet addr:192.168.31.239  Bcast:192.168.31.255  Mask:255.255.255.0       inet6 addr: fe80::725a:b6ff:fea6:86d7/64 Scope:Link       UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1       RX packets:4833 errors:1332 dropped:0 overruns:0 frame:666       TX packets:5589 errors:0 dropped:0 overruns:0 carrier:0       collisions:0 txqueuelen:1000        RX bytes:3266446 (3.2 MB)  TX bytes:1046654 (1.0 MB)       Interrupt:20 Memory:d3500000-d3520000 Can you explain closures (as they relate to Python)? I've been reading a lot about closures and I think I understand them, but without clouding the picture for myself and others, I am hoping someone can explain closures as succinctly and clearly as possible.  I'm looking for a simple explanation that might help me understand where and why I would want to use them. The second part of an exercise asks that I show:     There does not exist a surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$.     The first part was to show that these two spaces are separable in their respective $L^p$ norms.    I've really hit a wall on this one.  I know, in fact, that there does exist a surjective bounded linear map from $\ell^1(\mathbf{N})$ to $\ell^2(\mathbf{N})$.  So my intuition says that if there were also one going the other way, then the two spaces would have to be isomorphic, which is false .  But I don't know of any such theorem that I could apply to "the category of Banach spaces".    My only other idea is to argue by contradiction using the open mapping theorem, but nothing is coming to me...  My guess is that separability is also going to be important, given the first part of the exercise.  -Thanks. PHP regular expressions: No ending delimiter '^' found in Do I have to buy or need a 3D-enabled phone to use Google Cardboard? Google cardboard comes with 3D glasses. Does that mean that we will be able to watch 3D videos using a smartphone like the Moto-G (1st edition) which is not 3D enabled? In search of story: Survivor of war game can do no wrong I'm trying to help a teacher friend of mine with finding a short story he read when he was a teenager and has not been able to find since.  He described the story in the following way:  In a post-war world there is a setup in which Soviet/Russian soldiers are required to fight against American soldiers in an arena in which both sides have equal setup: a forest, a lake, etc. The winner of the 'game' has the right to govern for the next several years.  It's told from a first person point of view like you're watching the Olympic games and one American soldier gets shot, but is not killed.  He falls and other bodies fall on top of him so it seems the soviets win, however their last two soldiers happen upon him and he kills them first, rendering the United States victorious.  Given that he was the only survivor he has a sort of political amnesty in which he can do no wrong legally. He returns home and he essentially suffers from a form of PTSD.  The story ends with him watching a young girl next door get off the school bus; he walks to the neighbor's home, goes inside and, in front of the girl's parents follows the girl into her room and shuts the door, leaving the reader to assume whatever happens behind the door.  He's been looking for this story in different anthologies for some time.  Can anyone help?  Thanks so much! :) Pages: How to put a word between horizontal rules How can I make something that looks like this?  --------   Text   ---------  where the horizontal rules extend to the margin on either side? Font corruption: lines through characters I have a problem where a one-pixel high white line is displayed through certain letters of text. Almost always only a single character type is affected at once, and only in one font size (though that size can change over time). Most of the time things are fine, but this happens several times a day. It happens frequently in Firefox, but system dialogs, menus, etc. can also be affected. It's been happening ever since I upgraded to 10.10. Only restarting seems to fix it.  Two examples (in the first, only the larger "r" is corrupted):     Any help would be appreciated, thanks.  Edit: I've since noticed that I can (sometimes) make the fonts appear correctly by zooming in/out all the way and returning to the default in Firefox (one or two steps, then going back, does nothing) seems to make the problem go away temporarily.  Edit 2: I figure it's worth noting that the solution below doesn't fully work for me any longer (I'm now using Ubuntu 11.10). It does significantly reduce the frequency of this problem occurring.  Edit 3: Still around in 12.04. The fix provided by Vanni works perfectly now for me, but apparently doesn't for some.  Edit 4: This seems to be an xorg problem, with Vanni's answer fixing it for many Intel video cards. I've had this occasionally happen with AMD graphics cards in 13.10 and 14.04, but very rarely (only two or three times). I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.  According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.  BUT Newton's second law states that $a = F/m$, with $a$ the acceleration of a particle, $m$ its mass and $F$ the sum of forces applied to it.  I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don't comprehend why the mass, which is seemingly affecting the acceleration, does not affect the "time of impact".  Can someone explain this to me? I feel pretty dumb right now :) How is the Schroedinger equation a wave equation? Install Windows 7 with Bootcamp on OS X Yosemite with USB Key I have an iMac (bought in 2011) and I recently upgraded it with Yosemite. I am trying to install Windows 7 on it via Bootcamp.  However, its optical drive does not work, so I chose the USB key solution using the trick of modifying the file info.plist of Bootcamp (type 'usb bootcamp youtube' in google to see a video of this trick).  So I follow the process religiously and end up with the classic and famous boring screen 'No bootable device -- insert boot disk and press any key'.  So I tried to use Unetbootin (  ) to make my USB Key bootable, and tried to boot on it through the screen that appears when you maintain the Option key (Alt button) while starting the mac. Result: I never managed to have my Unetbootin-formatted USB key appear on this screen :(  I read some stuff about reFit (  ) and GParted, but I just don't know how to use them...  If someone managed to install Windows 7 on his/her iMac with Yosemite using a USB Key, please help me understand why I can't see the USB as a boot option. This is a question to experienced people that might help us shed some light on the issue.   We noticed a very strange behavior on our site, in Google Analytics. Some dude from Finland, namely, from Kouvola city is hitting one of our pages - only one page on our site, 'bout a hundred times per day, all with an average bounce rate of 90%+...  This is causing our overall bounce rate to go up by 1 to 3% per day... which is very disturbing.. since we're trying to do our best in order to keep it as low as possible. And obviously having it jumped from ~24% to 27%, just because of that crazy dude is not making us happy at all... We tried implementing a geo-targeted script in order to catch this particular visitor and deliver him a juicy message, and it seemed like it helped in the beginning, it has stopped for a day or two, but now he's back...   The geo-targeted script was also logging all IP addresses for page requests originating from Finland in order to find out more details and (in order to block them on the server level, later).. but thing is, it was all mainly cable or DSL connections with various, but not constantly repeating IPs... we are all wondering what is he up to really ?   I think that this page should be kept updated with ideas on how to combat this and perhaps someone could also shed light on what it might be ? What is the reason for doing this "bounce-rate attack", as I call it?  There was a similar question asked on stackoverflow earlier, with no meaningful answer - here - This question is in response to . The original post mentioned that they wish to retract their paper from a "fake" journal. I don't know what a fake journal is but better safe than sorry so I want to make sure what defines a fake journal. In the comments, other people also mentioned "shady" journals and "predatory" journals. This is the first time I encounter these descriptions so I would like to know more about what they entail. I would be interested in hearing about your experience with such journals as well, if any.