Isomorphism Between V and V**
On the canonical isomorphism between $V$ and $V^{**}$
Do electrical devices "take what they need" One concept of electronics I have a hard time understanding is if things like motors, actuators, solenoids etc. use as much power as they need or what you give them.   If a motor needs 12 volts and 500ma and I supply it with 12 volts and 3000ma will it only consume 500ma? Also, if I supply it with 15volts and 500ma what will happen?   It seems logical that an LED and a DC motor are way different when it comes to requiring/using electric where as an led has to be completely regulated and (I assume) a DC motor doesn't.   Is my understanding wrong? Execute bash script from URL Is the tabu package obsolete? Using a new document class/template with LyX? I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next? Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$ Prove $$\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n! \qquad\text{and}\qquad \sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0,$$ where $m \in \{0, 1, 2, \cdots, n - 1\}$.  To be honest, I tried to use some combinatorial ideas but was not able to see interconnections. Also, I had an idea to prove it using induction but failed to do that either. Help will be much appreciated! I just got stuck and don't see any continuation of solution for this problem How do you extract IP addresses from files using a regex in a linux shell? Semigroup analogue to the classification of finite simple groups? Is there a semigroup analogue to the classification of finite simple groups?  If so what are some of the major results?  --Edit, reference links--- Allow [tag:tag-name] syntax to link to any site The tag  and meta-tag  syntax generate much nicer looking results than merely surrounding your tag with [square brackets].    However, they only work when you're talking about the site you're on.  On Area51, in Chat, and on Meta sites, this is frequently not the case, leading to attempts at syntax like [[tag:failure]](https://superuser.com/questions/tagged/failure), which produces:    Hmm, must be some subtle syntax thing:   : [tag:failure](https://superuser.com/questions/tagged/failure) []: [[tag:failure](https://superuser.com/questions/tagged/failure)] : [tag:[failure]((https://superuser.com/questions/tagged/failure))] : &lt;a href="https://superuser.com/questions/tagged/failure"&gt;[tag:failure]&lt;/a&gt; : [tag:failure][1] \n\n [1]: https://superuser.com/questions/tagged/failure : [more text is a [tag:failure] too](https://superuser.com/questions/tagged/failure)   I give up!  How can I create a link to a tag on another site with tag markdown? I want to buy some stock photos like the ones below. What is this design called?  I don't even know how to start searching... How to prevent going to next row after editing a DataGridViewTextBoxColumn and pressing EnterKey? When I spoke with a friend of mine, I had noticed she used sentences similar to "I need to go buy food."   Is it correct to say "to go buy," or should I say "to go to buy"?    I know that I could say "I need to buy food," but I think that in "I need to go buy food," who is speaking is putting in evidence s/he needs to go and that s/he cannot stay any longer, or that her/his time to stay is limited. How to reinstall Ubuntu keeping my data intact? I want to reinstall Ubuntu keeping my data intact. I have 160 GB hardrive (sata or pata I don't know but it's slim and made in China) with a 40 GB ext3 partition, a 4GB swap memory and 3 other partition with a FAT32 file system. I have around 4GB space on my drive where Linux is installed.  I'd like to keep the data intact, especially the Downloads folder, desktop, and /var/www; And I no longer have access to any other machines or external storage devices. What was with the two different colored prison uniforms in Daredevil season 2? In Daredevil S02, we see two kinds of prison uniforms, full orange and full white. We see in the flashback that Wilson Fisk gets a white prison uniform but his current one was orange.  The Punisher was also given a white prison uniform but most of the prisoners had orange uniforms. What was with the two different colored uniforms? Does it have some significance or is it just random? Does it happen similar in real life US prisons too? How do I write a correct micro-benchmark in Java? What is a word for someone who is experienced and wise, but who deliberately acts naïve?    I don’t intend it for sarcastic use; I’m trying to describe someone succeeding in making people think that that person truly is naïve.   Is there a word for this? Which is higher — "hyper-", "ultra-" or "super-"? Splitting all lines in layer at vertices using QGIS I want to automatically split all lines in a QGIS layer at their vertices (). I've done a Google search and found , which is quite close but the workflow is complicated. Because I'll have to train my co-workers (who are unfamiliar with GIS) to use this tool, I want something as simple as a plugin or something that doesn't require GRASS. Since it's been a long time from 2010 - the time of , I wonder if there is any better way to achieve the same result? I hava Lenovo g580 laptop. I want to change disk to SSD drive, but I'm not sure if my laptop support SATA 3 (6Gbps).  I write following output:  dmesg | grep SATA [    3.190743] ahci 0000:00:1f.2: AHCI 0001.0300 32 slots 6 ports 6 Gbps 0x5 impl SATA mode [    3.199450] ata1: SATA max UDMA/133 abar m2048@0xd3617000 port 0xd3617100 irq 43 [    3.199455] ata3: SATA max UDMA/133 abar m2048@0xd3617000 port 0xd3617200 irq 43 [    3.518365] ata1: SATA link up 3.0 Gbps (SStatus 123 SControl 300) [    3.857921] ata3: SATA link up 1.5 Gbps (SStatus 113 SControl 300)   Is that means I Can use SSD disk in SATAa 6Gbps mode? Filter questions with no accepted answer I have some questions with answers, but none of the answers are acceptable (just wrong).  I'm sure there are a lot more people with the same problem.  Can you add a button to filter questions with answers but no accepted answer?  This way, people will see those questions and maybe try to offer a new perspective. Is there a list of error codes for Minecraft? Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.