If $M_1$ and $M_2$ are distinct maximal ideals of, then $R/M_1 \otimes _R R/M_2=0$
Show that $R/I\otimes_R R/J\cong R/(I+J)$
How to find a global minimum for $\frac{1}{2}x^tQx-b^tx$ Fibonacci sequence emerging from integer partitioning Is there a better name for this than "emphatic and"? In semi-poetic writing, I have had occasion to deviate from the standard prose list practice (interpose commas or semicolons between items, with an "and" preceding the final item), by utilizing a second or third and to separate three or four items.  That is,       Bob likes beer, wine and liquor.   The variant would be:     Bob likes beer and wine and liquor.   Now, the usage is obviously nonstandard and should be avoided in formal writing, but for those instances where poetic variation may be justified.    What is it called?  "Emphatic And" is the best I can coin on my own, but I wonder if there is a more established name for this variation. Because of the Rule of Two, is/was Sidious the strongest Sith ever? The Sith Rule of Two says: One to embody power, one to crave it. It's like a survival of the fittest.   If the apprentice must kill the master to be the master, that usually means the apprentice is stronger than the master. If this chain went on for many years, does this mean Sidious was the strongest Sith ever, just by the transitive property? Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied . Prove that if $f$ is differentiable on $ [a,b]$ and if $ f(a)=f(b)=0$ then for any real $k$ there is an $ x \in (a,b) $such that $$kf(x)+f'(x)=0 $$  As all the conditions of Rolle's theorem are satisfied one can say that there is at least one  $c \in (a,b) $ such that $f'(c) =0$ How should I proceed furthur ? How can I use this to get to the required equation ? I am looking to display my iPad screen wirelessly to an external display to demo applications.  I found  showing exactly what I want to do with an iPhone but no explanation as to what the hardware dongle used was.  The main thing is that there isn't a wire tethering the user to the external display. Why is AES resistant to known-plaintext attacks? At least it's my understanding that AES isn't affected by known-plaintext. Is it immune to such an attack, or just resistant? Does this vary for chosen-plaintext? How to sort strings in JavaScript I have a list of objects I wish to sort based on a field attr of type string. I tried using -  list.sort(function (a, b) {     return a.attr - b.attr })   but found that - doesn't appear to work with strings in JavaScript. How can I sort a list of objects based on an attribute with type string? How do I change my username? What's the difference between a method and a function? Can someone provide a simple explanation of methods vs. functions in OOP context? Double SOCKS5 proxy using SSH I was searching for a way to connect to one of my servers who is behind a jumpbox via SSH. I was able to do so by running the following command:  $ ssh -tt ptitpou@jumpbox ssh -tt ptitpou@targetserver   Now, I want to be able to use that server to access webservers on targetserver's network. For that, I followed  and I was able to successfully access the websites. The command I used was:   $ ssh -L 127.0.0.1:9999:localhost:9696 -tt ptitpou@jumpbox ssh -D 9696 -tt ptitpou@targetserver   The question I want to ask is how to use the ssh -o ProxyCommand to command in a slightly cleaner way. I tried to put the second part of the command as the proxy command and I had a successful SSH connection, but I was unable to use the proxy after that.   I've also tried  but the command line hangs after connecting to targetserver.  How can I do that? Am I wrong to try to use ProxyCommand option for this task? How to enter the Default Keyring password via the command line? Is there a way to enter the default keyring password using the command line?   For instance:  You have a remote setup of Ubuntu 10.10 thats set to auto login. You don't want to remove  the keyring password.  All right the system boots up and logs in automatically, then asks for the keyring password now at this point you can create ssh connections but you can't remote desktop.   What can you do to enter the keyring password at this point?  Also, to better clarify, this is from a remote connection using the command line. I have a Canon 7D, which has a crop factor of 1.6x.  When using a Canon EF-S lens I get the focal length stated on the lens, when using a Canon EF lens I get the focal length times 1.6 when used on the APS-C body. At least that's what I thought.  I just compared two lenses:   Canon EF-S 15-85mm f3.5-5.6 Canon EF 70-200mm f4   .  The top photo is shot with the 15-85, the bottom photo with the 70-200 - both lenses are set to 70mm. Now why do they look the same?  I thought I would get 112-320mm (70mm*1.6 crop factor). What did I misunderstand about the crop factor calculation? Lightroom also displays the photos as having "70mm" and not 112mm. In particular, I am referring to the Pearson product-moment correlation coefficient. The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this? What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$? I do not understand the difference between $\rightarrow$ and $\Rightarrow$. Sometimes I see implication truth tables labeled with the former, sometimes with the latter.  Aren't they synonyms of logical implication or is there any difference? Chrome unity shortcut acting up Whenever I click on my chrome shortcut I get a new window (as expected) but I also get a new Unity entry with a different icon (one from an iconset I had been using before upgrading to 14.04 - don't really remember the name). The new unity entry does not seem to originate from a correct .desktop entry because all the submenus are missing from it (New incognito window, New Window etc.) and it has a permanent tag '(1) Facebook' no matter the window title (see attached picture).  I have uninstalled and reinstalled chrome in hope that it would help which it did until restart but now I get the same behaviour.  Note that I haven't altered any .desktop files regarding chrome and I can only find one file:  /usr/share/applications/google-chrome.desktop which seems to be correct (with submenus etc.) Apply empty style to the entire bibliography Can I see images and watch movies inside the terminal emulator When do I use "can" or "could"? When should I use can? When should I use could? What is right under what context?