I rewrite N as kg m s^-2 and try to get Pmax, which is in Watts to kg m^2 s^-3 but when I do so I am left with an rad^2.
I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've been writing a  (the specifics of which are out of scope), which has me thinking about the problem because I decided to handle angle units as dimensioned quantities, which seemed natural to enable the unit conversion with degrees. The overall purpose of the library is to disallow operations that don't make sense because they violate the rules of dimensional analysis, e.g. adding a length quantity to an area quantity, and thus provide some built-in sanity checking to the computation. Treating radians as units made sense because of some of the properties that dimensioned quantities seemed to me to have:  The sum and difference of two quantities with the same dimension have the same physical meaning as both quantities separately. Quantities with the same dimension are meaningfully comparable to each other, and not meaningfully comparable (directly) to quantities with different dimensions. Dimensions may have different units that are scalar multiple (sometimes with a datum shift).  If the angle is treated as a dimension, my 3 made up properties are satisfied, and everything &quot;makes sense&quot; to me. I can't help thinking that the fact that radians are a ratio of lengths (SI defines them as m/m) is actually critically important, even though the length is cancelled out. For example, though radians and steradians are both dimensionless, it would be a logical error to take their sum. I also can't see how a ratio of something like (kg/kg) could be described as an &quot;angle&quot;. This seems to imply to me that not all dimensionless units are compatible, which seems analogous to how units with different dimensions are not compatible. And if not all dimensionless units are compatible, then the dimensionless &quot;dimension&quot; would violate made-up property #1 and cause me a lot of confusion. However, treating radians as having dimension also has a lot of issues, because now your trig functions have to be written in terms of $\cos(\text{angleUnit}) = \text{dimensionless unit}$ even though they are analytic functions (although I'm not convinced that's bad). Small-angle assumptions in this scheme would be defined as performing implicit unit conversions, which is logical given our trig function definitions but incompatible with how many functions are defined, especially since many authors neglect to mention they are making those assumptions. So I guess my question is: are all dimensionless quantities, but specifically angle quantities, really compatible with all other dimensionless quantities? And if not, don't they actually have dimension or at least the properties of dimension?
Integral of the square of the normal distribution. Is there is a way to exclude nested subdirectory specified by a path to that dir from grep recursive search? Or I have to use ack or find for this?  Here's what I want. Say I have this dir structure:  dir/nesteddir/match.txt otherdir/nesteddir/match.txt   How do I exclude first nesteddir only? Is it even possible using grep?  Most obvious answer $ grep -r --exclude-dir="dir/nesteddir" "stringToFind" . doesn't seem to work, nor do any of my experiments with various --exclude-dir paths using globbing, leading ./, etc.   Reading man page and googling didn't help, the only mention of this usecase I found is this question:   It was concluded that this is bug introduced in grep 2.12, but I'm using latest version (2.16) and grep's bugtracker () doesn't mention anything related to --exclude-dir, so I guess either it was fixed or it's an intended behaviour.   Would be really nice to get some clarification. I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two. I have something like this:  &lt;div class="content"&gt;     &lt;a href="#"&gt;A&lt;/a&gt; &lt;/div&gt; &lt;div class="content"&gt;     &lt;a href="#"&gt;B&lt;/a&gt; &lt;/div&gt; &lt;div class="content"&gt;     &lt;a href="#"&gt;C&lt;/a&gt; &lt;/div&gt;   When one of these links is clicked, I want to perform the .hide() function on the links that are not clicked. I understand jQuery has the :not selector, but I can't figure out how to use it in this case because it is necessary that I select the links using $(".content a")  I want to do something like  $(".content a").click(function() {     $(".content a:not(this)").hide("slow"); });   but I can't figure out how to use the :not selector properly in this case. I can enter U+0008 (backspace character) into a chat message I typed . I believe I tab-completed @rumtscho and fully typed @MarthaF (since she doesn't tab complete). However, other people tell me that a Unicode character was inserted into the message; I can't see it:  Originally, I abandoned this bug report for a lack of reproducibility. But on another machine, I can see the character and managed to reproduce it: press tab, then press backspace. It works anywhere in a message, not just in a @-ping. (Actually, it seems that you just need to un-focus the input box; clicking elsewhere then hitting backspace works, too)  First machine is Firefox 12 (Iceweasel) on Debian GNU/Linux AMD64, testing+unstable. No user scripts. Greasemonkey is installed, but disabled in the extension manager Second machine is Firefox 10 (Iceweasel) on Debian GNU/Linux AMD64, testing+unstable. No user scripts, Greasemonkey not even installed Third machine (just tested) is Firefox 11 (Iceweasel) on Debian GNU/Linux AMD64. Greasemonkey installed and enabled, and there is a global userscript. Does not happen on Chromium 18.0.1025.151, running on machine #3.  So far, that's all the machines I've tested on, and it happens on all of them. It only happens in chat. Easiest way to produce it is to click on the page background, somewhere outside the text box, to un-focus the text box. Then press backspace. Note that not all browsers will display the character, even if its there (check  to see if yours does) Difference between JOIN and INNER JOIN Both these joins will give me the same results:  SELECT * FROM table JOIN otherTable ON table.ID = otherTable.FK   vs  SELECT * FROM table INNER JOIN otherTable ON table.ID = otherTable.FK   Is there any difference between the statements in performance or otherwise?   Does it differ between different SQL implementations? Do tenses in a time clause never back-shift in reported speech? Do tenses in a time clause never back-shift in reported speech?  For example, does      "I went to Italy when I finished school."    become      She said she had gone to Spain when she finished school.   -or-   She said she had gone to Spain when she had finished school.   and does      "I will go to Italy when I finish school."    become     She said she would go to Italy when she finishes school.   -or-   She said she would go to Italy when she finished school. This seems to be one of those tricky examples. I only know one proof which is quite complicated and follows by localizing $\mathbb{Z}[\sqrt[3]{2}]$ at different primes and then showing it's a DVR. Does anyone know any simple quick proof? What is the radius of convergence of $\sum z^{n!}$? How to find the radius of convergence of $\sum z^{n!}$?   I'm used to applying the ratio test to power series of the form $\sum a_{n}z^{n}$, but for a different power of $z$, I am a bit stumped. What about $\sum z^{2n+a}$ for another example? Where $a\in \mathbb{R}$. What do you call the symbols list on a map? Every map has symbols that describe things. In the corner of a map, there is a list that explains what each symbol means.  What is the name of that list? (What title should I put above this list)? What documentation is needed for a tourist to drive a US citizen's car? Cycles in permutations of a given size Geometric meaning of the determinant of a matrix What is the geometric meaning of the determinant of a matrix? I know that "The determinant of a matrix represents the area of ​​a rectangle." Perhaps this phrase is imprecise, but I would like to know something more, please.  Thank you very much. This question attempts to collect a community-maintained list of quality books on the  programming language, targeted at various skill levels.  C is a complex programming language that is difficult to pick up on-the-go by reading online tutorials. A comprehensive book is often the best way to learn the language, and finding a good book is the first step. It is important to avoid badly-written books, and even more importantly, books that contain serious technical errors.  Please suggest edits to the accepted answer to add quality books, with an approximate skill level and a short blurb/description about each book. (Note that the question is locked, so no new answers will be accepted. A single answer is being maintained with the list)  Feel free to debate book choices, quality, headings, summaries, skill levels, and anything else you see that is wrong. Books that are deemed satisfactory by the C community here will stick around on the list; the rest will be regularly removed.  For books that have reviews by the Association of C and C++ Users (ACCU), a link to those reviews should be added along with the book.  See also:   Other C-related resources in the   A similar list for :      This question was discussed on  as part of the .The consensus was to keep it undeleted and actively maintained. Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$. Let A be a commutative ring with unity ring, M be a maximal ideal and $b\notin M$ . Show that there exists $q \in M, s\in A$ such that for every $a \in A$ we have $a=sba+qa$. Show that this is true only when $M$ is a maximal ideal.   Suppose if we take $A=2\mathbb Z$ and $M=4\mathbb Z$, $a=6.$ Then by the given statement $\exists$ $s\in A$, $q\in M$ s.t. $6=6(2s+q)$ $\implies$$s=\frac{1-q}{2}\implies q \text { is odd}$. But $q \in 4\mathbb Z.$  Please someone give some hints. how can solve this.  Thank you.. Can a virtualized machine have the CPU and RAM resources of multiple underlying physical machines? We are studying implementing some virtualized servers here, but we don't know what will be better suitable for us. Some folks are saying better have two huge servers, and others are saying have like a ten middle-end servers.  We have a legacy Visual Foxpro application, which nowadays run on Dual Xeon E5405 @ 2GHz and 16Gb of RAM. The currently server its getting too slow due the number of active users and process running on it. Virtualizing this server will give us the benefit of an faster disaster recovery.  So the question is, having like ten physical servers running at 1.7GHz and 4Gb of RAM, we could virtualize one server into 4 machines, and have one virtualized server running at 6.8GHz and 16Gb of memory? If yes, there is some how if one machine stops, automatically manage this virtual machine to another one, and execute the appropriate maintenance on it, and later back to it again? Why are my render times 30+ minutes, but other people's are ~3 minutes? Is there a difference between DR/evil and DR/unholy? Can I use apt-get or aptitude to install software to non standard location? When I install a software using apt-get it installs to default locations i.e to /usr/bin, /usr/lib, /usr/share and etc. For example when I install "Meld Diff Viewer" using  sudo apt-get install meld   and use whereis command to find its location, I get the following output  adnan@adnan-laptop:~$ whereis meld meld: /usr/bin/meld /usr/lib/meld /usr/share/meld /usr/share/man/man1/meld.1.gz   Is there any way to change the install location. Lets say if I want to install it in /usr/local/ can I do it using apt-get or aptitude? I know I can compile it from source and specify prefix option to configure script or make install but it would be better (and really easier) if I could do it using apt-get as I would be able to use uninstall, upgrade and other stuff that apt-get offers Path bar missing in file dialog after running software updater for Ubuntu 17.04 After running software updater, the path bar in the file dialog (for example the one you get when choosing Open File in in Google Chrome or Firefox) is missing. This is frustrating since it's no longer possible to copy a path from the terminal (for example) and paste it into the file dialog. Here is a screenshot of the dialog:     How can I get back the path bar?