Why is energy proportional to light's frequency?
Does a single photon's energy depend on frequency? (photoelectric effect)
$24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement. Well, this is an exercise problem from Herstein which sounds difficult:   How does one prove that if $|G|&gt;2$, then $G$ has non-trivial automorphism?   The only thing I know which connects a group with its automorphism is the theorem, $$G/Z(G) \cong \mathcal{I}(G)$$ where $\mathcal{I}(G)$ denotes the Inner- Automorphism group of $G$. So for a group with $Z(G)=(e)$, we can conclude that it has a non-trivial automorphism, but what about groups with center? I have just had my broadband upgraded to  which means my router has had to change. Previously I was using a Thomson TG585v7 ADSL thingy provided by my ISP. One nice thing about that router was that it would act as a local DNS and allow me to find my other machines on the network by using &lt;hostname&gt;.lan instead of IP addresses.  I've now switched to a Linksys WRT320N ethernet router which connects to my fibre modem, and which I've updated to the latest firmware (1.0.04). I have 2 machines on the network which I regularly want to connect to each other; one is running Windows 7 and the other is running OS X Lion.  The problem I'm having is that I'm unable to connect to my Win7 machine from the OS X machine using the Win7 machine's name. However, I'm able to ping the OS X machine from my Win7 machine using the hostname. BIGINT UNSIGNED value is out of range Is an empty set equal to another empty set? I have a definition that claims that two sets are equal A = B, if and only if:  $\forall x ( x \in A \leftrightarrow x \in B)$  An empty set contains no elements. If I define the sets:  A = $\emptyset$  B = $\emptyset$  then can I conclude that A $\neq$ B? Since they contain no elements? Or would I have to show that an elements exists in one but not the other? To me it seems that these are not equal, but I'm struggling to wrap my head around this.  Thanks, Paul Often assignments (or even papers) have a word count limit. That is not a big deal when using Word, but I don't know how to do that using LaTeX. My solution has been so far to compile the document and then do a rough word count of my pdf file, sometimes even copying the contents of the pdf file and pasting in Word to get a mostly correct Word count.  Is there any tool (maybe even an online tool), package, script or software to do that directly from my .tex document and still get the right word count (i.e., ignore commands, equations, etc)? Prove this inequality $\sum \cos{A}\ge\frac{1}{4}(3+\sum\cos{(A-B)})$ The probability of two dice summing to k is simple enough, make a diagram of the throws,  $$ \begin{array}{c}  &amp;|&amp;1&amp;2&amp;3&amp;4&amp;5&amp;6\\\hline 1&amp;|&amp;2&amp;3&amp;4&amp;5&amp;6&amp;7\\ 2&amp;|&amp;3&amp;4&amp;5&amp;6&amp;7&amp;8\\ 3&amp;|&amp;4&amp;5&amp;6&amp;7&amp;8&amp;9\\ 4&amp;|&amp;5&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}\\ 5&amp;|&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11\\ 6&amp;|&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11&amp;12\\ \end{array} $$  and the probability of a sum is just the length of the corresponding diagonal divided by $36$. For instance, $\mathrm{P}(\mathrm{sum} = 10) = \frac{3}{36} = \frac{1}{12}$. However, it's not as easy to draw a diagram for three dice or more, so how would a general formula look? Can I be automatically notified of prolonged blocking in SQL server? About once a week I have to resolve a blocking chain on a SQL Server 2005 database, caused by a long-lived read lock from an Access 2003 front-end. The lock is taken out whenever a user opens a certain form and is released once the user has finished scrolling through the form or closes it. Since many of our users open this form as reference, these locks stay around for a while. Any update to the table causes the blocking, and suddenly nobody can select from this table since they're all waiting on the first lock. This is quite a problem for us, since lots of apps rely on this data. I understand that this locking behavior is part of how Access works with linked tables.  I've been solving the problem from Activity Monitor,  whenever I find out about it. This is a problem not only because it takes me time to do it manually, but also because it's reactive. By the time I hear about it, it's already been a problem for a lot of people.  I'd like to know if there is an automatic way to check for these long-lasting blocking chains, and either be emailed or have the problem resolved automatically. The logic seems straightforward enough ("if any process matching this SELECT query has been blocking for longer than a minute, notify me/kill it") but I don't know how to implement this with SQL Server.  For what it's worth, I think the proper solution is to fix or rewrite the app. However, due to departmental politics, this is not an option for the next few months, so I'm looking for a stopgap. What does env x='() { :;}; command' bash do and why is it insecure? There is apparently a vulnerability (CVE-2014-6271) in bash:   I am trying to figure out what is happening, but I'm not entirely sure I understand it. How can the echo be executed as it is in single quotes?  $ env x='() { :;}; echo vulnerable' bash -c "echo this is a test" vulnerable this is a test     EDIT 1: A patched system looks like this:  $ env x='() { :;}; echo vulnerable' bash -c "echo this is a test" bash: warning: x: ignoring function definition attempt bash: error importing function definition for `x' this is a test   EDIT 2: There is a related vulnerability / patch:  which uses a slightly different test:  $ env 'x=() { :;}; echo vulnerable' 'BASH_FUNC_x()=() { :;}; echo vulnerable' bash -c "echo test"   unpatched output:  vulnerable bash: BASH_FUNC_x(): line 0: syntax error near unexpected token `)' bash: BASH_FUNC_x(): line 0: `BASH_FUNC_x() () { :;}; echo vulnerable' bash: error importing function definition for `BASH_FUNC_x' test   partially (early version) patched output:  bash: warning: x: ignoring function definition attempt bash: error importing function definition for `x' bash: error importing function definition for `BASH_FUNC_x()' test   patched output up to and including CVE-2014-7169:  bash: warning: x: ignoring function definition attempt bash: error importing function definition for `BASH_FUNC_x' test   EDIT 3: story continues with: I want to filter a java.util.Collection based on a predicate. (I'm going to link to this Stackexchange post concerning Nullary Operations: )  In general an  is a function $f:S^n \to S$, where $n$ denotes the arity of the operation, and a  is a function $f:S^0 \to S$.  It is clear that $S^n=S \times S \times \cdots \times S$ denotes the Cartesian product of a set with itself ($n$ times), however $S^0$ makes little sense to me.  One might define $S^0=\emptyset$. At first glance, that seems like a good choice. However then a nullary operation makes no sense, since it must be a function $f: A \to B$ where $A$ and $B$ are two sets representing the domain and codomain of the function. And note a function is defined in terms of relation, where a relation is a subset of the Cartesian product $A \times B$. So when we think of $A=S^0=\emptyset$ and $B=S$, so that we have a nullary operation $f:\emptyset \to S$, what is a a subset of $\emptyset \times S$? What even is $\emptyset \times S$? By definition of the Cartesian product, \begin{equation} \emptyset \times S = \{(a,b):a \in \emptyset\textrm{ and }b \in S\}. \end{equation} But there exists no $a \in \emptyset$! Therefore there exist no ordered pairs in our Cartesian product! Therefore $\emptyset \times S = \emptyset !$. Remember a function is a relation which is a subset of the Cartesian product. Therefore our relation is the empty set, and therefore also $f=\emptyset$.    Edit: We got the definition sorted out in the comments. Thanks especially to Hayden and Christoff for their great help. In summary, we figured out that $S^0=\{()\}$, the set containing only one element, the "empty $n$-tuple". Then if taking $S=\{1,2,...,k\}$, then a nullary operation $f:S^0 \to S$ is a function, i.e. some subset of $S^0 \times S = \{()\} \times S$. Looking at $\{()\} \times S$, this equals $\{((),1),((),2),...,((),k)\}$. Then a function is a special subset of this, so that each element of the domain (and there is only one element, namely $()$) is paired with exactly one element of the codomain. Therefore a function would have the form $f=\{((),a)\}$ where $a$ is one of $1,2,...,k$. Thank you for your help. Exporting PDF with Hyperlinked Attributes from ArcMap? I'm using ArcGIS 10.1 and would like to export a map to a pdf, preserving feature's attributes. I would like to be able to identify, for example, a point feature from the map on pdf with its underlying features (essentially hyperlink to a document or URL). I know one can export to such a pdf in ArcMap, with an advanced option of exporting features with attributes. I use Adobe Acrobat Pro v.10, and cannot seem to be able to find a way to bring these attributes up.   Is this possible? How to remove the WordPress version from some .css/.js files I know that I can use the following function to remove the version from all .css and .js files:  add_filter( 'style_loader_src', 'sdt_remove_ver_css_js', 9999 ); add_filter( 'script_loader_src', 'sdt_remove_ver_css_js', 9999 ); function sdt_remove_ver_css_js( $src ) {     if ( strpos( $src, 'ver=' ) )         $src = remove_query_arg( 'ver', $src );     return $src; }   But I have some files, for instance style.css, in the case of which I want to add a version in the following way:  function css_versioning() {     wp_enqueue_style( 'style',         get_stylesheet_directory_uri() . '/style.css' ,         false,         filemtime( get_stylesheet_directory() . '/style.css' ),         'all' ); }   But the previous function removes also this version. So the question is how to make the two work together? Are any fictional worlds available in some GIS format? Is there any fictional world (e.g. ,  etc.) which could be used in a GIS context?  For example, an MBTiles archive and a shapefile or any other format usable with OpenLayers / Polymaps / Leaflet? With the enthusiastic question of "Who wants ice-cream?", what is the more correct response?         (Not) I.   (Not) me.      Neither response is a sentence. The first response of "(not) I" sounds stuffy, like it should be followed with an indignant sniff. The second sounds like American idiom and acceptable for casual speech.    What do you say? I have an UTF-8, polish text in .tex file. When I open it with my LEd (LaTeX editor), it shows ok (all characters can be seen). But when I try to compile it, I get error:  Package inputenc Error: Keyboard character used is undefined (inputenc) in inputencoding `utf8'.   I have to copy the text, cut it and paste to Notepad++, change (not convert!) encoding from UTF8 to ANSI (the polish characters will be missed and replaces with some random characters). Than copy it again and paste to LEd (in that editor, characters display bad also). But now I can compile my pdf and in it, the encoding is right again.  Is there a way to set encoding in the way I will see characters in LEd propertly and I will be able to compile it and I will get good characters in pdf?  The begging of my code:  \documentclass[12pt]{report} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{graphicx} \usepackage{amsmath,amssymb,amsfonts} \usepackage{txfonts} I have a question:     Suppose $f$ is continuous and even on $[-a,a]$, $a&gt;0$ then prove that   $$\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$$   How can I do this? Don't know how to start. Correct use of "is" or "are" Possible Duplicate:          Would I use is or are in the following sentence?      The Pohutakawa Coast, Hauraki Gulf, and Waiheke Island is/are the backdrop for our day.   If I rewrote it so the subject (backdrop) starts the sentence, then it seems to me that as it is singular, the verb should be the singular is. But as it is written above, are seems less clumsy. Origin/reason for the expression "on the bus" instead of "in the bus" This is sort of a follow up to my question .  I was told a while ago that the reason why we use "on the bus" instead of "in the bus" is because back in the day buses were open, that is, they didn't have a roof.   Is this story correct or is there another reason why the correct expression is "on the bus", in spite of the fact that when one gets on the bus, he is actually inside the bus?