My nikon d3100 has broken flash... what can I use to replace it, externally?  I just want something small and lightweight, as fill flash. I have a large external flash unit, but it's HEAVY. Thanks! Claudia
I have read a lot about the SB-800/SB-900 but I am on a low budget (around ~120$). Is there an external flash that I can have to start learning to use it? I do not need TTL compatibility so it can be an older model. I have a Nikon D5000.
Do citizens migrate closer to their workplace within the town? By using the Path tool (F2, 7) I have found some laborers walking very long to eat at home or to warm up in winter.  If I build a house close to a Quarry or a Mine, will Stonecutters or Miners move automatically to this house to avoid long walking distances between the workplace and home?  Or can I assign some citizens to houses closer to their workplace? Prove for any $a&gt;1$ there exist a natural number, $N$, such that $a^n&gt;n$ for all $n \ge N$  My attempt:  By definition, for $N$ to be a natural number $1\le N \le ∞$ for any integer $N$.  By induction, the base case $n=1$ is true because $a^1&gt;1$ which is true.  Now assume that $a^k&gt;k$ is true, then it is also true for $n= k+1$.  Hypothesis  $a^{k+1}&gt;k+1$  Now I am not sure if I am on the right track I am stuck in a question where energy conservation is failing and momentum conservation is correct. I think I might be doing something wrong, that's why I'm asking this question. The problem is as follows:     A bullet of mass $25\,g$ is fired horizontally into a ballistic pendulum of mass $5.0\,kg$ and gets embedded in it. If the centre of pendulum rises by a distance of $10\,cm$, find the speed of the bullet.   (H.C. Verma, Centre of Mass, Q47)     Let the mass of the bullet be $m=25\,g$. Let the mass of the pendulum be $M=5\,kg$. Let the peak height be $h=0.1\,m$. Let the initial and final velocities be $u$ and $v$ respectively.  Method 1: (Momentum Conservation)  $$mu=(M+m)v \implies v=\frac{mu}{M+m}\\ \text{Also, }\frac{1}{2}(M+m)v^2=(M+m)gh\\ \implies u^2=2\biggl(\frac{M+m}{m}\biggr)^2gh\\ \implies u=201\sqrt2 \text{ m/s}$$  Method 2: (Energy Conservation)  Since both the masses move together after the collision, and because the velocity at highest point is null, therefore: $$\frac{1}{2}mu^2=\frac{1}{2}(M+m)v^2=(M+m)gh\\ \implies u^2=2gh\biggl(\frac{M+m}{m}\biggr) \implies u=\sqrt{402}$$    To summarize myself, I am curious about the following: Why do the results differ? Shouldn't the energy be conserved as well as the momentum? Since it should be, then what is the flaw in my calculations? I am writing a small matrix library in C++ for matrix operations. However my compiler complains, where before it did not. This code was left on a shelf for 6 months and in between I upgraded my computer from debian etch to lenny (g++ (Debian 4.3.2-1.1) 4.3.2 ) however I have the same problem on a Ubuntu system with the same g++.  Here is the relevant part of my matrix class:  namespace Math {     class Matrix     {     public:          [...]          friend std::ostream&amp; operator&lt;&lt; (std::ostream&amp; stream, const Matrix&amp; matrix);     } }   And the "implementation":  using namespace Math;  std::ostream&amp; Matrix::operator &lt;&lt;(std::ostream&amp; stream, const Matrix&amp; matrix) {      [...]  }   This is the error given by the compiler:     matrix.cpp:459: error: 'std::ostream&amp;   Math::Matrix::operator&lt;&lt;(std::ostream&amp;,   const Math::Matrix&amp;)' must take   exactly one argument   I'm a bit confused by this error, but then again my C++ has gotten a bit rusty after doing lots of Java those 6 months. :-) Set value of textarea in jQuery I am attempting to set a value in a textarea field using jquery with the following code:  $("textarea#ExampleMessage").attr("value", result.exampleMessage);   The issue is, once this code executes, it is not altering the text in the textarea?  However when performing an alert($("textarea#ExampleMessage").attr("value")) the newly set value is returned? I'm trying to load data from different tables using left outer joins into a QgsVectorLayer. The approach I'm following so far is the one from the developers cookbook . The underlying database is postgres. The query returns correct data, including a geometry column, however I can't figure out how to get the join inside the query to work with . As the table the data come from needs to be specified, is it even possible to do so?  Would approaching the problem using psycopg2 be more suited, and if so, is there a way to create a layer from the result set? The only way I can think of is creating an empty layer and adding each feature individually by looping over the result set. But possibly there is an easier way?  Sadly, using the builtin DB Manager is not an option. The layer has to be added programmatically. Form within a block I'm using drupal_get_form('event_signup_form') to embed my custom form inside a block. The form is being rendered as intended, but submitting the form triggers nothing.  The form function itself is called event_signup_form($form, &amp;$form_state) and the submit function is called event_signup_form_submit($form, &amp;$form_state) but it's not being called.  I am using  to show the form:  function event_block_view($delta = '') { $blocks = array(); if ($delta ...) { $blocks['content'] = drupal_render(drupal_get_form('event_signup_form')); } }   I managed to get this working - here is how (stub):  function hook_block_view($delta = '') { $blocks['content'] = drupal_render(drupal_get_form('event_signup_form')); }  function event_signup_form() { // Register form submit handler, same goes for validation handler $form['#submit'][] = 'event_signup_form_submit';  return $form; }  function event_signup_form_submit($form, &amp;$form_state) { // This is now triggered } Drawing users' attention to unrecoverable actions? How do you programmatically set an attribute? Factorial of 0 - a convenience? If I am correct in stating that a factorial of a number ( of entities ) is the number of ways in which those entities can be arranged, then my question is as simple as asking - how do you conceive the idea of arranging nothing ?   Its easy to conceive of a null element in the context of arrays, for example - so you say that there is only one way to present a null element.   But, in layman terms - if there are three humans $h1, h2, h3$ that need to be arranged to sit on three chairs $c1, c2, c3$ - then how do you conceive of a) a null human, and b) to arrange those ( that ? ) null humans ( human ? ) on the three chairs ?   Please note that referral to humans is just for easy explanation - not trying to be pseudo-philosophical. Three balls to be arranged on three corners of a triangle works just fine. So basically, how do you conceive of an object that doesn't exist, and then conceive of arranging that object ?  So, in essence ... is $0! = 1$, a convenience for mathematicians ? Not that its the only convenience, but just asking. Of course, there are many.  If yes, then its a pity that I can't find it stated like so anywhere.  If not, then can anybody suggest resources to read actual, good proofs ? Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$ Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$.   My approach:   Since $p$ is prime, it is of the form $6k+1$ or $6k-1$. Now if $p$ is of the form $6k-1$ then $(p+1)/2 = 3k$ which is not possible as $3|3k$.   So $p$ is of the form $6k+1$. Now $(p-1)/4 = 3k/2$ so $2\mid k$. So $p$ is of the form $12k+1$. But now, how to prove $k=1$?  Please help! Can you make multiple "if" conditions in Python? How many connected graphs over V vertices and E edges? Is there a way to calculate the number of simple connected graphs possible over given edges and vertices?   Eg: 3 vertices and 2 edges will have 3 connected graphs But 3 vertices and 3 edges will have 1 connected graph  Then 4 edges and 3 will have 4 connected graphs  Till such values...it is easy to see its  V choose E  But what about when the number of vertices are less than number of edges...how to calculate then?  I am not able to visualize that  Can it be a variation of the Stars and Bars problem  Like...number of ways 7 edges(balls) can be connected to (kept in) 5 vertices(bags) such that no vertex(bag) is isolated (is empty)  Here maybe we might have to consider the number of edges twice as each edge needs two vertices... How do I turn off some formats in GeoServer's WMS? I have published a couple of layers on my Geoserver.  To be complaint with the T&amp;C of my data provider, I need to block the access of some of those layers as Vector data. Hence I have already blocked the WFS services on these Layers.  I came to know that even on the WMS service, you can get Vector Data, if you use GeoRSS and some of the .   How do I block GeoRSS, SVG &amp; UTFGrid as formats in the WMS Service? Is there a way to include an entire text file as a string in a C program at compile-time?  something like:   file.txt:  This is a little text file  main.c:  #include &lt;stdio.h&gt; int main(void) {    #blackmagicinclude("file.txt", content)    /*    equiv: char[] content = "This is\na little\ntext file";    */    printf("%s", content); }    obtaining a little program that prints on stdout "This is a little text file"  At the moment I used an hackish python script, but it's butt-ugly and limited to only one variable name, can you tell me another way to do it? In Star Trek canon, what's the range of operation of Transporters? By "range of operation" of the transporter, I mean "distance up to which it could transport" or "distance from which it could transport something to its own location". The range of operation would have increased with time without a doubt but I want to know the average range at any period. It'll be better if you provide full stats of all times. How can I replace a string in a file(s)? Replacing strings in files based on certain search criteria is a very common task. How can I    replace string foo with bar in all files in the current directory? do the same recursively for sub directories? replace only if the file name matches another string? replace only if the string is found in a certain context? replace if the string is on a certain line number? replace multiple strings with the same replacement replace multiple strings with different replacements Inequality between $\ell^p$-norms I would like to add in QGIS real time weather data.  I found this  and this  and I tried to follow the example, but without any success.  I've added a WMS weather data layer for precipitation to the QGIS map, as follows:  First, the parameters for the service:  service = 'crs=EPSG:900913&amp;dpiMode=7&amp;featureCount=10&amp;format=image/png&amp;layers=precipitation&amp;styles=&amp;url=http://wms.openweathermap.org/service'   Next, create the raster layer, specifying WMS as the type:  rlayer = QgsRasterLayer(service, "precip", "wms")   Finally, add the precipitation layer to the map:  QgsMapLayerRegistry.instance().addMapLayers([rlayer])   the example didn't show any error in the code and no data was added to the weather layer either, I'm not sure why? To show that Fermat number $F_{5}$ is divisible by $641$. How can I show that  $F_{5}=2^{2^5}+1$ is divisible by $641$.