Light from an incandescent lamp
How is light emitted by an incandescent lamp
How to replace a string with a string containing slash with sed? I am looking for a way to replace a string in a file with a string that contains a slash by using sed.  connect="192.168.100.61/foo" srcText="foo.bar=XPLACEHOLDERX" echo $srcText | sed "s/XPLACEHOLDERX/$connect"   The result is:  sed: -e Expression #1, Character 32: Unknown option for `s' Zsh get terminfo keys with modifiers I am rendering my scene with only one sample but all the renders of the same picture have a different seed value. How can I combine them correctly? I wrote a java-program that loads all the images and takes the average pixel color for each pixel of the images. Is that a correct way of combining the images? It doesn't reduce the noise very much so I am not happy with it. What can I do? Suppose we have a set $S$ of real numbers. Show that   $$\sum_{s\in S}|s-x| $$   is minimal if $x$ is equal to the median.    This is a sample exam question of one of the exams that I need to take and I don't know how to proceed. Grep: The asterisk (*) doesn't always work If I grep a document that contains the following:  ThisExampleString  ...for the expression This*String or *String, nothing is returned. However, This* returns the above line as expected.  Whether the expression is enclosed in quotes makes no difference.  I thought the asterisk indicated any number of unknown characters? Why does it only work if it's at the start of the expression? If this is intended behavior, what do I use instead of the expressions This*String and *String? Why would spacetime curvature cause gravity? It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place? What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$? How to get Steam to recognize existing game files from a different source? Let's say I have a game bought on retail/other digital download and installed on my hard drive. I buy the same game (or a minor variant of it, say the GOTY edition) on Steam. It should be possible to use the existing installation to avoid the generally big downloads. This is very useful as it saves both bandwidth and time.   Previously, as far as I understood, Steam downloaded the game files directly to steam\steamapps\common\&lt;game_name&gt;. Since this folder would be created on starting the download, pausing and closing steam, copying the game files to this folder and then validating game files would make Steam absorb as much as possible and just download the missing files.  Currently, Steam downloads the files to steam\steamapps\downloading\&lt;game_id&gt; and then moves them over to the aforementioned folder once the download finishes. So first of all, what the final folder would be is not clear. So what would be the correct way of doing the same thing, that is, make steam use as much of the existing files as possible? Should the files be copied to downloading\*\, or should I figure out the actual folder (say via googling) and copy the files to steamapps\common\*\?  More specifically, I had a retail copy of Arkham City installed and I just bought the GOTY version on Steam. Now I tried both of the above things, in either case, the validating does not seem to do anything. Assuming I have the correct folder name steamapps\common\Batman Arkham City GOTY, according to , if I copy the files there, Steam seems to just continue with its 17GB download. If I copy it to steamapps\downloading\200260 then the download keeps stopping every few seconds with "Disk Write Error" after modifying 1 or 2 files, and I have to keep hitting resume. Launching an Applet fails? No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$. For some reasons, homomorphism is a very hard area for me to make improvements. I've been hitting the brick wall for almost 2 hours.   Prove that no homomorphism exists from $Z_{16}\oplus Z_2$ onto $Z_4\oplus Z_4$.  Assume a homomorphism $\phi$ exists from $Z_{16}\oplus Z_2$ onto $Z_4\oplus Z_4$. Then $\phi$ is an isomorphism.  Note that the $\left | \ker \phi \right |=2$ The $\ker \phi$ is also a normal subgroup for $Z_{16}\oplus Z_{2}$. We want possible normal subgroup of order 2. I.e., 2 elements in each normal subgroups.  By Lagrange's theorem, the order of each element in a group divides the order of a group so the possible order of the elements are 1 or 2. If the elements has order 1, then the Ker \phi cannot have 2 elements.  Hence, $\ker\phi$ = $\left \{ (0,0),(8,0) \right \}$ ,$\left \{ (0,0),(0,8) \right \}$,$\left \{ (0,0),(8,1) \right \}$, possibly.  By the First isomorphism theorem:  $\phi: Z_{16}\oplus Z_2 \rightarrow Z_2\oplus Z_2$  $\Psi: G/\ker \phi \rightarrow \phi\left ( Z_16\oplus Z_2 \right )=Z_2\oplus Z_2$  $g\ker \phi  \mapsto \phi(g)=\Psi(g\ker \phi)$  Any help is appreciated.  Edit: I know that $(2,0)$ has order $8$ in $Z_{16}\oplus Z_{2}$ but any elements in $Z_{4}\oplus Z_{4}$ does not have order $8$ which would have solved the question at the outset. But I would like a different route. What are the recommended textbooks for introductory calculus? Reasons why not to update an Ubuntu version to a newer/older kernel version How do I pack textures for sending off to a render farm Whenever i try to send a project off to a render farm such as sheepit, it says it needs the textures packing with the file in order to render correctly.  How would I do this? What is a suitable word to describe a place where two rivers meet? I've googled for a while and on some sites I've found the word "watershed" as the proposed word. Is it the word that best suits it? Screen resolution stuck at 1024x768 If $A=\left( \begin{array}{ccc} 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 1 \\ 1 &amp; 0 &amp; 0 \end{array} \right)$, find the rank of $A+A^2+A^3$  We have $\rho(A+A^2+A^3)\leq\rho(A)+\rho(A^2)+\rho(A^3) $ where $\rho(A)$ means rank of A.  Here $\rho(A)=3.$ Also $\rho(A^2)=3$ and $\rho(A^3)=3$  as $\det A\neq 0$ and $\det(A^2)=\det(A)\det(A)\neq 0$ and so on.   But how to get the desired result. Every convergent sequence in a metric space has a unique limit. Is there a \subsubsubsection command? I could do \subsection{} and \subsubsection{} but not \subsubsubsection{}. This command does not seem to be available in LaTeX. Is there an alternative command? I just installed a fresh Ubuntu 12.04 (Precise Pangolin).   I noticed that, there is no screensaver settings, which is fine. I like to control the period of time after which the blank screen is shown,which automatically locks the screen.  I do not want to enable screensaver. I only wish to be able to change the idle time period required to lock the screen automatically. It seems to me, it is by default around 10-15 minutes. To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$ How can I show   $\lim_{n \to \infty} a_n = 0$  $a_n = {1.3.5 ... (2n-1)\over 2.4.6...(2n)}$  I have shown that $a_n$ is monotonically decreasing. I thought to shown sequence is bounded from below then it automatically would converge and hence my question will be solve. But I'm unable to show its boundedness... Or there maybe another method to prove this. Thanks