Number of vertices after taking out an edge from a tree
Graph theory: Tree holds two sub-tree with an amount of vertices
I accidentally committed an unwanted file (filename.orig while resolving a merge) to my repository several commits ago, without me noticing it until now. I want to completely delete the file from the repository history.   Is it possible to rewrite the change history such that filename.orig was never added to the repository in the first place? ATI Radeon HD 7770 no GPU rendering? What's is the origin of Orbital Angular Momentum of electrons in atoms? Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with the probability of finding it being maximum a radial distance $R$ (=Bohr radius) away from the nucleus. This helps explain why the electron does not radiate EM radiation while in the atom.  But, with this understanding, I do not understand the source of the orbital angular momentum. Is it intrinsic like the spin? I'd like to show that, given to hermitian operators $A,G$ on a Hilbert space $\mathscr{H}$, the following identity holds: $$ e^{iG\lambda}A e^{-iG\lambda} = A + i\lambda [G,A] + \frac{\left(i\lambda\right)^2}{2!}[G,[G,A]]+\ldots+\frac{(i\lambda)^n}{n!}\underbrace{[G,[G,[G,\ldots[G}_{n\ times},A]]]\ldots]+\ldots $$ where $\lambda$ denotes a real parameter and $[\ \!,]$ indicates the commutator.  This is a proof left to the reader by Sakurai in his books on Modern Quantum Mechanics. How do I make an object face the mouse position, but only on one plane? How to Logout of an Application Where I Used OAuth2 To Login With Google? GDAL HDF4 Driver on Linux System I'm running code that works with MODIS HDF4 datasets on a Debian Linux distribution.  I am also running this code on a Windows machine.  On both the Windows and the Linux machines, I have the most recent GDAL version (gdal 1.11.1, np19py27_1), however on the Linux machine, GDAL doesn't seem to recognize HDF4 Drivers... it won't load or process any of the HDF4 datasets that are easily processed on the Windows machine (unfortunately this machine doesn't have enough space to run the full code).  Has anyone else encountered this problem?  Do I need to install an additional module on the Linux system? What is the easiest way to duplicate an activerecord record? I want to make a copy of an ActiveRecord object, changing a single field in the process (in addition to the id).  What is the simplest way to accomplish this? I realize I could create a new record, and then iterate over each of the fields copying the data field-by-field - but I figured there must be an easier way to do this. Perhaps something like this:  new_record = Record.copy(:id) Best way to find all factors of a given number Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form I need to express $$1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb  + \frac{1}{n + 1}\binom{n}{n}$$ in a simplified form.  So I used the identity $$(1+x)^n=1 + \binom{n}{1}x + \binom{n}{2}x^2 + \dotsb   + \binom{n}{n}x^n$$ Now on integrating both sides and putting $x=1$.  I am getting $$\frac{2^{n+1}}{n+1}$$ is equal to the given expression.But the answer in my book is  $$\frac{2^{n+1}-1}{n+1}.$$ Where does that -1 term in the numerator come from? Based  I'm trying to setup Tomcat Server, I have successfully installed it and tested it. Then I stopped it as recommended in the tutorial. I'm setting up "New Server Runtime Environment" as you can see under Tomcat Installation Directory is a windows directory, anyone knows the Ubuntu directory equivalent for this? Thanks. Increasing spacing between section number and title in the table of contents I'm using the simple ordinary \tableofcontents command to produce a table of contents, and I find that the resulting spacing between the section number and the section title is too small:    Can someone tell me how to fix this, please. My documentclass is memoir, if that matters. Why Cooper or Dr. Brand can't send message? I know that the Windows copy dialog (in Windows&nbsp;XP) stores the copy in memory first, and it is still copying after the dialog closes, so the time is off, but why is the estimation of the time it will take to make a copy so inaccurate, even when memory copying has been disabled (in Vista and Windows&nbsp;7)? It seems so arbitrary! How does the whole copy procedure work, and why can't Windows estimate it correctly? I just try to visualize some points using GeoServer to publish them as WMS and bind this WMS to my Openlayers website using the GeoServer internal Heatmap process to visualize it. I don't want to use the Openlayers Heatmap function.   But there seem to be some problems, look here:    I'm using this Openlayers implementation to bind my WMS URL:    Changing the params to:  params: {'LAYERS': 'test:points','TILED': true,'STYLES': 'heatmap'},   And using this as SLD to define the Heatmap:    Any ideas why this happens? What is the shape of a black hole? I was thinking; what shape does a black hole have?. By 'Shape', I mean its form (e.g, circle , cylinder, sphere, torus, etc..).  We usually think of black holes as if they're plugholes (e.g, a flat circular object), but what if they're spherical? A spherical black hole would make much more sense. I would imagine than a black hole shaped like a basketball would be capable of pulling more mass towards it than a flat one, as it has a higher surface-to-volume ratio to do so.  Edit I know that it's probably a sphere, but when you think about it, a cylinder could also be a potential shape. Is there evidence that adding salt to water prior to boiling can damage a stainless steel pan? I am trying to ask a question on SE, have some mock data in Excel I've copied, and am simply trying to paste in to my question.  I've done this before dozens of times, but suddenly am having this issue.  However, when I do so, I get prompted to upload an image. (This happens with Ctrl + V and also right click --> Paste):    Am I overlooking something?  Edit: Playing around, I can copy from Firefox/browsers and Word, and paste in to the box as usual. Excel seems to be the only one giving the issue so far.  Edit2:  are still having this issue. I recall being somewhat impressed by a novel I read a few years back – this book may be less than five years old – which featured a college-aged man.  He had a laptop which transformed into a troll goblin that served as his familiar.  In the story's universe, mages had switched to the Internet for most of their magic &amp; communication.  The main character was essentially a magical hacker, and spent much of the book fighting against his evil aunt (I think, I know it was a female relative) with the help of his cousin.  Older forms of magic were also featured, including using special paintings as magical portals, and spells being whistled by wizards.  It features a scene at a gas station where the laptop is disabled by a virus, and the main character whistles a spell to reanimate dinosaurs from the gasoline.  Is this ringing any bells? Mongodb: Possible to enlarge a capped collection? If a collection is created as capped, is it possible to increase the cap without losing data?  Or to increase the cap without recreating the whole collection?  Thanks