Count & sum no. of occurrences of each unique line in a file
sum pair of columns based on matching fields
A symmetry of graph $X$ is a permutation of the vertices that also happens to be a permutation of the induced edges. In particular, the distances between vertices are preserved by a symmetry. Show that the set of symmetries of $X$ is a permutation group of $\operatorname{V}(X)$. Compute the cycle index of the group for the Petersen graph.   Alright I am super confused. I have no idea how to even start. Can someone point me in the right direction. How do I show that something is a permutation group? How do I compute the cycle index of a graph? How do I delete files that are locked when no other app can delete them? So I found out that I had a Trojan on my external hard drive. My anti-virus app killed it, but it has created a bunch of random files on my computer which cannot be deleted. These are image files. They cannot be renamed - using any method - nor can they be moved, cut, copied, permanently deleted or even opened (in any program).  How can we rid these files from our system?  I have tried:   Right-click > Delete Shift+Delete (Permanently Delete) Swearing   and then:   FileASSASSIN from MalwareBytes Eraser program sdelete program several commands in cmd   but none of them have been successful. How can I completely obliterate these files? How do I check if an integer is even or odd? Java - Splitting a CSV file into an Array Why isn't the gamma function defined so that $\Gamma(n) = n! $? $$  \lim_{n\to\infty} n^{1/2} \int_{0}^{1} \frac{1}{(1+x^2)^n}\mathrm{d}x=0 $$  Is my answer correct? But I am not sure of method by which I have done. Can others in my party go through TSA PreCheck? If I have  (i.e. I have a KTN from TSA and the "pre-check" logo gets printed on my boarding pass) and a travel companion does not, can they go with me through the PreCheck security lines? This is assuming that the travel companion is booked in the same reservation on the same flights and is also a U.S. citizen and not on any no-fly or otherwise increased scrutiny lists.  I'm guessing the answer is no, but I haven't seen anything from TSA specifically addressing this. What is the advantage to crushed garlic over minced garlic beyond texture? I use a lot of garlic in my cooking, especially minced garlic.  But lately I've been doing some more recipes with crushed garlic and while I love the texture of cooked garlic, I can't see how it could be better than minced garlic for the overall taste.  Is there an advantage to crushed garlic over minced garlic, beyond texture? I have a simple cylinder which is mirrored on both the X and Y axis.  When I scale it along the X axis, the two halves of the cylinder overlap, rather than scale as it would before the mirror modifier was applied:    I haven't used Blender in a while and I know this is a simple fix. In the first half of Tenet, there is a scene where The Protagonist and Neil break into Freeport and find a glass wall with bullet holes (could only find a good photo with Christopher Nolan in it):  In the next scene, we find out that these bullet holes were caused by an inverted armed man entering the room (exiting the room from their perspective) and reverse-shooting the glass, which removes the bullet holes from the future-facing perspective. This all makes sense, but raises a question: how long were the bullet holes there in the first place? Were they in place as soon as the glass was installed, possibly years ago? Or even back when the glass was manufactured? Snap entire selection to the 3d cursor in edit mode Is there any way to snap an entire selection to the 3d cursor in edit mode?  Shift+S > Selection to Cursor snaps each individual vertex to the cursor, so the shape is lost: In an alternating current, do electrons flow from the source to the device? If electrons in an alternating current periodically reverse their direction, do they really flow? Won't they always come back to the same position? Distance between two hyperplanes I have two parallel hyper planes $$a^Tx=b_1,a^Tx=b_2$$ where $a \in \mathbb{R}^n, x \in \mathbb{R}^n ,b \in \mathbb{R}$ and I want to find the distance between the two. I have read that the distance between the two hyperplanes is also the distance between the two points $x_1$ and $x_2$ where the hyperplane intersects the line through the origin and parallel to the normal vector $\vec a$. These points are given by $$x_1=\frac{b_1}{\|a\|^2_2}a$$ and $$x_2=\frac{b_2}{\|a\|^2_2}a$$ Then the distance is $|x_1-x_2|$ but I don't really understand how we got $x_1$ and $x_2$. Is Ubuntu based on Debian unstable or Debian testing? which of the two it is? ST_Length (GEOM, true) for calculating distances in Geographic Reference System Clock displays incorrect time I've just installed 64-bit Ubuntu 11.04 and after I updated it, the clock stopped displaying the right time. It's now 8 hours behind my normal time. I've checked the Time and Date settings and the Location field is correct. What's even weirder is that the time displayed in Time and Date Settings adjusts itself after a few seconds and is correct. The time displayed in the task bar remains the same, however.  Any ideas? One of the answers in a reading exercise in my class today was:   100,000,000,000,000,000,000   ... which was the value of the highest denomination note ever issued. It was a 100,000,000,000,000,000,000 Pengo note, issued by Hungary in 1946. The students in my class wanted to know how they could say that last sentence in words in English. So I told them that I didn't know. They pointed out to me that if they wanted to read this bit of writing to someone they'd want to be able to use the words. Fair point.  Can anyone help?  [In case you're interested, a 100,000,000,000,000,000,000 Pengo note was worth about $0.20!] Springer llncs TOC not working Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$ I'm trying to prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$ I showed that both $n,m$ divides $nm/\gcd(n,m)$  but I can't prove that it is the smallest number.  Any help will be appreciated.