Prove that group of order 203 is abelian.
Nonabelian semidirect products of order $pq$?
Android app should send edits to edit queue if necessary rather than rejecting them I edited a question, on Stack overflow and when submitting preview, got red bar telling me my account isn't allowed to make suggested edits.  On the Sandbox android question it works fine, but that is editing an answer to my question.   The message I receive is:     Account is not allowed to suggest edits   Are the rules for suggested edits different for Android app? Solve $x^2+2=y^3$ using infinite descent? Why AUC =1 even classifier has misclassified half of the samples? I am using a classifier which returns probabilities. To calculate AUC, I am using pROC R-package. The output probabilities from classifier are:  probs=c(0.9865780, 0.9996340, 0.9516880, 0.9337157, 0.9778576, 0.8140116, 0.8971550, 0.8967585, 0.6322902, 0.7497237)   probs shows probability of being in class '1'. As shown, the classifier has classified all of samples in class '1'.  True label vector is:  truel=c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0)   As shown, classifier has misclassified 5 samples. But, AUC is:  pROC::auc(truel, probs) Area under the curve: 1   Could you please explain to me why it happens? I cannot submit my answer to    I am aware that my reputation is low. Also, spam posting is discouraged.  My answer includes a compilation of Android graphing libraries, with links, so fellow hackers do not have to Google each and every one of them.  I believe this answer is superior to the current answers, because it is updated to 03/2012 and covers more than 90% of all Android charting libraries.  How can I post the answer, or how can I increase my reputation without being able to post quality answers? The old school websites included just a bunch of links to other places, I am an old man!  Alternative solution would be to blog it, and just post a link to my blog, which is not optimal. Find The Last 3 digits of the number $2003^{2002^{2001}}$ Find The Last 3 digits of the number $2003^{2002^{2001}}$  BY number theory or otherwise,   Also i would like to ask is there a property observed in the numbers of the form $k^n$, where for some $k, n$ is varied then the digits of $k^n$ are periodic,  for example,  $2^n$,  its last digit is periodic with period 4, its second last digit is periodic $4\cdot 5 = 20$ its third last digit is periodic with periodic with period $20\cdot 5 =100$  I have observed this property with other numbers as well, though period might vary,for different values of $k$. My passport was detached from the front cover but all the pages are intact. what shall i do? Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form &quot;gravity wells.&quot; Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing? When a PHP application makes a database connection it of course generally needs to pass a login and password. If I'm using a single, minimum-permission login for my application, then the PHP needs to know that login and password somewhere. What is the best way to secure that password? It seems like just writing it in the PHP code isn't a good idea. Insert eps graphics with graphicx (file not found) Approximation algorithms for min vector subset-sum over GF(2) In  vzn asked about the following problem, which I'll call Vector-Subset-Sum.     Given a set of vectors $v_i$ over GF(2) and a target vector $y$, is there a subset of the $v_i$ summing to $y$?   In the answers, comments, and referenced papers I noted   The decision problem is in P. The natural minimization problem (finding the smallest subset) is NP-hard. It's related to the problem of finding sparse codewords in a linear code.   My question is: are there any known polynomial-time approximation algorithms for the minimization problem in (2)? I know very little about coding theory, so there may be some obvious or well-known approximation-preserving reductions to (3) that I have not seen. How many times has the matter in our solar system been recycled from previous stars? I've got a basic understanding of these facts:   The Universe is a little over 13 billion years old.  Our galaxy is almost that old. Our solar system is roughly 4.6 billion years old. The heavier elements (Carbon, oxygen, etc...) are only produced by stars.   When our solar system coalesced, the matter that makes up the planets came from a previous generation of stars.  (Meanwhile our Sun is busy making its own slightly-heavier elements, but those aren't ours.  Those belong to the next "generation" after our star dies.)  So we're all sitting on a rock whose matter was spewed out of a star (or stars) that preceded this solar system. But what I want to know is:  How many cycles of coalescing, fusing, nucleosynthesis, exploding -- and then repeating the cycle -- have this atoms in this ball of rock I'm standing on been through?    How do you know this?  Can you tell by the make-up of the matter in the solar system?  Looking around the Orion arm to see remnants of our former home? Exercise from Atiyah-Macdonald, Chapter 1, 2.iv) Let $A$ be a ring and let $A[x]$ be the ring of polynomials in an indeterminate $x,$ with coefficients in $A.$ Let $f=a_0 + a_1x+\cdots+a_nx^n \in A[x].$ $f$ is said to be primitive if $(a_0,a_1,\ldots,a_n)=(1).$     Prove that if $f,g\in A[x],$ then $f$ and $g$ are primitive $\Rightarrow$ $fg$ is primitive.   I know Gauss lemma holds true for UFDs, but in this case it isn't required $A$ to be UFD: is it possible to drop the assumption, or is some hypothesis missing here? No such file or directory? But the file exists! I've downloaded a game (Shank) but the bin file doesn't run. The error that is shown when I try to launch the executable is:  bash: ./shank-linux-120720110-1-bin: No such file or directory Distance function is continuous in topology induced by the metric The question is (from Topology without tears) that: Let $(X,d)$ be a metric space and $\tau$ the corresponding topology on $X$. Fix $a \in X$. Prove that the map $f:(X,\tau) \rightarrow \mathbb{R}$ defined by $f(x) = d(a,x)$ is continuous.  My first attempt was that let an open ball, $B_{\epsilon}(a)\subset \mathbb{R}$ and show that $f^{-1}(B_{\epsilon}(a)) \subset \tau$. Since $f(x) = d(a,x)$, $f^{-1}(B_{\epsilon}(a))=B_{\epsilon}(a) \in \tau$.   I am pretty sure the last sentence is wrong. I am not sure if every open ball is an open set in topology induced by metric space.  Please give me some hint and direction. Thanks How can I achieve the correct garden tap orientation when threading it in? I'm installing an external tap using a wall plate like this one:    And a tap like this one:    This might be a stupid question, but if I screw the tap into the wall plate it will end up at a certain angle. I can install the wall plate with that angle and the tap will end up with the correct orientation (i.e. pointing down). But what if I want to put another tap in later that has its thread cut slightly differently? How do I prevent it ending up upside-down or whatever? Are all the threads cut exactly the same in these taps?  This seems like a stupid design. Sweave.sty causing error in verbatim environment? I am trying to invite my son (IOS Pocket Edition) to my realms server (mac osx).   I keep getting the response "Could Not Invite The Provided Name" when I try to invite him. His name is all regular characters with no spaces . . . just letters and numbers.  Are the two game types incompatible, and if they are Is it possible to create the same type of 24/7 available server that is only open to him and other invitees like the OSX realms?   Thanks in advance for any clarification. Is it possible to detect a player consuming food items? In my rebuilding project I have counted 18 outlets and lights on one bedroom circuit that travels through 3 rooms. Is that ok? Seven-sided dice from five-sided dice with finite rolls I have a 5-sided dice, and I want to use it to simulate a 7-sided dice. Is there a way to do this with a finite number of rolls?