Idempotent elements on the quotient ring
Lifting idempotents modulo a nilpotent ideal
I was browsing through the apt folder to try my proxy settings and I was unable to find the apt.conf file in Ubuntu 11.04. Is there any alternative file for it?  Adding proxy settings to 99-synaptic in apt.conf.d does not help as it gets overwritten everytime I restart the system. Suppose $a_n \ge 0$ for all natural numbers $\Bbb{N}$ and $\sum{a_n}$ converges. Is it necessarily true that $\sum{(a_n)^2}$ converges?  I think yes.  Clearly as $a_n \ge 0$ it follows $(a_1+a_2+\dots+a_n)^2 \ge a_1^2+a_2^2+\dots+a_n^2 \ge 0$ and so $(\sum_{n=1}^{\infty}{a_n})^2 \ge \sum_{n=1}^{\infty}{a_n^2} \ge 0$.  As we are told $\sum{a_n}$ converges to say $L$ where $L$ is a real number it follows $L^2 \ge \sum_{n=1}^{\infty}{a_n^2} \ge 0$ and so therefore $\sum{(a_n)^2}$ converges.  Is this correct? How can I request a random row (or as close to truly random as is possible) in pure SQL? I've been trying to figure out how to change the chart from scientific notation to just show the 5 digit numbers. I've tried scale and scale ticks with not success.  How can I change the y-axis and data values to show the decimals not in scientific notation?  \begin{tikzpicture} \centering \begin{axis}[     width=300pt,     height=250pt,     axis lines*=left, % Don't display the top and right lines     ybar, % Display it as a bargraph     enlarge y limits={upper,value=0.2},     legend style={at={(0.5,-0.20)}, % -.20 y-axis     anchor=north,legend columns=-1},     ylabel={Densities},     nodes near coords,     every node near coord/.append style={ anchor=mid west, rotate=90},     symbolic x coords={Class1,Class3,Class5,Class7,Class9,Class11,Class13,Class15,Class17,Class19,Class21,Class23},     xtick=data,     xticklabel style={ inner sep=0pt, anchor=north east, rotate=70 },     nodes near coords align={vertical}, ] \addplot coordinates { (Class1,0.0968) (Class3,0.0887) (Class5,0.1452) (Class7,0.0726)     (Class9,0.0403) (Class11,0.0081) (Class13,0.0161) (Class15,0.0000)     (Class17,0.0161) (Class19,0.0081) (Class21,0.0000) (Class23,0.0081) }; \end{axis} \end{tikzpicture} How to calculate information included in R's confusion matrix I want know the formulas for the information highlighted in the confusion matrix in the picture below: Execution of a command locally after ssh tunneling I have a script file ./run_app.sh which contains of the following:  ssh -L 8888:localhost:8888 ubuntu@address ./run_website.sh   # it should be executed locally   but it tries to run the second line on the remote machine. Actually, I want to run it on my pc. Any idea? CDN: How is it possible that my DNS delivers a different IP depending on the visitors location? I found  how a CDN works. But there is one thing I don't really understand. Let's assume I setup multiple DNS servers at my location and they use the nameserver domains dns1.example.com, dns2.example.com and dns3.example.com. This DNS servers are able to deliver a server IP depending on the visitors location (ping, geo database, browser language or whatever). Now I update this nameserver settings for my domain www.example.org at the registry.  Now, the very first request on www.example.org with an expired TTL tries to resolve the domain. It asks:   the local .hosts/DNS, if TTL expired: the internet providers DNS, if TTL expired: the root DNS, if TTL expired: my local dns1.example.com   But if I understand it correct, the new IP is then added to all these nameserver caches until the TTL expires again. So how is it possible to send other IPs to the visitor depending on his location?  In  theandym said the request is "forwarded", but I don't think this is how a CDN works, because "forwarding" means lengthen the transmission way resulting a longer loading time. Or does a CDN require zero TTL for the domain?  Update1 Through  I found  describing how they optimized CDN performance. It did not explain how the CDN works in general, but there were interesting explanations like the following:     Thereafter, whenever a client attempts to fetch content hosted on the   CDN, the client is redirected to the node determined to have the least   latency to its prefix. This redirection however is based on the prefix   corresponding to the IP address of the DNS nameserver that resolves   the URL of the content on the client’s behalf, which is typically   co-located with the client.   This means Google checks at first the latency of all IP prefixes and defines a DNS resolution table (?) for all available prefixes. And if a visitor has the IP 198.51.100.231 the Google server IP is used, that is set for the prefix 198.51.100.0. But again: How does Google's DNS know which IP the visitor is using? Most visitors resolve Google's domain through their internet provider and by that the resolving is done through those external DNS servers or not?  As an additional example: If I start a DNS resolution for the domain facebook.com with different online tools (hosted in different countries) it is resolved to different IPs with different domains like:   31.13.92.36 Reverse: edge-star-mini-shv-01-frt3.facebook.com 31.13.76.68 Reverse: edge-star-mini-shv-01-sea1.facebook.com 31.13.69.228 Reverse: edge-star-mini-shv-01-iad3.facebook.com 157.240.2.35 Reverse: edge-star-mini-shv-01-ort2.facebook.com   After that I thought it could depend on the DNS server location used by the visitor, but I tried my own (Deutsche Telekom, Germany), Google's (8.8.8.8) and a major one from France (Orange) and they all returned for facebook.com the IP 31.13.92.36. Logical volume is not mounted but is in use. Please close all applications using this device (eg iscsi) $\phi \times \theta$ is faithful iff $(|Z(H)| ,|Z(K)|)=1$ for faithful characters $\phi \in Irr(H)$ and $\theta \in Irr(K)$ . I am trying to mount my ext4 (sdc6) partition from a live usb because that's how I deleted two unused partitions left from a prior install of ubuntu, using GParted. The swap is mounted. However, I can't edit fstab, or find anywhere to click in nautilus to mount sdc6. In the terminal, I get the error: "can't find /dev/sdc6 in fstab". I'm afraid to exit the usb and update grub if that partition isn't mounted. Is there any easy way to do this, or do I have to install gksu or some other editor? Or do I need to mount it as sda6?  Device     Boot Start     End Sectors  Size Id Type /dev/sda1  *     2048 3905535 3903488  1.9G  b W95 FAT32  Device     Boot     Start        End   Sectors   Size Id Type /dev/sdc1            2048   29362175  29360128    14G 27 Hidden NTFS WinRE /dev/sdc2  *     29362176   29566975    204800   100M  7 HPFS/NTFS/exFAT /dev/sdc3        29566976  487023432 457456457 218.1G  7 HPFS/NTFS/exFAT /dev/sdc4       487024638 1250263039 763238402   364G  5 Extended /dev/sdc5       728393728  740290559  11896832   5.7G 82 Linux swap / Solaris /dev/sdc6       487024640  728391679 241367040 115.1G 83 Linux  Partition table entries are not in disk order. Newtonian mechanics: massless particles Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$ This problem is from a practice exam I was working on.     What is the cardinality of the quotient $\mathbb{Z}[x]/(x^2-3,2x+4)$ ?   Thoughts. If I find a ring that is easier to handle then this then I can go from there. So I think this is isomorphic to $\mathbb{Z}_2[x]/(x^2-3,x+2)$. And then I am stuck.  Am I correct so far? What should I be looking to do from here?  Thanks for your time and your answers. Low output volume What's the difference between fit and fit_transform in scikit-learn models? I'm a newbie to data science, and I do not understand the difference between the fit and fit_transform methods in scikit-learn. Can anybody explain simply why we might need to transform data? What does it mean, fitting a model on training data and transforming to test data? Does it mean, for example, converting categorical variables into numbers in training and transforming the new feature set onto test data? What is the difference between #include  and #include "filename"? In the C and C++ programming languages, what is the difference between using angle brackets and using quotes in an include statement, as follows?   #include &lt;filename&gt;  #include "filename" Find the sum of $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$ User cards are no longer showing reputation or badges across the network If I run history, I can see my latest executed commands.  But if I do tail -f $HISTFILE or tail -f ~/.bash_history, they do not get listed.  Does the file get locked, is there a temporary location or something similar? Why did the Star Trek writers decide Warp 10 would be infinite? From  onward,  has a basically cubic scale from warps 1 - 9. But then, close to warp 10, it suddenly develops its own puzzling scale, as can be seen in .  In this scale, , occupying all points in the universe simultaneously and therefore effectively teleporting instantaneously.  My question is why have this confusing scale? Why not have a uniform cubic scale? Was there ever any "official" explanation for this?  Clarification: I'm looking for why the writers decided on this, not the "in-universe" explanation. Question 1: Let $x,y \in S$ such that $x\sim y$ if $x^2 =y^2\pmod6 $. Show that $\sim$ is an equivalence relation.    This is what I tried: Reflexive: $x^2\pmod6 = x^2$  implying $x\sim x$ Symmetry: suppose $x\sim y$, then  $x^2 =y^2\pmod6$ Operating by inverse of $x^2$ both sides we have $e=(x^2)^{-1} y^2\pmod6$ Then I have $y^2=x^2\pmod6$, hence $y\sim x$ I would like to get some corrections up to here because am not sure with this     Question 2. Find the orbits of the given permutation:    $$v:\mathbb{Z}\to\mathbb{Z}\quad\text{ defined by }\quad v(n)=n+3$$   Here is my solution which I would also want somebody to correct me! Let the relation $\sim$ be defined on $\mathbb{Z}$ by $a\sim b$ if $b=a+3$ I consider that the orbits of $v$ are the classes of $\mathbb{Z}$ with respect to $\sim$ given by  $\{b\mid b=a+3\}$. Thus I get only three orbits which are $\{1,4,7,10,…,3n-2\mid n\in \mathbb{Z}\}$, $\{2,5,8,…,3n-1\mid n\in \mathbb{Z}\}$, and $\{3,6,9,…,3n \mid n\in \mathbb{Z}\}$.