What Java library would you say is the best for consuming and parsing feeds? Requirements:   Embeddable Supports Atom &amp; RSS Has caching architecture Should be able to deal with any feed format the same way   (Please: one suggestion per answer.)
I'm using Java, and need to generate a simple, standards-compliant RSS feed. How can I go about this?
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6. I read the following two sources and I think I understand the structure of proofs involving WOP, but I am stuck on the open-ended part where you prove P(n-1) for the  following problem:    Use the well-ordering principle to show that n^3 - n is divisible by 6.    Any help would be greatly appreciated!   Note: After factoring out (n-1)^3 - (n-1) it took the form of n^3 - 3n^2 + 2n and the only difference between that and n^3 - n is "3n^2 - 3n" which I proved was divisible by 6 via induction. Is there a better way to solve this problem?  Edit: , post is useful however I not supposed to use induction for the main part of the proof. I want to add CaseComment and CaseHistory related list to my visualforce page.   &lt;apex:relatedList list=" " /&gt;  What should be the value for List attribute in the code defined above. When I added   &lt;apex:relatedList list="CaseHistory" /&gt; 'Histories' is also not working   &lt;apex:relatedList list="CaseComment" /&gt; 'CaseComments' is also not working  I get errors saying they are not valid child relationship name for entity Case.  Please help me out on this issue. Is the universe finite or infinite? Which is easier, pushing or pulling? It is generally assumed, from a person's perspective, that pushing a cart is more easier than pulling one. But why? Is there any difference in terms of force required to achieve the same amount of displacement?  Or is it merely human perception?  Why is it that almost all automobiles transfer torque to the back axle. But then, why do trains have engines in the front? Images can be pushed outside the boundaries of a post by using nested lists A   B   C   D   E   F             I don't even know. It just seemed weird.  Yes, I understand I could just avoid doing something like that. But the problem already exists with a single level.   Consider having 2 images in a post. Both exceed the maximum width of a post. One is nested in a list. Key to this issue is that my original images were much larger. They were automatically resized.  Image    List      I think it looks weird. Where does the word "torsion" in algebra come from? How to tail multiple files using tail -0f in Linux/AIX I tried tailing two files using the option:  tail -0f file1.log -0f file2.log   In Linux I see an error "tail : can process only one file at a time".  In AIX I see the error as "Invalid options".  This works fine when I use:  tail -f file1 -f file 2   in Linux but not in AIX.  I want to be able to tail multiple files using -0f or -f in AIX/Linux  multitail is not recognized in either of these OS. Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$ Let $(v_n)_{n \geq 1} \in \ell ^2$ be a fixed bounded sequence of real numbers. Define a mapping $T$ on $\ell ^{\infty}$ using the formula $$T(a_1, a_2,...)=(v_1a_1,v_2a_2,...), \, \, \, \, \, x=(a_1,a_2,...) \in \ell^{\infty}$$  We can use the fact that, $Tx \in \ell^2 $ for every $x \in \ell^{\infty}$ and $T: (\ell^{\infty},||\cdot ||_{\infty}) \rightarrow (\ell^{2},||\cdot ||_{2})$ is a linear operator.  Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$ for all $x \in \ell^{\infty}$    Here is what I tried:  $||Tx||_2 = \bigg( \sum v_k^2 a_k^2 \bigg)^{1/2} \leq (||x||_{\infty}^2 \sum v_k^2 )^{1/2}= (||x||_{\infty}^2 ||(v_k)||_2^2 )^{1/2} = ||(v_k)||_2 \cdot ||x||_{\infty}$  Is this OK? So this homework question is in the context of $\mathbb{R}$ only, and we are using Lebesgue measure.  The sum $A+B$ is defined to be $A+B=\{a+b|a\in A,b\in B\}$. The question is: If $m(A),m(B)&gt;0$, is it necessarily the case that $A+B$ contains an open interval?  This question is quite annoying, since it is quite difficult to calculate the sum even after you construct an example. However, it seems like no matter how I constructed a set of positive measure, there is a region that have a lot of point in it (yet this region is not necessarily dense). This suggest that when summed up, the holes should be covered up somehow and thus there would be an open interval, and so the answer is yes. Sorry for a rather vague idea, but I'm just not sure what to do with this problem. I have a feeling that somehow topology would have a way to capture precisely the idea above about a region with a lot of point.  (also, I think my middle school teacher mentioned this once, and I remembered the answer to be yes; but that is quite a while ago though)  Thank you. Any help will be appreciated.  EDIT2: So Camilo's answer is gone. I am looking at the convolution method right now. Because the convolution is continuous, if it is nonzero I am done. But then there is no guarantee that the convolution is nonzero even if $x\in A+B$. I still need help with this direction. Can someone give me some hints?  EDIT: Camilo's answer below essentially suggest the method of getting 2 open interval from regularity theorem, one cover a subset of A and one cover a subset of B such that the sum of the measure of these two subset is bigger than the measure of the larger interval. user99680's answer point to a wiki which show a method that essentially simply acquire an open set. After some thinking, I believe that these method simply can't be made to work. I constructed this example in the hope that it would convince you that it is the case:  Let $I_{0},I_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is nonzero and $m(I_{n})=9^{-n}$ and all of them are inside $[0,2]$. Let $J_{0},J_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is at least $3$ and $m(J_{3n})=m(J_{3n+1})=m(J_{3n+2})=\frac{m(I_{n})}{3}$. Let $O=\bigcup I_{n}$ and $H=\bigcup J_{n}$. Construct $A\subset O$ such that $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$. Construct $B\subset H$ such that $m(B\bigcap J_{n})=\frac{3m(J_{n})}{4}$. Now if you apply Camilo's method, it is possible that your $I$ would be one of the $I_{n}$ above, and your $J$ is one of the $J_{m}$ above. No matter which $I_{n},J_{m}$ you have, the argument does not work. Rewrite $m=3q+r$ where $0\leq r\leq 2$. If $q&lt;n$ then $m(J_{m})&gt;m(I_{n})$ so the longer interval have length $\frac{m(I_{q})}{3}$; $m(A\bigcap I_{n})$ is at most $\frac{3m(I_{q+1})}{4}=\frac{m(I_{q})}{12}$ and $m(B\bigcap J_{m})=\frac{3m(J_{m})}{4}=\frac{m(I_{q})}{4}$. Thus $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. If $n\geq q$ then $m(I_{n})&gt;m(J_{m})$ so the larger interval is of length $m(I_{n})$; $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$ and $m(B\bigcap J_{m})$ is at most $\frac{3m(J_{3n})}{4}=\frac{m(I_{n})}{4}$. Once again $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. Hence the Camilo's argument does not work. user99680's method does not work either, since you get $O$ and $H$ which is even bigger than any interval. On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity.  And I've read that the net electron drift is slow.  But electricity travels through the wire, essentially at c, and I want to understand that mechanism.  My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail.  Here's my conception, I'm hoping someone will fill in the holes, ha ha.  An electron moves into the wire.  It's got a kinetic energy.  After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell.  That electron then presumably does the same.  If this conception is simply wrong, please enlighten me.  The questions that arise:   Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way? If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be?  I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible? Why should a photon emitted by an electron be in the direction of travel?  Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction?  If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling. What is the mechanism by which electrons propagating increase the temperature of the material?  Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?  Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon.  By how much is this slower than light, and what is the speed of each interaction? How to add a modifier to a collection? My goal is to reduce the faces of an object using the decimate modifier. The object I'm editing has lots of vertex groups. Blender 2.8 only lets me add the decimate modifier to a single group at once which would take quite some time. I have already put all groups in a single collection.  How can I add the decimate modifier to the entire collection?  Do I have to add the modifier group by group? Though tangentially related to another post on MathOverflow (), the questions below are mainly out of curiosity. They may be very-well known ones with very well-known answers, but...    Suppose $\Sigma$ is a sigma-algebra over a set, $X$. For any given topology, $\tau$, on $X$ denote by $\mathfrak{B}_X(\tau)$ the Borel algebra over $X$ generated by $\tau$.     Question 1. Does there exist a topology, $\tau$, on $X$ such that $\Sigma = \mathfrak{B}_X(\tau)$?   If the answer to the previous question is affirmative, it makes sense to ask for the following too:     Question 2. Denote by ${\frak{T}}_X(\Sigma)$ the family of all topologies $\tau$ on $X$ such that $\Sigma = \mathfrak{B}_X(\tau)$ and let $\tau_X(\Sigma) := \bigcap_{\tau \in {\frak{T}}_X(\Sigma)} \tau$. Is $\Sigma = \mathfrak{B}_X({\frak{T}}_X(\Sigma))$?   Updates. Q2 was answered in the negative by Mike (). Implement a Selective Comment Ban When I installed my SSD I just mounted with discard and didn't sweat it. However today I was reading about the pros and cons of using fstrim instead and decided to run the program to get an idea of how long it would actually take (still with my partitions mounted with discard). The command took several minutes on both my root and home partitions. For my home partition I used -v and got this:  $ sudo fstrim -v /home /home: 137494052864 bytes were trimmed   This is more than the amount of free space on the partition!  $ df -h /home Filesystem      Size  Used Avail Use% Mounted on /dev/sda2       206G   78G  118G  40% /home   Subsequent runs finish in less than a second, eg:  $ sudo fstrim -v /home /home: 0 bytes were trimmed   Surely if I have always had the partition mounted with discard, fstrim should not trim a large amount of data like that? The discard option is definitely enabled, here are the relevant fstab lines:  UUID=xxxxxxxx...    /          ext4   noatime,discard,errors=remount-ro  0      1 UUID=xxxxxxxx...    /home      ext4   noatime,discard,errors=remount-ro  0      2   And mount output lines:  /dev/disk/by-uuid/xxxxxxxx... on / type ext4 (rw,noatime,discard,errors=remount-ro,stripe=128,data=ordered) /dev/sda2 on /home type ext4 (rw,noatime,discard,errors=remount-ro,stripe=128,data=ordered)   The SSD is a TOSHIBA THNSNS256GMCP. Why does this happen? What packages do people load by default in LaTeX? I'm getting the impression from reading the answers written by some of the real experts here that there are quite a few little packages that just tweak LaTeX2e's default behaviour a little to make it more sensible here and there.  Rather than try to pick these up one by one as I read answers to questions (and thus risk missing them), I thought I'd ask up front what LaTeX2e packages people load by default in (almost) every document.  As this is a "big list" question, I'm making it CW.  I don't know if there are standard rules across all SE/SO sites for such questions, but on MathOverflow the rule is generally: one thing (in this case, package) per answer.  I guess that if a couple of packages really do go together then it would be fine to group them.  This is perhaps a little subjective and a little close to the line, so I'll not be offended if it gets closed or voted down!  (But please explain why in the comments.)  Also see our community poll question: Website display problem - across all browsers whenever I go to  or  the page loads like this:    How can I fix this? Benchmark (hash rate) for SHA-3 (SHAKE128) To estimate the time for brute-force attack we need to compute keyspace size divided by hash rate, where the hash rate (hash/second) varies depending on the computer's capabilities.  The website  shows the hash rate for different computers.  Can you explain the following two confusing phenomena?   The hash rate decreases as the message size increases. Core i3 has a higher hash rate than Core i7 for SHAKE128. How to automatically restart a linux background process if it fails? Import PLY doesn't display vertex colors I'm trying to import a .PLY mesh in Blender. I've troubles with colors: the mesh appear in a grayscale palette. Other softwares open it correctly (eg. MeshLab).  This is the header of the PLY file:  ply format binary_big_endian 1.0 comment created by Geomagic Sculpt Exporter. element vertex 182488 property float x property float y property float z property uchar red property uchar green property uchar blue element face 364980 property list uchar int vertex_indices end_header   Any tips? Thanks! 0 ram free on ICS I'm new to the ICS os, coming from Gingerbread from another phone. The phone's quite nice and fast when I first used it, but just this morning it started exhibiting weird actions. Camera360 doesn't open up automatically when I click it, the Camera closes for no reason, Pocket restarts when an article has an image, and TTPod resets the song to the previous song on my widget in the middle of a new song I'm playing.  I checked out the ram, and and was surprised to see 500+ mb used, 0 mb available. I looked at the list of programs and I see the usual culprits like Facebook, but the ram they're using doesn't add up to 500+ mb. Yeah, I know that the whole ram indicated isn't usable by the apps, but I don't think I've done anything to warrant the 0 mb. I close my apps. There are times when there's free 4 to 5 mb, but I think that too shouldn't be the case. I tried installing Advance Task Killer, it listed less than 10 apps, killed it, still the ram is what it is above.   I did a reboot, and now it reads 300+ mb usage, 200 something free.   What can I do? How do I ensure an app's closed on ICS? I installed GoLaucher because it has a handy task killer and I can see the ram freed in an instant, but I would like to know if there's a better way to handle the RAM.