Even Digit Series (2,4,6,8,20,....)
Generating ordered combination of numbers
How come SG-1 couldn't get back to Earth? In Stargate SG-1 S02E16, , SG-1 (Captain Carter, Teal'c and two other members, who replaced Colonel O'Neill and Dr Jackson) is "trapped" on planet in binary system, where second star has risen and is slowly raising temperature - Samantha Carter says, in one moment, that it's going to reach 200°F soon - and dialing device is locked mid-dial. Yet, SGC manages to dial the planet and send them instructions how to repair the device and off-world team makes it back.  Why didn't they come back when Earth first dialed P9Q-281 to contact SG-1? I mean, from my understanding, stargate wormhole is two-directional, meaning it doesn't matter which end it was activated from, yet it seems like it is one-directional from the events of this episode... Our group has determined that buying (almost exclusively) money and points is the way to go.  Most kingdom cards are ignored, or are bought very sparingly. This has lead to games feeling 'samey' and has taken a lot of the fun out for us.  What strategies should we use to counter ""?  Or are house rules needed here? Can't install Oracle Java 8 in Ubuntu 16.04 How can I maintain open ssh connection and use it from shell scripts? Currently i invoke the following:  $ ssh me@host.com my_cmd   This is slow and not easy to automate safely. I would like to establish ssh connection once and have some script that will forward my commands to host.com and print output.  Is that possible ?  Adding my machine to authorized_keys is not an option for me and it wouldn't solve slowness issue. How to add horizontal cylinder at end of cube Limit of some specific "almost Riemann" sums I'm just beginning my journey with calculus, and this problem is giving me hard time.  $$\lim_{n \to \infty} \sum_{k=1}^n \frac{k}{{n^2+k}}$$  I calculated first three sums: $$\frac{1}{2}, \frac{16}{30}, \frac{117}{220}$$ From that I guessed that the limit is $$\frac{1}{2}$$. The hard part, though, is proving it.    I reckon that the squeeze theorem should be used here, but I can't seem to find anything useful. (The only sequences I was able to figure out give me limits of 1 and 0, so it's not something I can use)  Maybe you guys can give me some ideas or theorems that can be of use here? I know that this problem could be probably solved using some more advanced calculus techniques, but I'm not familiar with derivatives and integrals yet, and this problem is in the limits section of my problem book, so I'm not supposed to use anything more advanced. OGR DXF to KML conversion Linux ACL behaviour: settings the mask changes 'ls' output, but not actual permissions It might be the time of night, but this is puzzling me. Picture the following.  [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x  3 root root     4096 Feb  9 21:53 . drwxr-xr-x 25 root root     4096 Feb  9 21:54 .. drwxr-x---  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# setfacl -m m::rwx foo [root@node1 acltest]# getfacl foo/ # file: foo # owner: root # group: testuser user::rwx group::r-x mask::rwx other::---  [root@node1 acltest]# ls -la . total 24 drwxr-xr-x   3 root root     4096 Feb  9 21:53 . drwxr-xr-x  25 root root     4096 Feb  9 21:54 .. drwxrwx---+  2 root testuser 4096 Feb  9 21:53 foo [root@node1 acltest]# su - testuser [testuser@node1 ~]$ cd /acltest/foo/ [testuser@node1 foo]$ ls -la . total 16 drwxrwx---+ 2 root testuser 4096 Feb  9 21:53 . drwxr-xr-x  3 root root     4096 Feb  9 21:53 .. [testuser@node1 foo]$ touch bar touch: cannot touch `bar': Permission denied   In words: I create a directory foo, with mode 0750, root as owner and testuser as the group. (testuser is the private group of testuser, but that doesn't matter.)  The getfacl command correctly shows no ACL's on this directory and there is not mask yet. The mask will be set accordingly to the group permissions if I would add a named group or user now.  If I explicitly set the mask to rwx now, the group permissions as shown by ls change too. I know it happens the other way around (the mask changes when the group permissions change), but this seems puzzling.  The more puzzling because the getfacl output does not show the group permissions as rwx but - as said - ls does.  Which one is right? Apparently, the output of getfacl is right, because testuser cannot write to foo. As expected, by the way, because I did not grant the testuser group any permissions to do so.  It goes on. I cannot allow the testuser group write permissions on foo by just using chmod. I have to explicitly set an ACL using setfacl -m g:testuser:rwx foo to allow testuser to finally touch foo/bar.   Can someone explain the rationale behind the difference in the outputs of getfacl and ls? I know it can be tricky to have normal permissions go together with ACL's, but this seems plain wrong. (Though I expect to be missing something glaringly obvious ;))  I have already seen Local server updates for the network I have setup one computer on our network as the file server. Because Internet here in Tanzania is both slow and expensive I would like that one system to download all the updates and then the other 10 computers on the network to get those update files from the server. I'm a bit of a noobie to Ubuntu, but really want to learn how to get this working smoothly so as to help other NGOs and schools here in Tanzania. Brendon Create instance of generic type in Java? Does an Enlarge/Reduce spell on a druid affect the beast form if the druid Wild-Shapes? If a druid (multiclassed into sorcerer) casts Enlarge on himself so that he becomes a Large humanoid (approximately twelve feet tall), and he then Wild Shapes in a brown bear, is the brown bear form normal size or doubled in all dimensions? What could cause a toilet to leave the flapper up and keep running? I have an American Standard toilet I installed last year. I don't know much about plumbing, but I was able to install this toilet. It seems to function okay, except for what I think is a mechanical problem.  Sometimes when the toilet is flushed, the flapper doesn't close and water keeps running.  The handle feels like it's slightly stuck in the up position.  I looked inside the tank once when it was doing this, and the chain attached to the handle was slack. I don't understand why the flapper isn't closing.  I've tried putting more slack in the chain and loosening the plastic nut that holds the handle on the toilet, but it doesn't seem to be helping.    How can I fix this? Am I being scammed by a sugar daddy? How do I get rid of this unwanted bar from Eclipse? Standard error of a ratio I have a linear regression and two estimates, say A and B and their standard errors. I need to find the standard error of a ratio A/B [or A/(1-B)].  I guess the main problem is that I don't know the correlation between A and B. I also guess that makes this unsolvable, since the correlation plays a major role. Is this correct?  If I knew it, what would be the way to calculate the standard error? Lagrangian of an effective potential If there is a system, described by an Lagrangian $\mathcal{L}$ of the form   $$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$   where $T$ is the kinetic energy and $V$ the potential energy, it is also possible to define the total energy $E$ of the system   $$ E = T + V =\frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) - \frac{k}{r}.\tag{2}$$  If the angular momentum $M$ is defined by $$ M = m r^{2} \dot{\phi},\tag{3}$$ then $E$ can be written as  $$ E = \frac{m}{2}\dot{r}^2 + \underbrace{\frac{M^2}{2mr^2}-\frac{k}{r}}_{V_\textrm{eff}\left(r\right)},\tag{4}$$  where the last two terms are written as new, "effective" potential $V_\textrm{eff}\left(r\right)$.    In addition, using the definition of $M$, the Lagrangian $\mathcal{L}$ can be written as  $$ \mathcal{L} = \frac{m}{2}\dot{r}^2 + \underbrace{\frac{M^2}{2mr^2}+\frac{k}{r}}_{-V_\textrm{eff}\left(r\right)},\tag{5}$$  where the sign of $V_\textrm{eff}\left(r\right)$ has been changed, since $\mathcal{L} = T-V$. But from this argument, it appears that there are two different possible ways to construct the same effective potential. This seems to me contradictory. Where is my mistake? Does the proof of Bolzano-Weierstrass theorem require axiom of choice? DMed for the first time yesterday and one of the things I feel I need to sort out, among other comments, improvements, and similar, is how combat itself is actually initiated. The main example I want to use involves  attempting to generate surprise conditions by players. Here the characters have entered a ruined city and generally been noisy about the whole thing - using a spell to make their voice louder and literally ask if there is anyone about. Any enemies around probably know what something is about to kick off but arguably don't know precisely what. After resting the PCs head up a long flight of steps to a temple on the edge of the city. At the top only one crests and finds 3 bandits lounging around, chatting, and doing whatever bandits do in their spare time. After a brief exchange of pleasantries a combat starts:  DM &quot;The bandit spits in your direction 'we're not done looting the temple, so you can clear off', and starts raising his crossbow as his mates emerge from their cover behind the pillars... PC &quot;I cast Firebolt at Bandit Keith&quot; DM &quot;Hang on, I hadn't finished, everyone rolls for initiative...  Which sparked a debate about whether or not the PC could preemptively cast/attack before the combat starts by &quot;instant actioning&quot; (as above) as I was describing the start of the combat. As far as the bandits are concerned a lone half-elf who is pretty heavily armed has popped up in front of them, not even tried to be diplomatic, and ended up saying something rather suggestive about their mothers. The PC then asked about it being &quot;surprise&quot; because the bandits wouldn't necessarily expect an attack, but my view of &quot;surprise&quot; is closer to an ambush where one party is unaware of the other's existence. (This precise example is close to how  works, however this specific PC was always the first of the party to go into rooms (only one with darkvision) and consistently felt they should get free rounds at the start of combat based on declaring attacks before I could &quot;start&quot; the combat.) The second example the party came to more bandits, who were not alert immediately, in an underground room. They used magic to yell something obscene at the bandits and shut off all the torches so the bandits were effectively blinded. At this point they wanted to burst into the room casting spells, swinging maces, and playing some &quot;meaty chords&quot; (the bard's words, not mine). Again they wanted surprise arguing that, despite the fact that the bandits were yelling and cursing in confusion, they couldn't be sure they were actually being attacked as such. In the end a character with darkvision wanted to sneak in to a corner and again wanted surprise based on passing stealth rolls, so they would start the &quot;combat&quot; by firing a crossbow. At that point I think I relented because it was clear that they would do anything to try and win combats in a single round. In a nutshell, my question is: &quot;how liberally can the concept of surprise be applied to combat - is it only when one party is literally unaware of a threat (as I read the rules), or just when they are caught slightly off guard by the exact situation?&quot; NB I already plan to address the attempts at interrupting descriptions with actions next session, because it happened at other times and actually threw me off quite a bit. I am trying to compile a list of the different ways to come up with the closed form for the sum in the title. So far I have the famous Gauss story, the argument by counting doubletons, and using generating functions. Is there any other (significantly) different way to discover the closed form?  To clarify, Gauss's method was to take $1+2+3+\dots+n$, write it backwards, and add it up. I am new to the amsart document class. For some reasons \author (etc..) is not showing after I use \maketitle. This is my tex:  \documentclass[12pt,reqno,a4paper]{amsart}  \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{mathrsfs}  \usepackage{amsthm}  \usepackage{latexsym}  \usepackage{pictexwd} \usepackage{pdftricks} \usepackage{natbib} \usepackage{setspace} \usepackage{color} \usepackage[affil-it]{authblk}  \begin{document}  \title{Temptation, Asymmetric information and Committment}  \author{Mark}  \affil{University of Leicester}  \date{February 2014}  \maketitle  \begin{abstract} To be written \end{abstract}  \section{introduction}  ...  \end{document}   and this is the output:   can anybody help me out?