Why do Dwellers return from the Wasteland by themselves?
Dwellers return automatically after finding a low amount of items in Wasteland
Chromatic Number The smallest number of colors needed to color a graph $G$ is called its chromatic number, and is often denoted $\chi(G)$.  Show that if graph $G$ is simple, then $$ \chi \ge \frac{V^2}{V^2 - 2E}. $$ Are C++ enums signed or unsigned? And by extension is it safe to validate an input by checking that it is &lt;= your max value, and leave out >= your min value (assuming you started at 0 and incremented by 1)? Can I revert to the Mountain Lion style labels instead of Mavericks tags? How? Counting and rasterizing polygon overlaps in ArcGIS Desktop? How do you take a vector layer with overlapping polygons and turn it into a raster where each cell counts the number of polygons containing that cell?    We are looking at polygons of fire burn areas between 1976 to 2000 and want to see how many fires would be contained in each raster cell. How to create individual chapter PDFs from included TeXs? My document structure has   one file with preamble (i.e. MainTex) and around 75 individual .tex files (i.e. Chapter_01, Chapter_02, ..., Chapter_75) representing each chapter.   I am using \include command to create a one big PDF file, the output is MainTex.pdf. Life is all good up to this point.   If I have to create individual PDF for each chapter then do I need to run 75 times with each chapter name and rename the PDF manually to match to chapter name. Because if I include only Chapter_01 and run it creates PDF named as MainTex.pdf.  Is there a way I can automate this workflow? Object rotate in a strange way today i run into another problem. i dont know how i have done it (probably i clicked sth what i should not click) - anyway - since that moment my objects are behaving totally different when i try to rotate them. the objects are now rotating around the pivot point but they keep their alignment - not sure if i am clear. eg. if u would rotate a plane which is lies flat on the ground it makes the rotation but the faces of the plane would still be up and dont which shouldn't be the case with the "normal" rotation that i know. so i want to understand what i have done (because this kind of rotation could be also usefull sometimes for me) and how can i return it in the case it happens again. In The Dark Knight Rises, at the beginning of the film Bane kidnapped a guy from the plane, then he drew blood from the guy he kidnapped. And then throughout the movie I didn't see any news regarding this kidnap scene. But, before the end of the movie we find out that the guy kidnapped by Bane was Dr Pavel. Bane needed him to convert the fusion project into a nuclear bomb and Dr Pavel was the only guy who could have done it.   But I don't understand, why did he draw blood from Dr Pavel? Suppose we are in $\mathbb R^n$. What can we say about the sign of $\Delta u(\vec x)$ if u($\vec x$) has a local max/min at $\vec x$? I've tried looking at the reverse of the second partial derivative test and it seems to suggest that $\Delta u(\vec x) \leq 0$ if $\vec x$ is a min and $\Delta u(\vec x) \geq 0$ if $\vec x$ is a max. However, I'm not convinced of this result. Can somebody point me towards a statement (theorem, etc.) involving the above. I appreciate the help. bash is not terminating I'm trying some things with my shell. This includes the following command:  kill $$  My expectation was that the shell would log me out and terminate itself. But instead the bash persists without change.   Any idea why?  I ran this command on different environments (archlinux, debian). The behavior was always the same. Why is the well ordering principle counter-intuitive? I read  that while 'The Axiom of Choice agrees with the intuition of most mathematicians; the Well Ordering Principle is contrary to the intuition of most mathematicians'. I don't understand why this is so. According to Wikipedia, 'the well-ordering principle states that every non-empty set of positive integers contains a least element'. This is quite a straightforward definition. Is it the way you derive the equivalence of the Axiom of Choice and well ordering principle that makes it counter-intuitive or the definition of the least element? How to format a USB drive? Possible Duplicate:             How to format a pen drive in Ubuntu? I have this pen drive which I made bootable using some other system (OS). But I need to format it from my Ubuntu 12.04. Please guide me. On thanksgiving day a woman posted in a facebook group that her father had just passed away (left her money) and in good deed because it was thanksgiving she was offering to pay people’s debts. Well I inboxed her and she pretty much wants me to open up a bank account with First Tech Credit Union and give her my log in and password info. Ofcourse its sketchy!   So I questioned her and asked why she wanted that instead of her sending me the money directly from her bank to mine. She then responded because she wants to keep records of my debts. (She asked for proof and I sent her screenshots ONLY of my outstanding balances) I heard about the depositing checks scam so I questioned her about how she would deposit the funds and she said cash.  Her facebook page is 100% legit, I screenshotted her pics and family profiles etc. We came to an agreement that I would only accept her help if she sends me a picture of her ID before me sending this info.   She literally just wants to deposit the money to me, She isn’t asking me to send nobody money from that account or anything. Of course the account will be empty when I provide it to her. When she does deposit the money I am planning to immediately change the password and obviously stay watching my account activity while she deposits the funds.   She actually also provided pics of other accounts she funded. My question is, is this a scam? And if so how could she possibly scam me? Specially if i have her information and A pic of her ID. She is a christian lady and looks like she has a good heart, We talked about my struggles and she actually looked into why I needed to be assisted with the money. By no means was she pushy or anything. I want to believe that she just wants to help me but I am also too skeptical. How do I parse command line arguments in Java? Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$ Duplicate:    I want an pseudo random number generator that can generate numbers with no repeats in a random order. For example: random(10) might return 5, 9, 1, 4, 2, 8, 3, 7, 6, 10 Is there a better way to do it other than making the range of numbers and shuffling them about, or checking the generated list for repeats?  Edit: Also I want it to be efficient in generating big numbers without the entire range.  Edit: I see everyone suggesting shuffle algorithms. But if I want to generate large random number (1024 byte+) then that method would take alot more memory than if I just used a regular RNG and inserted into a Set until it was a specified length, right? Is there no better mathematical algorithm for this. I run a large bulletin board and I get spammers every now and again. My moderation team does a good job filtering them out but every time I IP ban them they seem to come back (I'm pretty sure it's the same person on some occasions, as the post patterns are exactly the same as are the usernames) but I'm afraid to ban them by IP address every time.  If they are on a dynamic IP address, I could be banning innocent users later down the line when they try to get to my forum through SERPs, but if I ban only via static IPs I know that I'm only banning that one person.  So, is there a way to properly determine if an IP address is static or dynamic?  Thanks. How do I use variables in a sed command? I tried the following code to replace QQ with ZZ, but it doesn't do what I want:  var1=QQ sed -i 's/$var1/ZZ/g' $file   However, this code does what I want:  sed -i 's/QQ/ZZ/g' $file   How do I use variables in sed? The quotient norm on $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$. I try to show that the norm on the quotient space $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$, where $x = (x_n)_{n \in \mathbb{N}} \in \ell^{\infty} (\mathbb{N})$. My attempt is the following:     By definition, the quotient norm $\| \cdot \|_{\ell^{\infty} / c_0}$ is defined as   $$ \| x + c_0 (\mathbb{N}) \|_{\ell^{\infty} / c_0} = d( x + c_0 (\mathbb{N}), 0 + c_0 (\mathbb{N}) ), $$   which can be re-written as    $$ \| x + c_0 (\mathbb{N}) \|_{\ell^{\infty} / c_0} = \inf \{ \| x + y \|_{\infty} \; | \; y \in c_0 (\mathbb{N}) \}. $$   Since $0 = (0,0,...) \in c_0 (\mathbb{N})$, it follows that   $$ \| x + c_0 (\mathbb{N}) \|_{\ell^{\infty} / c_0} \leq \| x \|_{\infty} = \sup_{n \in \mathbb{N}} |x_n|. $$   I thought about using Bolzano-Weiserstrass' Theorem at a certain point, but I am not sure how to obtain the wished equality from here.    Any help is appreciated. Thanks in advance. Sum of the series:$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\cdots$ I have a question where i couldn't find any clue. The question is  $$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\frac{1\cdot3\cdot5}{1\cdot2\cdot3\cdot4\cdot5\cdot6}+\cdots$$  I could get the general term as $t_n=\frac{1\cdot3\cdot5\cdot7\cdots(2n-1)}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdots2n}$  I have also tried it to form the sequence in the telescopic form.But couldn't get. Any hint will be appreciated. Energy-momentum tensor transformation I've been trying to find how the energy-momentum tensor changes if we add a total derivative to the lagrangian: $$L\to L+\mathrm d_\mu X^\mu.\tag{1}$$   From the answer key:  $$T^{\mu\nu}\to T^{\mu\nu}+\partial_\lambda F^{\lambda\mu\nu}\tag{2}$$ Where $$F^{\lambda\mu\nu}=\frac{\partial X^\lambda}{\partial(\partial_\mu\phi)}\partial^\nu\phi -\frac{\partial X^\mu}{\partial(\partial_\lambda\phi)}\partial^\nu\phi.\tag{3}$$ Is the above answer right? I'm not able to get this result! any help?