Scoping problem?
Variable scoping in Module
Quantum Entanglement - What's the big deal? Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement?  I used to think I understood it - that 2 particles, say a light-year apart spatially, could affect each other physically, instantly.  Here I would understand the "big deal".  On further reading I've come to understand (maybe incorrectly) that the spatially separated particles may not affect each other, but in knowing one's properties you can infer the other's.  If that it the case, I don't see what the big deal is... 2 things have some properties set in correlation to each other at the point of entanglement, they are separated, measured, and found to have these properties...?  What am I missing? Is it that the particles properties are in an "un-set" state, and only when measured do they get set?  (i.e. the wave-function collapses).  If this is true - why do we think this instead of the more intuitive thought that the properties were set at an earlier time? I live &amp; work in the UK.  Having pretty much exhausted all of the avenues I can find for saving (none of which have great returns anyway at the moment, obviously), I have recently started looking to buy my first house.  I have a reasonable sum saved up for a deposit, but I'm wondering what to do with that in the mean time, as a fair amount of it is not currently earning any interest. For the moment, I have put any surplus, that I'm not earning interest on into premium bonds, just in the off-chance that I win something with it, but this is obviously more of a lottery than an investment, and I'm not 'expecting' to win anything noteworthy with it.  Ideally, I would like to buy a house within the next year or so, so investing in the stock market is not really an option, as I understand the commonly accepted advice is that you invest with a minimum 5 year horizon.  What other options do I have for any surplus cash while I look for a house? Discontinuous derivative. Could someone give an example of a ‘very’ discontinuous derivative? I myself can only come up with examples where the derivative is discontinuous at only one point. I am assuming the function is real-valued and defined on a bounded interval. How do I work with the Card Layout in the NetBeans GUI builder? Sturm-Liouville Questions In thinking about Sturm-Liouville theory a bit I see I have no actual idea what is going on.  The first issue I have is that my book began with the statement that given  $$L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  the problem $L[y] \ = \ f$ can be re-cast in the form $L[y] \ = \ \lambda y$.  Now it could be a typo on their part but I see no justification for the way you can just do that!  More importantly though is the motivation for Sturm-Liouville theory in the first place. The story as I know it is as follows:  Given a linear second order ode   $$F(x,y,y',y'') = L[y] = a(x)y'' + b(x)y' + c(x)y = f(x)$$  it is an exact equation if it is derivable from a differential equation of one order lower, i.e.  $$F(x,y,y',y'') = \frac{d}{dx}g(x,y,y').$$  The equation is exact iff  $$a''(x) - b'(x) + c(x) = 0. $$  If $F$ is not exact it can be made exact on multiplication by a suitable integrating factor $\alpha(x)$.  This equation is exact iff  $$(\alpha(x)a(x))'' - (\alpha(x)b(x))' + \alpha(x)c(x) = 0 $$  If you expand this out you get the Adjoint operator  $$L^*[\alpha(x)] \ = \ (\alpha(x)a(x))'' \ - \ (\alpha(x)b(x))' \ + \ \alpha(x)c(x) \ = 0 $$  If you expand $L^*$ you see that we can satisfy $L \ = \ L^*$ if $a'(x) \ = \ b(x)$ &amp; $a''(x) \ = \ b'(x)$ which then turns $L[y]$ into something of the form  $$L[y] \ = \ \frac{d}{dx}[a(x)y'] \ + \ c(x)y \ = \ f(x).$$  Thus we seek an integratiing factor $\alpha(x)$ so that we can satisfy this &amp; the condition this will hold is that $\alpha(x) \ = \ \frac{1}{a(x)}e^{\int\frac{b(x)}{a(x)}dx}$  Then we're dealing with:  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \alpha(x)f(x)$$  But again, by what my book said they magically re-cast this problem as  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ \alpha(x)c(x)y \ = \ \lambda \alpha(x) y(x)$$  Then calling  $$\frac{d}{dx}[\alpha(x)a(x)y'] \ + \ ( \alpha(x)c(x)y \ - \ \lambda \alpha(x) )y(x) \ = \ 0$$  a Sturm-Liouville problem.  My question is, how can I make sense of everything I wrote above? How can I clean it up &amp; interpret it, like at one stage I thought we were turning our 2nd order ode into something so that it reduces to the derivative of a first order ode so we can easily find first integrals then the next moment we're pulling out eigenvalues &amp; finding full solutions - what's going on? I want to be able to look at $a(x)y'' \ + \ b(x)y' \ + \ c(x)y \ = \ f(x)$ &amp; know how &amp; why we're turning this into a Sturm-Liouville problem in a way that makes sense of exactness &amp; integrating factors, thanks for reading! There's a story my grandpa use to tell me when I was younger, about the sole survivor of of an attack on a mining vessel in space. The man lives in space for months/years, ignored by the company he worked for and never rescued. Then when he thinks he is being rescued, it's actually another set of raiders who attack him and kidnap him.  He then wakes up in captivity in some sort of prison inside of an asteroid, and has a word tattooed on his forehead. My grandpa called him Ronin (that's what the tattoo on his forehead said) but I don't know what the character's real name is. Anyways, he learns that he has the ability to teleport after having a brush with death and decides to make his way back to Earth so that he can exact revenge on the mining company who abandoned him and left him floating to die.  Does anyone know what this story or book may be? My grandpa told it to me when I was little, he said that he got it from a book he use to love reading when he was younger. I'm assuming the book is very old (possibly pre 1940's as he was born in the 20s). I can't ask him as he is no longer alive. I'm also unsure as to whether or not all the details in the story he told me, are the same as in the original. Let $f : \mathbb{R}^n → \mathbb{R}_∞$ be a function and let $C ⊂ dom f$ be a convex set.  $$**Part I**$$ Prove that $f$ is a convex function if and only if $f$ is convex over every line $L_{v,x_0}$ where $L_{v,x_0} := \{x_0 + tv : t \in \mathbb{R}\}$.  i.e. f is convex iff when restricted to any line, it be convex on that certain line.  So essentially to handle this proof I need to show that convexity for $f$ holds when its convex over any arbitrary line, and on the converse it does not hold when $f$ is not convex over that arbitrary line. If $f$ is convex then,  $$\forall x,y \in C, a \in [0,1]$$ it holds that $$f(ax+(1-a)y) \leq af(x) + (1-a)f(y) \space \space\space\space\space\space\space\space\space\space\space\space (1)$$  EDIT: $$**Part II**$$  Let $f : \mathbb{R}^n \to \mathbb{R}_∞$ be a function.   I want to prove that $f$ is convex over the line $L_{v,x_0}$ iff $\psi : \mathbb{R} \to \mathbb{R}_∞$  $\psi(t) := f (x_0 + tv)$, is convex over $I (x_0, v )$.  where $L_{v,x_0}:= \{x_0 + tv : t ∈ \mathbb{R}\}$, and $I(x_0,v):=\{t \in \mathbb{R} : x_0 + tv \in C\}$  Any help is very much appreciated How to get more info out of the uninformative Windows 8 BSOD? Getting attributes of Enum's value Setting up PyCharm to reference ArcPy? How would I setup  to recognize import arcpy?   I'd like to use PyCharm to develop and debug geoprocessing tool. Solve for $x$: $2^x=4x$ Given that $x$ is a positive integer. By using methods of trial and error as well as plotting two lines: $y=2^x$, $y=4x$ on a graph and find their intersection point, we can easily solve for $x$ which is equal to 4. However, I do not know how to solve this using only equation. Can anyone help me? This is a follow-on from my  about samples from a distribution.  Suppose $X_1 \ldots X_{n-1}, X_n$ are random variables all following some fixed distribution $D$. How do I prove that $P(X_n &gt; X_1 \wedge \ldots \wedge X_n &gt; X_{n-1}) = \frac{1}{n}$ (this is true intuitively and experimentally). I've just updated to 11.10 and now my embedded terminal in gedit does not match my default terminal. I hate looking at a white and black terminal. Does anyone know how to make the embedded terminal match the default terminal?  This is a screenshot:    I want my embedded terminal in gedit to match my default terminal. Crash adding comment Empty Disk when trying to install dual-boot system I recently purchased an SSD to speed up my computer experience. Before, I had Windows 7 and Ubuntu in a dual-boot system. The plan was to install Windows 8 on the SSD and then set aside ~30GB for the system files of Ubuntu.  I installed Windows 8 just fine on the SSD, then I booted the Ubuntu install CD to make my partitions like always - but GParted tells me the entire SSD is unallocated. Now I am afraid I will lose my Windows installation if I try to do anything to it.  Why does GParted think there is no partition on the SSD? Shouldn't it be 4 Partitions, like the Windows installer told me?  And is it possible to ignore this and install Ubuntu on the hard disk (where it, frankly, already is) and somehow make it possible to install GRUB on the SSD to revert my dual-boot system without damaging the installed Win8? Removing all \n\r characters from a node XSLT? wondered if you could help me please? I have node in xml that is as followed  $LOG: 08880xbpnd $ fhdsafidsfsd df sd fsd f sd fsd  I was wondering is there anyway to make all the text go on to one line so that it then can be passsed through to a javascript function? so it would turn out like this   $LOG: 08880xbpnd $fhdsafidsfsddfsdfsdfsdfsd What is the best way to convert an array to a hash in Ruby In Ruby, given an array in one of the following forms...  [apple, 1, banana, 2] [[apple, 1], [banana, 2]]   ...what is the best way to convert this into a hash in the form of...  {apple =&gt; 1, banana =&gt; 2} How long do seasons last? In the Kittens Game, how long (in real life minutes) do seasons last? What is the function of the "Sticky edges" on/off setting in displays? I have installed Ubuntu 12.04 (Precise Pangolin). If I open System Settings &gt;&gt; Displays there is a new (?) on/off button for a setting named Sticky edges.  Can someone tell me what this setting is supposed to control? Design simulates perfectly but won't work on FPGA