Lights don't emit anymore
Why are lamps and mesh lights not illuminating anything?
Installing Broadcom Wireless Drivers What are the differences between Generics in C# and Java... and Templates in C++? 1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation:  if $C = A+B$  or  $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = \frac{A}{B}$ $$\frac{\Delta C}{C} = \frac{\Delta A}{A}  + \frac{\Delta B}{B}$$ if $C = A^m$ $$\frac{\Delta C}{C} = |m|\frac{\Delta A}{A}$$   These formulas are derived from the expression for the differential of a function of multiple variables:  if $C = f(A,B)$ $$ dC = \frac{\partial C}{\partial A}dA + \frac{\partial C}{\partial B}dB \Rightarrow \Delta C = \frac{\partial C}{\partial A}\Delta A + \frac{\partial C}{\partial B}\Delta B$$  and I think that makes sense because the value C is just a function of two variables that happen to be measurements.  2) But this morning, I was told that this is wrong and I should actually use these instead:  if $C = A+B$  or  $C = A-B$ $$(\Delta C)^2 = (\Delta A)^2 + (\Delta B)^2$$ if $C = AB$ or $C = \frac{A}{B}$ $$\left(\frac{\Delta C}{C}\right)^2 = \left(\frac{\Delta A}{A}\right)^2  + \left(\frac{\Delta B}{B}\right)^2$$  which are apparently derived from a general formula:  $$(\Delta C)^2  = \left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...$$  or   $$\Delta C  = \sqrt{\left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...}$$  3) So:   Why is this formula better?  Where does it come from? What does it actually represent? (Do I recognize the shape of a norm in that last formula?)  What is wrong with the formula of the differential?   I'm asking a lot, but the propagation of uncertainty always confused the ship out of me. Let $A \in {M_n}$ is nonsingular and each eigenvalue of $A$ is either $+1$ or $-1$.Why $A$ is similar to ${A^{ - 1}}$? Can anybody please help me to prove this:  Let $p$ be greater than or equal to $1$. Show that for the space $\ell_p=\{(u_n):\sum_{n=1}^\infty |u_n|^p&lt;\infty\}$ of all $p$-summable sequences (with norm $||u||_p=\sqrt[p]{\sum_{n=1}^\infty |u_n|^p}\ )$, there is an inner product $&lt;\_\,|\,\_&gt; $ s.t. $||u||^2=&lt;u\,|\,u&gt;$ if and only if $p=2$. No room for a new \dimen Validity of maximising log-likelihood for maximum likelihood estimation For reasons owing to mathematical convenience, when finding MLEs (maximum likelihood estimates), it is often the log-likelihood function---as opposed to the standard likelihood function---which is maximised.  From what I've gathered, this approach is deemed valid as a result of the monotonically increasing nature of the (natural) logarithm function.  My understanding of a monotonically increasing function is: for all $x$ and $y$ (defined on a subset of the reals), if $x \leq y$ then $f(x) \leq f(y)$.  This, however, does not appear to be the case for all log-likelihood functions; for example: for the log-likelihood $\text{Gamma}(3, 5)$ function, if $x = 0.15$ and $y = 0.46$, then $f(x) = -0.59$ and $f(y) = -1.19$.  Clearly, I've misunderstood this concept. Fundamentally, I guess I'm asking can somebody (preferably mathematically) demonstrate why:  $$ \hat{\theta} = \text{argmax} \text{ } L(\theta) = \text{argmax} \text{ } \text{log} \text{ } L(\theta) $$  where $\hat{\theta}$ is the MLE for a given likelihood function. Is there any difference between mapping and function? I wonder if there is any difference between mapping and a function. Somebody told me that the only difference is that mapping can be from any set to any set, but function must be from $\mathbb R$ to $\mathbb R$. But I am not ok with this answer. I need a simple way to explain the differences between mapping and function to a lay man together with some illustration (if possible).  Thanks for any help. Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$ Why does Beamer's table of contents items link to the second slide in a section? When I include a table of contents in a Beamer slide show, each section entry in the TOC ends up linking to the second slide in that section. I would have expected it to link to the first slide. What am I doing wrong?:  \documentclass{beamer}  \begin{document} \begin{frame}{Test TOC}   \tableofcontents \end{frame}  \section{Section 1}  \begin{frame}   \frametitle{Test 1} \end{frame}  \begin{frame}   \frametitle{Test 2} \end{frame}  \end{document}   Just to clarify: when I click Section 1 in the TOC, it takes me to the slide Test 2.  UPDATE: I am actually not sure if it takes me to slide Test 2. When I click the link, the viewer (Evince and Okular) displays most of Test 2, but with a tiny strip of the slide Test 1 visible at the top of the window. I suspect that the viewer may treat the link as pointing to the very bottom of slide Test 1 and then aligns that with the top of the window. Could this be the explanation? When do merchants start paying the actual value of items without bonus effects and perks? How does stuff glow in the dark? Which is the preferred way to convert an Enum to a String in .NET 3.5?   Enum.GetName Enum.Format ToString   Why should I prefer one of these over the others? Does one perform better? Update 2014-04-17 04:47 UTC: Stable, with some odds and ends to clean up      The main MSO/MSE sites are stable, but there are plenty of corners left to sweep. For details, see:    Not all of them mind you, just Meta Stack Overflow into Meta Stack Exchange.  I'll have you know, factually, that we really did believe this would take place in six-to-eight weeks when it was , but we've finally got a tentative date established.  If things go according to plan, we'll begin the operation shortly after 8:30 PM EDT on the 16th, completing everything within a few hour window. Ideally, all service disrupting endeavors will be completed within the first hour, which include:   The availability of Meta Stack Overflow The availability of Stack Overflow (more on this shortly) The availability of Chat on Meta Stack Overflow   As you know, we'll be bolting on a standard issue per-site meta on Stack Overflow, while breaking the link between what will have become Meta Stack Exchange and Stack Overflow. There's some irritable innards in that particular region, so we'll be asking folks to expect the unexpected during the maintenance window. Affected sites will be in and out of read-only mode, or quite possibly just down for maintenance while we're doing the actual break.  I'll be posting a system message on both Meta Stack Overflow as well as Stack Overflow itself 24 hours before we begin the actual work.   Did I say tentative in a six-to-eight-something time frame again? Why yes, I did - we're currently running some tests on the dev tier to simulate the split as closely as possible, so that we can better anticipate quirks that we need to address prior to actually doing it.  Once the sites have actually been stood up functionally on the production tier, we're going to get to work on finishing touches. This will include things like site settings (which determine bits of text you see in the question prompts, rep thresholds, etc) and all sorts of other fine tuning.  Once we're done:   Stack Overflow will have a blank, empty child meta site just like every other site The new Meta Stack Exchange will be up and running All rooms on Chat Meta Stack Overflow will be moved to Chat Meta Stack Exchange  I'll send over about 150 - 200 questions from MSE to MSO, most of which will be tag or SO-specific feature related posts that got buried by the network stuff without resolution.   If the tentative date moves, I'll update this post with the new date. However, we do not anticipate this happening any later than Saturday, April 19 - in the case that we see down time we can't mitigate and need to do it on a weekend.  The ground work is basically done, we're finishing up sanity now with a great deal of confidence, and we're pretty certain that we'll hit between those dates, if not directly on the tentative 16th.  Questions? Kvetch? Anonymous confessions? Answer below, and I'll address each in comments. Subsample of a random sample: random sample? Let's say you have a large random sample of soccer players in Europe but you are only interested in what happens in Spain. Could you reduce your sample to players in Spain and still call it a random sample (but of a different population)? If not, how would you call that subsample and which specific precautions should you take to be able to make inferences on the population of spanish soccer players?  My feeling is that using that subsample would be fine as long as it is large enough, but maybe I am missing something. How to check if list item already exist when adding it with Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable. I'm trying to solve exercise 2.11 from Folland's Real Analysis.    Firstly, how do we show that $f_n$ is Borel measurable on $\mathbb{R} \times \mathbb{R}^k$? I really have no idea how to show this when we have separately Borel measurable functions.  Next, I can't show that $f_n\to f$ pointwise.   For any $(x,y)\in \mathbb{R}\times \mathbb{R}^k$,   $f_n(x,y)=n[f(a_{i+1},y)(x-a_i)-f(a_i,y)(x-a_{i+1})]=n[x[f(a_{i+1},y)-f(a_i,y)]+\frac{1}{n}[f(a_i,y)-f(a_{i+1},y)]]$,   but because of the $n$ outside the bracket, I can't show that this converges to $f$. How can I show this? Also, how can I conclude from this fact that every function on $R^n$ that is continuous in each variable separately is Borel measurable?  I would greatly appreciate any suggestions, hints, or solutions. Does a surjective ring homomorphism have to be surjective on the unit groups? My 5 year- old daughter is constantly defiant! My 5-year old daughter is very defiant.  It started getting bad about 6 months ago. She doesn't do what she is told, and any time she hears the word "no" she throws terrible, dramatic fits, screaming ridiculously loud, and in some cases hitting.  She refuses to make eye contact when I warn her to stop doing something even when I am down at her eye level and it takes multiple orders to finally get her to look at me. She constantly tells me no.  I feel like I constantly tell her no and that she feels this gives her the right to tell her father and I no.  I have tried time outs which are not effective at all; she only throws a fit the whole time, never seeming to run out of wind. Spankings are only effective until the shock of the action itself wears off and then she returns to the same behavior.  My husband and I recently took away ALL of her toys/ possessions being she is a pretty materialistic child (she loves getting toys and always wants something new). We told her that if she was good and listened and stopped telling us no and throwing fits, that after three days we would let her choose three boxes of toys to bring back in her room. This worked but as soon as she got those three boxes unpacked, we packed them back up because she went right back to the no's and fit-throwing within a few hours.  I am mainly the one disciplining her and I feel she is definitely the most defiant with me. I believe in explaining to her why things are not OK and why I tell her no, but I really don't feel it helps and I never feel as if she listens to what I tell her.  I am at my wits' end and feel like a failure of a mother. She is my first and only child, and the only grandchild on both sides of our family. She is an angel at school but home is completely different.  I need help figuring this out but nobody I talk to really has any advice for me. I am at the point where I am wondering if she or I need counseling because I feel out of options. Is there a difference between foo(void) and foo() in C++ or C? Consider these two function definitions:  void foo() { }  void foo(void) { }   Is there any difference between these two? If not, why is the void argument there? Aesthetic reasons?