Why does my camera's indicator light produce so many reflections off a window?
Why does a mirror split my laser beam?
Say we have the following sample and we are trying to estimate the variance of the sample mean of the population.  X = [0, -1, 2, 10, -3]   If I take an increasing number of bootstrap (e.g. 100, 1000, 10,000, 100,0000), the bootstrap distribution of the sample mean gets narrower and narrower. In other words, I can make the bootstrap distribution arbitrarily narrow.   Given the above, what's the point of using a different number of bootstrap samples here? And wouldn't this mean that I could make the standard error of the mean arbitrarily small by just taking more and more bootstrap samples? What am I missing?  Please note that I am doing a proper bootstrap sample in the sense that each bootstrap sample has the same exact size as the original sample (input array). i know that|$S_n$|=$n!$ and |$A_n$|= $\frac{n!}{2}$ but i'm not sure where to go from there. Thanks. Is it safe to delete the file Caches, in the Library of the Mac OS X Hard Drive?  It's a pretty big file, 3.56 GB, Caches reminds me of logs i don't need or browser cookies.   Is it safe to delete the folder "Caches"? How to create a page like this? I'm a LaTeX newbie. I want to create a page layout like in the picture below on every page.  Can someone help please? Thanks. I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? Let $A,B \in \mathbb{M}_n (\mathbb{C})$. If $A^2B + BA^2 = 2ABA$ then exist $k \in \mathbb{N}$ where $(AB-BA)^k = 0$.  I tried solve with minimal polynomial, but I did not have much effect. Hide textfield blinking cursor Luggage, connecting flights and customs question for USA I'm flying to the USA, from Australia, through LAX and catching a connecting flight 6 hours later, think it's the same ticket, booked all at once. I've never traveled before, and I'm wondering what happens with customs.   Do I collect my bags at LAX so they can be checked? Do I have to check in at every airport or is it all done when I catch the first flight? There are 4 flights on my itinerary. How to fix slow wireless on machines with Intel wireless cards? I have looked through all the previous questions but turning power management off for the Wi-Fi card didn't work. This problem seems to be with the Lenovo Thinkpads. I switched to Ubuntu 11.10 from Windows 7 3 days ago so I'm new to the operating system. Say I have the following CSS and HTML code:    #header {   height: 150px; } &lt;div id="header"&gt;   &lt;h1&gt;Header title&lt;/h1&gt;   Header content (one or multiple lines) &lt;/div&gt;     The header section is fixed height, but the header content may change.  I would like the content of the header to be vertically aligned to the bottom of the header section, so the last line of text "sticks" to the bottom of the header section.  So if there is only one line of text, it would be like:   ----------------------------- | Header title | | | | header content (resulting in one line) -----------------------------   And if there were three lines:   ----------------------------- | Header title | | header content (which is so | much stuff that it perfectly | spans over three lines) -----------------------------   How can this be done in CSS? When should the "Not an Answer" flag be used? What are the main reasons the elves did not show up in force to defeat Sauron? During The Great Battle of the Last Alliance, there were an estimated 100,000 elves that fought with the armies of Isildur. This was one of the first scenes in the first LOTR movie. However, in the trilogy, it appears that only a small number of elves show up to Helms Deep and overall left the majority of the fighting to the humans. Why did the elves not participate during the rest of the war? Get month name from Date Could someone please explain the differences between the 3 fitting methods, method = c("CSS-ML", "ML", "CSS"), in Arima?  If I run the code below I get an error message, but if I specify method="ML" in Arima it runs fine.  So I was curious what the difference was between the 3 fitting methods.  Code with error:  library("fpp")  tsTrain &lt;- window(hsales,end=1989.99)  pvar&lt;-1:10 dvar&lt;-1:2 qvar&lt;-1:7  OrderGrid&lt;-expand.grid(pvar,dvar,qvar)  n &lt;- function(a,b,c) {Arima(tsTrain, order=c(a,b,c))} ModFit &lt;- do.call(Vectorize(n, SIMPLIFY=FALSE), unname(OrderGrid))   Fixed Code:  library("fpp")  tsTrain &lt;- window(hsales,end=1989.99)  pvar&lt;-1:10 dvar&lt;-1:2 qvar&lt;-1:7  OrderGrid&lt;-expand.grid(pvar,dvar,qvar)  n &lt;- function(a,b,c) {Arima(tsTrain, order=c(a,b,c),method="ML")} ModFit &lt;- do.call(Vectorize(n, SIMPLIFY=FALSE), unname(OrderGrid)) Simple one really.  In SQL, if I want to search a text field for a couple of characters, I can do:  SELECT blah FROM blah WHERE blah LIKE '%text%'   The documentation for App Engine makes no mention of how to achieve this, but surely it's a common enough problem? How do you make corrections to a published paper? Let $G$ be a finite group and suppose there exists $f\in\text{Aut}(G)$ such that $f^2=\text{id}_G$, i.e., $f$ is its own inverse, and such that $f$ has no fixed points other than the identity $e$ of $G$, i.e., $f(x)=x\Rightarrow x=e$. Show that $G$ is necessarily abelian.   While trying to do this exercise I noticed two facts.  First, $g$ and $f(g)$ have the same order because $o(f(g))|o(g)$ and, applying $f$ again and using $f^2=\text{id}_G$, $o(f(f(g)))=o(g)|o(f(g))$ and, once the order of any element is $\geq 1$, it follows that $o(g)=o(f(g))$. Also, it's easy to see that $g$ and $f(g)$ commute.  Second, there cannot exist such an automorphism if the order of $G$ is even, because $f(e)=e$ and we can form pairs like $\{g,f(g)\}$ with $f(g)\neq g$ that are invariant under $f$, i.e., $f(\{g,f(g)\})=\{g,f(g)\}$. But once the order of $G$ is even, proceeding with the construction of the pairs, we'll end up with just one element $\neq e$, so we must have some $\gamma\in G\setminus{e}$ with $f(\gamma)=\gamma$, contradicting the hypothesis.  Let $n$ be the order of $G$ and let's fix an enumeration of the elements of $G$, say $G=\{g_1,\ldots,g_n\}$. My approach was the following. For each $\sigma\in S_n$, let $x_{\sigma}=\prod_{i=1}^ng_{\sigma(i)}$. Then we have that $f(x_{\sigma})=x_{\sigma^{\prime}}$. If it's shown that $f(x_{\sigma})=e\;\forall\;\sigma\in S_n$, then we'd have $x_{\sigma}=e\;\forall\;\sigma\in S_n$, which implies that $G$ is abelian. The problem is that $S_n$ has $n!$ elements while $G$ has $n$ elements, so there repetitions among the $x_{\sigma}$, and we cannot apply directly the reasoning of the last paragraph.  Is this the right way, or is there an easier manner to solve this? If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$? Can spells with movable areas of effect be moved out of sight or behind obstacles? With spells like Moonbeam or Flaming Sphere, how should we treat the movement of their areas-of-effect when it comes to passing them behind a thick pillar or around a blind corner?  Should we treat any movement of them as if they are being 're-cast' (and so requiring a clear unobstructed view)? Or could a mage presumably will them somewhere out-of-sight? Linear algebra is a very well-behaved part of mathematics. Soon after you have mastered the basics you got a good feeling for what kind of statements should be true -- even if you are not familiar with all major results and counterexamples.  If one replaces the underlying field by a ring, and therefore looks at modules, things become more tricky. Many pathologies occur that one maybe would not expect coming from linear algebra.  I am looking for a list of such pathologies where modules behave differently than vector spaces. This list should not only be a list of statements but all phenomena should be illustrated by an example.  To start the list I will post an answer below with all pathologies that I know from the top of my head. This should also explain better what kind of list I have in mind.