Why does everyone seem to assume that gravitational waves will always be very small?
How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments?
Can druids Wild Shape into creatures other than beasts? Under Wild Shape it says "assume the shape of a beast" you have seen before. Does this mean they can only transform into creatures that have the beast type, such as bear, wolf, crocodile, etc.? Or can they turn into things with other types, like dragon, monstrosity, humanoid, fiend, etc.? How can I change the master volume level? Using this code  [DllImport ("winmm.dll")] public static extern int waveOutSetVolume (IntPtr hwo, uint dwVolume);  waveOutSetVolume (IntPtr.Zero, (((uint)uint.MaxValue &amp; 0x0000ffff) | ((uint)uint.MaxValue &lt;&lt; 16)));   I can set the wave volume but if the master volume is too low this won't have any effect.  Thanks for any help. Usage and origin of "sister" in expressions like "sister company, sister ship, sister site" etc One who has potential, but never gives the effort to show it.   What would be the best word or words that match this description? When & How often do 4e Monster powers recharge? How often should I roll power recharge rolls and at which point in the monster's turn do I re-roll them?  I'm trying to find the official definition of the recharge mechanic in the online compendium and I'm not seeing it there. In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$.  says that "there is a bias against roots in the denominator of a fraction". But such fractions are well-defined and I'm failing to see anything wrong with $\frac{1}{\sqrt{2}}$ - in fact, IMO it is simpler than $\frac{\sqrt{2}}{2}$ because 1 is simpler than 2 (or similarly, because the former can trivially be rewritten without a fraction).  So why does this bias against roots in the denominator exist and what is its justification? The only reason I can think of is that the bias is a relic of a time before the reals were understood well enough for mathematicians to be comfortable dividing by irrationals, but I have been unable to find a source to corroborate or contradict this guess. Compute $\Gamma(2.7)$ All I know of the Gamma function is $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}e^{-x}\text{ d}x$$ and the recursive formula $$\Gamma(\alpha) = (\alpha-1)\Gamma(\alpha - 1)\text{.}$$ A friend asked me to try to find $\Gamma(2.7)$. I assume this involves complex analysis, which I have absolutely no background on (except for the basic Euler formula). Using Wolfram, I found that  $$\Gamma(2.7) = e^{0.434821}$$ which suggests to me perhaps writing out $e^{-x}$ as a Taylor series: $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}\sum\limits_{i=1}^{\infty}\dfrac{(-x)^{i}}{i!}\text{ d}x$$ but alas, this doesn't look helpful.  How does one derive that $\Gamma(2.7) = e^{0.434821}$? Why isn't apt full-upgrade getting an updated software key signature for skype After a recent apt update &amp;&amp; apt full-upgrade I started getting the following error when running apt full-upgrade subsequently: Get:4 https://repo.skype.com/deb stable InRelease [4,502 B]                                         Err:4 https://repo.skype.com/deb stable InRelease   The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: https://repo.skype.com/deb stable InRelease: The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: Failed to fetch https://repo.skype.com/deb/dists/stable/InRelease  The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: Some index files failed to download. They have been ignored, or old ones used instead.  Is there a way to correct this, or is it down to Microsoft/Canonical to produce/update the necessary key signatures? Why can't I define a static method in a Java interface? biblatex, biber, is it possible to \printbibliography between two years? With biblatex and Biber, is it possible to print all the bibliography (\printbibliography) from (let's say) 2003 to 2008 in one section? And then in another section print all the bibliography from 2009 to 2016? In HP-UX server, grep -r option is not working In unix server grep -r option is not working. OS is HP-UX.  If grep -r is not working any alternative way to do recursive search without -r option? In CodeGear Delphi 2007, how can I turn specific warnings and hints off? I am attempting to turn off H2077 - Value assigned to 'varname' never used. How can I create a new extensible symbol? Given an arbitrary thin vertical symbol, can I create a new math delimiter from it (and if so, how)?   Edit: Ideally, I would like to be able to create an extensible symbol, either built out an existing normal symbol, or even made from scratch.  Edit 2: I am pretty sure that what I am after is an explanation of how to create a .tfm file for an extensible symbol (which Werner's answer describes the general structure of, but not how to make one).    For example, let's say I wanted to use the \dagger () or \wr () symbol as a delimiter, and write expressions like    \[\left\ldagger \sum_{n=1}^\infty a_n \right\rdagger\]   where the symbol scaled appropriately. Would there be any distinction between declaring a symmetric delimiter (like \vert), as opposed to one that has inherently different "left" and "right" versions like [ and ]?  Now, even being unaware of the inner workings of TeX, I imagine that there has to be lots of information in the fonts for how a delimiter is to be scaled in different situations, and if I try to make my own delimiter, this information won't be present. Would I need to get deep into FontForge or equivalent to achieve my custom delimiters, or is there an easier way? Do lenses have focal planes or focal spheres/ellipsoids? How to catch the "Login Failed" event? I want to show a custom block, only when log in has failed. So from visibility settings I have to put a PHP code that returns TRUE only when the login has failed.  But how could I "catch" that event? Do I have to use variable_get(..)? And if yes, how could I use that?with what attributes?  Thank you. Badge symbol in notification is of the site you're on, not where badge was earned If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric One of my columns is called from. I can't change the name because I didn't make it. Am I allowed to do something like SELECT from FROM TableName or is there a special syntax to avoid the SQL Server being confused? Nonlinear function continuous but not bounded I would like an example of a map $f:H\rightarrow R$, where $H$ is a (infinite dimensional) Hilbert space, and $R$ is the real numbers, such that $f$ is continuous, but $f$ is not bounded on the close unit ball $\{ x\in H : \|x\| \leq 1\}$.  Actually, $H$ could be replaced by any Banach space (but not just a normed space-- that's too easy).  My motivation is that if $f$ is linear, this is impossible; but I have next to no intuition about non-linear functions.  Edit: Here's an example for $c_0$ which is even differentiable (disclaimer: I found it here: ).  Define $f:c_0\rightarrow F$ (where F is your field, real or complex) by $$ f(x) = \sum_{n=1}^\infty x_n^n \qquad (x=(x_n)). $$  You can estimate the sum by a geometric progression, so it does converge.  A bit of checking shows that f is Frechet differentible (so certainly continuous).  But $f(1,1,\cdots,1,0,\cdots)=n$ (if there are $n$ ones) so $f$ is not bounded on the closed unit ball.  What I don't immediately see is how to adapt this to $\ell^2$, say. Convert DOS line endings to Linux line endings in Vim If I open files I created in Windows, the lines all end with ^M. How do I delete these characters all at once?