We have a Ranger and a Battlemaster in the party, and the Ranger thinks that he can benefit from the Colossus Slayer bonus to damage both during his Action and again later in that same round if the Battlemaster gives him an extra attack using Commander's Strike (which uses the Ranger's Reaction)...because Colossus Slayer only states "You can deal this extra damage only once per turn" and doesn't specify it has to be only on the Ranger's turn.   Since the Reaction is happening on the Battlemaster's turn, he reasons that Colossus Slayer is still only "once per turn" (it just happens to be on two different people's turns).
PHB says 'once per turn,' so, it would seem that a Rogue with Sentinel, for example, could "consistently" deal Sneak attack twice per round (whether the enemy triggers an OA or the melee weapon attack provided by the Feat).  So, can rogues deal sneak attack damage with any weapon attack outside their turn? (obv. one that meets the standard requirements--finesse, adv or adj ally)
Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula $m + Lr$, where $L$ is the Cholesky lower factor so that $S=LL^T$ and $r = (r_1,...,r_n)^T$.  What about if one wants samples from singular Gaussian i.e. $S$ is still symmetric but not more positive definite (only positive semi-definite). We can assume also that the variances (diagonal elements of $S$) are strictly positive. Then some elements of $x$ must have linear relationship and the distribution actually lies in lower dimensional space with dimension $&lt;n$, right?  It is obvious that if e.g. $n=2, m = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, S = \begin{bmatrix} 1 &amp; 1 \\ 1 &amp; 1\end{bmatrix}$ then one can generate $x_1 \sim N(0,1)$ and set $x_2=x_1$ since they are fully correlated. However, is there any good methods for generating samples for general case $n&gt;2$? I guess one needs first to be able identify the lower dimensional subspace, then move to that space where one will have valid covariance matrix, then sample from it and finally deduce the values for the linearly dependent variables from this lower-dimensional sample. But what is the best way to that in practice? Can someone point me to books or articles that deal with the topic; I could not find one. Is normal extension of normal extension always normal? 100 apples are/is considered as a large number of apples how can i display the latest items from another site collection I have a web application, with three site collections . and i want inside my team site to be able to display the latest pages that  have been added to my enterprise wiki site collection. so what are the available approaches which i can follow?  Thanks in advance for any help.  Regards A skydiver jumps out of a plane from a height of $2200$m. The skydiver's height, $h$ meters above the ground, can be modeled by the function $$s = 2200 - 4.9t^2$$ How fast is the skydiver falling at $t = 4$s?  If the skydiver is approaching a height of $2200$m, I reasoned that I could use the following definition to find the solution $${f(x+h)-f(x)\over h}$$ I entered the function into this definition and got stuck when I got to this$$f'(x) = \lim_{x\to 0} {2200-4.9t^2-9.8th-4.9h^2\over h}$$ Where can I go from here? Can I continue with this method or did I make a mistake a few steps back? New Solution  How does this look? How do I set up my LaTeX document to enable me to cite from my BibTeX bibliography? This may be an overly simplistic question but please bear with me...  I have a BibTeX bibliography containing all of my references, set up using BibDesk. I am now trying to cite these references in my LaTeX documents. Following the advice on the LaTeX wikibooks page, I have included the following lines into my LaTeX document...  \bibliographystyle{plain} \bibliography{/Users/Graeme/Documents/References/BIBliography.bib}   ... where BIBliography is my .bib file, created in BibDesk.  Unfortunately, when I cite something in the document, using \cite{citekey} and typeset the document, the log tells me that there were undefined references. In the .pdf that is produced, there is a [?] where the references should be.  Am I doing something wrong? Do I need to store my .bib for in a particular location? I know there can be some errors that mean you need to typeset the document several times, but I have tried countless times to no avail.  I would be very grateful if someone could help out. Viruses: Adaptation to a new host through repeated host jumps A friend told me, during a 3 minute discussion, that viruses that are endemic in host $A$ and make repeated jumps to host $B$ but can't be transmitted between individuals of species $B$, may slowly adapt (through these repeated jumps) to be able to be transmitted between individuals of host $B$ and become epidemic.  I don't know much about epidemiology. I don't understand how a virus population that is endemic to host $A$ may adapt to host $B$ with repeated jumps while the viruses that jump to host $B$ are dead end because they cannot be transmitted further more. Or Are these viruses able to jump back to host $A$ to bring back their newly acquired adaptations to host $B$?  Also, I might misunderstand the meaning of "repeated host jumps transmission". I first thought it meant repeated jumps from a reservoir population in host $A$ to host $B$, but it is also possible that it describes the dynamic of a virus population that is adapted to jump from species to species and they actually gain this ability by keeping jumping and jumping. But then, how could a virus species get adapted to jump from species to species? I'm a bit confused…. Can you give me some hints about this process of cross-species transmission through repeated jumps? Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$ The second part of an exercise asks that I show:     There does not exist a surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$.     The first part was to show that these two spaces are separable in their respective $L^p$ norms.    I've really hit a wall on this one.  I know, in fact, that there does exist a surjective bounded linear map from $\ell^1(\mathbf{N})$ to $\ell^2(\mathbf{N})$.  So my intuition says that if there were also one going the other way, then the two spaces would have to be isomorphic, which is false .  But I don't know of any such theorem that I could apply to "the category of Banach spaces".    My only other idea is to argue by contradiction using the open mapping theorem, but nothing is coming to me...  My guess is that separability is also going to be important, given the first part of the exercise.  -Thanks. What's the arc length of an implicit function? While an explicit function $y(x)$'s arc length $s$ is easily obtained as  $$s = \int \sqrt{1+|y'(x)|^2}\,dx,$$   is there any formula for implicit functions given by $f(x,y) = 0$? One can use the implicit differentiation $y'(x) = -\frac{\partial_y f}{\partial_x f}$ to obtain  $$s = \int\sqrt{1 + |\partial_y f / \partial_x f|^2}\,dx,$$  but that still requires (locally) solving for $y(x)$. Is there any formulation that does not require this, e.g. another implicit equation involving $s$?    Thoughts so far:  One could rewrite $s$ as  $$s = \int |\nabla f|\, |\partial_x f|dx,$$  or symmetrize to  $$s = \int |\nabla f|\, \underbrace{(|\partial_x f|dx + |\partial_y f|dy)}_{(*)}/2$$  where $(*)$ might be strongly related to $|df|$ I guess (though it's not identical due to the $|\cdot|$), but then? Can a function be differentiable at the end points of its (closed interval) domain? Assume $f$ has a domain of $[a,b]$. Is it possible that $f$ is differentiable on the closed interval $[a,b]$, or must the maximal domain for $f'$ be $(a,b)$? Skype window problem in Ubuntu 14.04 Transparent textured planes produce black artifacts How does Cooper get out of the black hole? In the movie Interstellar,  Cooper (played by ) enters a black hole and sends a message to Murph (his daughter). Later, he is found by rangers, but I don't understand how he gets out of the black hole?  As far as I know, nothing can get out of a black hole, as it has extremely high gravity. I just did my first install of any Linux OS, and I accidentally selected "Desktop GUI" in the install, but I want to build everything myself. Is there any way by which I can remove the GUI environment without re-installing OS? I've just executed a long-running process from the bash prompt. In hindsight, I wish I'd run time on it, or noted down the time at which I kicked it off.  Is there any way of getting this information retrospectively? The .bash_history doesn't seem to include timestamps.  In my particular case it's Mac OS X, but I'm interested in general Unix/Linux solutions.  To clarify, the process has now completed, and I'd prefer not to run it again unless absolutely necessary! It seems the .NET Regex.Replace method automatically replaces all matching occurrences.  I could provide a MatchEvaluator delegate that returns the matched string after the first replacement, rendering no change, but that sounds very inefficient to me.  What is the most efficient way to stop after the first replacement? Tracker icon is misaligned in activity page Redirect 301 with hash part (anchor) # Linear functional on a Banach space is discontinuous then its nullspace is dense.