Does the Spirit Guardians spell hurt friendly creatures if they were not visible at the time the spell was cast?
Can Spirit Guardians affect enemies through walls?
Is the current obtained using Ohm's law that which passes through the resistor or that which passes through the circuit? Shouldn't the current passing through a resistor be lesser than that which passes through a circuit? My understanding is that since Current = Charges/Time. If there exists a resistance to the flow of charges, then that must mean the charges slow down, meaning that more time is required to pass through a point. So, the current should then decrease. But, since this opposition to the flow of charges doesn't exist in the ENTIRE circuit, it should really only decrease the current in the resistor, right? Am I confusing the resistance of the resistor with the resistance of the wire? Any help will be appreciated! Thanks a bunch for lending me some of your time :D Are there any expressions that describe going from a bad to a worse situation? Are there idioms or expressions in English that describe going from one bad situation to one that's even worse?  I heard "between a rock and hard place" but this describes a dilemma not really a transition. I am looking for an expression that describes someone trying to get out of a bad situation but after much effort, the situation only got worse. SHA-256 "almost unique"? I have seen numerous references on the internet of people describing SHA-256 as generating an "almost unique" hash.  . there are more.  Is there some mathematical basis to the almost uniqueness? I would have thought that as SHA-256 is an evenly-distibuted (?) hash algorithm which can accept any message (infinitely many) as an input and produces a fixed length (finite) hash - then there will in fact be an infinite number of each possible output - which I would think hardly qualifies as "almost unique".  Is there a basis for this statement? Weak solutions to the Neumann's problem (Evans PDE) Let $U$ be connected. A function $u \in H^1(U)$ is a weak solution   of Neumann's problem   \begin{equation} (*)\qquad\left\{ \begin{array}{rl} -\Delta = f &amp; \text{in } U \\ \frac{\partial u}{\partial \nu} = 0 &amp; \text{on } \partial U \end{array} \right. \end{equation}   if   $$ \int_U Du \cdot Dv \; dx = \int_Ufv \; dx $$   for all $v \in H^1(U)$. Let $f\in L^2(U)$. Prove $(*)$ has a weak solution   if and only if   $$ \int_U f \; dx =0. $$   For the only if part I set $v=1$. However I do not see where to start the if part. I was thinking of the Lax-Milgram theorem. That's where I'm now. I'm a mathematician interested in abstract QFT.  I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator.  I understand from the Wikipedia article that requiring that energy stay positive forces $T$ to be represented by an anti-unitary operator.  But I don't see how this forces $T^2=-1$.  (Or maybe it doesn't force it, it merely allows it?)  Here's another version of my question.  There are two distinct double covers of the Lie group $O(n)$ which restrict to the familiar $Spin(n)\to SO(n)$ cover on $SO(n)$; they are called $Pin_+(n)$ and $Pin_-(n)$.  If $R\in O(n)$ is a reflection and $\tilde{R}\in Pin_\pm(n)$ covers $R$, then $\tilde{R}^2 = \pm 1$.  So saying that $T^2=-1$ means we are in $Pin_-$ rather than $Pin_+$.  (I'm assuming Euclidean signature here.)  My question (version 2): Under what circumstances are we forced to use $Pin_-$ rather than $Pin_+$ here?  (I posted a  on physics.stackexchange.com last week, but there were no replies.)    EDIT: Thanks to the half-integer spin hint in the comments below, I was able to do a more effective web search.  If I understand correctly, Kramer's theorem says that for even-dimensional (half integer spin) representations of the Spin group, $T$ must satisfy $T^2=-1$, while for the odd-dimensional representations (integer spin), we have $T^2=1$.  I guess at this point it becomes a straightforward question in representation theory: Given an irreducible representation of $Spin(n)$, we can ask whether it is possible to extend it to $Pin_-(n)$ (or $Pin_+(n)$) so that the lifted reflections $\tilde R$ (e.g. $T$) act as an anti-unitary operator. Expression Versus Statement I'm asking with regards to c#, but I assume its the same in most other languages.  Does anyone have a good definition of expressions and statements and what the differences are? how does the circuit of a basic Variable speed electric drill work? i am trying to 'automate' the control of an electric drill motor that im taking from a garden variety Variable Speed drill (from Harbor Freight)  it has a universal AC motor which I basically undertand and a DPDT switch to reverse direction and a triac citcuit to vary speed    Question 1 . i see 4 wires going to the 'field/Stator coil(s)'. Are there 2 seperate field/stator coils here? is this to provide low/high power.  I think in theory , you only need 1 coil with 2 wires and that coil is wired in series with the brushes... is that right?   how does this circuit work with 2 coils.  Question 2 . how does this variable speed circuit work.  is the wiring diagram correct (it doesnt show a variable resistor and it doesnt show what drives the control input of the traic? why are there two switches in the thing? does switch 2 close at high speed and thus shunt around the triac?  please see the attached 4 diagrams iPad won't turn on after a complete battery drain My iPad mini retina is out of warranty,  I forgot to plug in my iPad after the critical battery warning and it went some minutes following the warning. I was not worried because same thing had happened a few times before and iPad was perfectly okay after charging it. However, this time I remember seeing a flash of blue screen immediately after it went black. Then, I plugged it in an waited for a while and tried starting it. Ever since, it fails to start hanging on the apple logo with white background screen.   I tried to connect to my Mac but nothing showed up in iTunes. I am worried now. Can I troubleshoot this or is it broken and needing repair? I find it funny that Java (or the java.util library) does not have a built-in function to calculate difference in dates. I want to subtract one date from another to get the elapsed time between them. What is the best way to do this?   I know the simple way is to take the difference of the time in milliseconds and then convert that into days. However, I wanted to know if this works in all cases (with daylight saving, etc.). Unable to delete recup_dir.1 folder A folder was created when I used a utility to recover pictures from a cd card that I deleted by mistake.  Now I can't delete it or move it. I am told I am not the owner of it even when I am logged on as root.  How can I delete the recup_dir.1 folder from my machine? How to run a program without typing the full path? System utilities such as ls don't need to have the full path typed before executing them. However, to execute Netbeans, I have to type /home/chris/netbeans-7.0.1/bin/netbeans. How can I make it so that I only have to type netbeans? Difference in meaning and use of future perfect forms Log of products to sum of logs Where are static variables stored in C and C++? Can I look at the upgrade log after a distribution upgrade? I've upgraded to Ubuntu 12.04 and did it . I didn't look at the "packages to remove" section before clicking next - I've done Ubuntu upgrades many times and assumed it was just the normal set of obsolete library packages etc. But I do tend to watch the terminal text go by and see what it's doing, and I saw it removing a number of packages I wanted. I guess these are packages that aren't on the CD that can't co-exist with the new Ubuntu.  Anyway, I want to find which packages have been removed. So does the update log get saved somewhere?  Then I can start doing some grepping on it and then reinstall the packages I did want. Is there any way to hide taskbar labels and not combine taskbar buttons? There are three options for customizing taskbar buttons in Windows 7:   Always combine, hide labels Combine when taskbar is full Never combine   Is there any way to hide labels and not combine taskbar buttons? Or even better, to exclude only certain applications from combining?  My main problem is that I switch a lot between two instances of a single application, and having to hover over combined icon and then choosing the correct one. Alt-Tabbing is not a good alternative when I'm switching between more than three applications; clicking on taskbar only once is what I'm looking for. Optimal estimation of a single parameter given data at different scales Let $A,B,C,D$ be independent normal random variables distributed according to $\mathcal{N}(0,\sigma^2)$ and $E = A+B+C+D$.  The goal is to provide an optimal estimate of $\sigma^2$ given samples of $A,B,E$ but not $C,D$.  In this case optimal refers to minimising the root-mean square deviation of the estimate $\hat{\sigma}^2$:  $$RMSD(\hat{\sigma}^2) = \sqrt{\mathbb{E}\left[\left(\hat{\sigma}^2-\sigma^2\right)^2\right]}$$  I can think of a simple approach to estimate $\sigma^2$ given samples of $A,B$ which is to simply compute the sample variance. Also I know that the variance of $E$ is $4\sigma^2$ so I could compute the sample variance of $E$ and divide it by 4 to get an estimate of $\sigma^2$. However it should be possible to combine the information from both $E$ and $A,B$ to improve estimation $\sigma^2$. Could you outline the approach to use both sets of information? Additional horizontal space when the last line of an environment is full I have created an environment env which just adds a \medskip and some text (say "Blablabla") after the text inside \begin{env} ... \end{env}. The problem is that if the last line is full, then I get an additional horizontal space between the text and "Blablabla".  Here is an MWE:  \documentclass{article} \newenvironment{env}{ ENVIRONMENT:\par }{ \medskip \par\noindent Blablabla }  \begin{document}  \section*{First case: the last line is not full}  \begin{env} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nulla malesuada porta tortor non vestibulum. Vivamus vel tincidunt purus. Curabitur quam arcu, suscipit sed diam sed, ornare efficitur felis. Duis at arcu iaculis, viverra ligula sit amet, hendrerit eros. Proin finibus venenatis sollicitudin. Nunc ullamcorper sem ut lacinia posuere. Integer pulvinar nulla lorem, ut pulvinar ipsum egestas at. Duis quam ipsum, posuere ac pulvinar vitae, auctor non leo. \end{env}  \section*{Seconde case: the last line is full}  \begin{env} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque suscipit vitae neque eu gravida. Quisque et enim quam. Integer elementum diam a ex laoreet, ac egestas lacus volutpat. Nunc ullamcorper non urna tincidunt ultrices. Etiam eu ultricies diam. Proin mollis, nunc sit amet volutpat varius, ipsum tellus bibendum nulla, in eleifend lacus felis pellentesque nisl. Phasellus laoreet, libero quis auctor congue, nulla nulla aliquam metus, in hendrerit arcu justo quis tortor. Nunc nec nisi euismod, consectetur tellus nec, suscipit libero.  \end{env}  \end{document} Should I always use a comma before a quote? On this site I see hundreds if not a thousand questions being asked about issues with a Wireless LAN adapter not being detected/recognized by Ubuntu. Some mainstream adapters appear to be utterly broken in Linux support, while others just require some simple steps to get it to work.  The options to get it to work appear to be infinitely huge and I have no clue where to get started!  What is considered 'best practice'? What order of things to try is most efficient in terms of time, effort and imposes minimal risk to my Ubuntu installation? Please help me save time and guide me what to do, step by step.