Besides the actual fellowship and Elrond, who else attended the meeting in Rivendell? In the movie, it looks like there are around 20 or so attendees. Who were they? How closely does this match the book?
In Peter Jackson's film The Fellowship of the Ring, when the Council of Elrond takes place it shows a total of 22 members:    We all know the names of the ones who were part of the Fellowship, but I want to know who are the rest of the people in the council. Who are the elves that came with Legolas? The men next to the dwarves? The three old men sitting next to Boromir? Or the two elves next to Aragorn?  Starting from left to right:   Frodo Gandalf Elf Elf Legolas Elf Old Man Old Man Dwalin Gloin Gimli Nori Old Man Boromir Old Man Old Man Elf Elf Aragorn Elladan Elrond Elrohir
"An operator is hermitian". Implications? Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter.  The first part of his second postulate can be stated as:      Every dynamical variable may be represented by a Hermitian operator whose eigenvalues represent the result of carrying out a measurement of the value of the dynamical variable...   My question is: just how much can we deduce from saying that the some of the operators involved in Quantum Mechanics are Hermitian?  When I use the word Hermitian, I am referring to the property that $A=A^+$ where $A$ is an operator and $A^+$ is the adjoint of $A$.  Does an operator being Hermitian automatically imply that there will exist eigenfunctions and eigenvalues corresponding to this operator?  Does being Hermitian imply that, should there exist eigenfunctions corresponding to this operator, they will form a complete and orthonormal set?  That any wavefunction can be expanded in terms of these eigenfunction?  Just how much is hidden in the word "Hermitian"? Positive AND Negative reputation show as +-1 How can I develop my Android game for different phone resolutions? In the  there are lots of numbers on display, including 1000, 2500 or 10000. The display is erratic though:    Same number, two displays. Both appear valid to me: 1000 or 1,000 but please, make it consistent. My eyes hurt! :) I just found , but there it's discussing the whole network while I'm asking just for that specific page. For a start. How to get Debian codename without lsb-release I am trying to create a script that requires me to print the debian codename so that I may echo it into the sources.list file.  I am trying to make this script work across any version of Debian, so I had hoped to set a bash variable of the release codename. This would be simple to do (with lsb_release -c), however our deployment images do not contain lsb_release by default - and with this script being required to fix the sources.list, installing lsb-release with apt-get would not be an option.  I have found numerous ways to get the release number and other info about the system, but cannot find a reliable place to get the codename.  Any ideas would be greatly appreciated!  (OS I am testing this with is Debian Squeeze) Evaluate : $1+\frac{2}{6}+\frac{2\cdot 5}{6\cdot 12}+\frac{2\cdot 5\cdot 8}{6\cdot12\cdot 18}+\ldots$ Evaluate : $$1+\frac{2}{6}+\frac{2\cdot 5}{6\cdot 12}+\frac{2\cdot 5\cdot 8}{6\cdot12\cdot 18}+\ldots$$  thought: I have tried to manipulate the series so that the sum upto n terms , can be simplified. But I can't figure out any profitable result. What is the icon next to Spotlight in menu bar, and how to remove it? What is this icon   in OS X menu bar and how do you remove it? Is it better to difference a series (assuming it needs it) before using an Arima OR better to use the d parameter within Arima?  I was surprised how different the fitted values are depending on which route is taken with the same model and data. Or am I doing something incorrectly?  install.packages("forecast") library(forecast)  wineindT&lt;-window(wineind, start=c(1987,1), end=c(1994,8)) wineindT_diff &lt;-diff(wineindT)  #coefficients and other measures are similar modA&lt;-Arima(wineindT,order=c(1,1,0)) summary(modA) modB&lt;-Arima(wineindT_diff,order=c(1,0,0)) summary(modB)  #fitted values from modA A&lt;-forecast.Arima(modA,1)$fitted  #fitted from modB, setting initial value to the first value in the original series B&lt;-diffinv(forecast.Arima(modB,1)$fitted,xi=wineindT[1])   plot(A, col="red") lines(B, col="blue")   ADD:  Please note I am differencing the series once and fitting arima (1,0,0) then I am fitting arima (1,1,0) to the original series. I am (I think) reversing the differencing on the fitted values for the arima(1,0,0) on the differenced file.   I am comparing the fitted values - not the predictions.  Here is the plot (red is arima(1,1,0) and blue is the arima (1,0,0) on the differenced series after changing back to the original scale)  :    Response to Dr. Hyndman's Answer:  1) Can you illustrate in R code what I would need to do in order to get the two fitted values (and presumably forecasts) to match (allowing for small difference due to your first point in your answer) between Arima (1,1,0) and Arima(1,0,0) on the manually differenced series? I assume this has to do with the mean not being included in modA, but I am not entirely sure how to proceed.  2) Regarding your #3. I know I am missing the obvious, but are not $\hat{X}_t = X_{t-1} + \phi(X_{t-1}-X_{t-2}) $ and $\hat{Y}_t = \phi (X_{t-1}-X_{t-2})$ the same when $\hat{Y}_t$ is defined as $\hat{X}_t - X_{t-1}$? Are you saying I am "undifferencing" incorrectly? An integration question to be solved without using differentiation under the integral sign. Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory In  gravity, the action is the usual  but now the Torsion tensor is allowed to vary as well (in usual GR, it is just set to zero).  Variation with respect to the metric gives:  $$R_{ab}-\frac{1}{2}R g_{ab}=\kappa P_{ab} \quad (1)$$  where $P_{ab}$ is the canonical stress energy tensor.  Variation with respect to the torsion tensor ${T^{ab}}_c$ gives:  $${T_{ab}}^c + {g_a}^c{T_{bd}}^d - {g_b}^c {T_{ad}}^d = \kappa {\sigma_{ab}}^c \quad (2)$$  where ${\sigma_{ab}}^c$ is the .  By contracting that equation, I can see that if the spin tensor is zero, the Torsion tensor is identically zero:  $${T_{ab}}^c + {g_a}^c{T_{bd}}^d - {g_b}^c {T_{ad}}^d = \kappa {\sigma_{ab}}^c = 0$$ $$ {g^b}_c({T_{ab}}^c + {g_a}^c{T_{bd}}^d - {g_b}^c {T_{ad}}^d) = 0$$ $$ {T_{ab}}^b + {g_a}^b{T_{bd}}^d - {g_b}^b {T_{ad}}^d = 0$$ $$ {T_{ab}}^b + {T_{ad}}^d - 4 {T_{ad}}^d = 0$$ $$ {T_{ad}}^d = 0$$ $${T_{ab}}^c + {g_a}^c{T_{bd}}^d - {g_b}^c {T_{ad}}^d = 0 \quad \Rightarrow \quad {T_{ab}}^c =0$$  My understanding is that:  The spin tensor and the stress energy tensor, are defined entirely in terms of whatever matter Lagrangian we add to the theory.  Therefore, from above, the equations in vacuum are exactly the same as normal GR (so solving for outside matter, only the boundary conditions with the matter could be different).  Assuming my understanding up to here is correct, my line of questioning is:   How is the Spin tensor (and hence Torsion) related to the concept of material with intrinsic spin? Hopefully answered by 1, but if the matter has zero intrinsic spin, yet we have an extended "spinning" body, is the spin tensor still zero (as I'd consider that orbital angular momentum then)? Does this mean Einstein-Cartan predictions are identical to normal Einstein GR if (and only if) the instrinsic spin of any particles and fields in the theory are zero? I've been getting this undefined symbol building with this command line:  $ gcc test.cpp Undefined symbols:   "___gxx_personality_v0", referenced from:   etc...   test.cpp is simple and should build fine.  What is the deal? I am planning on spending 90 days in Schengen zone countries.  I will be taking a cruise between Lisbon and Barcelona.  Do the days at sea count against the 90 days allowed for staying in the Schengen zone? I have been hit with a homework problem that I just have no idea how to approach. Any help from you all is very much appreciated. Here is the problem  Prove the equation: $a^{\log_b c} = c^{\log_b a}$  Any ideas? How do I match any character across multiple lines in a regular expression? Choosing between $z$-test and $t$-test Background: I'm giving a presentation to colleagues at work on hypothesis testing, and understand most of it fine but there's one aspect that I'm tying myself up in knots trying to understand as well as explain it to others.  This is what I think I know (please correct if wrong!)   Statistics that would be normal if variance was known, follow a $t$-distribution if the variance is unknown CLT (Central Limit Theorem): The sampling distribution of the sample mean is approximately normal for sufficiently large $n$ (could be $30$, could be up to $300$ for highly skewed distributions) The $t$-distribution can be considered Normal for degrees of freedom $&gt; 30$   You use the $z$-test if:   Population normal and variance known (for any sample size) Population normal, variance unknown and $n&gt;30$ (due to CLT) Population binomial, $np&gt;10$, $nq&gt;10$   You use the $t$-test if:   Population normal, variance unknown and $n&lt;30$ No knowledge about population or variance and $n&lt;30$, but sample data looks normal / passes tests etc so population can be assumed normal   So I'm left with:    For samples $&gt;30$ and $&lt;\approx 300$(?), no knowledge about population and variance known / unknown.   So my questions are:   At what sample size can you assume (where no knowledge about population distribution or variance) that the sampling distribution of the mean is normal (i.e. CLT has kicked in) when the sampling distribution looks non-normal? I know that some distributions need $n&gt;300$, but some resources seem to say use the $z$-test whenever $n&gt;30$... For the cases I'm unsure about, I presume I look at the data for normality. Now, if the sample data does looks normal do I use the $z$-test (since assume population normal, and since $n&gt;30$)? What about where the sample data for cases I'm uncertain about don't look normal? Are there any circumstances where you'd still use a $t$-test or $z$-test or do you always look to transform / use non-parametric tests? I know that, due to CLT, at some value of $n$ the sampling distribution of the mean will approximate to normal but the sample data won't tell me what that value of $n$ is; the sample data could be non-normal whilst the sample mean follows a normal / $t$.  Are there cases where you'd be transforming / using a non-parametric test when in fact the sampling distribution of the mean was normal / $t$ but you couldn't tell? Now the cubs are growing, fed on mom's milk, but mom herself hasn't eaten in five months, and is getting thinner by the day.   What does in mean here, and how would the meaning of that piece change if for were used? I have a problem understanding the proof of Rencontres numbers (Derangements) I understand the whole concept of Rencontres numbers but I can't understand how to prove this equation  $$D_{n,0}=\left[\frac{n!}{e}\right]$$  where $[\cdot]$ denotes the rounding function (i.e., $[x]$ is the integer nearest to $x$). This equation that I wrote comes from solving the following recursion, but I don't understand how exactly the author calculated this recursion.  $$\begin {align*}  D_{n+2,0} &amp; =(n+1)(D_{n+1,0}+D_{n,0}) \\ D_{0,0} &amp; = 1 \\ D_{1,0} &amp; = 0  \end {align*} $$ Multiplexing UART I'd like to interface my main microcontroller's hardware serial port to more than one device at the same time. My understanding is that UART on my microcontrollers is based on an active-low 5V TTL.  (I know what I'm explaining here can be technically achieved by using more suited protocols, such as SPI and I2C, but my project requires to be only implemented using UART.)  Here's a pseudo-schematics chart of what I'm trying to achieve:         &ndash; Schematic created using   Please note that:   I don't want to use a second UART interface on the master, or any of the slaves. Only one slave at a time is going to transmit or send data on the line to the master. (e.g. If the slave 1 is transmitting data, slave 2 and 3 should remain idle.) Whatever the master is transmitting can, and should be received by all of the slaves. All of the slaves should be hot-pluggable, meaning they could be removed or inserted at any time. The RX and TX wires to the master are parallel between each slave, so no daisy chaining.   So, my questions are as follows:   Assuming the correct impedance is considered, I shouldn't need an additional circuit to transmit data from the master's TX line to any of the slave's RX line simultaneously. Is this correct? I understand that without current limiting resistors between slaves' TX line and the master's RX line, if any of the devices begin to broadcast data, the line between the devices will short circuit and I risk damaging them. Is this correct? Assuming the items 1 and 2 are correct:  a) Would just some current limiting resistors be enough to use?  b) Can I use 74-series logic gates instead of resistors? Between options a and b above, what route should I choose? For a reliable 115200 baud rate connection, will the switching frequency of a 74HC08 AND gate suffice to be incorporated?   EDIT: I'm well aware of other well-suited protocols such as SPI and I2C. There's a reason I'm using UART, and that's because the optiboot bootloader that is used on the master's mcu communicates over UART, albeit UART's obvious limitations.  Also, while daisy-chaining is definitely a clever approach, due to breaking the 4th requirement, it also breaks bootloader functionality.  The devices could also be USB-to-Serial chips, and using SPI-to-USB or I2C-to-USB would not be feasible in this project.  So, I'd appreciate if you could focus on the 6 questions listed here instead, and share your UART knowledge. Human & Alien captured, observed by higher beings From a collection of short stories I read at least 30 years ago. :/  This is going to be incredibly vague, so apologies in advance.  A human and alien (blob/octopus-like...I think) from warring races are captured by an unidentified higher intelligence and put in an enclosure (more like a zoo habitat rather than a prison cell). They are separated by an invisible barrier and can see each other.  I think they were both trying to escape or trying to figure out how they could kill the other first. There was a bulldozer/loader type vehicle they could use at one point to build a shelter (or something).  I believe they were crafting makeshift weapons as well. There was no communication between the two as far as I remember.  The main tension in the story seemed to be was the race to get to the other first.  This has been stuck in my head forever. I know its a very common theme.  The short stories may have included Asimov. Each  has a compiled cost that contributes towards the  compiled character formula limit.  What are the current compiled costs associated with each formula function?