Exponentiation of cardinal numbers
exponentiation of cardinal number
Do class spells take up spell slots? So I'm fairly new and ended up being the Cleric in my also fairly new group. I haven't played a caster before and the book says that at level 1 I have Bless and Cure Wounds. Do I need to assign these to a spell slot or do I have them inherently (not to be confused with a cantrip; I know I'd have to use a slot to cast them)? For an architectural visualization, I would like to use MakeHuman models, but:   Only get them to render white with a black outline (on reflection surface too, if possible). Interact with light like normal human bodies in the scene (cast shadows, etc).   I can do the outline in freestyle, but any in-Cycles solution would be appreciated (OSL?) IndentationError: unindent does not match any outer indentation level MPPT charging a li-ion battery I just designed this MPPT solar charge controller which outputs 4.2 V regulated via MPPT, it uses the SPV1040 IC. This will be used on a satellite with 4 side panels, each with 8 solar cells in parallel outputting 2.6 V at approximately 122 Ma. Each panel will have this exact circuit and all the outputs will be connected in parallel to a 3.7 V lithium ion camera battery.  When active only 1 solar panel will be active and the other MPPT circuits will be offline or providing a very low amount of current. How should I connect the 4.2v to the battery, just directly or using some sort of controller to stop charging at 4.2v? Keep in mind the battery will always have a load and it will charge for around 50m in a 90m cycle due to being eclipsed. I would obviously like the battery to last as long as possible so I am not sure what are the implications of constantly having a battery connected to 4.2 V during 50m. Thanks.   The schematic was made based off a simulation made using the ST Edesignsuite directly from the provider.  Excuse my previous question about this, wasn't properly worded. Considering phrases of the form "I left [the] X", what causes some words to need a "the" before them, while it sounds awkward with others?  Needs "the":   I left the office I left the bank I left the house I left the courthouse   Awkward with "the":   I left work I left social media I left New York   Either way works:   I left [the] school I left [the] church Is there a way to condition output on a given date? I'd like to be able to print text that varies depending on whether the date matches a given date string  For example  suppose there was a command   \iftoday#1#2#3   which printed #2 if \today matched the string in #1 and #3 otherwise.  So a sample of my proposed usage would be:     \iftoday{February 3, 2016}{There's no garbage today}{Please put out the garbage}    I've tried various commands like pdftexcmd's strcmp, to no avail.    I suspect the problem may have to do with matching the string generated by \today.    While on screen it appears that \today returns February 3, 2016. I can't get it to match February 3, 2016 when I compare strings.  Obviously, I'd be perfectly happy if I could get this to work by represent today's date in any of the standard date formats.  Thanks very much in advance for any suggestions. Let $R$ be a UFD. Then for any two elements $a,b \in R \setminus \{0\}$ $ab \sim \gcd (a,b){\operatorname{lcm} (a,b)}$.   My attempt :  Let $d = \gcd (a,b)$.Then $d|a$ and $d|b$.Then $\exists x,y \in R$ such that $a = dx$ and $b = dy$.Now it is to be shown that $c = dxy$ is the lcm of $a,b$.Which I find difficulty to show.It is clear that $a|c$ and $b|c$. Now if $u$ is any common multiple of $a$ and $b$.Then $dx|u$ and also since $y|b$ we have $y|u$ i.e. $dxy|u^2$ $\implies c|u^2$.But I have to show $c|u$ to complete the proof which I fail to prove.Please help me to complete the proof.  Thank you in advance. If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated. I'm answering this question:     Let $M$  be a module. Show that if  $M$ is not Noetherian then $M$ has a submodule $N$ such that $N$ is not finitely generated but $A$ is finitely generated whenever $N &lt; A ≤ M$.   The solution starts as follows (I'm following a given solution): Let $Y$ be the set of non-finitely-generated submodules of $M$. If $(N_α)$ is a chain in $Y$ then $Q= \bigcup_αN_α $ is in $Y$, else $Q$ is f.g., which implies $Q=N_α$ for some $α$, whence $N_α$  is f.g., contradiction.  I don't understand why if $Q$ is f.g., then $Q=N_α$ for some $α$? Am I missing some fact?  Thanks! Is a DSL splitter required, if only a Modem is attached to the line? Two "if"s in a row I am trying to create a flowchart with Tikz. Since it is a long one, it spans three pages. So after creating a node to stop, I am continuing to the next page using \newpage command. Unfortunately some elements in page 1 are connected to page 2, 3 and vice versa. So when I try to create the arrow connection, it is not possible since the \newpage command comes in between. I am sharing the code with you for info. Could  anyone help me to improve the flowchart so that I could direct the arrows among multiple pages. My sample code is below:  \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} \newpage \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} \newpage  \begin{tikzpicture} \node 1 \node 2 ........ \draw[arrow] (node1)--(node2) \draw[arrow] (node2)--(node3) ---- \end tikzpicture} I'm looking for one word which describes what a student who missed classes needs to do in order to complete his missing.   For example if he missed biology class he needs to seat with the teacher and study this missed class together with her and then he get the mark for this missed class. Someone -who isn't native English speaker- told me that it's called "rework". But I looked for it in some dictionaries (such as ) and I didn't find such definition.   : "SCHEDULE of reworks of missed classes" Do virtual particles actually physically exist? How to prove a general matrix invertible given by as below?  How to prove that $A^TA+I$ is always invertible for $\forall A \in \mathbb{R}^{n\times n}$? What does the phrase "Underfull \hbox (badness 10000) in paragraph" actually mean? What does the actual phrase above mean? Primes dividing a polynomial Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. How does Linux kernel compare to microkernel architectures? I read once that one advantage of a microkernel architecture is that you can stop/start essential services like networking and filesystems, without needing to restart the whole system. But considering that Linux kernel nowadays (was it always the case?) offers the option to use modules to achieve the same effect, what are the (remaining) advantages of a microkernel? What are the various physical mechanisms for energy transfer to the photon during blackbody emission? Hot questions no longer work on iPad (ok on iPhone) Installation of latest version R for linux First I typed  sudo gedit /etc/apt/sources.list   after that I got one sources list then I typed  deb http://cran.rstudio.com/bin/linux/debian wheezy-cran3/   then I get the error like this  No command 'deb' found, did you mean:  Command 'derb' from package 'icu-devtools' (main)  Command 'deb3' from package 'quilt' (main)  Command 'debc' from package 'devscripts' (main)  Command 'dwb' from package 'dwb' (universe)  Command 'xdeb' from package 'xdeb' (universe)  Command 'debi' from package 'devscripts' (main)  Command 'dab' from package 'bsdgames' (universe) deb: command not found   How should I proceed?