I got the above named error after changing an eqnarray envrmt to align envrmt. I was wondering if align does not work with doc class scrartcl, but the mwe of other users also seem to work like that. Also the error can't be in the formula, as in a sample formula like below the same problem occurs.  Any ideas?  \documentclass[a4paper,12pt]{scrartcl}  \usepackage[ngerman]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath, amssymb, graphicx} \usepackage{color}  \newcommand{\eq}{\begin{equation}} %Shortcuts für num. Einzelformel \newcommand{\eeq}{\end{equation}} \newcommand{\eqs}{\begin{align}} %Shortcuts für ausgerichtete num. Formelsysteme \newcommand{\eeqs}{\end{align}}  \begin{document}      \eqs a&amp;=b+c\\ de&amp;=fg+hi \eeqs  \end{document}
I know from the  that it is not possible to introduce direct abbreviations like \newcommand{\bal}{\begin{align}} % doesn't work \newcommand{\eal}{\end{align}}   % doesn't work  or \newcommand{\bal}{\align}    % doesn't work \newcommand{\eal}{\endalign} % doesn't work  What is puzzling me is that \newenvironment{foo}{\align}{\endalign}  does work, at least if one is well-behaved enough to diligently type \begin{foo}...\end{foo}, since \foo...\endfoo won't work either. I'd really appreciate some help to shed some light on what is going on behind the scenes :-)
Non abelian Lie group with abelian Lie algebra EDIT:  My question was poorly worded.   I wasn't asking about showing $\ln(1+x) &gt; \frac{2x}{2+x}$ for $x&gt;0$.   What I wanted to know is why the lower bound provided by $ \frac{2x}{2+x}$ was so tight for small positive values of $x$. This is addressed in robjohn's answer. Automatically keep current version of config files when apt-get install Linethrough/strikethrough a whole HTML table row I have searched through the internet and in AskUbuntu, but I could not find a working solution for my little problem.  The RTL8723ae WLAN is behaving strangely on Ubuntu 14.04 and drops the WLAN connection constantly. I am using the notebook MSI GE40 and have already seen on the web that there are other people having the same problem but there was no permanent solution. The problem did not exists on the original Windows 8 on the device and the router is a TP-Link, which I can control (channel change and so on, I use WPA2-PSK WLAN security). I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's equations. These equations are invariant under many transformations (Lorentz transformation, rotations, spatial and temporal translations, etc. By the way is there a way, maybe from group theory, to find all the possible transformations that leaves the equation(s) invariant?) which imply as many conserved quantities thanks to Noether's theorem. In wikipedia I can see an equation that seems to give all the conserved quantities () but it involves the Lagrangian and I'm not sure whether the formula is valid for all systems whose Lagrangian is possible to obtain. Equal standard errors for all levels of a categorical factor in lmer I have a question about the standard error of mixed model parameters estimated using the lmerTest package.  I have 12 sites with 6 treatments over each site. I measured a response variable (biomass_of_insects) (which has a Gaussian distribution).   library (lmerTest)   model &lt;- lmer(biomass_of_insects ~ as.factor(treatments) + (1 | sites))   However, the model summary shows the same standard error for every treatment (see below: 114.065). Why is the standard error always the same?   Fixed effects:                                Estimate    Std.err      df       t        p (Intercept)             501.333     80.656  66.000   6.216 3.91e-08 *** as.factor(treat)F       126.667    114.065  66.000   1.110    0.271  as.factor(treat)I        -8.333    114.065  66.000  -0.073    0.942      as.factor(treat)I+F1/3  -75.000    114.065  66.000  -0.658    0.513    as.factor(treat)I+F2/3   18.333    114.065  66.000   0.161    0.873     as.factor(treat)I+F3/3   15.917    114.065  66.000   0.140    0.889 Do the automatic success and failure rules apply to skill checks? We had a rule check tonight that we couldn't answer. On the Pathfinder wiki I could only find info on natural 20s and 1s in regards to attack rolls and saves in combat.  Do they also apply to skill checks? What is wrong with this deduction to show that within a multiplet different state has different square angular momentum? I am watching Susskinds's lecture , in which he introduced square angular momentum operator $L^2$, which can be written as $$ L^2=L_z^2+L_-L_++L_z $$ where $$ L_\pm=L_x\pm iL_y $$  Besides, he argued that the spectrum of $L$ can only be $m,m-1,\cdots,-m+1,-m$ in which $m$ is an integer or half-integer. If we denote $|m\rangle$ the eigenvector corresponds to eigenvalue $m$, we have $$ L_\pm|l\rangle=|l\pm 1\rangle\;\text{or}\;0 $$  In the lecture he showed that $L^2|m\rangle=m(m+1)|m\rangle$ for $m$ the highest eigenvalue, by $$ \begin{align*} L^2|m\rangle&amp;=L_z^2|m\rangle+L_-L_+|m\rangle+L_z|m\rangle\\ &amp;=m^2|m\rangle+0+m|m\rangle\\ &amp;=m(m+1)|m\rangle \end{align*} $$  Then he left an exercise to show that for any $-m\leqslant l&lt; m$, we also have $|l\rangle$ is an eigenvector of $L^2$ with eigenvalue $m(m+1)$.  In the lecture, he hinted by showing that it suffices to show that $L^2$ commutes with $L_i$ for $i=x,y,z$, which gives us $$ L^2|m-1\rangle=L^2L_-|m\rangle=L_-L^2|m\rangle=L_-m(m+1)|m\rangle=m(m+1)L_-|m\rangle=m(m-1)|m-1\rangle $$  I believe it is true since I find the   online.   However, my question is that, why the following proof is wrong.  I tried to mimic the proof for $|m\rangle$ to have that  $$ \begin{align*} L^2|k\rangle&amp;=L_z^2|k\rangle+L_-L_+|k\rangle+L_z|k\rangle\\ &amp;=k^2|k\rangle+L_-L_+|k+1\rangle+k|k\rangle\\ &amp;=k^2|k\rangle+|k\rangle+k|k\rangle\\ &amp;=(k^2+k+1)|k\rangle \end{align*} $$  which shows that $|k\rangle$ does not have eigenvalue $m(m+1)$ but $k^2+k+1$ for $k&lt;m$. I am thinking about a wizard who has a rat familiar (from the  spell), and has the  spell prepared. Can he use his familiar's senses to teleport into another room (where the familiar is hiding) by looking through the eyes of the rat and casting misty step?  The wizard could use his action to switch to the familiar's senses and then use his bonus action to cast the spell. This would greatly reduce the "blind and deaf" time he experiences from doing this. Is there a way to unlock PDF documents? I realize most PDF documents are locked for a reason, but I spend several hours a week editing datasheets provided directly from my vendors to be sent to customers. Obviously it's very annoying and somewhat of a show-stopper when I download a datasheet in PDF format, then I am not able to draw boxes, add comments, or draw arrows to the supplied product.  One of our vendors told us the way around that was to print a physical copy, then scan it in as a PDF - not the most technological or aesthetically pleasing solution I have found.  I at least would like to be able to print the PDF to another PDF so that the new copy is unlocked for editing. Is there any way around this? What statistical test to use for discrete predictor and response variables? I'm doing a statistical analysis of a model for college. It's modelling a bear catching fish and I'm asking will the amount of time taken to digest the fish have an effect on the amount of fish caught? (stupid question I know!) So the predictor variable is the amount of fish the bear can eat before it needs to digest and the response variable is the amount of fish it catches. The predictors varies between 1 and 30 in integers and the response is also in integers. I repeated each level of the predictor 5 times creating a sample size of 150 altogether. I was thinking of just using a simple correlation test such as cor.test in R, but I've read online that this is for continuous data. Does that matter or would this test still be appropriate? Thanks a million, Eamon Finding conditional distribution Let $X$ and $Y$ be independent $Exp(1)$-distributed random variables. Find the conditional distribution of $X$ given that $X + Y = c$ ($c$ is a positive constant).  this is my idea:  $$f_{X \mid X+Y}(x\mid c) = \frac{f_{X,X+Y}(x,c)}{f_{X+Y}(c) } $$  if this is the right definition then i might calculate the righthand side to obtain the distribution but Iam unsure How much money do I need to make in order to generate 1k/month for the rest of my life? Is that even possible? If yes, in what way? Edit: I am 30 years old. Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$ For an odd prime $p$, prove that any primitive root $r$ of $p^n$ is also a primitive root of  $p$   So I have assumed $r$ have order $k$ modulo $p$ , So $k|p-1$.Then if I am able to show that $p-1|k$ then I am done .But I haven't been able to show that.Can anybody help me this method?Any other type of prove is also welcomed. Question involving the Cauchy-Goursat Theorem Show $\int_C \frac{dz}{(z-z_0)^n} = 2\pi i$ when $n = 1$ and 0 when $n \gt 1$   I'm not entirely sure how to approach this one.  Any help would be much appreciated. Preloading images with jQuery As the title asks, why didn't the basilisk bite received in the Chamber of Secrets destroy the Horcrux inside the bitten person?   Yes, I know Fawkes quite quickly healed the bite wound with his phoenix tears, but when Harry used the basilisk fang to destroy Tom Riddle's diary the destruction of that Horcrux was immediate. When Ron hit the locket with the Sword of Gryffindor, it was destroyed immediately. Although the destruction of the ring occurred off-page, Dumbledore used the Sword of Gryffindor to destroy it, so presumably, like the locket, it was gone right away. Nagini died straightaway when Neville decapitated her. The destruction of the Hufflepuff cup happens off-page. The diadem seems to have been destroyed by Fiendfyre immediately as well, as when Harry examined it outside the Room of Requirement it was already leaking a blood-like substance, and then it cracked in half. When Voldemort hit Harry with Avada Kedavra in the forest, Harry woke up in limbo with the last fragment of Voldemort's soul - that awful flayed baby-like being - separated from him immediately.   Is there a logical/canon-based explanation for why the fragment of Voldemort's soul residing in Harry wasn't destroyed upon Harry being bitten by the basilisk?  NOTE: I've read the HP Wiki's entry on Horcruxes; however, I find the HP Wiki to be inconsistent in its accuracy, so I'm hesitant to accept the Wiki's explanation on the matter. I'd prefer an explanation constructed from information in the books or a statement by JKR, or the like. What is the maximum number of Locations Discovered that one can achieve in Skyrim? To debug a JACK/Pulseaudio issue, I want to understand when and why the pulseaudio daemon is started by systemd (on Fedora).  Using:  $ ps -o'pid,ppid,args' `pgrep pulse`   I see that the pulseaudio daemon is being started by systemd (pid=1)   PID  PPID COMMAND 2738     1 /usr/bin/pulseaudio --start   However, I was unable to find any unit-file on my system containing pulseaudio or even just pulse.  My specific questions are:  A) Is there a way to determine the systemd unit that caused the creation of a specific process (in my example output, process 2738, the PA daemon)?  B) Are there alternative approaches to find out which unit-dependency chain or other settings of systemd resulted in the invocation of /usr/bin/pulseaudio --start?