I want to use the align environment inside a list but the equation shouldn't be centered with respect to the pagewidth but with respect to the intented block of the list.   A minimal example:  \documentclass[12pt,a4paper]{amsart} \usepackage[utf8]{inputenc} \begin{document} Some text.. \begin{itemize}     \item Very import point:     \begin{enumerate}         \item Yet another very important point substantiated by a long equation         \begin{align*}             x^2+y^2+5\int_{10003}^{10033455}\sin x\;dx+\tan^2(74638263x^2)=1.         \end{align*}      \end{enumerate} \end{itemize} \end{document}   I want to have the long equation centered under point (1).
I have equations inside an environment which has a larger left-margin than the main text (analogous to an enumerate/itemize environment, implemented with the changepage package's adjustwidth environment). Just as equations in enumerate/itemize behave, the equations are centered with respect to the entire text, rather than just the width of the container environment. I want the latter behavior.  I'm trying to accomplish this by wrapping all display-math in minipages. Namely, I'm modifying the mathdisplay environment in amsmath.sty as follows:  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother   This is almost working, but there are some issues with spacing which I don't understand how to fix. Here's how the the normal \[ ... \] and numbered \begin{equation} ... \end{equation} look with the above modification:      My main confusion is why the numbered version is behaving so differently from the unnumbered. But all in all I want to fix this so that the spacing above and below is even as it usually is. Any help is appreciated, thanks.  Edit: Here's a compilable example:  \documentclass{amsart}  \usepackage{lipsum} \usepackage{calc} \usepackage{changepage}  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother  \setlength{\parindent}{0pt}  \begin{document}  \lipsum[1]  \begin{adjustwidth}{20pt}{} \lipsum[2] \[ x \mapsto \hom(-,x) \]  \lipsum[3] \begin{equation}   y \mapsto \hom(y,-) \end{equation} \lipsum[4] \end{adjustwidth}  \lipsum[5]  \end{document}
For example, the radiation dominated cosmology, the energy density of radiation is proportional to $a^{-4}$ and the volume is proportional to $a^3$, where $a$ is the scale factor. So the total energy of radiation is propotional to $a^{-1}$. So where is the loss of energy of radiation? Is it because the gravitational field has the energy? Does $\nabla_aT^{ab}_{\rm matter}=0$ represent the conservation of energy and momentum of matter field in GR? How do you protect a camera and lens while photographing in rain or snow? I've been trying to photograph lightning lately, as we have had some great storms in Colorado. I've had some difficulty getting a good vantage point, however, as almost all of these storms include rain as well. To keep my camera from getting drenched (I have weather-sealed lenses, but my camera body, a Canon 450D, is not weather sealed as far as I can tell), I've had to shoot under the eve of a building or under a thick canopy of trees, however that has greatly limited my ability to adapt to the changing weather and get get a vantage point on the best lightning.  Is there any equipment, something I can purchase or something home-made that has easy-to-find parts, that can help me protect my lens from the rain while still being able to shoot? Additionally, I've been getting rain on a UV filter I have on the front of my lenses, simply to prevent rain from getting on the front lens element itself. However, once a storm really gets going, so does the rain. Is there a simple solution to keep rain off the front of the lens? What are useful websites for scouting GIS related jobs? MLE for Poisson-binomial distribution I am looking for the maximum likelihood estimator (MLE) for the .  I understand the derivation of the MLE for a  and a , but I am unable to derive the MLE equation for the Poisson-binomial distribution. Word for two collections that do not have any elements in common I'm looking for a word for when you have a collection A and a collection B and they have no overlap.  In mathematical terms: the relation between two sets where the intersection is empty. Like in this Venn diagram:    The word that keeps popping up in my mind is disparate sets, but I don't feel that completely covers the meaning when I look at the definition, because that doesn't seem to preclude overlapping sets that are different:     disparate   1. distinct in kind; essentially different; dissimilar:   disparate ideas. Discoveryd Alternative to Replace mDNSResponder Argument? This is a direct follow-on to . , I'd add the "-AlwaysAppendSearchDomains" argument to the mDNSResponder plist file so that all local resolver lookups added the search domains, regardless of whether there was a period in the label to be looked up. For example, whether I try to ssh to hostname foo.bar or foo, the search domain of baz.com should be tried, not only for the latter case, as was (and is) the default behavior.   Now, it looks like the mDNSResponder is gone, replaced with discoveryd. I cannot find a similar option to get it to always appending the search domain. Suggestions? I'd rather not go the route of using a non-default local resolver, but I'd consider it as an option. For now, I'll just type in the long FQDNs, but I'd really rather not.  Thanks, Pete What prefixes should be used on reference designators for components of various types?  I think we can all agree that "R##" refers to a resistor, "C##" refers to a capacitor, and "L##" refers to an inductor.  Beyond that, it appears to be a mishmash of conventions.    I've seen both "IC" and "U" used for chips.   "Q", "T", and "M" have been used for transistors and MOSFETs.  Ordinarily, "D##" is used for diodes, but LEDs and Zeners get special treatment on some boards.    What standards are available for reference, and who endorses them?  JEDEC, ISO, IEEE, and other standardization bodies are welcome references (though I'd prefer an inexpensive standard), but I'm also curious to see what's used at various companies other than my own.    Edit:  What I'd really like to see is a list in an answer here which complies with the standard (even if it's just a quote). I've got a circuit in the basement carrying a handful of outlets.  This circuit has no ground wire.  I want to add a couple of outlets and want them to be grounded.  I may even want gfci outlets on them in the future.  I have no reasonable way of getting a ground wire to the panel but I do have easy access to another circuit that does have a ground wire.  Is it acceptable to borrow or share a ground wire between circuits?  If not, why not?  Both circuits are 20A with 12 AWG wire. I'm looking at buying a second-hand Mac, probably one that does not include an OS installation disk.  How can I scan it to make sure that it has not had security threats installed on it?  Is there a CD or DVD image I can boot it up with to perform this scan offline?  Edit: prospective machine would be a 2011- or 2012-vintage MacBook Pro.  Also note that I don't have reliable access to high-speed internet, so solutions that involve downloading 5GB over the Internet are not ideal.  For others, though,  may be helpful. Why are useful questions on StackOverflow being closed as non-constructive? Useful threads are being closed as "not constructive:"     This question is not a good fit to our Q&amp;A format. We expect answers to generally involve facts, references, or specific expertise; this question will likely solicit opinion, debate, arguments, polling, or extended discussion. See the .   For example,  was very useful for me since I am new to obfuscation and the question gave me a start. Also that question has lots of votes and bookmarks - these alone are the  markers of usefulness. The question is closed anyway. No idea why.  Same happened to my question, , which received one bookmark immediately.  I was waiting for an answer with the two products downloaded and installed.  I desired that experienced people would share their thoughts and point me to the better one. No. Closed. I.e. I must go to some other forum and ask there or I must search on Google and write down the pros and cons of each myself. I am not asking questions just because I have tons of time and want to chat; I need an answer, that's why I am asking. I am asking because I think that SO has the most professional people to answer and because I didn't find a good answer in Google.  I saw other questions closed which I myself found to be useful and I bookmarked some of the closed questions.  UPDATE  If I want people who have an experience which I do not have with some software products and I want to see which product is better in the terms of usability and reliability, not just better in terms of the price or has a better official website or better described on the official website, how do I ask this question? Or is this a question which I cannot ask on SO? I.e. this sort of information is not available on SO?  Is this one breaking the rules as well:  ? What is the fastest way to get from Courmayeur/Aosta to Milan? I found "A sledgehammer to crack a nut" as one example. What are some others? sample make file for creating more than one exe files with different directory Ubuntu 13.10 to 14.04 Lts does not upgrade, keeps showing error The update from Ubuntu 13.10 to 14.04 LTS does not work it keeps showing me an error as could not calculate the upgrade, even when I want it to get updated from the terminal it says the same error. I did not use the beta its the final Ubuntu 14.04 LTS.I have restarted my laptop for like 5-10 times no change. Disabling the software sources also does not help. Function is Continuous When Restricted to Closed Sets Which Cover the Space Suppose that $\{A_i\}$ is a finite collection of closed sets in $X$ such that $X = \bigcup A_i$, and $f : X \to Y$ restricted to each $A_i$ is continuous. Then $f$ is continuous.   Okay. The base case ($n=2$) is just the pasting lemma. I am having a little trouble with the inductive case, specifically with what the hypothesis is and how to deal with continuity with respect to subspaces. I believe the inductive hypothesis is to assume that any function over a topological space that is the union of $n-1$ closed sets such that the function restricted to each of these $n-1$ closed set is continuous must be continuous over the whole space. Then I assume I have a topological space $X = \bigcup_{i=1}^n A_i$, where each $A_i$ is closed, and a function $f : X \to Y$ such that $f|_{A_i}$ is continuous for each $i$. Thus $X = \bigcup_{i=1}^{n-1} A_i \cup A_n$, where $C = \bigcup_{i=1}^{n-1} A_i$ is closed since it is a finite union of closed sets. If I can show $f|_C$ is continuous, then I simply apply the pasting lemma to finish the problem. Give $C$ the subspace topology, and notice that each $A_i$ is closed in $C$. Thus we have a topological space $C$ that is the union of $n-1$ closed. But do I still have continuity $f$ restricted to $A_i$ since I am no longer considering them subspaces of $X$ but of $C$? When one says $f|_{A_i}$ is continuous, is one saying that $f$ is continuous when restricted to $A_i$ and $A_i$ is given the subspace topology?  EDIT:  I think I figured out the lemma I need. Claim: Let $A$ and $C$ be subspaces of $X$ such that $A \subseteq C$. Topologize $C$ with subspace topology with respect to $X$. Then the subspace topology on $A$ as a subspace of $X$ (call it $\tau_X$) is the same as the subspace topology of $A$ as a subspace of $C$ (call it $\tau_C$).   Proof: Let $U$ be open in $X$. Then $A \cap U$ is some open set in $A$ as a subspace of $X$. Since $C$ is a subspace of $X$, $C \cap U$ is open in $C$ as a subspace of $X$. Then $A \cap (C \cap U) = (A \cap C) \cap U = A \cap U$ is open in $A$ as a subspace of $C$, thereby proving $\tau_X \subseteq \tau_C$. Now let $O$ be some open set in $C$ as a subspace of $X$. Then $A \cap O$ is some open subset of $A$ as a subspace of $C$. But $O = C \cap U$ for some open set in $X$. Therefore $A \cap O = A \cap (C \cap U)= A \cap U$, which is also open in $A$ as a subspace of $X$. Hence $\tau_C \subseteq \tau_X$  Kind of obvious. But it was hard to spot the need for this lemma when I was considering subspace of subspaces and continuous functions, etc. Am I right in thinking this is the lemma I need? Why is King Arthur female? Why is Iskander tall? I've watched both the Fate/Zero and Fate/Stay Night anime (including the Unlimited Blade Works movie), but none of the visual novels, so no spoilers from that unless they are light spoilers. One thing that bothered me was that despite the fact that heroic spirits are defined by the public opinion/view of them, some heroes had qualities that were in direct opposition of what the public thought.  We know that heroic spirits, being sealed on their Throne of Heroes, are meant to be completely unchanged. This is the entire point of the Throne of Heroes. But this seems to be in opposition of the previous fact that heroic spirits are defined by what others think they are. Then there are Counter Guardians who are completely different, I believe, in that they are not sealed on their Throne of Heroes.  One particularly important Counter Guardian of the series is Arturia, or Saber. Arturia is female, despite the fact that she was treated by even her contemporaries as male, and has gone done in history as male. In fact, there isn't even any small hint as to Arturia's gender being anything other than male in our history, or the history of the Nasuverse (I believe). This being true, shouldn't Arturia be male?  This not being the case shouldn't Arturia be erased, or else create instability in the World? Same with Iskander. In history he is known for being pretty short, even for a Macedonian. That he is very tall means there is an incongruity with human knowledge and true fact.  Furthermore, in the Unlimited Blade Works movie Archer is revealed to be Heroic Spirit Emiya. If Heroic Spirit Emiya is summoned before he is even a hero, or acquired his gift from the World, etc., then how is it that Heroic Spirit Emiya is even strong at all? The power of a Servant being based on their popularity at the time of their summoning, Emiya should be weaker than pretty much every other Servant, and then some.  Maybe I'm just over-analyzing things, or I have some misconception. In any case, answers are appreciated. How to make \hl (highlighting) to automatically place incompatible commands in \mbox? The soul package provides a useful command \hl for highlighting text. However, \cite, \ref, and some other commands (maybe equations too) must be placed within an \mbox in order for \hl to work properly.  Is there any way to make this automatic? Meaning that to modify \hl (and other commands provided by soul) to put everything except plain text in an \mbox?  \documentclass[12pt]{article} \usepackage{soul} \begin{document}  \section{1}\label{sec} This is to show that \textbackslash{hl} fails to highlight texts containing citations or reference!  \hl{ This is one line containing a citation \mbox{\cite{}}}  \hl{ This is one line containing a reference \mbox{\ref{sec}}}   \end{document} Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix crossfade between 2 videos using ffmpeg Can an ideal in a commutative integral domain be its own square? If $I$ is a non-zero proper ideal of a commutative integral domain, is it possible for $I$ to be its own square?