The latest xelatex update make the beamer ball disappeared
XeLaTeX update [20201004] and item ball in Beamer
I was doing a package removal with apt-get remove but then realized I should have done a --purge along with it to remove the configuration files.  Can I remove the packages configuration files easily or do I need to reinstall the package and then remove with a --purge? "There are no comments" vs. "There is no comment" Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values? Word for a temporary project name I need a poll inside my content types.  Sometimes the users create an article and like to create a poll directly into the node they created. They don't want to create an extra poll with no connection to the original article.  So how can I get the poll functionality inside a different content type? Object selection box with eyedropper Why is 'that' sometimes optional before dependent clauses? copy and paste doesn't work in terminal Is there an easy way to calculate the residue at one of the poles of a rational expression of the form $\frac{1}{1+z^n}$?  I end up having to add a bunch of polar-form complex numbers in the denominator which I have no idea how to do except to convert them to rectangular coordinates, which becomes really messy.  I feel like there ought to be simple pattern/rule for such a canonical expression. Do downvotes on Meta truly mean something different? It is often said that voting on Meta means something different than voting on regular sites. Upvotes mean "I agree", and downvotes mean "I disagree".  However, I submit that this is not the case. Downvoting of a question has one effect in particular: censorship.  Once a question reaches -8 votes, it disappears from the front page. It can still be found; it isn't deleted. But all it takes is a net 8 downvotes for a question to be more or less lost without a direct link.  You might say that a net 8 downvotes obviously means that the community doesn't agree or want that. Well... does it? Particularly on polarizing issues, a question can temporarily get -8 votes as different people come online and see it. Maybe certain people with a certain belief all see it at once and downvote it a lot.  The front page is how most people find stuff they want to talk about, vote on, or answer. Removal from the front page means that most people will not find it without being pointed directly to it. Once a question hits -8, it is unlikely to be upvoted again. Edits will be irrelevant, new answers won't matter. The question is basically exiled.  The problem is that, on polarized topics, fast mass downvoting can quash any idea that is not popular with the most active members. After all, the most active members are the ones who are most likely to be online and see it. If a bunch of MSO regulars see it and downvote it, it goes away. Someone who checks MSO maybe once a day is less likely to be able to catch the question before it is exiled. This gives undue power to members who are most active on MSO, simply because they have more free time to spend on MSO.  I think this is a significant problem for polarized topics. It becomes very difficult to adequately discuss something that a significant number of active members dislike, even if the community at large doesn't mind.  Consider . It currently stands at +9/-8. Initially, in the first few hours, the question was heavily downvoted and even closed. However, after a day, it was upvoted and reopened.  This shows that a question can initially have a negative response, but later get a positive one. And you can check; any edits I did to the question were relatively minor. The question posted as is was initially negative, but ultimately positive.   If that -8 happened to all come first, odds are good that the +9 and the reopen would never have happened. Those 9 people would never have had the chance to weigh in on the subject. And that's wrong.  It is wrong for someone's potential vote to not matter just because they don't visit MSO multiple times in a day. It is wrong for someone's potential vote to not matter just because they have a different sleep schedule from many of MSO's members.  The problem is one of timing. Heavy dislike from active members who quickly see the question and downvote it can kill a question before someone who might upvote it ever even sees it.  I suppose the best suggestion would be to either lower the -8 threshold (or remove it altogether) or keep it from kicking in until 1-2 days has passed. If the question isn't active, it'll already be off the front page. And if it is active, then enough people will have seen it to know if the threshold represents a real consensus or just the fast-acting few. Complex number isomorphic to certain $2\times 2$ matrices? I have been trying to prove this, but I am having trouble understanding how to prove the following mapping I found is injective and surjective. Just as a side note, I am trying to show the complex ring is isomorphic to special $2\times2$ matrices in regard to matrix multiplication and addition. Showing these hold is simple enough.  $$\phi:a+bi \rightarrow \begin{pmatrix} a &amp; -b \\ b &amp; a \end{pmatrix}$$  This is what I have so far:  Injective: I am also confused over the fact that there are two operations, and in turn two neutral elements (1 and 0). Showing that the kernel is trivial is usually the way I go about proving whether a mapping is injective, but I just can't grasp this.  $$ \phi(z_1) = \phi(z_2) \implies \phi(z_1)\phi(z_2)^{-1} = I = \phi(z_1)\phi(z_2^{-1}) = \phi(z_2)\phi(z_2^{-1}).$$  So if we can just show that the kernel of $\phi$ is trivial, then it also shows that $z_1 = z_2$. The only complex number that maps to the identity matrix is one where $a = 1$ and $b = 0$, $a + bi = 1 + 0i = 1$.  Using a similar argument for addition we can just say that the only complex number $z$ such that $\phi(z) = 0\text{-matrix}$, is one where $a=0$ and $b=0$, $a+bi=0+0i=0$.   Surjective:  I forgot to add this before I posted, but I honestly don't really understand how to prove this because it just seems so obvious. All possible $2\times2$ matrices of that form have a complex representation because the complex number can always be identified by its real parts and since the elements of the $2\times2$ matrix are real then the mapping is obviously onto.  I have always had trouble understanding when I can say that I have "rigorously" proved something, so any help would be appreciated! Consider this:  \documentclass{article} \usepackage[framemethod=TikZ]{mdframed}  \begin{document} \begin{mdframed}[innerrightmargin=0pt] TEXT\end{mdframed} \end{document}   This produces a frame that is much wider than its content:    I know this is not a bug: the mdframed documentation mentions a userdefinedwidth parameter that defaults to \linewidth. But how can I get a mdframed frame that has the same width as its content?   (What I actually need is a box with rounded corners and shading options; breaking over multiple pages isn't necessary. mdframed seemed like the easiest way to get the box, but if it's too much hassle to make it size to content, it would be useful to know so I can try pure tikz.) Proper usage of "since" and "from" with regard to duration of time I've downloaded the new iOS 8 update on my iPhone 5 but am getting second thoughts about actually installing it.  Is there a way for me to delete that download or am I at the point of no return? Related:    The helpcenter has . It still links to the  for further details. Besides that, the question ban message .  Now that we have the helpcenter, could the following changes be implemented?   Link to the help center instead of the meta post Remove the link to the meta post from the help center, and instead incorporate its contents into the helpcenter itself Which is correct?     How much is the two fares?      How much are the two fares? Does a filament of lamp still have resistance when no current flows, and if yes, why? Does a filament lamp still have resistance when no current flows? What happens if I combine Ur-priest and prestige class to exceed 10 effective spellcasting levels? Suppose I have a human character who invested 5 levels on Wizard, 2 on Ur-priest(by appropriate feat chain), and 8 levels of Mystic Theurge, net level of 15. This allows you to cast spells as stated in 10th level Ur-priest Spells per day table. Now, assume that I leveled up, and I choose Mystic Theurge as the next level class. This makes me to look up Ur-priest table for Level 11, which does not exist. In this case, what happens to my divine spells per day? Does it continue to progress "in the same pattern", as Hellfire Blast progresses with Hellfire Warlock-Legacy Champion build? Does it stop and I only get Wizard spells per day? Or, isn't it allowed to do so?  I am totally aware that although the answer is "yes", it does not mean it means spells over 9th level will be granted to my character unless I take Improved Spell Capacity, which requires me to be epic. What I am curious is the progression of spells per day of existing spells.  P. S. Don't ask me how to satisfy the requirements. This is possible by combining Apprentice (Criminal), Iron Will and Great Fortitude as level-up feat, and Spell Focus (evil) as a Wizard bonus feat (RAW, it is a "Spell Focus" feat, anyway.) It's fairly straight forward to fix up a single orphaned SQL user to a login using:     EXEC sp_change_users_login 'Auto_Fix', 'user'   I could script this, but is there an existing stored procedure which automatically tries to fix up every orphaned user in a given database? Proximal Operator Fixed Point Property for Matrices $\newcommand{\prox}{\operatorname{prox}}$ $\newcommand{\argmin}{\operatorname{argmin}}$ $\newcommand{\dom}{\operatorname{dom}}$  Recall again that the proximal operator for vectors $\prox_{f}: R^n \rightarrow R^n$ of $f$ is defined as:  $\prox_f(v) := \argmin_{x} \left(f(x) +(1/2)\|x-v\|_2^2 \right) $,  where $f: R^n \rightarrow R \cup \infty$ is a closed proper convex function and $\|\cdot \|_2$ is the Euclidean norm. $\prox$ is strongly convex and not everywhere infinite, so there it will have a unique minimizer for every $v \in R^n$  The crucial property of proximal operator is that $x^*$ minimizes $f(x)$ iff $x^* = \prox_f(x^*)$, i.e. $x^*$ is a fixed point of $\prox_f$.  Let us consider the proof of this property. The first part, namely, that if $x^*$ minimizes $f$ then $\prox_f(x^*)=x^*$, is trivial:  $f(x) +(1/2)\|x-x^*\|_2^2 \le f(x^*) = f(x^*) +(1/2)\|x^*-x^*\|_2^2$  The second part uses the notion of subdifferential. In the proof authors say that $\tilde{x}$ minimizes  $f(x) +(1/2)\|x-v\|_2^2$  i.e. $\tilde{x} = \prox_f(v)$ iff $0 \in \partial f(\tilde{x}) + (\tilde{x}-v)$,   where the sum is of a set and a point. Recall the definition of the subdifferential:  $\partial f(x) = \{ y$ |  $ f(z)\le f(x) + y^T(z-x)$ $\forall z \in \dom{f}\}$  Take $\tilde{x}=v=x^*$, it follows that $0 \in \partial f(x^*)$ so $x^*$ minimizes $f$.  Question 1:  Consider proximal operator defined for matrices now:  $\prox_f(Y) := \argmin_{X} \left(f(X) +(1/2)\|X-Y\|^2 \right)$,  where $X$ is some real $m$ by $n$ matrix. What norm function should be taken in the definition of the $\prox$ in this case? Frobenius? Or spectral norm (induced 2nd norm) which is the largest eigenvalue (is spectral norm even differentiable?)? Or something else?  Question 2:   Can the norm for the definition of $\prox$ in case of matrices be chosen in different ways? What conditions does the proof above impose on the norm function?