Tikz multiline node with center align
Manual/automatic line breaks and text alignment in TikZ nodes
VS10 debugger error: Test host process exited unexpectedly Under what circumstances will a passive HDMI-to-VGA adapter work? I have bought a no-brand, passive HDMI Male to VGA Female adapter, to link up a PC with a more dated monitor. It did not work.  After doing some reading, I have learned that buying such an adapter is often discouraged because in many cases it will not convert the signal from Digital to Analog, or the Motherboard/CPU on a specific computer might not be compatible with that particular adapter.   So my question is: seeing how there are so many of these passive adapters on the market, are there circumstances under which they actually do suffice to connect an HDMI output to a VGA input? Or are they generally just a rip-off?  Example of the kind of adapter I bought: How to easily build your own Linux Distro? I wanted to have a go at creating my very own Linux Distribution. Could you suggest some nice and easy-to-follow tutorials (preferably text based and not videos). I have heard something about Arch Linux but I don't know how to go from there. What do I need? Determine group G as cyclic If $G$ has no proper subgroup, prove that $G$ is cyclic of order $p$, where $p$ is a prime number.     I know that since $G $is a group with no proper subgroups, $g \in G$ is not just the identity. I don't know where to go from there. Evolution of the (phenotypic) facial features of the indigenous people of (west/central) Africa I am not even remotely an expert in this field; I just got curious, so help me.   First of all, let us remove all human sentimental attributes from this question (such as connotations of  or emotional reactions thereof) and ask it from a purely scientific point of view. The typical facial feature of a West/Central African person (the so-called ) exhibits a wide nose, a lack of nasal bridge projection (similar to many Asian noses) and a prognathous skull shape that resembles more closely to our ancestor Homo Heidelbergensis than many other indigenous phenotypes from other parts of the world do.  I agree that this claim sounds anecdotal, and is certainly not true of all Africans (for example, Ethiopians), but one cannot dismiss it simply on grounds of ethical policing. I cannot help but notice that many of my African friends remind me of our shared ancestry (with no disrespect meant whatsoever), as is clear from the photographs below, one of a supposed Homo Heidelbergensis and one of a random African Homo Sapiens of today.     My question is the following. What is the reason behind this seeming resemblance? Is this appearance an illusion and possibly a construct of a prejudiced mind, or does this have a valid scientific answer? For example, are most Africans closer to our ancestors than the rest of humanity is? How does evolution answer this question?  Thank you for your help. There are a variety of characters that are not legally encodeable in XML 1.0, e.g. U+0007 ('bell') and U+001B ('escape'). Most of the interesting ones are non-whitespace 'control' characters.    It's clear from (e.g.)  and others that it's  -- but can anyone illuminate me as to why the XML spec forbids these characters?   It seems like it could have been required that they be encoded in escapes, e.g. as &amp;#x0007; and &amp;#x001B; respectively, but perhaps there's a practical reason that the characters were forbidden rather than required to be escaped?  Answerers have suggested that there is some motivation towards avoiding transmission control characters, but Unicode includes many other control-like characters (consider U+200C "zero width non joiner"). I recognize there may be no good reason for this behavior, but I would still like to understand it better.  It's particularly frustrating because when those character values appear in other encodings data formats, I end up "double-escaping" new XML documents that need to encode this. Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$ Suppose I want to find the minimal polynomial of the number $\sqrt[3]{2} + \sqrt{3}$.   Now that means I want to find a  unique polynomial that is irreducible over $\Bbb Q$ such that $f(x)=0$. Now I know that because   $\sqrt[3]{2} + \sqrt{3}$ belongs to $\Bbb Q( \sqrt[3]{2} , \sqrt{3})$  it might be degree $2$, $3$ or $6$ and does not belong to $\Bbb Q( \sqrt[3]{2})$ so it cannot be of degree $3$ or  $\Bbb Q( \sqrt{3})$ so it cannot be of degree $2$.  So it is of degree $6$. I think my sayings are a bit intuitive and not formal and lack rigorous. Couldn't it belong to another extension of degree $2$? or $3$? I can't answer that. Why checking only those $2$ is enough? Or is it wrong at all to say that? What is a polite substitute for badass (used as a noun)? How are quantum gates realised, in terms of the dynamic? When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions.  In some sense, these are rather mysterious objects, in that they perform "magic" discrete operations on the states. They are essentially black boxes, whose inner workings are not often dealt with while studying quantum algorithms. However, that is not how quantum mechanics works: states evolve in a continuous fashion following Schrödinger's equation.  In other words, when talking about quantum gates and operations, one neglects the dynamic (that is, the Hamiltonian) realising said evolution, which is how the gates are actually implemented in experimental architectures.  One method is to decompose the gate in terms of elementary (in a given experimental architecture) ones. Is this the only way? What about such "elementary" gates? How are the dynamics implementing those typically found? How do I run specific sudo commands without a password? On one particular machine I often need to run sudo commands every now and then. I am fine with entering password on sudo in most of the cases.  However there are three sudo commands I want to run without entering password:   sudo reboot sudo shutdown -r now sudo shutdown -P now   How can I exclude these commands from password protection to sudo? Rounding up to next power of 2 I want to write a function that returns the nearest next power of 2 number. For example if my input is 789, the output should be 1024. Is there any way of achieving this without using any loops but just using some bitwise operators? What are the dangers of accepting gifts from unknown accounts on Steam? A user named 'steamfairy1' gifted me a game on Steam. I don't know this user, their profile shows no games, no friends and zero hours played. The profile of 'steamfairy1' was created the day I received the gift.  It very much looks like a scam, but I can't figure out how the scam is supposed to work. What's the worst thing that could happen if I accept the gift? Any idea what the trick here is? It could be just a random act of kindness and I'm just paranoid…  I contacted the Steam support, but they were unhelpful as usual: responding in the wrong language and with a canned one-liner that didn't make a whole lot of sense or had much to do with my question.  Keywords (not really tags, but I want this to be searchable): steamfairy, steam fairy Question mark or bold citation key instead of citation number Under what assumptions can a semigroup $(S,*)$ be embedded into a group? I need a list of integers from 1 to x where x is set by the user.  I could build it with a for loop eg assuming x is an integer set previously:  List&lt;int&gt; iList = new List&lt;int&gt;(); for (int i = 1; i &lt;= x; i++) {     iList.Add(i); }   This seems dumb, surely there's a more elegant way to do this, something like the Is a set without limit points necessarily closed? According to the definition on Rudin' Principles of Mathematicial Analysis, closed set is defined as:      $E$ is closed if every limit point of $E$ is a point of $E$.   Then I have a question: if a set has no limit point, is it necessarily closed? I think this idea doesn't contradict the definition of closed sets. Am I right?  And another question is #10 in Chap.2 of Rudin's:      Let $X$ be an infinite set. For $p\in X$ and $q\in X$, define    $d(p,q)=0$ when $p=q$. Otherwises,$d(p,q)=1$.    I have known that every set in the metric space is closed. To prove it, we can show that the complement of any set is open, which is quite trivial. My question is: how can we prove that every set is closed just by checking according to the definition of closed set, i.e. how can we show that every limit point of any arbitrary set $E$ in the metric space is a point of $E$?   Thanks in advanced! Suppose that I have a group $G$ of order $p^{2}q$ for two distinct primes $p$ and $q$.  I need to first show that one of its Sylow subgroups is normal.  I start by letting $H$ be a Sylow $p$-subgroup and $K$ be a Sylow $q$-subgroup.  If $K$ is not normal, then letting $r$ denote the number of Sylow $q$-subgroups, I have that $r|p^{2}$ and $r\equiv 1$(mod $q$).  I also have by the second Sylow theorem that $r\neq 1$.  So $r = p$ or $p^{2}$.  If $r = p^{2}$, I can write out the Sylow $q$-subgroups, and count their combined elements to show that $H$ is uniquely determined and then again imply Sylow number $2$ to obtain that $H$ is normal.  But if $r = p$, then I cannot see how to proceed.  Can anyone give any advice?  Thank you.  ( I am happy to provide more detail for the $r = p^{2}$ case if it is desired or appropriate. ) How does damage dealt increase as you level up I've recently taken over as GM in my group.  We are all new to RPGs except for our original GM, so they decided to run an adventure path so it would be easier to change GMs if they had to stop playing.  Along this path, we had one CR 4 encounter that took us an hour, almost killed our bloodrager and knocked our brawler unconscious. When we leveled up, our GM told us to increase the damage we did by "one level," so my 1d6 became 2d6 and my friend's 2d6 became 4d6.  I saw no problem with this as a player, but I was looking over the adventure path and later encounters that also have a CR of 4 could be ended in one turn by our bloodrager. This would make encounters really boring, and my goal is to avoid boredom.  My question is: As you level up, how does the damage you do increase? Does it go up like my GM said so that at level 3 my rapier does 3d6 and the bloodrager's earth breaker does 6d6, or does it go up by some other method?  I have read the PHB and I don't think that what the GM was saying is correct, but being a first-time player I wasn't sure if had just missed something, so I figured I should ask elsewhere. I have been racking my brains over how in bloody hell can you have a different header for the title (or first) page of a document.   I am not asking here how I can not have a header by clearing the page style for this page using \thispagestyle{plain} or something of the sort but how can I have a different header just for the very first page.   Please help as I have a deadline to meet.   So far, I have not been able to find anything useful on TeX.SE.   Here is some of my code to give you some idea of what I want to achieve:  \documentclass[12pt]{article} \usepackage{amsmath} \usepackage[margin=2.5cm]{geometry} \usepackage[utf8]{inputenc} \usepackage{amsfonts} \usepackage{fancyhdr} \usepackage{hyperref} \usepackage{graphicx} \usepackage{csc} \pagestyle{fancy} \fancyhead[L]{**Left Header for all pages**}\fancyhead[R]{**Right Header for all pages**} \lhead{**Left Header for just the first page**} \rhead{**Right Header for just the first page**} \title{Problem Set 1}         \author{MyBloodyName} \date{January 31, 2017} \begin{document}     \maketitle     \newpage     Easier? \end{document} How to connect to Android through SSH over 3G/4G public IP?