When light is moving from a less dense medium to a more dense medium, does the reflected ray ever have a higher intensity than the refracted ray?
Relation between intensity of light and refractive index
MWE:  \documentclass{article}  \usepackage{listings}  \begin{document}  IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII hardware/software  \end{document}   This results in this output:    If \usepackage{listings} is commented out, the hyphenation rules return to normal:    And just to note, in the actual environment I'm working in, it will also hyphenate between hard•ware, while with listings enabled, it hyphenates hardware/•software, as in the first image:    Two questions:   Why is this happening? Is there a way to disable this? I don't really want this behaviour just because I'm typing code occasionally in a document. I have some basic data on emission reductions and cost per car:  q24 &lt;- read.table(text = "reductions  cost.per.car     50  45     55  55     60  62     65  70     70  80     75  90     80  100     85  200     90  375     95  600     ",header = TRUE, sep = "")   I know that this is an exponential function, so I expect to be able to find a model that fits with:      model &lt;- nls(cost.per.car ~ a * exp(b * reductions) + c,           data = q24,           start = list(a=1, b=1, c=0))   but I'm getting an error:   Error in nlsModel(formula, mf, start, wts) :    singular gradient matrix at initial parameter estimates   I've read through  on the error I'm seeing and I'm gathering that the problem is probably that I need better/different start values (the initial parameter estimates makes a little more sense) but I'm not sure, given the data that I have, how I'd go about estimating better parameters. I am able to locate files in a folder containing a specific text string using this command:  grep -lir 'string' ~/directory/*   How do I move the files that appear in the above result to another location? We have played a 7-team competition, all seven teams met, we eliminated the team with the lowest points. After that the remaining six teams played knock out games and the three winning teams will go direct to semi-finals.  We decided that 4 teams should be picked to go for semi-final and that the best loser will join the other three to make it four teams to battle at the semi-final and final.  During the quarter final games, one team is beaten 2-0, another is beaten 3-0 and the third team is beaten in a penalty shoot-out by 4-0.  Now should you want a best loser to join the other three teams making four teams to play in the semi-final, who among these three teams would be in the best losers position. How do I find out what tool a shortcut is triggering? I used to have problem with connecting two objects, because when I smooth the final object, there was a darker line on the connected parts (for example when I was making head, I've had eyes darker this way). Then I found out that I can get rid of it by hitting Ctrl+N, but I don't realy know what it does. I can just see that the lines are gone. So, what does Ctrl+N do? Which commit has this blob? Given the hash of a blob, is there a way to get a list of commits that have this blob in their tree? How do I install an application from a .dmg disk image? I've downloaded Firefox and it's now sitting on my desktop as Firefox.dmg. When I double click on Firefox.dmg it opens up a window with Firefox in it so I can use it - does this mean the application has been installed?    Community Wiki'd the question because I think it's a worthwhile question to have on the site for pointing people to, it's not exactly intuitive to do and not a question I think I deserve any rep from. What's the difference between an inverter with a bubble at the input and one with a bubble at the output? See , page 2: the internal logic diagram for the MM74HC138.    The diagram shows logic inverters with bubbles at the input or at the output. Is there an actual difference between them? I'm working on a mac, I use the package TikZ and it works. But I have problems when I want use ellipse or diamond ex :  \documentclass{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[ellipse] {Ellipse}; \end{tikzpicture} \end{document}   If somebody could help me thank you ! What are the “spam” and “rude or abusive” (offensive) flags, and how do they work? When flagging, there are two special case options: spam and rude or abusive.   What is spam, and when should I flag content as such? What is considered offensive, rude or abusive content? How does the spam flag differ from the rude or abusive flag? What is the effect of these special flags? When are these flags removed? Expanding a parent  to the height of its children I have a page structure similar to this:  &lt;body&gt;   &lt;div id="parent"&gt;     &lt;div id="childRightCol"&gt;       /*Content*/     &lt;/div&gt;     &lt;div id="childLeftCol"&gt;       /*Content*/     &lt;/div&gt;   &lt;/div&gt; &lt;/body&gt;   I would like for the parent div to expand in height when the inner div's height increases.  Edit: One problem is that if the width of the child content expands past the width of the browser window, my current CSS puts a horizontal scrollbar on the parent div.  I would like the scrollbar to be at the page level. Currently my parent div is set to overflow: auto;  Can you please help me with the CSS for this? Greek pdf bookmarks I am puzzled with sections titled with Greek characters. They do appear in the pdf's Content list, though not correctly.  For example, in my thesis--written in English with LyX, based on the KOMA-script--I choose to include a translation of the summary in Greek (=Περίληψη). The "raw" code for the (unnumbered) chapter title reads: \addchap{\textgreek{Per\char208lhyh}}. In the final .pdf file (using pdflatex) the respective entry appears as Per208lhyh. Using the unicode option for the hyperref package does not fix the problem.  Update detail: the document (should) not only contain Chapter or Section titles in Greek, but normal text as well.  I have found some relevant references within tex.stackexchange and elsewhere (e.g., , the manual of the textgreek package, , ). However, I cannot extract a concrete answer.  How can Greek characters appear correctly as bookmarks in the .pdf's Content list?  Note, the information of this Q&amp;A applies to/under LyX as well. I am looking for a word that would describe someone who always goes out of their way to take their time and do a good job. Sort of the opposite of half-assing something.  I am looking for something that is more about a work ethic than a technically proper way of doing things. Something like canonical or protocol would not be a good fit. $t^3$ is never equal to Let $t$ be a real number such that $t^2=at+b$ for some positive integers $a$ and $b$. Then for any choice of positive integers $a$ and $b$, $t^3$ is never equal to: (A). $4t+3$ (B). $8t+5$ (C). $10t+3$ (D). $6t+5$  We have $t^3 = at^2+bt$ and so for (A) we have $t^3 = 4t+3 = 4(at^2+bt)+3$. I don't see how to continue since this is a cubic equation. Is there an easier way of finding a contradiction? What is the simplest SQL Query to find the second largest value? Allow an edit to notify downvoters: "I think I've fixed the issue now - please check" In Rey's vision, whose voice says "These are your first steps"? Why don't we treat rubbish the same as spam? Spam gets fairly heavily punished - 100 reputation penalty, if I recall correctly, and the content itself gets hidden in the revision history.  Now if we just have some rubbish:     dfajiojaifojadiofjadhigaowkokaomdiovnuiyhioqejgioqejgio   I'm not talking about someone posting a question or comment as an answer (i.e. possibly just not knowing the rules or being frustrated with not having the required privileges), or someone making some really horrible attempt at answering the question, I'm talking about an answer that clearly shows absolutely no observation of any content on the page.  This, in my opinion, causes a similar amount of harm to the site - I'm inclined to say the fact that someone posts spam isn't as important as the fact that they're posting something that needs to be deleted, since we're likely going to delete it pretty quickly, and they're (likely) behaving maliciously, or am I wrong?  Why don't we treat this equally harshly, or why do we treat spam as harshly as we do?    Side notes:  I'm sure I've seen a few times where users get punished for posting spam when their link is likely actually relevant to the question and useful (should I flag these? They are still link-only answers, so they shouldn't really come back, and often I'm just not sure enough). While false positives are bad, it seems worse that we're treating worse behaviour better.  I'm assuming that's not what "abusive" in this reason is referring to: (I'm also not sure, off the top of my head, how this one gets treated)     It is offensive, abusive, or hate speech A diffeomorphism whose tangent map preserves dot products is an isometry. I'm having trouble solving the following problem.  If $F:\mathbb{R^3} \to \mathbb{R^3}$ is a diffeomorphism such that $F\ast$(the tangent map of $F$) preserves dot products, show that $F$ is an isometry. (Hint: Show that $F$ preserves lengths of curve segments and deduce that $F^{-1}$ does also.)  I'm trying to proceed as in the hint, but I'm stuck on the first step, showing the $F$ preserves lengths of curve segments. Moreover, how does showing that both $F$ and its inverse preserves length of curve segments show that it is an isometry. And how do I characterize the curve segments. I would appreciate any solutions, hints or suggestions. Can I travel to France with Fiktionsbescheinigung (Fiction Certificate) of Germany