Print screen img - png/eps loses quality with no scaling
My pixel perfect picture gets blurry when compiled in LaTeX
I am currently using Ubuntu 12.04 because the latest upgrade 14.04 is not working in my system. I need to install the latest Adobe Flash Player 17 plugin, but it only allows me to install up to version 11.02, so media files cannot be opened. It says that Adobe Flash Player 17 is not compatible with my system. Showing that if $\lim_{x\to\infty}xf(x)=l,$ then $\lim_{x\to\infty}f(x)=0.$ Let $l \in\mathbb{R} $ and $ f:(0,\infty) \to \Bbb R $ be a function such that $ \lim_{x\to \infty} xf(x)=l $ .  Prove that  $ \lim_{x\to \infty} f(x)=0 $.  Any help would be appreciated - I found this difficult to prove Minkowski Metric Signature When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}   $$ where $ x^0,x^1,x^2,x^3 $ come from $ x^{\mu} : \mu = 0,1,2,3 $, and $ c $ is the speed of light. The first resource I had access to--I have to do a bit of digging for the exact paper--of course addressed that this invariant takes the tensor form: $$ ds^2 = g_{\mu \nu}dx^{\mu}dx^{\nu} $$ as well. This two things I've seen in all of my texts and online resources regarding resources. The element in question that varies between authors, is the time coordinate, $ x^0 $. When it was first explained to me, it was using the standard Cartesian representation for the spatial portion of the coordinates, and the time coordinate was labeled as $ x^0 = ict $. Squaring gives $ (x^0)^2 = -c^2t^2 $, and applying differential calculus, we get $ (dx^0)^2 = -c^2dt^2 $. Sensible and expected to have the tensor formula spit out the Minkowski Metric. The author then later explicitly states the coordinates are $ x^0 = ict, x^1=x,x^2=y,$ and $x^3 = z$.  My questions is then, why is it most authors on the subject omit the imaginary unit on the time coordinate? For example, .   The only reason I can fathom omission is if the author is using metric signature $ [+,-,-,-] $, where I started off learning the theory with signature $ [-,+,+,+] $ which may be the reason seeing the time coord with no imaginary unit seems dissonant to me. All help appreciated!  Edit: After reading the other answers, my questions is now one of why and how (mathematically) do we obtain the Minkowski Metric Signature. More specifically the one element with a different sign. I'd like to be able to easily transfer large files wirelessly, fast, between Android devices - preferably without requiring root.  As a secondary objetive, it wouldn't hurt if the same solution could be used, to transfer files between the Android devices and a Windows PC.   Specifically, I'm trying to exchange files between my Nexus 7 (Android 4.2.2) and Samsung Galaxy S2 (Android 4.0.4).   Bluetooth is simply too slow, so that's out of the question Transfer via the Internet is also not an option, hence so is cloud-based solutions Only Nexus 7 supports NFC, so that's out too  looked promising and very simple, but does not work on "Devices that don't have WiFi Tethering setting, such as the Nexus 7"   Wi-Fi direct ( and up) seems to be a decent lowest common denominator between my two devices, however...  Galaxys S2's native Send via Wi-Fi Direct sees the Nexus, but seems to get stuck in the "Connecting..." most times. When there finally seems to be breakthrough, I get "Waiting..." and a spinning circle. Even if it worked, it would only allow me to send from the Galaxy S2 to the Nexus 7, as a similar option os not present on the Nexus 7.  J4velin's  is no longer available in the Play Store, with the following explanation:     WiFi Direct drivers are broken on many devices, which led to users leaving negative reviews for this app. As I don't see any sense in keeping a free app published when only getting 1-star-ratings (for an issue which only your device manufacturer can fix), the app is no longer available at the Play Store.   Nick Adams'  seems flaky at best. Invations from Nexus 7 to Galaxy S2 are never received. Invitations from Galaxy S2 are mostly received, but even when accepting promptly, the peers doesn't always show as connected. When they finally do, usually after quite a long wait, I can select a file to send but it's never transferred -  "Transfer failed" it says almost immediately in the notification bar.  budius inc's  is working slightly better, but still very unreliable. I actually managed to (occasionally) send files both ways, but never when attempting connection from the Nexus 7. To send from the Nexus 7 to the Galaxy S2, I had to go through this akward manoeuvre:   Share the file on the Nexus 7 via the WiFi Shoot intent Start the Receive WiFi Shoot app on the Galaxy S2 Invite the Nexus 7 from the Galaxy S2 (never the other way around!) Accept the invitation on the Nexus 7 Press the Shoot button on the Galaxy S2   Take the whole switching back and forth between devices, and garnish with random delays or failures in any step of the process...  Is there really no easy, reliable, fast way to transfer files directly between different Android devices?  Generally, my experience with Wi-Fi Direct is all but positive...   A device often won't even see a device lying next to it Sometimes, it will see the other device, only to have it disappear from the list, before I have the chance to connect When I do have a chance, invations are not realiably received (from Galaxy S2 to Nexus 7 mostly reliable, but never worked the other way around) When invitations are received (and accepted), a partnership rarely manages to be setup ("invited" or "connecting") And even when that happens, some apps can't seem to transfer files through it...   *Sigh*  Maybe J4velin's explanation pretty much sums up the sad state of Wi-Fi Direct on Android, which otherwise seemed as the best solution to my quest? I would like to set up memoir so that when I use \footnote{foo}, foo is displayed in the margin with the proper label and preferably break over pages.  There is an option \footnotesinmargin which gives almost exactly what I need, only justified. I want it to use ragged2e and change alignment based on even/odd page so that the margin note is always flushed towards the main text area and allows hyphenation on the side of the edge.  \documentclass[12pt, draft]{memoir} \footnotesinmargin \usepackage{polyglossia} \setmainlanguage{english} \usepackage{fontspec} \defaultfontfeatures{Ligatures=TeX} \setmainfont[Ligatures=TeX,Numbers=OldStyle]{Minion Pro} \usepackage{kantlipsum}  \begin{document} \kant[1]\footnote{\kant[1]} \kant[2]\footnote{\kant[2]} \kant[3-5] \end{document}   Possible partial work-around  I have remembered a nice thesis based upon the Classic thesis template and found the  which indeed contains a possible solution:  \usepackage{marginnote} \usepackage{ragged2e} \newcommand{\sidemark}[1]{#1.{\:}}  \newcommand{\marginelement}[2][0]{%   \marginnote{%     \strictpagechecktrue     \checkoddpage     \ifoddpage%       \RaggedRight\footnotesize%     \else%       \RaggedLeft\footnotesize%     \fi%     #2%   }[#1\onelineskip]% }%  \newcommand{\sidenote}[2][0]{%   \footnotemark%   \ignorespaces%   \marginelement[#1]{%     \sidemark{\thefootnote}%     \ignorespaces#2%   }%   \unskip% }%   Nevertheless, I would still prefer a memoir-specific solution with the re-definition of footnotes when used with the option \footnotesinmargin mainly for the sake of portability. This work-around also does not work with hyperref (there is no hypertext connection) and does not break over pages automatically. Recently, I found this , that allows you to generate a 3D model from a 2D image.   It works very well and you can download an OBJ file. Vertex are colored and when I import it using Blender, I can't see any Vertex color.   Using Cycle (I prefer a internal solution if it exists) according to some answers I've found on Blender Stack Exchange, I patched some nodes : Attribute -> Diffuse BDSF -> Material Output.  Unfortunately, I can't get it works, the model stills black.    When I open the OBJ file, I see that color per vertex are there :  v 43.747554 107.000000 69.000000 0.470588 0.380392 0.309804 v 43.780163 115.000000 64.500000 0.427451 0.337255 0.266667 v 43.782527 107.000000 68.500000 0.470588 0.380392 0.309804 v 43.801902 115.000000 65.000000 0.427451 0.337255 0.266667 v 43.806461 107.000000 69.500000 0.470588 0.380392 0.309804 v 43.821703 115.000000 64.000000 0.427451 0.337255 0.266667 v 43.838352 108.000000 68.500000 0.466667 0.376471 0.305882 v 43.854670 106.000000 69.000000 0.482353 0.392157 0.321569 v 43.856176 108.000000 69.000000 0.466667 0.376471 0.305882 v 43.873876 106.000000 69.500000 0.482353 0.392157 0.321569 v 43.888855 110.000000 68.000000 0.466667 0.376471 0.305882 v 43.891471 109.000000 68.000000 0.466667 0.376471 0.305882 v 43.892733 110.000000 67.500000 0.466667 0.376471 0.305882 v 43.895170 108.000000 68.000000 0.466667 0.376471 0.305882 v 43.900904 109.000000 68.500000 0.466667 0.376471 0.305882 v 43.907584 107.000000 68.000000 0.470588 0.380392 0.309804 v 43.917898 115.000000 65.500000 0.427451 0.337255 0.266667 v 43.925000 111.000000 67.500000 0.454902 0.364706 0.294118   According to some answers here, Blender import more easily the vertex color of a PLY file so I tried to convert to PLY with two different sites :   1. meshconvert .com : Give me a 3.5 Mo file  2. greentoken.de/onlineconv : Give me a 2.3 Mo file  (Of course, if you know some other sites I could try, it interest me)  I guess that color data are lost with greentoken (not sure).   When I import the 3.5 Mo PLY file in blender, I need to be in textured display mode, then I think I see my vertex color value but in black &amp; white instead of RGB, that is weird. Anyway, I can't get it work  EDIT 1 : I opened PLY files and color vertex aren't there... I need to find a better converter   EDIT 2 : I tried www.ofoct.com/3d-model-file-for-3d-printer-converter it doens't take vertex color into account. In fact, in each PLY files I converted with the various sites here, there is a common line :      comment Created by Open Asset Import Library -    (v3.2.0)   (the version varies)  EDIT 3 : In fact it seems that model converted by Green token, keep the vertex color. That is weird because that's the smallest file :   ply format ascii 1.0 comment Created by Open Asset Import Library - http://assimp.sf.net (v3.1.187496374) element vertex 29793 property float x property float y property float z property float nx property float ny property float nz element face 59582 property list uint uint vertex_index end_header 82 103 6.37528 0.40963 0.0331735 0.911648 82 102 6.57043 0.272087 0.235193 0.933088 82.6603 103 6.5 -0.14071 0.043367 0.9891 82 103.935 6.5 0.201161 -0.136681 0.969976 81.5475 103 7 0.825371 0.0489484 0.562465 83 102 6.62244 -0.248588 0.147929 0.957247 83 103 6.56417 -0.411487 -0.0867124 0.907281 81.5819 104 7 0.787841 -0.0338904 0.614946 82 105 6.63886 0.0715144 -0.131383 0.988749 83 104 6.77321 -0.431167 -0.171652 0.885794 83.6781 102 7 -0.470137 0.061235 0.880467 83.6327 103 7 -0.543939 -0.0905203 0.834228 83 105 6.96709 -0.445324 -0.163091 0.880391 84 103 7.23724 -0.520118 -0.141377 0.842313 84 104 7.47775 -0.546517 -0.195833 0.814229 84 102 7.16782 -0.416323 -0.021798 0.908955 83.3508 101 7 -0.314426 0.156435 0.936304 84 101 7.22581 -0.280388 0.0301462 0.959413 84.9009 101 7.5 -0.339848 -0.0219793 0.940223 84.6939 102 7.5 -0.435242 -0.0925323 0.895546   As you can see, nx, ny and nz correspond to RGB values.. A book on quantum mechanics supported by the high-level mathematics I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators etc, certainly the modern mathematics). If there isn't something similar please give me a reference to the book that is strictly supported by mathematics (given a set of mathematically descripted axioms author develops the theory using mathematics as a main tool). Calculating sequential numbers into sorted table using ArcGIS Desktop? Is there a way to calculate a sorted field with sequential numbers?  I have seen  that outlines how to calculate sequential numbers, but this is always calculated on FID order, not on sorted order.  #Pre-logic Script Code: rec=0 def autoIncrement():      global rec      pStart = 1       pInterval = 1      if (rec == 0):           rec = pStart       else:           rec += pInterval       return rec  #Expression: autoIncrement()   An example of what I'm trying to do.  I've used an advanced sort to sort by year, month, day, and now want to have sequential numbers in the Seq field.  You'll see that my OBJECTID field is not in order, so the above code won't work.    Can this be done either in the Field Calculator or using an Update Cursor in arcpy? When to use self over $this? In PHP 5, what is the difference between using self and $this?  When is each appropriate? Why do you have to use copy_to_user()/copy_from_user() to access user space from the kernel? If a character who was under the effect of a growth potion (double their height and eight times their weight) and weighed 2,400 lbs. was able to use Dimension Door to teleport 400 feet or more into the air, directly above a Huge-sized monster, and fell on it, how much damage would the falling creature - and the monster - take?  I would assume both would take the 20d6 max for the falling over 200 feet, but is there a estimation on additional damage for the falling creature's size?  According to the splat calculator, at 500 feet you'd be falling at 196 km/hr, and it would expend 1.6 million joules of energy, the equivalent of over 3,000 mid-sized cars hitting an object at 60 km/hr.  A 2,400-lb. barbarian falling 500 feet is like dropping a mid-sized Toyota Corolla off a 50 story building onto a monster - it should do some damage. Where can I find the location of downloaded .deb files?  I want to copy this folder before I reinstall Ubuntu so I don't have to redownload the packages.  I am running Ubuntu 12.10 32-bit.  How can I do this? Can Recovery Mode install OS X onto a blank SSD? How to find the real user home directory using python? ASP.NET MVC: Weird characters in error page Ice skater increase of energy This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero so we have conservation of angular momentum. This implies that $\omega$ increases to keep $I\omega$ constant, but then $K_{rot}=\frac{1}{2}I\omega^2$ doesn't stay constant, it increases. This implies that there is work done, but what force is doing this work? How to find the most common name in passwd file What's the difference between the snap folder in /home/UserName and the snap folder in root (/)? Where do electrons in electricity come from? Where do the electrons come from when an electric generator is making electricity?  Is from the air?  Would a generator work in a vacuum?  Electrons have mass so where would they be pulled from if there is nothing? Selecting a security team that includes at most one of the oldest man or oldest woman A security company consists of $7$ men and $6$ women. Determine the number of ways to form the night shift team of $3$ men and $3$ women if it can include at most one of the oldest man or oldest woman.  I know the first step is to pick $3$ from each group which is   $_6C_3 \cdot _7C_3 $  but I am not sure how to account for the "include at most one of the oldest man or oldest woman"   The answer is $_6C_3 \cdot _7C_3 + _6C_3 \cdot _5C_3 + _6C_2 \cdot _5C_3 $  Also, how do I account for it in my calculations if I want to include the oldest man and oldest woman from the group?