Is it physically possible for an object to achieve the speed of light if it is in a gravitational field strong enough and the mass does not collide before it attains a velocity of $c$? It is true that the mass of the object approaches infinity as its speed approaches $c$, but maybe there could be an (almost) infinitely powerful gravitational field (increasing in strength as the mass speeds up) originating from a very long distance away, which could accelerate the mass to this impossible speed? I ask this because it appears that you would not need an infinite amount of fuel for taking the object to the speed of light.
Most of you if not everybody will agree that the stronger the gravitational pull, the faster an object will fall. For example, on a planet with 50 times the gravity of Earth, any object will hit the ground on that planet much quicker than it would on Earth. So taking all of these into the equation, does it mean that at a blackhole, an object will fall at an infinite speed because of the infinitely strong gravitational pull of the blackhole?
Can I use Minecraft PC textures and worlds in Pocket Edition? Now that I've discovered that I can host a , I'd like to know if is it possible to use the textures and maps of the PC version for the pocket version.  I'm planning to visit Peru and Machu Picchu. It would be really cool to entice them for the voyage by letting them play a  in their favourite video game. Unfortunately, this God of Deceit world looks really sophisticated. I don't believe the Pocket Edition would be able to play it. Why does a monopole not radiate energy in electodynamics? Respawning the Ender Dragon Lie Algebra of U(N) and SO(N) U(N) and SO(N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? A limit ordinal $\gamma&gt;0$ is said to be indecomposable iff $\nexists\alpha,\beta&lt;\gamma$ such that $\alpha+\beta=\gamma$.  In view of this definition, I’m trying to prove the equivalence of the following statements for limit ordinals $\gamma$:  (1) $\gamma$ is indecomposable.  (2) $\alpha+\gamma=\gamma$ $\forall\alpha&lt;\gamma$.  (3) $\gamma=\omega^\alpha$ for some $\alpha\in\mathrm{ON}$.  I’ve been able to get $(1)\implies(2)$ and $(3)\implies(1)$, but I have nothing more than scratch work for $(2)\implies(3)$.  Any suggestions would be appreciated. The following MWE compiles (for me)  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=newest} \usetikzlibrary{external} \tikzexternalize[prefix=figures/externalized/]   \begin{document} \begin{figure}     \centering     \begin{tikzpicture}          \begin{axis}  %           \addplot3[surf,mesh/rows=129,mesh/cols=129,mesh/ordering=y varies] table[x=X,y=Y,z=psi] {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.dat};              \addplot3[contour gnuplot,mesh/rows=129,mesh/cols=129,mesh/ordering=y varies] table[x=X,y=Y,z=psi] {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.dat};          \end{axis}      \end{tikzpicture}     \caption{ciao} \end{figure} \end{document}   where the data file is . If I de-comment the first \addplot3 and comment the second one, then I get an error. The final part of the log file (the interesting one, I think) is  ===== 'mode=convert with system call': Invoking 'pdflatex -shell-escape -halt-o n-error -interaction=batchmode -jobname "figures/externalized/prova-figure0" "\ def\tikzexternalrealjob{prova}\input{prova}"' ======== \openout3 = `prova.auxlock'.  runsystem(pdflatex -shell-escape -halt-on-error -interaction=batchmode -jobname  "figures/externalized/prova-figure0" "\def\tikzexternalrealjob{prova}\input{pr ova}")...executed.  \openout3 = `prova.auxlock'.   ./prova.tex:22: Package tikz Error: Sorry, the system call 'pdflatex -shell-esc ape -halt-on-error -interaction=batchmode -jobname "figures/externalized/prova- figure0" "\def\tikzexternalrealjob{prova}\input{prova}"' did NOT result in a us able output file 'figures/externalized/prova-figure0' (expected one of .pdf:.jp g:.jpeg:.png:). Please verify that you have enabled system calls. For pdflatex,  this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or som ething like that. Or maybe the command simply failed? Error messages can be fou nd in 'figures/externalized/prova-figure0.log'. If you continue now, I'll try t o typeset the picture.  See the tikz package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.22    \end{tikzpicture}  ?  PGFPlots: reading {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.da t} Runaway argument? {\pgfkeyssetvalue {/pgfplots/execute at begin plot visualization}{}\pgfkeyssetv alue \ETC. ./prova.tex:22: TeX capacity exceeded, sorry [main memory size=5000000]. &lt;argument&gt; ...5e-1],2Y7.753628e-3]}{2Y8.20894\ETC.  l.22    \end{tikzpicture}  If you really absolutely need more capacity, you can ask a wizard to enlarge me.   Here is how much of TeX's memory you used:  20761 strings out of 493054  547383 string characters out of 6134761  5000001 words of memory out of 5000000  23958 multiletter control sequences out of 15000+600000  3640 words of font info for 14 fonts, out of 8000000 for 9000  1141 hyphenation exceptions out of 8191  62i,4n,84p,728b,1519s stack positions out of 5000i,500n,10000p,200000b,80000s ./prova.tex:22:  ==&gt; Fatal error occurred, no output PDF file produced!   similar (or the same) error appears if externalization is not enabled/used.  My TeX distribution is TeX Live on Mac OS X 10.9.5 and I use TeXShop as editor.  Once I (partially) solved a  on Windows+MikTeX+TeXniccenter by modifying/adding options to the command executed when compile button is pressed. I say partially since I actually solved the problem for some data file. Then I experienced the same problem with larger datafile and/or different plots (I don't remember anymore) and didn't find a way out, no matter how much I extended the memory.  What should I do now? Mac OS X Darwin: how to reset admin password? Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password? Add field "tome" to biblatex entries I need to add a new field in the @book or @InProceedings entries: this field is "tome", for I have for instance the following title:  Francesco Bertolini, Società di trasmissione orale: mito e folclore, in Lo spazio letterario della Grecia antica, a cura di G. Cambiano, L. Canfora e D. Lanza, vol. I, tomo I, Salerno, Roma 1992, pp. 47--75.   So the following code is not enough:  @InProceedings{ bertolini:1992,   author                   = "Francesco Bertolini",   title                    = "Società di trasmissione orale: mito e folclore",   booktitle                = "Lo spazio letterario della Grecia antica",   editor                   = "G. Cambiano and L. Canfora and D. Lanza",   publisher                = "Salerno",   location                 = "Roma",   year                     = "1992",   volume                   = "1,   pages                    = "47--75", }   Using othes codes, I was able only to produce the "tome" field, but with a general trouble about the other fields:  \DeclareSourcemap{   \maps[datatype=bibtex]{     \map{       \step[fieldsource=tome,fieldtarget=usera]     }   } } \DeclareFieldFormat{usera}{tomo\space{#1}}   \DeclareBibliographyDriver{book}{%   \usebibmacro{author/editor}%   \setunit{\labelnamepunct}\newblock   \usebibmacro{title}%   \newunit\newblock   \usebibmacro{journal+issuetitle}%   \setunit{\bibpagespunct}%   \printfield{pages}%   \newunit\newblock   \printfield{usera}%   \usebibmacro{finentry}} \renewcommand*{\finentrypunct}{}   (useful for articles, but not for my case). By real, I'm not able to understand  which bibmascros I have to invocate...  I tried to write a biblatex-tome.dbx:  \ProvidesFile{biblatex-tome.dbx}   \DeclareDatamodelFields[type=field,datatype=literal,skipout=false]{tome}   \DeclareDatamodelEntryfields{tome}   Inside the main .tex file I put just this code:  \DeclareFieldFormat{tome}{\mkbibacro{tome}\addcolon\space #1} \newcommand*{\patchmoretome}[1]{   \xpatchbibdriver{#1}%     {\printfield{tome}}     {\printfield{tome}%           \newunit\newblock      \printfield{tome}}%     {\typeout{patching #1 to include more tome succeded}}%     {\typeout{patching #1 to include more tome failed}}% } % patch all drivers \patchmoretome{article} \patchmoretome{book} \patchmoretome{collection} \patchmoretome{inbook} \patchmoretome{incollection} \patchmoretome{inproceedings} \patchmoretome{manual} \patchmoretome{periodical} \patchmoretome{proceedings} \patchmoretome{report} \patchmoretome{thesis}   but it doesn't print the field in bibliographic entry. So I'm very confused about a (re)writing of driver While talking about ships and countries, is it a good practice to use the feminine form?  For example:  "Her economy" - while referring to a country's economy "Her flag (or deck etc)" - while referring to a ship  Is this practice common? Is it used today? Cannot get 2 raster files of same cell size to align ArcMap 10.2 Let $x = (a, b), y = (c, d) \in \mathbb{Z}^2$. What is the condition on $a, b, c, d$ so that ${x, y}$ is a basis?   My answer: $ad\neq bc$ and $gcd(a, c) = gcd(b, d) = 1$.  The first condition ensures that they aren't the same vector; the second ensures that we can actually "get" all of the integer values/lattice points.  Is this correct?  Thanks. How soon until I can take my newborn to take a walk outside? I understand that newborn's immune system is still weak and crowds/strangers are to be avoided. Knowing this, how soon can I take my newborn outside, for example to take ~1 hours walk in a non-crowded park? Any particular things to pay attention to when doing this? Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$ I can't crack this one.      Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$ (the only constraint is that  $a,b,c,z \in \mathbb{Z}$ and $c\neq 0)$ Are any of the USB ports on a Macbook Pro "always on" Always on USB ports will provide power to a device even when the laptop is shut down. Obviously this can be problematic for battery issues, but sometimes a user wants this capability all things considered.  Do the Macbook Pro offer this on any of the USB ports and if not is there any chance its wired and just has to be enabled? Xubuntu Dropbox icon fail I am trying to balance underbraces in the equation below, how can I ensure that both underbraces at the same depth?  \begin{equation} y = \underbrace{ \left [ x^2 + r^2 (a^2+\frac{a^{0.3}}{b}) \right]}_\text{growth rate} \times  \underbrace{ C_0}_\text{initial} \end{equation} Animagi (Sirus specifically) and wands? I have 3 questions about animagus transformation and wands      Does animagus transformation require the use of a wand?   If yes, where does the wand go after the wizard transforms?   Again, if 1 is yes, how did Sirius transform into a dog in Azkaban?     Note that 2 and 3 are invalidated if the answer to 1 is no. If so, is it mentioned anywhere in the books, or can be implied by something in the books, that wand use is not required? I don't think Sirius managing to do it in Azkaban can be used as a proof here, as in Book 3 Wormtail needs a wand to change back into a rat Is there a grammatical term for moving a word to the front or back of a sentence? There is a function in Arabic grammar where you may bring forward in sentence order a word - as well as deferring it.  For example: if the sentence order is Subject - Verb - Object, you can bring the object forward to be before the subject,  yielding Object - Verb - Subject or Object - Subject - Verb.  Similarly, if you have Noun Phrase - Verb Phrase, you can move the verb phrase forward so you get Verb Phrase - Noun Phrase.  This is used to add emphasis to the item brought forward. The same applies to moving the item to the end of the sentence.  Is there a grammatical term in English that represents this function or functions? I started to read about Diffie-Hellman exchange and I encountered a problem which I don't know how to solve.  Given $g=3$, $p=131$, $g^x\bmod p=112$, $g^y\bmod p=74$, compute $g^{xy}\bmod p$   $113$ $110$ $112$ $111$   How could I compute $g^{xy} \bmod p$? Or at least verify which one is correct. Any idea? Why was Dumbledore worried by the cut in Harry's arm? In the Goblet of Fire, Harry is cut in the arm by Pettigrew. When Dumbledore learns it, he's extremely worried and wants to check Harry's arm.  Why?     When Harry told of Wormtail piercing his arm with the dagger, however, Sirius let out a vehement exclamation and Dumbledore stood up so quickly that Harry   started. Dumbledore walked around the desk and told Harry to stretch out his arm.   Harry showed them both the place where his robes were torn and the cut beneath   them.      "He said my blood would make him stronger than if he'd used someone else's,"   Harry told Dumbledore. "He said the protection my - my mother left in me - he'd   have it too. And he was right - he could touch me without hurting himself, he   touched my face."      For a fleeting instant, Harry thought he saw a gleam of something like triumph in   Dumbledore's eyes. But next second. Harry was sure he had imagined it, for when   Dumbledore had returned to his seat behind the desk, he looked as old and weary   as Harry had ever seen him.      "Very well," he said, sitting down again. "Voldemort has overcome that particular   barrier. Harry, continue, please.     Edit:  Plz explain this sentence specifically:     "Dumbledore walked around the desk and told Harry to stretch out his   arm."