Consider the following :   A\input{foo1}C  A\input{foo2}C  A\input{foo3}C  A\input{foo3} C   with foo1.tex containing "B", foo2.tex containing "B%" and foo3.tex containing "B\n%".  In the first case, we obtain "AB C", in the second "ABC" and in the third "AB C" and in the fourth "AB  C" (with double space).  Up to here we can think that A\input{foo}C is equivalent to A&lt;insert foo&gt;\n C.  But,  \begin{equation} \input{bar} \end{equation}   with bar.tex containing "a=b" will not produce the expected error (two \n makes an empty line inside the equation).  Question  So my question is : what \input{foo} is equivalent to ? Is there a conditional addition of \n when the file does not finish by % or something ?  I'm not asking how to get rid of the extra space, but, on the contrary, how to conserve this extra space when replacing \input{foo} by the content of foo.bar.  Non equivalence with an extra newline  Let foo.tex containing only "A"  \input{foo}B   will produce the same as "A\nB" but  \input{foo} B   will produce a larger space between A and B wich is not equivalent to "A\n B".
Intro  I'm working on a lightweight package that allows you to put any content (typically LaTeX code) in an environment, then use that content multiple times, each time scanned separately, so you can use it both as verbatim output and interpreted as LaTeX.  Its main purpose is to typeset LaTeX code and its 'result' side-by-side; useful for documenting TeX packages without having to copy/paste code. But it has other purposes as well.  After experimenting with \scantokens until I gave up in tears, I arrived at the filecontents environment, which almost solved my problem singlehandedly!  The Problem  The problem is, when reintroducing filecontented code through \input, LaTeX adds an implicit newline at the end, which translates to whitespace that I can't seem to get rid of.  I've seen many semi-related questions floating around, with answers employing techniques like:   reading a file line-by-line, using \everyeof in some clever way, playing with \endlinechar or using packages such as catchfile   but none of them provides a clear answer to the following question:  The Question  How can I \input a file without getting the implicit newline?  Minimal Working Example  \documentclass[margin=1mm]{standalone}  \usepackage{filecontents}  \begin{filecontents*}{tmp.tex}     \LaTeX{}\end{filecontents*}  \begin{document}     \fbox{\input{tmp.tex}} \end{document}     Note the extra whitespace to the right of the box.  Note also that I'm definitely not adding any explicit whitespace. Even a manually produced file (so, not using filecontents) with no newlines at all exhibits the same problem.
Is uncertainty principle a technical difficulty in measurement? Is the uncertainty principle a technical difficulty in measurement or is it an intrinsic concept in quantum mechanics irrelevant of any measurement?  Everyone knows the thought experiment of measuring the position of an electron. One can detect electron's position by hitting it with a photon, due to Compton scattering the collision of the photon with electron will change electron's momentum. This experiment is used to explain uncertainty principle to layman, but it is over simplified, isn't it? It also gives an impression that if there was a better suited experimental method the uncertainty principle becomes irrelevant.   I personally think it is intrinsic as it arises from the non-zero commutator of position and momentum operators irrespective of the measurement process. Am I right?  EDIT: My question is similar to certain extent to  and . The answers there are nice but they focus on explaining basics of quantum mechanics more than they comment on the technical difficulty part. In the answers of question 2 there are statements like "So, it's not a knowledge limit" and "you're sort of correct when you say it's an observational limit" without further comments  To summarize, assume hypothetically we managed to find a way in the future where we can have a look at an electron without disturbing it by measurement or causing its wave function to collapse, would the uncertainty principle still hold in such a case?? Why/Why not? Calculationg base-resistor between microcontroller and transistor I'm curious, when connecting my 2N2222 transistor's base to a PWM output pin on my Arduino, I know the Arduino can deliver a maximum of 40mA current. The 2N2222 only requires around 5 to 10 mA on it's base to switch the collector and emitter. Now, when calculating the base-resistor under "normal" conditions where I'm merely switching it directly from Vcc, the following applies:   However, when putting in a 500 ohm or 1K resistor in (1K for 5mA) directly it works great. But putting it in between the Arduino and the transistor, the transistor doesn't switch.  I suspect thus, that the resistance is too high of the base-resistor. Therefore, we may very well not need a base-resistor.  But, according to spec, the Arduino can deliver 40mA. So, am I correct in assuming the folling: 1) I should calculate the perceived resistance that the Arduino is giving, if it goes high to 5Volt and only gives 40mA, and then 2) Subtract that from the 500ohm resistor needed to make the transistor operate optimally.  Example:    So, I'm theorising that I have to then put in a 375 ohm resistor in to make the total resistance between the Arduino and the base resistor 500 ohm.  Somehow this doesn't feel right. Keep in mind, I'm not an electronic engineer, so I might have the cat by the tail here :P Group of order $pqr$, $p < q < r$ primes Multiple Author and email with location? I am trying to add multiple Author with their email and location but not working.  I am trying to get something like this     first_person^1 , second person^2, third_person^3            {1^mail, 2^mail, 3^mail}@gmail.com                   institution name                      location Continuous bijection from $(0,1)$ to $[0,1]$ Does there exist a continuous bijection from $(0,1)$ to $[0,1]$? Of course the map should not be a proper map. General relativity (gravitation) in time and one spatial dimension I don't have any idea of general relativity but intend to learn. Is it a good idea to study general relativity in two dimensions (time and single spatial dimension) in the begining to get good idea on the subject? If it is, then please give some references for such a treatment. Access a glyph on fontspec using a GID (Glyph ID) I'm trying to access a glyph, but it's only mentioned in the "Basic Latin and Latin 1" set for a font. The glyph has no name or unicode ID, but it does have a glyph ID or GID. fontspec doesn't mention possibilities for using this glyph. Neither does Adobe in the adobe feature file syntax:   I'd still like to be able to access a glyph through its ID, since it's the only way I can access it (I think).  My specific case requires to access the glyph ID 554 from Stevens Titling Pro Sable Brush. I will only post this font if it's strictly necessary, since I don't like to distribute these fonts to the wide world.  I posted an MWE containing another (free) font. This is not the font I intend to use, but perhaps a starting point to try and access glyphs manually.   \documentclass{article}  \usepackage{fontspec} \setmainfont{EB Garamond}  \parindent=0pt \begin{document}  Some text int EB Garamond. How can I access glyph 123 now?  \end{document} \sum caused \sqrt to not be slanted Getting an "Authentication token manipulation" error when trying to change my user password I am logging in to my Ubuntu Server using my username. Once I am logged in I am typing passwd command. Entering a new password but a second after getting following error messages:  passwd: Authentication token manipulation error passwd: password unchanged   What is wrong here? How can I change my password otherwise if I don't have access to that server physically, i.e. I am connecting remotely with ssh using terminal. I got a stomach flu or I got the stomach flu or I got stomach flu? Calculate Euler equations of fluid dynamics without division? I'm working on the calculation of the  with the . Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division.  At the moment the Euler equations look like this:  $$ \frac{\partial}{\partial t} \begin{pmatrix} \rho \\ \rho v_1 \\ \rho v_2 \\ \rho v_3 \\ \rho E \end{pmatrix} = -\mathrm{div} \begin{pmatrix} \rho v_1 &amp; \rho v_2 &amp; \rho v_3 \\  \rho v_1^2 + p &amp; \rho v_1 v_2 &amp; \rho v_1 v_3 \\  \rho v_2 v_1 &amp; \rho v_2^2 + p &amp; \rho v_2 v_3 \\  \rho v_3 v_1 &amp; \rho v_3 v_2 &amp; \rho v_3^2 + p \\  (\rho E + p) v_1 &amp; (\rho E + p) v_2 &amp; (\rho E + p) v_3 \end{pmatrix} $$  As you can see, I first need to calculate $\frac{\rho v_1}{\rho}$ to get $v_1$ so I can calculate e.g. $\rho v_1^2$ Prove that a continuous function on a closed interval attains a maximum For a given inner product space $V$, I would like to prove the inequality $$\|\mathbf{x}+\mathbf{y}\|^2 + \|\mathbf{x}-\mathbf{y}\|^2 = 2(\|\mathbf{x}\|^2 + \|\mathbf{y}\|^2).$$  We see that $$\|\mathbf{x}+\mathbf{y}\|^2 + \|\mathbf{x}-\mathbf{y}\|^2 = \langle\mathbf{x}+\mathbf{y},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{x}-\mathbf{y},\mathbf{x}-\mathbf{y}\rangle,$$  which by linearity $$=\langle\mathbf{x},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{y},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{x},\mathbf{x}-\mathbf{y}\rangle - \langle\mathbf{y},\mathbf{x}-\mathbf{y}\rangle.$$  I've been trying to figure out how to go about this proof using linearity in the second argument of an inner product, but my textbook does not say that linearity necessarily holds in the second component. If it does, how would I go about the rest of this proof? If not, should I be potentially using some aspect of conjugate symmetry to prove this statement? I'm relatively new to ring theory so this is probably a simple question.  Its easy to see that a finite ring that is commutative and has no-zero divisors (i.e. an integral domain) must have multiplicative inverses.  I am wondering if we can rearrange these properties and always get implication or produce finite rings with only 2 of the above properties.  Explicitly my questions are:  1) Does a finite ring that is commutative with multiplicative inverses always have no-zero divisors? (EDIT: this one is pretty easy too, let $xy=0$ and assume $x\neq 0$. then $x^{-1}xy=x^{-1}0$. Hence, $y=0$ as desired.)  2) Is a finite ring that has multiplicative inverses and no zero divisors always commutative?  If these are actually simple exercises, I'd just like a hint to get started with the proof or any counterexamples.  Thanks :) The title is probably very confusing, but here's the situation:  I'm animating a flat grid curve by shrink-wrapping it onto a moving plane in order to get a uniform wave animation, it looks like this:    Before I render it, i want a bevel. What I did then was simply adding a bevel to the curve, making the curve look like this:    Now, when activating the shrinkwrap modifier, I expexted that only the curve would be shrinkwrapped, but alas, the bevel did the same:    As seen by the blue spots, the curve has been completely flattened along with the bevel.  How can I avoid this? I tried using a wave modifier instead of shrinkwrap, but this modifier doesn't seem to make perfectly round waves like this:    So, any thoughs on how to solve this?  Thanks for reading! How do I prevent Apache from answering requests for domains I don't host? Proxy setting for R I consider the co-finite topology on $\mathbb{R}$ that is $$\{G\subset \mathbb{R}, card(\mathbb{R}\setminus G)&lt;+\infty\}\cup \{\emptyset\}$$  What are the convergent sequences in this space .  thank you Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.  If $f$ is not constant  then $f(\mathbb{C})$ is dense set in $\mathbb{C}$, but how can I use that line does not intersect the image set? coloring the page numbers in the table of contents