How do I find a replacement rear axle?
How do i know which wheels will fit my bike?
pdfx: incomplete CIDset in some fonts I try to compile a document as pdf/x and pdf/a with pdfx under LuaLaTeX, and I am already quite successful. One thing still poses problems though: With some fonts I get the following error if I check the resulting pdf/a file with Acrobat: "CIDset in subset font is incomplete (font contains glyphs that are not listed)" (VeraPDF gives the same error, so the issue seems to be real).  Here's a MWE:  \RequirePackage{filecontents} \begin{filecontents*}{\jobname.xmpdata} \Title{Test}       \Author{Simon Spiegel}       \Language{de-DE} \end{filecontents*} \documentclass {article} \usepackage{fontspec} \setmainfont{Palatino Linotype} [Ligatures={TeX,Common}, Extension = .ttf, ] \usepackage[a-3b]{pdfx} \begin{document} Test \end{document}   I realise that not everyone will be able to compile this MWE due to the proprietary font, but since the problem only occurs with specific fonts, I had to use this example.  The pdfx manual mentions this error, but only in relation to XeLaTeX. According to the manual, it should not occur with LuaLaTeX.  From what I understand, this seems to be at least to some degree a problem of this specific font, but since I am relying on it, I am looking for a way to fix it.  EDIT  Here's a new MWE with a bunch of fonts which are hopefully more common (the paths have to be adapted of course).  \RequirePackage{filecontents} \begin{filecontents*}{\jobname.xmpdata} \Title{Test}       \Author{Simon Spiegel}       \Language{de-DE} \end{filecontents*} \documentclass {article} \usepackage{fontspec} \setmainfont{Georgia} [Ligatures={TeX,Common}, Extension = .ttf, ]  \newfontfamily\fontone{Verdana} [Ligatures={TeX,Common}, Extension = .ttf, ] \newfontfamily\fonttwo{Cambria} [Ligatures={TeX,Common}, Extension = .ttf, Path = {/Users/simi/FontExplorerX/C/Cambria/} ] \usepackage[a-3b]{pdfx} \begin{document} Test  \fontone Test  \fonttwo Test \end{document}   All these fonts give me the same error. I wonder if this only happens with .ttf OpenType fonts. How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? If $f^2$ is Riemann Integrable is $f$ always Riemann Integrable? What does protection from [quality] do? Example 1) Let's say I have some random creature with protection from white, and my opponent plays , a white card with the effect "Destroy all creatures." Can my creature with protection from white be destroyed by a white card that isn't actually targeting it specifically?  Example 2) I was playing a match with a friend where I had  on the field against his 3 zombies. Is he able to declare his zombies as blockers even though Elite Inquisitor has "protection" from zombies?  If he can declare them as blockers, does protection mean that no damage is dealt by the zombies to  Elite Inquisitor? I've been trying to prove that given a ring $R$ and a collection of ideals $\{I_{\beta}\}_{\beta \in B}$ in $R$, the set $$\sum_{\beta \in B} I_{\beta}=\{f_1+\cdots+f_r:f_j \in I_{\beta_j}, \mbox{ for some } I_{\beta_j}\}$$ is an ideal and is the smallest ideal containing $\cup_{\beta \in B} I_{\beta}$.  I've already proved when I only have two ideals, and so, using induction, I've seen it for finite sums. But I don't see how to generalise that to an arbitrary family of indexes (maybe infinite) $\beta$.   Could someone please give me a hand? Thank you. Irreducible polynomial which is reducible modulo every prime How to show that $x^4+1$ is irreducible in $\mathbb Z[x]$ but it is reducible modulo every prime $p$?   For example I know that $x^4+1=(x+1)^4\bmod 2$. Also $\bmod 3$ we have that $0,1,2$ are not solutions of $x^4+1=0$ then if it is reducible the factors are of degree $2$. This gives that $x^4+1=(x^2+ax+b)(x^2+cx+d)$ and solving this system of equations $\bmod 3$  gives that $x^4+1=(x^2+x+2) (x^2+2x+2) \pmod 3$. But is there a simpler method to factor $x^4+1$ modulo a prime $p$? Distance between surfaces I have TeX Live 2013 installed via MacTeX on my Snow Leopard laptop.  I copied the following code from page 247 of version 2.10 of pgfmanual:  \documentclass[a4paper,12pt]{report} \usepackage{tikz} \usetikzlibrary{decorations}  \begin{document}  \begin{tikzpicture} \node (a) {A}; \node (b) at (2,1) {B}; \draw (a) -- (b); \draw[decorate,decoration=brace] (a) -- (b); \draw[decorate,decoration={brace,mirror},red] (a) -- (b); \draw[decorate,decoration={brace,mirror,raise=5pt},blue] (a) -- (b); \end{tikzpicture}  \end{document}   Yet somehow I get this error:  ./Untitled2.tex:11: Package pgfkeys Error: I do not know the key '/pgf/decorati on/brace' and I am going to ignore it. Perhaps you misspelled it.  See the pgfkeys package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.11 \draw[decorate,decoration=brace]                                       (a) -- (b); ?    Is this a bug? Are there any distinct finite simple groups with the same order? In finite group theory, it's often quite easy to show that there are no simple groups of a given order $n$.  My question is different: is there some natural number $n$ such that there are two non-isomorphic simple groups of order $n$?  The two easiest families of finite simple groups - $\mathbb{Z}_p$ for $p$ a prime and $A_n$ for $n\ge5$ - clearly don't yield any examples.    It should be possible to check this using the , but I don't know enough about the fabled 'sixteen infinite families of groups of Lie type' to do the check myself.  Also, if the answer is 'no', I'd be much more interested to see an elementary(ish) proof than I would be to see a proof that relies on over 3,000 pages of non-stop hard group theory. Is the converse of Cayley-Hamilton Theorem true? The question is motivated from the following problem:     Let $I\neq A\neq -I$, where $I$ is the identity matrix and $A$ is a real $2\times 2$ matrix. If $A=A^{-1}$, then the trace of $A$ is   $$ (A) 2 \quad(B)1 \quad(C)0 \quad (D)-1 \quad (E)-2$$   Since $A=A^{-1}$, $A^2=I$. If the converse of  is true, then $\lambda^2=1$ and thus $\lambda=\pm1$. And then $\rm{trace}(A)=1+(-1)=0$.   Here are my questions:   Is  $C$ the answer to the quoted problem?  Is the converse of Cayley-Hamilton Theorem, i.e.,"for the square real matrix $A$, if $p(A)=0$, then $p(\lambda)$ is the characteristic polynomial of the matrix $A$" true? If it is not, then what's the right method to solve the problem above? If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$ If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$   I was practicing quadratic equation questions online but I am stuck on this question.  I found the values of roots $a= 1$, $b= 1/2$ How do I access previous promise results in a .then() chain? Fancy vertical timeline I'd like to have a timeline as similar as possible to this with the addition of being able to add a logo at the left of each textbullet, but I've got no clue at all:    Thanks very much in advance for any help :)  p.s. I've stumbled upon this answer () but I don't how to modify it to get what I want! Breadboard Confusion I just received the following breadboard in a electronics starter pack I purchased.    I am a little confused in how I would go about prototyping on this board, all the tutorials I have read state that the breadboard should have a positive and negative  input on it. But it appears this one doesn't.  Could anyone help clear my confusion? How do I get adequate depth of field in macro photography? I have been messing around with some Macro Photography using the techniques (and a reversal ring) described in a  by @ My main issue is that I am having a hard time getting the subject into focus. There are times when the center is blurred and the outside is in focus or the center in focus and the outside out of focus. What are ways to get as much of the subject in focus?   I am using a Nikon D5100, I have a 18-55mm kit lens but I find the 55-200mm lens easier to use for shooting. I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner)  In the Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55,\ldots$ each term after the first two is the sum of the two previous terms. What is the sum to infinity of the series: $$\frac{1}{2} + \frac{1}{4}+ \frac{2}{8} + \frac{3}{16} + \frac{5}{32} +\frac{8}{64} + \frac{13}{128} +\frac{21}{256} +\frac{34}{512}+ \frac{55}{1024} + \cdots$$  Now, I solved this using an infinite geometric matrix series (incorporating the matrix version of the relation $a_n= \frac{a_{n-1}}{2}+ \frac{a_{n-2}}{4}$), and my students, after much hinting on my part, googled the necessary string to stumble across Binet's formula (which allows one to split the series into two simple, if rather messy, geometrics). Both of these are good methods, but neither really seems plausible for a challenge set for 15-18 year olds under exam conditions. So how is one supposed to do it? Inhumans vs. Mutants in the Marvel Universe What's the difference between those two? Aren't Inhumans supposed to be an evolution of the human race "forced" by the Kree? Which is almost the same as Mutants, the natural evolution of the human race...  What exactly am I missing? Strange character when using listings package Workflow for UV orientation How to I deal with unwrapped UVs orientation?   Delete the default Cube. Add a Cylinder Edit mode and edge select the Top and the Bottom and a single connecting edge. Make them into seams UV Unwrap (standard Unwrap mode)   The unwrapped UV now shows two circles above a row of quads. I can save this and open it in an image editor and paint over those areas and get the texture to align on the cylinder back in blender.  But, the pattern(just happens to be text) that was inserted in place of the row of quads is now upside down on the model. Any attempt to flip or align just makes things worse, from upside down to mirrored or the Top/Bottom not aligning.  So my real question is how could I have known that the quads represented an upside down view of the world?  Do other blender users export UVs and mark them with arrows and colours just to see how they align on a model before actually painting for real?  I tried selecting the edges in step 3 in different orders before making them into seams and it made no difference.  I also looked at the Normals but they appear to be only Inside/Outside not Up/Down.  Blender 2.70 Determine file type of an image I'm downloading some images from a service that doesn't always include a content-type and doesn't provide an extension for the file I'm downloading (ugh, don't ask).  What's the best way to determine the image format in .NET?  The application that is reading these downloaded images needs to have a proper file extension or all hell breaks loose.