Question about the speed of light
Does the speed of light vary in non-inertial frames?
I've been writing in English for many years, but there are certain recurring issues that come up in my writing, which I can't seem to resolve permanently. Primarily I have a problem with punctuation. In my native language, commas are very commonly used. One would place a comma to separate any portion of the sentence that serves a specific grammatical role. At least, this is the case according to the rules I was taught in school. I can see when I write in English that there are extraneous commas, but I can't always figure out which ones, and why. When dependent clauses require commas, when do they allow them, and when are they definitely incorrect? I have latitude and longitude as 19.0649070739746 and 73.1308670043945 respectively.   In this case both coordinates are 13 decimal places long, but sometimes I also get coordinates which are 6 decimal places long.   Do fewer decimal points affect accuracy, and what does every digit after the decimal place signify? How do I edit/access Chrome app properties on GNOME? How to assign permanent drive letters to removable USB hard drives I have scripts that expect specific drive letters for hard drives. Windows sometimes assigns the different drive letters (e.g. I expected my Maxtor drive to be E:, but it's now F:, therefore my scripts will fail), depending on the order of how the drives are plugged into my laptop.  In Windows 7, how do I assign a permanent drive letter to a drive? Quadratic Formula in Complex Variables Does addition imply an order? Consider any integer, suppose a number 3. We can break any such integer down into a sequence of 1's. So, we can write: $$ 3\equiv1+1+1 $$ 3 represents what we get when we add 1 to 1 to another 1. Conceptually, what I am getting confused with, is the fact that notionally, at least according to this definition, there is one unit at the beginning, to which we add another, and yet a third. There seems to be a sequence here, which would imply there being an order. Am I missing something obvious? Question statement is as in the title:     $\varphi:G\to H$ is a Lie Group Homomorphism, then $\ker \varphi$ has Lie algebra $\ker D_e \varphi$   Since $\varphi$ is a Lie group homomorphism, in particular it is continuous. As $H$ must be Hausdorff, every point set is closed, and hence $\{e\}$ is closed in $H$, which implies that $\ker\varphi = \varphi^{-1}(e)$ is closed as well.  So $N=\ker\varphi$ is an embedded Lie subgroup of $G$. Therefore, the inclusion $j:N\to G$ is a Lie Group homomorphism, and induces a Lie algebra homomorphism $D_e j :T_e N \to T_e G$. So I only need to show that $D_e j$ is in fact an isomorphism between $T_e N$ and $\ker D_e \varphi$.  But I'm stuck at this point. I know that for $X\in T_e N$, we have, for $f\in C^{\infty}(H)$,  $$ D_e\varphi (D_e j(X))(f)=D_e j (X)(f\circ \varphi)=X(f\circ \varphi\circ j)=0$$  So $D_ej(T_e N) \subset \ker D_e \varphi$.  At this point, I can either show inverse inclusion: that is, for every $X\in \ker D_e \varphi$, we can find $Y\in T_e N$ such that $D_e j (Y)=X$, or for all $f\in C^{\infty}(G)$, $Y(f\circ j)=X(f)$  Or I can somehow show that dimensions of the two spaces are the same.   But I can't proceed from here.  It'd be great if someone could help me Why does a light object appear lighter in your peripheral vision when it's dark? So, I am not sure I can reproduce it via images, but the steps are:  1) At night, open a window and have a look at the surface of the earth  2) Suppose there's an object that reflects a tiny amount of light  3) When you actually try to focus your eyes at this object, you either don't see anything (depends on the amount of light it reflects) or you can hardly see it  4) When you focus your eyes on something that is 3-10 metres away, you can easily see this object with your ambient vision. Not the details, but it seems that it reflects more light.   Why does it happen? Why do I get a black rectangle instead of my external picture? I write some of my network notes in TeX. I wanted to make a table, and inside it insert an image:   .   I wrote a document:  \documentclass{article} \usepackage[demo]{graphicx} \usepackage{booktabs} \usepackage{array}  \begin{document} \begin{tabular}{m{3cm}m{3cm}m{5cm}} \toprule Configuration for ... &amp; Commands &amp; Topology\\ \midrule PPP: CHAP, PAP &amp; \#sh int se 0/0/0  &amp; \includegraphics[width=4cm, height=4cm]{chappap.png}\\  &amp; &amp; \\ \bottomrule \end{tabular} \end{document}   But instead of my network topology image, I see only this: .   I don't know what is wrong, cause my image is 100% in the same dir, as my *.tex file.  EDIT:  Changed my code as @Jubobs suggested, now everything is as I wanted:  \documentclass{article}     \usepackage{graphicx}     \usepackage{booktabs}     \usepackage{array}      \begin{document}     \begin{tabular}{m{3cm}m{3cm}m{5cm}}     \toprule     Configuration for ... &amp; Commands &amp; Topology\\     \midrule     PPP: CHAP, PAP &amp; \#sh int se 0/0/0  &amp; \includegraphics[width=4cm, height=4cm]{chappap.png}\\      &amp; &amp; \\     \bottomrule     \end{tabular}     \end{document} How do I completely remove Ubuntu 12.04 on my Mac? I have dual booted Ubuntu 12.04 on my Mac using disk utility and the rEFIt tool.The battery life is very bad and therefore I want to switch back to Ubuntu 10.04 . How can I completely remove the 12.04 partition? Unitl now I haven't found the option to enable the curved representation of connectors between nodes. The  doesn't mention such an  option. Is there a keyboard shortcut? Does a creature with Lifelink provide lifegain equal to its power, or the defender's toughness? I have recently began playing a deck that has a number of creatures with lifelink in it.  I want to be certain I understand the mechanic and the following question occurred to me.  Which damage total do you use to determine the life gain from lifelink?  I had assumed that if  a 3/3 creature with lifelink was blocked by a 2/2 creature that the life gain total would be 2, the maximum that the blocker can absorb before dying.  This seems to be incorrect, as when I read the example attached to CR 119.4c      [...] attacks with a 3/3 creature with wither and lifelink. It’s blocked by a 2/2 creature, [...]. The damage event starts out as [3 damage is dealt to the 2/2 creature, 2 damage is dealt to the 3/3 creature]   Have I been short changing myself? Prove the statement 'World is not flat' In my graph theory book exercise, I found a problem that:     Prove that the World is not flat using Mathematics     This picture is used in the exercise, but no idea of applying it.  I would have used the angles don't add to $180^\circ$, but the author is using a fourth city. How do you search through flags in the manpages? Whenever I search the manpages, I'm almost always trying to find out what's going on with a specific flag. For example, when searching the man pages for  I was searching the for -f flag. I'm not sure how to say, quickly get to the flag which is here:  OPTIONS    General options        -f FORMAT, -r FORMAT, --from=FORMAT, --read=FORMAT   and filter out stuff like:  iconv -t utf-8 input.txt | pandoc | iconv -f utf-8              or  pandoc -f markdown -t latex hello.txt   I've tried searching for /-f, and I've looked at  and tried (^|\s)-f($|\s\) but it was invalid. So I'm wondering how do you quickly search less for "only the flag -f"?  Would love your thoughts or some other tool that you use to quickly go through documentation Should I round my uncertainty to nearest hundred? I was doing some exercises on error propagation when I came across this problem:  $4\pi^2/(0,034 \pm 0,004 \space s^2/cm)$  I calculated my uncertainty to be $\Delta$ = 136 $cm/s^2$  And so the hole thing gives me: $(1200 \pm 136) \space cm/s^2$.  Now going into my question I rounded $4\pi^2/0,034 = 1161.12993$ to $1200$ which makes sense since my uncertainty is 136 but in the solution to this problem $136$ is rounded to $100$ and that's not making much sense to me.  So should I always round my uncertainty to the nearest hundred (assuming my uncertainty has 3 digits)? Firefox 37.0.2 not opening (removing firefox did not help) runing ubuntu 14.04 LTS Why can you see virtual images? Zero vector of a vector space I know that every vector space needs to contain a zero vector. But all the vector spaces I've seen have the zero vector actually being zero (e.g. $\mathbf{0}=\langle0,0,\ldots,0\rangle$). Can't the "zero vector" not involve zero, as long as it acts as the additive identity? If that's the case then are there any graphical representations of a vector space that does not contain the origin? What features of Mavericks are beneficial to you? This question serves to share and collect the enhancements that make a large difference to how you use your Mac.   Please post one feature per answer. Please also check to see if your answer has already been posted - duplicate answers will be deleted. To search answers for this question use  (directly from the question page) in addition to your search terms in the search box in the upper right hand corner of this page.  The best answers will not only list a feature, but provide details on how to configure that feature, and provide an image of how to use the feature to be more efficient or effective with Mavericks. I'm trying to find a movie with an underground facility with people wearing white suits. The people have been affected such that they show no curiosity. There is one person that does and asks one of his co-workers where a tube leads to.      At the end there is an uprising where everyone gets to see the surface and sunlight.   What is the name of this movie?