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I have enabled MathJax on the site. There are no Latex images being displayed. Please post any problems. I'll leave it enabled for the next hour or so and switch back to images until we are 100% ready.
Greg Bernhardt said:I have enabled MathJax on the site. There are no Latex images being displayed. Please post any problems. I'll leave it enabled for the next hour or so and switch back to images until we are 100% ready.
dextercioby said:So I wrote the LaTex code for y=x^2 and a dubious thing appeared (below). Do these essentially replace the nicely looking LaTex images and to make them we'd still have to type the LaTex code ?
y=x^2
dextercioby said:So, Greg, it's the image which changes and the lower space on the server occupied by the tinier pictures, right ?
jhae2.718 said:The align environments seem buggy, plus some markup in my blog posts don't render. I'm trying to troubleshoot now.
Nebuchadnezza said:Why the sudden change?
Sorry to say I really hate the new look. The images are smaller, and arew just ugly compared to the old font. Please bring back imgtex =)
jhae2.718 said:Greg, during the test was the math rendered with cmr font? (Didn't look like it, but hard to tell...)
flyingpig said:Please don't fix what's not broken!
QuarkCharmer said:So, we can't click anymore to see the latex code? :(
Greg Bernhardt said:Right click on the equation to get a menu.
I'm seeing some pretty serious problems in the post preview on Firefox 4: large chunks of the post text just don't show up. It doesn't seem to be a problem with the HTML or MathML markup, but rather with the way the browser's rendering engine interacts with it, because if I scroll down far enough to put the preview out of view and then back up, it'll look different. Plus, I can select sections of text to make them show up, but then other sections of the preview (and even of the page, outside of the preview) flicker in and out of view as I change the selection. A lot of the problem areas seem to start at instances of the / operator in the math, so perhaps the way that's being rendered is messing things up somehow. I suppose this could be a problem with MathJax itself, but I've been to several other sites that use it and never had this problem before (including the site where I originally posted the exact same thing I quoted), so there must be something specific to PF that is contributing to this problem somehow. (A sample screenshot attached - notice how part of the second matrix equation is cut off, as well as most of the lines above and below it. At other times multiple entire paragraphs would be missing.)However, you can _convert_ an amount of kinetic energy measured in one frame to another frame, if you know their relative velocity. If you're working at low speeds, the easy (approximate) way to do this is to just calculate the relative velocity, as you did. So if the train observer measures a kinetic energy K = \frac{1}{2}mv^2, the ground observer will measure a kinetic energy of \frac{1}{2}m(v + V)^2, or
K + \sqrt{2Km}V + \frac{1}{2}mV^2
(in one dimension).
If you get up to higher speeds, or you want an exact expression, you'll have to use the relativistic definition of energy. In special relativity, the kinetic energy is given by the difference between the total energy and the "rest energy,"
K = E - mc^2
One way to figure out the transformation rule is to use the fact that the total energy is part of a four-vector, along with the relativistic momentum,
\begin{pmatrix}E/c \\ p\end{pmatrix} = \begin{pmatrix}\gamma_v mc \\ \gamma_v mv\end{pmatrix}
where \gamma_v = 1/\sqrt{1 - v^2/c^2}. This four-vector transforms under the Lorentz transformation as you shift from one reference frame to another,
\begin{pmatrix}E/c \\ p\end{pmatrix}_\text{ground} = \begin{pmatrix}\gamma & \gamma\beta \\ \gamma\beta & \gamma\end{pmatrix}\begin{pmatrix}E/c \\ p\end{pmatrix}_\text{train}
(where \beta = V/c and \gamma = 1/\sqrt{1 - \beta^2}), so the energy as observed from the ground would be given by
E_\text{ground} = \gamma(E_\text{train} + \beta c p_\text{train})
The kinetic energy is obtained by subtracting mc^2 from the total energy, so you'd get
K_\text{ground} = \gamma(E_\text{train} + \beta c p_\text{train}) - mc^2
which works out to
K_\text{ground} = \gamma K_\text{train} + (\gamma - 1) mc^2 + \gamma\beta c p_\text{train}
where K is the relativistic kinetic energy and p is the relativistic momentum.
If you wanted it in terms of energy alone:
K_\text{ground} = \gamma K_\text{train} + (\gamma - 1) mc^2 + \gamma\beta\sqrt{K_\text{train}^2 + 2 mc^2 K_\text{train}}
You might start to notice a similarity to the non-relativistic expression above (K + \sqrt{2Km}V + \frac{1}{2}mV^2), and indeed, if you plug in some approximations that are valid at low speeds (\gamma \approx 1, \gamma - 1 \approx V^2/c^2, K_\text{train} \approx \frac{1}{2}mv^2 \ll mc^2), you will recover exactly that expression.
diazona said:...I'm seeing some pretty serious problems in the post preview on Firefox 4...
jhae2.718 said:Greg, are we on MathJax 1.1? Edit: dumb question, you're linking to their CDN.
A bit of Googling suggests that there exist rendering problems with FF 4.*.
Hm... the site I took my example from also uses MathJax 1.1:jhae2.718 said:Greg, are we on MathJax 1.1? Edit: dumb question, you're linking to their CDN.
A bit of Googling suggests that there exist rendering problems with FF 4.*.
but there are no rendering errors.MathJax v1.1
using local STIX fonts
TeX Input Jax v1.1
HTML-CSS Output Jax v1.1
mml Element Jax v1.1
tex2jax Extension v1.1
MathZoom Extension v1.1
MathMenu Extension v1.1
TeX/noErrors Extension v1.0.1
TeX/noUndefined Extension v1.0.1
Firefox v4.0
Mark44 said:Pages with any appreciable amount of LaTeX take a lot longer to load, it seems. For example, this page took about 15 - 20 sec. to load.