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  1. How do I change my IE6 browser running on windows XP to display the proper theme for the website, which I guess is the same as allowing the website to choose its own colors? Thx in advance
  2. I am still using IE6 'cus of other unrelated isues, but I think this problems effects most browsers 'cus I've seen others complain of the same or a similar thing. On physicsforums.com some1 complained of a problem very similar to what I described, latex code displaying as nearly unreadable or unreadable white marks against a black background. That person described it as an anit-aliasing problem, which it might be, I don't know. But a forum mentor said that these images were stored that way on the server, implying that they were, perhaps, incorrectly formated when initially posted, and that one
  3. Thx all for the replies. I should have known the problem was mathematica's [wolfram alpha] behavior when doing certain calculations.
  4. Hi, I'm sure this has been asked many times before, and I tried to find a sticky for this, but can some1 plz tell me the easiest way to get latex code to display properly when I'm browsing the math & physics forums? The code usually displays for me as unreadable white marks against a black gackground. I usually click on the code and then try and piece together what it's saying from the written LaTex code. Thx in advance.
  5. I noticed some unexpected behavior in the real-valued f(x)=(1+x)^1/x, as a function of real numbers, when plotting it on wolfram alpha. I inputed: plot (1+x)^1/x from x=-0.0000001 to x=0.0000001 and saw that it unexpectedly seemed to oscillate near zero. I took a closer look with: plot (1+x)^1/x from x=-0.00000000001 to x=0.00000000001 and saw that it definitely seems to oscillate near zero. My original rough graph on paper using a hand calculator suggested the curve was smooth near zero, and even windows calculator's 32 decimal places were unable to reveal the oscillation when I manua
  6. aswoods at S.O.S. Mathematics CyberBoard :: View topic - mean nearest neighbor in 3d helpfully pointed out that Gradshteyn and Ryzhik 3.381.10, and Wolfram Alpha agree that the integral from 0 to infinity of x^3 e^(-ax^3)dx = 1/3 gamma(4/3) a^(-4/3) so the mean nearest neighbor distance in 3d is: <r> = [4 pi rho] integral from 0 to infinity r^3 e^(-[4/3] pi rho r^3) dr <r> = 1/3 gamma(1/3) ([4/3] pi)^(-1/3) rho^(-1/3) <r> = 0.55396 rho^(-1/3) <r> = 3.93 light-years for the 23 star systems within 12.5 ly :)
  7. since what we really want is the average distance to the nearest star system, and atlasoftheuniverse.com reports 23 star systems within 12.5 ly (35 stars but 3 trinaries, 6 binaries, and 14 singles), we have: rho = 23/([4/3]pi 12.5^3) rho = 0.0028113 star systems/cubic light-year rho is only an estimate since some of the star systems near the outer edge of the volume (of 12.5 ly radius) might have nearest neighbors outside the volume and some star systems just outside the volume might have nearest neighbors inside. since the integral of x^3 exp(-a x^3)dx doesn't seem to be integrable, I
  8. Modest at http://hypography.com/forums/physics-mathematics/21509-mean-nearest-neighbor-distance-3d.html was helpful in pointing me to this link: Probability, statistical optics, and ... - Google Books And now I need to integrate: integral of x^3 exp(-a x^3) dx, with a = constant, but I couldn't. Hopefully, it's an easy integral and and someone will figure it out. In a 3-dimensional random distribution, the basic idea for finding the average distance from any given particle to its nearest neighbor begins with: P®dr = [1 - integral from 0 to r of P®dr][4 pi r^2 pho dr] (1) whe
  9. Hi. In 3 dimensional Euclidean space with the usual metric, d=[(delta x)^2+(delta y)^2+(delta z)^2]^1/2, I'm trying to figure out the average distance between nearest neighbors in a randomly distributed sample of particles. My best initial guess for the average distance from any given particle to its nearest neighbor is d_nearest neighbor_mean=(volume/n)^1/3 where n particles are randomly distributed in a 3 dimensional volume. The question originated when I wondered what was the average distance between stars in the solar neighborhood. atlasoftheuniverse.com gives 35 stars (including the Su
  10. i'm confused about how COBE (the Cosmic Background Explorer) measured the frequency peak of the Cosmic Microwave Background (CMB). the following seems clear to me and relatively straightforward: for black body radiation, i.e., for an ideal photon gas in local thermodynamic equilibrium with matter, e.g., the surface of last scattering of the CMB, the spectral radiance, I_nu (T) = [2h/c^2][nu^3/(exp(h nu/[k T])-1)] or I'_lamba (T) = [2hc^2][1/lamba^5(exp(h c/[lambda k T])-1)] <forgive my clumsy notation, i don't know how to do LaTeX notation>, peaks at nu_max or lambda_max, respectively,
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