Recent content by neginf

How do you find matrices a,b,c satisfying a=b*c*b^-1 b=c*a*c^-1 c=a*b*a^-1 ?

http://www.sciencedaily.com/releases/2012/08/120823111507.htm 1. Does this mean space might be smooth down to any scale ? 2. Can virtual particles appearing and disappearing effect paths of photons traveling through space ?

Thank you both for the replies. Sorry question 3 wasn't specific enough. Could physical space have a different topology than the usual R^3 ?

Is it known if space: 1. is "grainy" or smooth ?, 2. has singular points ?, 3. is like R^3 ?

Does the universe's flatness mean that non Euclidean geometry isn't important in physics?

Were the observations Whitewolf4869 asks about done by COBE, WMAP, etc. ? Can flat universes have different possibilities for topologies like flat surfaces can ? At any fixed time, is the spatial universe a 3 manifold ?

If f(x) has a period of 2*pi and |f(x)-f(y)| <= c*|x-y|^a where a and c are positive constants, why are are n-th Fourier coefficients <= c*(pi/n)^a ? Help or hints would be appreciated.

Thank you very much.

Maybe I should have asked if it had no gaps instead of using the word "continuous". Is the answer to 1. "no" because the molecules are mostly gaps to start with and have gaps between them ? Does this mean many things in ordinary life are mostly empty space ? Does the surface of calm water...

1. Do adjacent water molecules fit together so tightly that water is "continuous" ? 2. If the answer to 1. is "no", what is in between them ? 3. What would the surface of a calm puddle look like if magnifed so individual molecules could be seen?

Sorry, n. I tried it with 4 and it seemed not to hold, the inequality. Tried with 2 and same problem.

Thank you for writing back. The inequality is n is even C(n,n/2)/2^(n+1) > 1/(2*sqrt(n)). "Sharp form fo Stirling's inequality" is sqrt(2*pi*k) * k^k * e^-k < k! < sqrt(2*pi*k) * k^k * e^-k * (1+1/(4*k)) Is it right? Tried with 4. With Google books, by clicking on the book in...

In this link is a part of a book on approximations of functions. http://books.google.com/books/about/An_Introduction_to_the_Approximation_of.html?id=VTW2cmjC43YC I'd be thankful if someone would explain how the inequality near the top of page 17 was gotten.

1. When a cup of water is in a freezer, for a while, some of it's ice and some of it's liquid. Does that mean the liquid part has not hit freezing temperature yet or does the changeover from liquid to solid take a while, even at freezing temperature? 2. When a pot of water gets hot...

Thank you both. x-ct=x'-ct'=0 so x-ct=anything*(x'-ct').