Recent content by pmsrw3

Got some answers to this on mathoverflow.net. It turns out there ARE continuous bijections ℝ^2×ℝ^2×ℝ^2/E+(2) -> ℝ^3.

This is a question that comes from my research. I know next to nothing about topology, so I'm not able to assure myself of the answer. The problem is this: I'm watching an animal move in two dimensions. At three successive points in time I have three positions, (x1,y1), (x2,y2), (x3,y3). But...

For a circle of radius r, equally spaced points are r e^{\frac{2\pi i k}{n}}. The product of the lengths of the n-1 line segments joining one of those points to each of the others would be n r^{n-1}. That is, it's just r^{n-1} times the value for the unit circle, since each line is now longer by...

It's very, very hard. Like quantum mechanics and supercomputers hard.

That's true, but it's not what I said. Even multiplying by the number of atoms in the entire universe doesn't noticeably increase it. What do you mean by the outcome of GN? That doesn't make any sense to me. What's confusing about this? The answer is clearly "No".

The fundamental idea is that you never get more energy out than you put in.

GN is so much more enormously big than the number of atoms in a (finite) universe, that it doesn't really matter if each universe contains 1 atom or 10100 or even 1010100. At the level of approximation we're dealing with, that's still basically just a tiny bit more than GN of atoms.

We're taking the absolute value. A complex number x+yi is like a vector -- it has a length and a direction. The length is called the absolute value -- a term you've probably heard before, meaning, for real numbers, the number with a positive sign. For complex numbers \text{absolute value of }x+y...

Look up "dehydration". Sulfuric acid is a powerful dessicant.

What is that, exactly? I'm unclear on what the "interesting property" is. Obviously you can express any number as a sum of differences between a series of smaller numbers. I tried googling "collapsing sum" but found nothing helpful.

I don't understand. What does this have to do with game theory?

Think a little about step 3.

I wasn't familiar with this, but based on those links, it should be the same. In particular, if you look at the second, the correction from ACF to PACF is calculated from the covariance matrix. Covariances, like correlations, are mean-corrected.

What does "from mechanical side" mean?

Ah! Well, that's at least one condition you didn't mention. You didn't say in the OP that f was periodic. But it still doesn't seem to work. For instance, the Laplace transform of cos(t) is s/(1+s2). This goes to 0 as s->infinity, but cos(0) = 1.