Link o' the Day

American Scientist has an interesting article about the future of computer storage (hint: video). Via /.

Wish me luck on my math midterm tomorrow.

In case you were wondering, this is the General Implicit Function Theorem:

Assume F maps Rn+k to Rk and is continuously differentiable. Also assume DyF(x0, y0) is an invertible k by k matrix (where x is a point in Rn and y in Rk). Lastly, assume that F(x0, y0) = 0. (0 = {01 ... 0k})

Then, there exists r > 0 and the continuously differentiable function G(x) such that

1. F(x, G(x)) = 0 for all x such that ||x - x0|| < r

2. If F(x, y) = 0, then y = G(x) for all x, y such that ||x - x0|| < r and ||y - y0|| < r

3. DxF(x, G(x)) + DyF(x, G(x))DG(x) = 0 where DG(x) = DyF(x, y)-1DxF(x, y)

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