Set Theory in Javascript

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Vortex Solution to Navier Stokes Equations

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This is a solution I found to the Navier Stokes equations . It uses the flow lines of the Hopf Fibration (which is basically just a way of covering the entire 3D space in circles). The flow lines can be seen in this image below: You can see my paper here. Solution to Navier-Stokes equation . Unfortunately I won't get a million pounds for winning the Clay Millennium prize because this is a compressible not incompressible solution. :( Oh, well. Nice try! I think it's pretty nice anyway. :) Also it uses the nice identity: which paramaterizes the Pythagorean quadruples!
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An Exceptional Supersymmetry

An Exceptional Supersymmetry It is proposed in this article a way to construct an exceptional supersymmetry distinct from the family of usual supersymmetries usually labelled by N. (N=1, N=2, N=4 and N=8). It relies on the special properties of the root system of E 8 . It is a different kind of super-symmetry in that the superpartners don't have the same charge but together the charges from all the particles in the representation form a group. In a nut-shell we are assigning spins to elements of the E8 algebra and promoting them to super-symmetry operators. The special properties of E8 allows us to do this. Introduction The similarities between  N=8 Supersymmetry with 256 generators and the group E8 with 248 generators is suggestive that there might exist a combined structure with properties of both. Noting that E8 can be split into a bosonic part (a representation of O(16) ) and a fermionic part a spinor representation of O(16). We can assign a "spin" to each...
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Could the Universe be a Giant Knot?

Idea is that the state of the Universe is represented by a knot. The complex amplitude is given by a knot invariant. This is the sum of histories. A history is a series of slicings which return the knot to the unknot. Knot states related by Reidmeister moves are equivalent. The cosmological time of a knot is the 'unknotting' number. One possible flaw is that there are an infinite number of families of knots with 'unknotting number' 1. However, many of these may have very low amplitudes. The amplitudes might be given by the knot polynomials , e.g,for some constant,k,q: \[ q\psi(K_0) = e^{ik}\psi(K_+) - e^{-ik}\psi(K_-) \] and \( \psi( unknot ) = 1 \) . The question is, how would one relate a knot to a curved 3 dimensional manifold? What would the curvature be? Where would the points of space-time be? Does it satisfy: \[ \sum\limits_{K_2}\Delta(K_1,K_2)\Delta(K_2,K_3) = \Delta(K_1,K_3) \]
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