Given a smooth compact Riemannian manifold , the incompressible Euler equations can be written in abstract index notation as where is a time-dependent scalar field (representing pressure), and is a time-dependent vector field (representing fluid velocity). Here is the Levi-Civita connection associated to . One can recover from (up to constants), so I will abuse […]
A quantum computing protocol makes it possible to extract energy from seemingly empty space, teleport it to a new location, then store it for later use
The following problem was posed by Erdös and Graham (and is listed as problem #437 on the Erdös problems website): Problem 1 Let be integers. How many of the partial products , , , can be squares? Is it true that, for any , there can be more than squares? If one lets denote the […]