Given a graph G and an integer k, the H-free Edge Editing problem is to find whether there exist at most k pairs of vertices in such that changing adjacency results without any induced copy H. Nontrivial polynomial kernels are known for some graphs H with 4 vertices, but starting from 5 only if either complete or empty. This suggests conjecture no other least where admits kernel. Towards this g...

We prove that the 2D finite depth capillary water wave equations admit no solitary solutions. This closes existence/non-existence problem for waves in 2D, under classical assumptions of incompressibility and irrotationality, with physical parameters being gravity, surface tension fluid depth.