The database of molecular motions, MolMovDB (http://molmovdb.org), has been in existence for the past decade. It classifies macromolecular motions and provides tools to interpolate between two conformations (the Morph Server) and predict possible motions in a single structure. In 2005, we expanded the services offered on MolMovDB. In particular, we further… (More)
when can 1 × t be tiled by positive and negative copies of rectangles which are similar (uniform scaling) to those in the list? We prove that such a tiling exists iff t is in the field (a, b,. .. , c). When can rectangle 1 × t be packed by (finitely many) squares? Dehn 1903 gave the answer: If and only if t is rational. For irrational t he showed 1 × t not… (More)
We determine the Desarguesian planes which hold r-nets with ovals and those which hold r-nets with hyperovals for every r ≤ 7.
Let K be a finite extension of the p-adic field Qp and let F (X, Y) and G(X, Y) be one-dimensional formal group laws over the ring of integers OK of K. Let φ(X) be a homomorphism from F to G which is defined over the ring of integers O Cp of the completion Cp of Q alg p. In this paper we prove that if ker(φ) is finite then there is a discretely valued… (More)
Let T be a tile made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be tilable by finitely many Q-weighted tiles with the same shape as T , and necessary and sufficient conditions for a square to be tilable by… (More)