O bodech obratu
We consider circular annuli with Poncelet's porism property. We prove two identities which imply Chapple's, Steiner's and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.
We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from to This estimate yields some continuity properties of the flow map for the topology of , provided one takes its quotient by the continuous group action of given by translations. We also prove that without taking this quotient, for any the flow map at time is discontinuous as a map from , equipped with the weak topology of to the space of distributions The argument relies in an essential...