The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks to zero all higher eigenvalues march o...

We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is possible that quantum deformations of these extremal solutions are the endpoint of Hawking evapo...

Cobots are devices for human/robot interaction, in which axes of motion are coupled to one another by computer-controlled continuously variable transmissions rather than individually driven by servomotors. We have recently built a cobot with a three-dimensional workspace and a 3-revolute parallelogram-type mechanism. Here we present control methods for the display of virtual surfaces and for fr...