For large-scale sparse saddle point problems, Peng and Li [12] have recently proposed a new alternating-direction iterative method for solving nonsingular saddle point problems, which is more competitive (in terms of iteration steps and CPU time) than some classical iterative methods such as Uzawa-type and HSS (Hermitian skew splitting) methods. In this paper, we further study this method when ...

An adaptive feedback method for tracking and stabilizing unknown or slowly varying saddle type steady states of conservative dynamical systems is described. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. Meanwhile, a controller, involving both filters in parallel, works perfectly. As a specific example, the Lagrange point L2 ...

We provide a lower bound on the number of closed characteristics on singular energy levels of second-order Lagrangian systems in the presence of saddle-focus equilibria. The hypotheses on the Lagrangian are mild, and the bound is given in terms of the number of saddle-foci and a potential function determined by the Lagrangian. The method of proof is variational, combining techniques to minimize...

We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The sad...

It is shown that any convex function can be approximated by a family of differentiable with Lipschitz continuous gradient and strongly convex approximates in a “self-dual” way: the conjugate of each approximate is the approximate of the conjugate of the original function. The approximation technique extends to saddle functions, and is self-dual with respect to saddle function conjugacy and also...

We calculate quantum-mechanically exact wave functions of resonances in spectra of the hydrogen atom in crossed external fields and prove the existence of long-lived decaying quantum states localized at the Stark saddle point. A spectrum of ground and excited states reproducing the nodal patterns expected from simple quadratic and cubic expansions of the potential in the vicinity of the saddle ...

High temperature superconducting (HTS) surface resonators have been used as a low loss RF receiver resonator for improving magnetic resonance imaging image quality. However, the application of HTS surface resonators is significantly limited by their filling factor. To maximize the filling factor, it is desirable to have the RF resonator wrapped around the sample so that more nuclear magnetic di...