The problem of controlling the position of a pair of point vortices using a strain field or a field of a single souce/sink is considered. The problem dimension is reduced by averaging over the fast rotation of vortices around the center of vorticity. Control is assumed to be function of rotation phase only. For the case of the strain field actuation, optimal control problem is posed in three di...

The concepts of bounded boundary rotation and parabolic domain are used to define certain new classes analytic functions such as V 1 , q m g , id="M3"> R id="M4"> T id="M5"> Q...

Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show that there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle, or it is an indecomposable continuum.

We review the Johnson–Moser rotation number and the K0-theoretical gap labelling of Bellissard for one-dimensional Schrödinger operators. We compare them with two further gap labels, one being related to the motion of Dirichlet eigenvalues, the other being a K1-theoretical gap label. We argue that the latter provides a natural generalization of the Johnson–Moser rotation number to higher dimens...

The fundamental boundary value problem in the function theory of several complex variables is the ∂-Neumann problem. The L2 existence theory on bounded pseudoconvex domains and the C∞ regularity of solutions up to the boundary on smooth, bounded, strongly pseudoconvex domains were proved in the 1960s. On the other hand, it was discovered quite recently that global regularity up to the boundary ...

The classical panel method has been extensively used in external aerodynamics to calculate ideal flow fields around moving vehicles or stationary structures in unbounded domains. However, the panel method, as a somewhat simpler implementation of the boundary element method, has rarely been employed to solve problems in closed complex domains. This paper aims at filling this gap and discusses th...

In this paper, a discrete robust adaptive iterative learning control is proposed for a class of uncertain nonlinear systems with unknown control direction and random bounded disturbances. Based on a new design methodology, the problem of unknown sign and upper bound of the time-varying input gain parameter can be solved. In order to deal with the uncertainties from random bounded disturbance an...

On-chip ESD protection circuits realized with novel diode structures without the field-oxide boundary across the p/n junction are proposed. A PMOS (NMOS) is especially inserted into the diode structure to form the PMOS-bounded (NMOS-bounded) diode, which is used to block the field oxide isolation across the p/n junction in the diode structure. Without the field oxide boundary across the p/n jun...

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...