A new variational characterization of solutions for an important class of nonlinear operator equations is obtained. The result obtained is used to derive sharp necessary and sufficient conditions for the solvability of such operator equations. Examples of the applicability of the results obtained to nonlinear Dirichlet problems and global differential geometry are discussed.

In this paper, we propose a nonlinear model for magnetic levitation systems which is validated with experimental measurements. Using this model, a nonlinear control law based on differential geometry is firstly synthesized. Then, its real-time implementation is developed. In order to highlight the performance of the proposed control law, experimental results are given.

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...

We consider the nonlinear function used in the Advanced Encryption Standard (AES). This nonlinear function is essentially inversion in the finite field GF(2), which is most naturally considered as a projective transformation. Such a viewpoint allows us to demonstrate certain properties of this AES nonlinear function. In particular, we make some comments about the group generated by such transfo...

Abstract:In this paper, under some assumptions a nonlinear controller based on differential geometry theory of nonlinear control system and pole-assignment method is designed, and applied to synchronize output signals of high dimensional chaotic system. Using the method, we can synchronize output signals formed by linear or nonlinear composition of single or multiple state variables of the chao...