Nonlinear feedback shift registers (NFSRs) are an important type of sequence generators used for building stream ciphers. The shift register used in Grain, one of eSTREAM finalists, is a cascade connection of two NFSRs, which is also known as nonlinear product-feedback shift registers proposed in 1970. This paper provides a series of algorithms to decompose a given NFSR into a cascade connectio...

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, ...

We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by complex topologies that include both shortand long-ranged connections. With an exemplary time-resolved analysis of asymmetric nonlinear interdependences bet...

In this paper we start developing the so-called Klein’s formalism on dual Lie algebroids. The nonlinear connection associated to a regular section is naturally obtained. Particularly, this connection is found for the Hamiltonian case. Mathematics Subject Classification: 17B66, 53C05.

We revisit the concept of observation error for nonlinear observers of nonlinear systems. In order to obtain a coordinate free notion of such an error we define it using fiber bundles over the system manifold. The new notion ties in nicely with Brockett’s and Willems’ classical description of nonlinear systems as bundles as well as with the related description of observers as bundles due to van...

Nonlinear resonant magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc.) The resonant behaviour of slow MHD waves is confined in a narrow dissipativ...

This paper proves approximation order properties of various nonlinear subdivision schemes. Building on some recent results on the stability of nonlinear multiscale transformations, we are able to give very short and concise proofs. In particular we point out an interesting connection between stability properties and approximation order of nonlinear subdivision schemes.