We survey continuous and discrete regularization methods for first-kind Volterra problems with continuous kernels. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on computation of the Volterra adjoint operator, an anticipatory operator. In this survey we pay special attention to partic...

This paper proposes a new reduced complexity Volterra model called S-PARAFAC-Volterra. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique. It takes advantage from previous results where an algorithm for the estimation of the memory and the order of the Volterra model has been presented. The proposed mod...

In this paper, the new hybrid adaptive Volterra filter was proposed to be applied for compensating the nonlinear distortion of memoryless nonlinear systems with saturation characteristics. Through computer simulations as well as the analytical analysis, it could be shown that it is possible for both conventional Volterra filter and proposed Volterra filter, to be applied for linearizing the mem...

This paper introduces a computationally e cient Gauss-Newton type adaptation algorithm for parallel-cascade realizations of truncated Volterra systems with arbitrary, but nite order nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. The complexity of our system is comparable to the c...

This paper presents performance analysis of an adaptive Volterra/Hybrid equalizer in a nonlinear magneto-optic data storage channel. In a data storage system, nonlinear intersymbol interference (ISI) is one of the limiting factors for high storage density. Volterra and Hybrid (combination of linear and Volterra) equalizers are proposed and developed for compensation of nonlinear ISI. The use of...

The present paper is concerned with the nonparametric identification of mechanical systems with mild nonlinearities using a Wiener-Volterra model. The paper employs some classical developed results to describe the discrete-time Volterra models using orthonormal Kautz functions. If the two parameters of these filter sets, associated with a Volterra series truncation, are properly designed, the n...

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the u...

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body for...