In this article we introduce a novel multiple-input-multiple-output (MIMO) spatial filter (SF) which can be applied as a preprocessing scheme to uniform linear arrays, preserving the Vandermonde structure of the steering vectors while changing the amplitude and the phase gradient of the steering vector in a nonlinear fashion. The new scheme is therefore titled Vandermonde Invariance Transformat...

A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) entropy ($\mathcal{K}$), both having attracted attention over past decades, a invariant called concentration ($\mathcal{A}$) introduced in present study. The defined as normalised mean distance between reconstruction vectors, evaluated...

• Generalising confluence to up garbage. Critical pair analysis for Back-tracking free recognition of graph languages. The transformation graphs and graph-like structures is ubiquitous in computer science. When a system described by graph-transformation rules, it often desirable that the rules are both terminating confluent so rule applications an arbitrary order produce unique resulting graphs...

In this paper we consider several nonlinear systems of algebraic equations which can be called “Prony-type”. These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes criti...

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties which we call Vandermonde varieties. They are closely related to the varieties consisting of all linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e., when the dimension of a...

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties which we call Vandermonde varieties. They are closely related to the varieties of linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e. when the dimension of a Vandermonde var...

We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fullyextended, orthogonal iCRSs are confluent modulo identification of hypercollapsing subterms. As a corollary, we obtain that fully-extended, orthogonal iCRSs have the normal form property and the unique normal form property (with respect t...