Background and Aims: Production of acoustic cavitation by sonication has been recently recommended as a targeted treatment. The experimental results from studies indicate that the activity of cavitation generated by bi- or multi-frequency ultrasound irradiation is higher than that caused by single frequency irradiation. In this study, effects dual (1 MHz and 40 kHz) and single frequency soni...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Until now the representation (i.e. plotting) of curve in Parallel Coordinates is constructed from the point ↔ line duality. The result is a " line-curve " which is seen as the envelope of it's tangents. Usually this gives an unclear image and is at the heart of the " over-plotting " problem; a barrier in the effective use of Parallel Coordinates. This problem is overcome by a transformation whi...

3 Linear operators 12 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Bounded linear operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Linear functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Algebraic dual spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5 Dual spaces . . . . ....

We survey some recent results due to myself, Nicola Pace and Gábor P. Nagy. A dual k-net of order n in the finite projective plane PG(2, q) over the finite field GF (q) consists of a k ≥ 3 pairwise disjoint point-sets (components), each of size n, such that every line meeting two distinct components meets each component in precisely one point. Dual k-nets are truly combinatorial objects; nevert...

In this paper we show how to split the root-locus plot for an irreducible rational transfer function into several individual algebraic plane curves, like lines, circles, conics, etc. To achieve this goal we use results of a previous paper of the author to represent the Root Locus as an algebraic variety generated by an ideal over a polynomial ring, and whose primary decomposion allow us to isol...

Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the degree of finite fields and have algebraic degree no more than 4. In this paper, several new infinite families of bent functions are obtained by adding the the...

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.