A new methodology to characterize nonlinear systems is described. It is based on the measurement over the time series of two quantities: the "Dynamical order" and the "Self-correlation". The averaged "Scalar" and "Perpendicular" producís are introduced to measure these quantities. While this approach can be applied to general nonlinear systems, the aim of this work is to focus on the characteri...

Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product. Bounds and computable expressions for structured eigenvalue condition numbers are derived for these classes of matri...

We examine whether the fact that QCD is chirally invariant at short distances necessarily leads to the prediction that hadrons form approximate parity doublets, as has been recently put forward by Glozman and collaborators. We show that this is not the case, and we exhibit some of the pitfalls of trying to link the operator product expansion to the hadron spectrum. We illustrate our arguments w...

These rings admit numerous algebraic and geometric realizations, but one of the historically first constructions, dating to the work of Steinitz in 1900 completed later by Hall, was given in terms of what is now called the classical Hall algebra H (see [Ma], Chapter II ). This algebra has a basis consisting of isomorphism classes of abelian q-groups, where q is a fixed prime power, and the stru...

Generalized scalar operators were introduced by C. Foia~ [4] and a detailed study of such operators can be found in the monograph [3]. An important subclass consists of regular generalized scalar operators which enjoy properties not shared by all generalized scalar operators. For example, the sum and product of commuting generalized scalar operators S and T need not be generalized scalar operat...

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

In a recent paper [I. P. Neupane and D. L. Wiltshire, Phys. Lett. B 619, 201 (2005).] we have found a new class of accelerating cosmologies arising from a time–dependent compactification of classical supergravity on product spaces that include one or more geometric twists along with nontrivial curved internal spaces. With such effects, a scalar potential can have a local minimum with positive v...

This paper investigates the implications of using a modern super-scalar processor in the safety-critical domain. Firstly, a description of current certification practice and devices is given as background. This is followed by an assessment of how the certification argument and its supporting evidence are affected by the use of a super-scalar processor. Two types of modern processor are consider...

This work examines force modeling and softwarebased commutation for closed-loop control of planar linear motors, motivated by the need for a robust and versatile planar robot for precision assembly. The approach taken is to make measurements of the static and dynamic force capabilities of the motor as directly as possible, and determine the applicability of simple models commonly used. Measurem...