Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

Shared parenting, law and policy: considering power within the framework of autopoietic theory

This paper uses the last few decades’ developments in the area of shared parenting to explore power within the framework of autopoietic theory. It traces how, prompted by turbulence from the political subsystem, family law has made several unsuccessful attempts to solve the perceived problem of post-separation dual-household parenting. It agrees with Luhmann and Teubner that closed autopoietic systems’ developments are limited by their normative and cognitive frameworks, and also argues that changes, which have occurred in family law, show that closed social systems do not function in total isolation. It considers power as ego’s ability to limit alter’s choices. In our functionally differentiated society, with its recent proliferation of communication, power appears more diffuse and impossible to plot into causal one-way relationships.

A structuration theory perspective on the institutional change in Higher Education sector

Budgeting system has been traditionally viewed as a control mechanism rather than a communication tool to facilitate the institutionalisation of organisational change. A good budgeting system not only reflects the organisational reality but also socially constructs the reality. This paper uses the structuration perspective to understand budget-related behaviour in a UK research-intensive university and especially, study the role of budgeting system in achieving organisational sustainability. Giddens’ structuration theory offers a valuable framework for the study of the duality of structure and emphasises on the structural properties of social systems. Based on the semi-structured interviews with top management and budget holders, it is concluded that in this specific context, budgeting system may place a significant role in establishing and legitimising institutional change.

Elucidating the structure of chiral molecules by using amplified vibrational circular dichroism: from theory to experimental realization

Recent experimental observations of enhanced vibrational circular dichroism (VCD) in molecular systems with low-lying electronically excited states suggest interesting new applications of VCD spectroscopy. The theory describing VCD enhancement through vibronic coupling schemes was derived by Nafie in 1983, but only recently experimental evidence of VCD amplification has demonstrated the extent to which this effect can be exploited as a structure elucidation tool to probe local structure. In this Concept paper, we give an overview of the physics behind vibrational circular dichroism, in particular the equations governing the VCD amplification effect, and review the latest experimental developments with a prospective view on the application of amplified VCD to locally probe biomolecular structure.

Categories & order systems: Claude Parent and The Serving Library intersections of architecture, art and editorial design

This paper discusses the work of Claude Parent and The Serving Library, considering the critiques generated by their intersecting of architecture, art and editorial design. Through focus on the ways in which hosting environment, architecture and forms of expanded publishing can serve to dissolve disciplinary boundaries and activities of production, spectatorship and reception, it draws on the lineage of 1960s/70s Conceptual Art in considering these practices as a means through which to escape medium specificity and spatial confinement. Relationships between actual and virtual space are then read against this broadening of aesthetic ideas and the theory of critical modernity.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

Poisson stability for impulsive semidynamical systems

In this paper, the concept of Poisson stability is investigated for impulsive semidynamical systems. Recursive properties are also investigated. (C) 2009 Elsevier Ltd. All rights reserved.

LaSalle`s theorems in impulsive semidynamical systems

We consider a semidynamical system subject to variable impulses and we obtain the LaSalle invariance principle and the asymptotic stability theorem for this semidynamical system. (C) 2009 Elsevier Ltd. All rights reserved.

Formal validation of automated policy refinement in the management of network security systems

Policy hierarchies and automated policy refinement are powerful approaches to simplify administration of security services in complex network environments. A crucial issue for the practical use of these approaches is to ensure the validity of the policy hierarchy, i.e. since the policy sets for the lower levels are automatically derived from the abstract policies (defined by the modeller), we must be sure that the derived policies uphold the high-level ones. This paper builds upon previous work on Model-based Management, particularly on the Diagram of Abstract Subsystems approach, and goes further to propose a formal validation approach for the policy hierarchies yielded by the automated policy refinement process. We establish general validation conditions for a multi-layered policy model, i.e. necessary and sufficient conditions that a policy hierarchy must satisfy so that the lower-level policy sets are valid refinements of the higher-level policies according to the criteria of consistency and completeness. Relying upon the validation conditions and upon axioms about the model representativeness, two theorems are proved to ensure compliance between the resulting system behaviour and the abstract policies that are modelled.

Photoluminescence behavior of Eu(3+) ion doped into gamma- and alpha-alumina systems prepared by combustion, ceramic and Pechini methods

Al(2)O(3):Eu(3+)(1%) samples were prepared by combustion, ceramic, and Pechini methods annealed from 400 to 1400 degrees C. XRD patterns indicate that samples heated up to 1000 degrees C present disordered character of activated alumina (gamma-Al(2)O(3)). However, alpha-Al(2)O(3) phase showed high crystallinity and thermostability at 1200-1400 degrees C. The sample characterizations were also carried out by means of infrared spectroscopy (IR), scanning electron microscopy (SEM) and specific surface areas analysis (BET method). Excitation spectra of Al(2)O(3):Eu(3+) samples present broaden bands attributed to defects of Al(2)O(3) matrices and to LMCT state of O -> Eu(3+), however, the narrow bands are assigned to (7)F(0) -> (5)D(J),(5)H(J) and (5)L(J) transitions of Eu(3+) ion. Emission spectra of samples calcined up to 1000 degrees C show broaden bands for (5)D(0) -> (7)F(J) transitions of Eu(3+) ion suggesting that the rare earth ion is in different symmetry sites showed by inhomogeneous line broadening of bands, confirming the predominance of the gamma-alumina phase. For all samples heated from 1200 to 1400 degrees C the spectra exhibit narrow (5)D(0) -> (7)F(J) transitions of Eu(3+) ion indicating the conversion of gamma to alpha-Al(2)O(3) phases, a high intensity narrow peak around 695 nm assigned to R lines of Cr(3+) ion is shown. Al(2)O(3):Eu(3+) heated up to 1100 degrees C presents an increase in the Omega(2) intensity parameter with the increase of temperatures enhancing the covalent character of metal-donor interaction. The disordered structural systems present the highest values of emission quantum efficiencies (eta). CIE coordinates of Al(2)O(3):Eu(3+) are also discussed. (C) 2007 Elsevier Inc. All rights reserved.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.