Flow Invariance on Stratified Domains

This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with non-Lipschitz data. This is done via the identification of a new multifunction, the essential velocity multifunction. Properties of this multifunction are investigated and used to establish the relevant invariance criteria

Reflexive law, corporate social responsibility and the evolution of labour standards: the case of working time

Through an empirical study of working time in the United Kingdom, we explore the scope for initiatives based on corporate social responsibility (CSR) to engender voluntary action by employers to raise labour standards. Our evidence suggests that a CSR-based approach faces considerable problems of implementation in this area, in large part because the legal mechanisms which might underpin CSR ('reflexive law') have not yet been effectively developed.corporate social responsibility, labour standards

Opting Out Of The 48-Hour Week – Employer Necessity Or Individual Choice? An Empirical Study Of The Operation Of Article 18(1)(B) Of The Working Time Directive In The UK

The EU Working Time Directive has so far had little impact on an ingrained culture of long-hours working in the UK. Case studies suggest that the use of individual opt-outs from the 48-hour limit on weekly working time is a principal reason for this. However, removal of the individual opt-out (currently under consideration at EU level) is unlikely to make much difference to UK practice in the absence of a wider review of working time policy. In particular, the UK’s individualised system of workplace bargaining is currently ill-placed to adapt to a continental European model of working time regulation.working time, labour standards, collective bargaining, European Union

Hamilton-Jacobi theory for optimal control problems on stratified domains

This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used to establish Hamiltonian criteria for weak and strong invariance. Finally, we use these characterizations to show that the minimal time function and the value function for a Mayer problem, both over stratified domains, satisfy and are the unique solutions to a proximal Hamilton-Jacobi equation