The synthesis of some acylglycines and related oxazolones

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Common law and the origin of shareholder protection

This paper examines the origins of investor protection under the common law by analysing the development of shareholder protection in Victorian Britain, the home of the common law. In this era, very little was codified, with corporate law simply suggesting a default template of rules. Ultimately, the matter of protection was one for the corporation and its shareholders. Using c. 500 articles of association and ownership records of publicly-traded Victorian corporations, we find that corporations afforded investors with just as much protection as is present in modern corporate law and that firms with better shareholder protection had more diffuse ownership

Common law and the origin of shareholder protection

This paper examines the origins of investor protection under the common law by analysing the development of shareholder protection in Victorian Britain, the home of the common law. In this era, very little was codified, with corporate law simply suggesting a default template of rules. Ultimately, the matter of protection was one for the corporation and its shareholders. Using c.500 articles of association and ownership records of publicly-traded Victorian corporations, we find that corporations afforded investors with just as much protection as is present in modern corporate law and that firms with better shareholder protection had more diffuse ownership

Liquid drop splashing on smooth, rough and textured surfaces

Splashing occurs when a liquid drop hits a dry solid surface at high velocity. This paper reports experimental studies of how the splash depends on the roughness and the texture of the surfaces as well as the viscosity of the liquid. For smooth surfaces, there is a "corona" splash caused by the presence of air surrounding the drop. There are several regimes that occur as the velocity and liquid viscosity are varied. There is also a "prompt" splash that depends on the roughness and texture of the surfaces. A measurement of the size distribution of the ejected droplets is sensitive to the surface roughness. For a textured surface in which pillars are arranged in a square lattice, experiment shows that the splashing has a four-fold symmetry. The splash occurs predominantly along the diagonal directions. In this geometry, two factors affect splashing the most: the pillar height and spacing between pillars.Comment: 9 pages, 11 figure

Capillary-gravity waves: The effect of viscosity on the wave resistance

The effect of viscosity on the wave resistance experienced by a 2d perturbation moving at uniform velocity over the free surface of a fluid is investigated. The analysis is based on Rayleigh's linearized theory of capillary-gravity waves. It is shown in particular that the wave resistance remains bounded as the velocity of the perturbation approches the minimun phase speed, unlike what is predicted by the inviscid theory.Comment: Europhysics Letters, in pres

A note on leapfrogging vortex rings

In this paper we provide examples, by numerical simulation using the Navier-Stokes equations for axisymmetric laminar flow, of the 'leapfrogging' motion of two, initially identical, vortex rings which share a common axis of symmetry. We show that the number of clear passes that each ring makes through the other increases with Reynolds number, and that as long as the configuration remains stable the two rings ultimately merge to form a single vortex ring

Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Sport, physical activity and the establishment of Health and Wellbeing Boards in Nottingham and Nottinghamshire

This paper will examine the emergence of Health and Wellbeing Boards in Nottinghamshire and the City of Nottingham and explore the implications for sport and physical activity. At the time of writing the transfer of responsibilities for Public Health and the establishment of Health and Wellbeing Boards in both the City of Nottingham and within Nottinghamshire County Council are considered to be relatively advanced by the Strategic Health Authorities, the respective local authorities and by the boards of the two Primary Care Trusts. "Shadow"� Health and Well being Board have been established in both authorities and they have been meeting regularly for s everal months. Public health and commissioning staff have also been successfully relocated and new strategies and priorities are starting to emerge. Nottingham and Nottinghamshire have traditionally acknowledged the role of sport and physical activity to the wider determinants of public health and given a relatively high priority to the contribution that sport and physical activity can make to the ir preventative health and early intervention agendas. This paper will look at the transition to Health and Wellbeing boards to assess how the role of sport and physical activity may be changing and to identify opportunities for its contribution to policy and practise in the future. It will examine both the theory and practise behind the emerging governance arr angements, the strategic objectives and priorities, and the developing evidential base for future policy and delivery within the two areas