Established gambling operators have argued that person-to-person wagering on Internet ‘betting exchanges’ represents unfair competition. In this paper we suggest that, in fact, betting exchanges have brought about significant efficiency gains by lowering transaction costs for consumers. We test this hypothesis using matched data on UK horse racing from betting exchanges and from traditional bet...

We give an overview of variational formulations of second-order linear elliptic PDEs that are based on integration by parts (or, equivalently, on Green’s identities).

The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modiied Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A nite element method for discretization of the Stefan problem is...

Weak lensing leads to the non-Gaussian magnification distribution of standard candles at given redshift z, p(μ, z). We derive an accurate and convenient analytical method for computing p(μ, z). Our method is based on the unique mapping between the magnification of a source and the local smoothness parameter α̃, the ratio of the density of matter smoothly distributed in the beam connecting the ob...

We establish a simpliied form of the axisymmetric Fokker-Planck-Landau operator. In doing so, we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three dimensional operator 6]. A symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical propertie...

For the Burgers’ equation as an example for a hyperbolic conservation law, we have considered in our previous paper [CGK] a weak formulation with a stabilization to handle discontinuities, commonly called a viscosity approach. Numerically, this was realized by locally introducing degrees of freedom around the discontinuities by means of an adaptive wavelet method in an a-posteriori fashion. In ...

We deal with initial-boundary value problems describing vertical vibrations of viscoelastic von Kármán-Donnell shells with a rigid inner obstacle. The short memory (Kelvin-Voigt) material is considered. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the penalization method.

A time-dependent system modeling the interaction between a Stokes fluid and an elastic structure is studied. A divergence-free weak formulation is introduced which does not involve the fluid pressure field. The existence and uniqueness of a weak solution is proved. Strong energy estimates are derived under additional assumptions on the data. The existence of an L2 integrable pressure field is e...

We study a linear fractional Fokker–Planck equation that models non-local diffusion in the presence of a potential field. The non-locality is due to the appearance of the 'fractional Laplacian' in the corresponding PDE, in place of the classical Laplacian which distinguishes the case of regular diffusion. We prove existence of weak solutions by combining a splitting technique together with a Wa...