L² -estimates for the evolving surface finite element method

In this paper we consider the evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a suitable variational formulation in time dependent Sobolev space we proposed and analysed a finite element method using surface finite elements on evolving triangulated surfaces. An optimal order H¹ -error bound was proved for linear finite elements. In this work we prove the optimal error bound in L² (Γ(t)) uniformly in time

On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick

In this paper we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is to use special solutions to the harmonic map heat flow in order to reparametrize the equations of motion. This idea is widely known from the Ricci flow as the DeTurck trick. By introducing a variable time scale for the harmonic map heat flow, we obtain families of numerical schemes for the reparametrized flows. For the curve shortening flow this family unveils a surprising geometric connection between the numerical schemes in [5] and [9]. For the mean curvature flow we obtain families of schemes with good mesh properties similar to those in [3]. We prove error estimates for the semi-discrete scheme of the curve shortening flow. The behaviour of the fully-discrete schemes with respect to the redistribution of mesh points is studied in numerical experiments. We also discuss possible generalizations of our ideas to other extrinsic flows

Intra-industry trade and labour market adjustment: A reassessment using data on individual workers

We re-examine the relationship between intra-industry trade and labour reallocation, using individual-level data on manufacturing worker moves in the United Kingdom. The contribution of this analysis is twofold. First, we estimate the impact of intra-industry trade on worker moves between occupations as well as between industries. Second, we run individual-level regressions that allow us to control for worker heterogeneity. Our results suggest that intra-industry trade does have the stipulated attenuating effect on worker moves, both between occupations and between industries, but that this effect is relatively small compared to other determinants of labour reallocation

The major transcriptional regulatory protein of herpes simplex virus type 1 includes a protease resistant DNA binding domain

Herpes simplex virus type 1 expresses five immediateearly (IE) polypeptides. In the absence of functional Vmw175 (the product of IE gene 3) activation of transcription of later classes of viral genes and repression of IE gene expression does not occur. The recognition of specific DNA sequences by Vmw175 requires, as determined by sensitivity to mutation, a part of the protein highly conserved in the corresponding proteins of related herpes viruses. However, mutations in other parts of the protein can also disrupt specific DNA binding. This paper shows that the DNA binding domain of Vmw175 can be liberated as a functional unit by digestion with proteinase K. Analysis of mutant Vmw175 proteinsshowed that the proteinase K resistant domain has an amino terminus between amino acid residues 229 and 292, while its carboxy terminus is between residues 495 and 518. Mutations outside this region which affect DNA binding by the intact protein do not eliminate binding of the proteinase K resistant domain. This implies that direct DNA binding by Vmw175 involves a linear subsection of the polypeptide, and that mutations in other parts of the polypeptide which affect DNA binding of the whole protein do so by indirect means

Hormone replacement therapy

Martha Hickey, Jane Elliott, Sonia Louise Daviso