Scaling Behaviour of the Maximal Growth Rate in the Rosensweig Instability

The dependence of the maximal growth rate of the modes of the Rosensweig instability on the properties of the magnetic fluid and the external magnetic induction is studied. An expansion and a fit procedure are applied in the appropriate ranges of the supercritical induction $\hat B$. With increasing $\hat B$ the scaling of the maximal growth rate changes from linear to a combination of linear and square-root-like scaling. The scaling of the corresponding wave number alternates from quadratic to primarily linear. For very small $\hat B$ the dependence of the maximal growth rate on the viscosity is given. Suggestions are made for experiments to test the predicted scaling behaviours.Comment: 8 pages, 4 figures; to appear in Europhys. Let

Equivariant smoothing of piecewise linear manifolds

We prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a challenge posed by Thurston in dimension three and confirms a conjecture by Kwasik and Lee in dimension four in a stronger form.Comment: revised version, accepted by Math. Proc. Cambridge Philos. So

Editor’s Note

With this issue, Law and Contemporary Problems initiates a new practice of offering occasional mini-symposia on topics which deserve treatment, but may not fill an entire issue. The topics we have chosen certainly deserve treatment. The questions of policy posed by the prospect of additional urban growth in the eighties demand far more thoughtful attention than they have yet had. The relevance of an examination into the control of political and ideological dissent is manifest as we contemplate world events of the past year. We are pleased to offer these two brief symposia. We will introduce others from time to time in future issues. David Lang

When is the underlying space of an orbifold a manifold?

We classify orthogonal actions of finite groups on Euclidean vector spaces for which the corresponding quotient space is a topological, homological or Lipschitz manifold, possibly with boundary. In particular, our results answer the question of when the underlying space of an orbifold is a manifold.Comment: 29 pages, combined with former arXiv:1509.06796, title updated, to appear in Trans. Amer. Math. So

Towards OpenMath Content Dictionaries as Linked Data

"The term 'Linked Data' refers to a set of best practices for publishing and connecting structured data on the web". Linked Data make the Semantic Web work practically, which means that information can be retrieved without complicated lookup mechanisms, that a lightweight semantics enables scalable reasoning, and that the decentral nature of the Web is respected. OpenMath Content Dictionaries (CDs) have the same characteristics - in principle, but not yet in practice. The Linking Open Data movement has made a considerable practical impact: Governments, broadcasting stations, scientific publishers, and many more actors are already contributing to the "Web of Data". Queries can be answered in a distributed way, and services aggregating data from different sources are replacing hard-coded mashups. However, these services are currently entirely lacking mathematical functionality. I will discuss real-world scenarios, where today's RDF-based Linked Data do not quite get their job done, but where an integration of OpenMath would help - were it not for certain conceptual and practical restrictions. I will point out conceptual shortcomings in the OpenMath 2 specification and common bad practices in publishing CDs and then propose concrete steps to overcome them and to contribute OpenMath CDs to the Web of Data.Comment: Presented at the OpenMath Workshop 2010, http://cicm2010.cnam.fr/om