3 An introduction to rigidity 7 3.1 Local rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Full rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Strong (Mostow) Rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 The Zimmer program . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Non-substitutability is a property of Multiword Expressions (MWEs) that often causes lexical rigidity and is relevant for most types of MWEs. Efficient identification of this property can result in the efficient identification of MWEs. In this work we propose using distributional semantics, in the form of word embeddings, to identify candidate substitutions for a candidate MWE and model its sub...

We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover...

We show the H 1 scattering for a one dimensional nonlinear Schrödinger equation with a non-negative, repulsive potential V such that V, xV ∈ W 1,1, and a mass-supercritical non-linearity. We follow the approach of concentrationcompacity/rigidity first introduced by Kenig and Merle.

We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S2 × R3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than connection metrics.