Collapsing in theL2Curvature Flow

Non-collapsing in Mean-convex Mean Curvature Flow

We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence. We follow [4] in defi...

Collapsing Closures

A description in the Jacobs and Langen domain is a set of sharing groups where each sharing group is a set of program variables. The presence of a sharing group in a description indicates that all the variables in the group can be bound to terms that contain a common variable. The expressiveness of the domain, alas, is compromised by its intractability. Not only are descriptions potentially exp...

Collapsing functions

We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for (21), then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than the least w...

On Collapsing Narrowing

Collapsing floating-point operations

This paper addresses the issue of collapsing dependent floatingpoint operations. The presentation focuses on studying the dataflow graph of benchmark involving a large number of floating-point instructions. In particular, it focuses on the relevance of new floating-point operators performing two dependent operations which are similar to “fused multiply and add”. Finally, this paper examines the...