Sobolev homeomorphic extensions

Voiculescu Theorem, Sobolev Lemma, and Extensions of Smooth Algebras

We present the analytic foundation of a unified B-D-F extension functor Extr on the category of noncommutative smooth algebras, for any Fréchet operator ideal ^ . Combining the techniques devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth algebras and Fréchet operator ideals. A key notion involved is r-smoothness, which is verified for the algebras of smooth functio...

On self-homeomorphic dendrites

It is shown that for every numbers m1, m2 ∈ {3, . . . , ω} there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.

Homeomorphic alignment of weighted trees

Motion capture, a currently active research area, needs estimation of the pose of the subject. For this purpose, we match the tree representation of the skeleton of the 3D shape to a pre-specified tree model. Unfortunately, the tree representation can contain vertices that split limbs in multiple parts, which do not allow a good match by usual methods. To solve this problem, we propose a new al...

Homeomorphic Embedding for Online Termination

Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper we investigate and clarify for the rst time, both intuitively and formally, the advantages of such an approach over one using well-founded orders. Notably we show that the homeomorphic e...

Homeomorphic meshes in Rd