Search results for "Variant"

L 2-topological invariants of 3-manifolds

1995

We give results on theL2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, along with some analytic results on geometric 3-manifolds, are used to compute theL2-Betti numbers of compact 3-manifolds which satisfy a weak form of the geometrization conjecture, and to compute or estimate their Novikov-Shubin invariants.

Sobolev embeddings, extensions and measure density condition

2008

AbstractThere are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the Wm,p-extension domains for 1<p<∞. As a corollary we prove that the property of being a W1,p-extension domain, 1<p⩽∞, is invariant under bi-Lipschitz mappings, Theorem 8.

Minimal forbidden words and symbolic dynamics

1996

We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.

Locality of order-invariant first-order formulas

2000

A query is local if the decision of whether a tuple in a structure satisfies this query only depends on a small neighborhood of the tuple. We prove that all queries expressible by order-invariant first-order formulas are local.

Invariant measures for piecewise convex transformations of an interval

2002

When is the Haar measure a Pietsch measure for nonlinear mappings?

2012

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.

A short proof of a theorem of Ahlfors

1988

In [1] Ahlfors proved that the Weil-Petersson metric of the Teichmfiller space is K~hler. A new proof was given by Fischer and Tromba [5] in a purely Riemannian setting of Teichmfiller theory [3]. We shall provide yet another proof that slightly shortens the argument of Fischer and Tromba. We begin with a brief review of the Fischer-Tromba approach to Teichmiiller theory [3-5]. Let M be a compact connected oriented 2-dimensional manifold without boundary.

Brauer characters and coprime action

2016

Abstract It is an open problem to show that under a coprime action, the number of invariant Brauer characters of a finite group is the number of the Brauer characters of the fixed point subgroup. We prove that this is true if the non-abelian simple groups satisfy a stronger condition.

Equivariant Triviality of Quasi-Monomial Triangular $$\mathbb{G}_{a}$$-Actions on $$\mathbb{A}^{4}$$

2014

We give a direct and self-contained proof of the fact that additive group actions on affine four-space generated by certain types of triangular derivations are translations whenever they are proper. The argument, which is based on explicit techniques, provides an illustration of the difficulties encountered and an introduction to the more abstract methods which were used recently by the authors to solve the general triangular case.

The structure of the state representation of shift invariant controllable and observable group codes

2000

AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.