If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in...

The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in Hausdorff based on locally compactable neighborhood systems without considering strictly (metrized) Borel variety. null extension gives rise to quasi sigma-semiring sigma-neighborhoods, which are rectifiable view Dieudonné n-space. concepts symmetric signed measure, un...

Abstract. We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation ...

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by 1nite energy paths. The main technique we use is the time reversal. This approach is di3erent from what B. Driver used to prove quasi-invariance for the pinned Brownian motion on a compact Riemannian manifold. c © 2002 Elsevier Science B.V. All rights reserved.

A measure-scaling quasi-isometry between two connected graphs is a that quasi- $$\kappa $$ -to-one in natural sense for some >0$$ . For non-amenable graphs, all quasi-isometries are any , while amenable ones there exists at most one possible such an graph X, we show the set of forms subgroup $$\mathbb {R}_{>0}$$ call (measure-)scaling group X. This invariant under quasi-isometries. In context C...