We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every homomorphism from an ergodic full group to a separable group is continuous. We also find bounds for the minimal number of topological generators (elements generating a dense subgroup) of full groups allowing us to dist...

Let G be a semisimple algebraic group over a local field K of characteristic p. If the universal covering map Gsc → G is inseparable then no open subgroup of G(K) is finitely generated. Otherwise, for any compact open subgroup G with probability 1 two randomly chosen elements generate an open subgroup of G(K). Our main tool is a recent theorem by R. Pink characterizing compact groups linear ove...

1. Non-commutative probability spaces In general, a non-commutative probability space is a pair (A, τ), where A is a unital algebra (over the field of complex numbers C) and τ a linear functional with τ(I) = 1, where I is the identity of A. Elements of A are called random variables. Since positivity is a key concept in (classical) probability theory, this can be captured by assuming that A is a...

We discuss a recent method proposed by Kryukov and Walton to address boundary-value problems in the context of deformation quantization. We establish a connection with our approach and comment on the virtues of both formalisms.

The effects of parametric uncertainty in stable state space systems are analyzed by averaging the state covariance over the statistics of the uncertain parameters. For natural frequency uncertainty, this computation is related to the Fourier transform of the probability density function of the uncertain parameter. Equipartition and incoherence are illustrated for a single mode oscillator. Avera...

We provide a simple proof that the kth gap, A *, for the Mathieu operator-dz/dxs + 2~ cos (2x) is A& = 8(~/4)* [(k-l)!]-* (1 + o(k-s)), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.

introduction: deep neck space infections (dnsi) are serious diseases that involve several spaces in the neck. the common primary sources of dnsi are dental infections, tonsillar and salivary gland infections, malignancies, and foreign bodies. with widespread use of antibiotics, the prevalence of dnsi has been reduced. common complications of dnsi include airway obstruction, jugular vein thrombo...

in this paper, we study fuzzy substructures in connection withhv-structures. the original idea comes from geometry, especially from thetwo dimensional euclidean vector space. using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. we connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as hv-groups...

the following study aims to present an innovative approach for design. participatory design is the model of direct involvement of different social groups in the design from functional tools to environments, social institutions and businesses. diverse collection of practices has been developed to support this direct involvement by participatory design. people are invited to participate during di...