We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C *-algebras. In particular, our results apply to the largest class of simple C *-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the...

In this paper we relate two topological invariants of a separable C*-algebras. The first is the shape invariant first studied by Effros and Kaminker [EK] and then developed further by Blackadar [B]. The second invariant is the isomorphism class of a C*-algebra in the asymptotic homotopy category A introduced by Connes and Higson [CH]. We prove that two separable C*-algebras are shape equivalent...

The first definition of semiprojectivity for C-algebras was given by Effros and Kaminker in the context of noncommutative shape theory ([3]). A more restrictive definition was given by Blackadar in [1]. Loring introduced a third definition, which he termed weak semiprojectivity, in his investigations of stability problems for C-algebras defined by generators and relations ([9]). Recently Neubüs...

Simple and nuclear C-algebras which fail to absorb the Jiang-Su algebra tensorially have settled many open questions in the theory of nuclear C-algebras, but have been little studied in their own right. This is due partly to a dearth of invariants sensitive to differences between such algebras. We present two new real-valued invariants to fill this void: the dimension-rank ratio (for unital AH ...

Let A be a C-algebra. The Cuntz semigroup W (A) is an analogue for positive elements of the semigroup V (A) of Murray-von Neumann equivalence classes of projections in matrices over A. We prove stability theorems for the Cuntz semigroup of a commutative C-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces. Let SDG denote the ...

The Great Plains low-level jet (LLJ) is an important element of the low-level atmospheric circulation. It transports water vapor from the Gulf of Mexico, which in turn affects the development of weather over the Great Plains of the central United States. The LLJ is generally recognized as a complex response of the atmospheric boundary layer to the diurnal cycle of thermal forcing. Early studies...

B. Blackadar [1] constructed for the first time an example of a symmetry (or an automorphism of period two) of the CAR algebra (or the UHF algebra of type 2) whose fixed point algebra is not AF (or approximately finite-dimensional). This was soon extended to produce an example of finite-group actions on UHF algebras whose fixed point algebras are not AF [5] and then of compact-group actions [12...

The modeling of the atmospheric boundary layer during convective conditions has long been a major source of uncertainty in the numerical modeling of meteorological conditions and air quality. Much of the difficulty stems from the large range of turbulent scales that are effective in the convective boundary layer (CBL). Both small-scale turbulence that is subgrid in most mesoscale grid models an...

This paper introduces two changes of the turbulence parameterization for the EMEP (European Monitoring and Evaluation Programme) Eulerian air pollution model: the replacement of the Blackadar in stable and O’Brien in unstable turbulence formulations with an analytical vertical diffusion profile (K(z)) called Grisogono, and a different mixing height determination, based on a bulk Richardson numb...