Sentence examples for dense ranges from inspiring English sources

We will say thatMandNare quasisimilar if there exist quasiaffinities (i.e. bounded one-to-one operators with dense ranges)XandY, commuting withT, such that (XM −=Nand (YN −=M.

The Impact of Dense Range Data on Computer Graphics.

They grouped themselves with the overachievers, immersed in a dense range of activities.

Surface reconstruction from dense range data has been an active area of research for several decades.

Our system uses a standard video camera and DLP projector, and produces dense range images at 60 Hz with 100 um accuracy over a 10 cm working volume.

For eachϕ∈Hom K1(A), R) with dense range inRwe construct a closed derivationδinAwhich generates a one-parameter automorphism groupαofAsuch thatτ(δ u) u* =2πiϕ([u]) for any unitaryu∈D.

We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range.

We show that there is then a Hilbert space H K), a contractive operator W: K→H K), and a selfadjoint operator S=S(U) in H K) such that W*W=PJP, W has dense range, and SW=WUP.

As another application of the construction of derivations, we show that ifAis aC*-algebra of the above type andα∈HInn(A) has the Rohlin property and comes fromϕ∈Hom K1(A), R) with dense range as in Kishimoto and Kumjian (preprint), then the crossed productA×αZis again of the same type; in particularA×αZis an AT algebra.

Case II: Suppose T does not have dense range.

(iv) Suppose T does not have dense range.