The Novikov Conjecture for Linear Groups

Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(n,K) is exact, in the sense of C^*-algebra theory.     

A synthesis of crambescidin 359

A potentially biomimetic synthesis of the guanidine-containing marine natural product crambescidin 359 via a double Michael addition of guanidine to a suitably functionalised bis-enone is reported.     

Studies of prereactions during MOVPE growth of wide band-gap II/VI semiconductors: the effect of pyridine upon the gas-phase reactions between H2S and Me2Zn

The effect of pyridine addition upon the gas-phase reactions of hydrogen sulphide (H₂S) with dimethylzinc (Me₂Zn) in the presence of pyridine has been investigated and compared with results from reactions of H₂S with Me₂Cd. The deposits of ZnS which form have been analysed and consist of particles in the nanocrystalline size range of mainly the hexagonal phase. The average particle size within the deposits depends on both the concentration of pyridine in the gas phase and the temperature at which the reactants are mixed. Pyridine may bind through the lone pair of the nitrogen to surface metal atoms of growing particles, inhibiting further growth of the particle.     

Mapping Surgery To Analysis III: Exact Sequences

Using the constructions of the preceding two papers, we construct a natural transformation (after inverting 2) from the Browder-Novikov-Sullivan-Wall surgery exact sequence of a compact manifold to a certain exact sequence of C ^*-algebra K-theory groups. Mathematics Subject Classification (1991): 19J25, 19K99     

Mapping Surgery to Analysis I: Analytic Signatures

We develop the theory of analytically controlled Poincaré complexes over C ^*-algebras. We associate a signature in C ^*-algebra K-theory to such a complex, and we show that it is invariant under bordism and homotopy. The authors were supported in part by NSF Grant DMS-0100464.     

Thermoelastic waves in a constrained isotropic plate: incompressibility at uniform temperature

Thermoelastic waves are investigated which propagate throughan isotropic plate which is constrained to be incompressibleat uniform temperature. This is an example of a deformation–temperatureconstraint, also known as a strain–temperature constraint.The boundaries of the plate are taken to be traction free andeither isothermal or insulated. Dispersion relations are derivedand expanded asymptotically in the long-wave low-frequency limit.The short-wave limit is also discussed. The higher modes areinvestigated numerically. Graphical comparison with the unconstrainedmaterial is also presented.     

Stress-intensity factors for a semi-infinite plane crack with a wavy front

The stress-intensity factors for a semi-infinite plane crack with a wavy front are determined when the crack faces are subjected to normal and shearing tractions. The results are derived using asymptotic methods and are valid to O(²) where =A/1; A is the amplitude and is the wavelength of the wavy front. The normal and shearing tractions are in the form of line loads parallel to the crack front.The results are then used to evaluate, in a qualitative manner, the growth characteristics of a semi-infinite plance crack with a wavy front under combined mode loading. This provides a possible explanation of crack front segmentation observed experimentally.     

Synthesis and Evaluation of GdIII‐Based Magnetic Resonance Contrast Agents for Molecular Imaging of Prostate‐Specific Membrane Antigen

Magnetic resonance (MR) imaging is advantageous because it concurrently provides anatomic, functional, and molecular information. MR molecular imaging can combine the high spatial resolution of this established clinical modality with molecular profiling in vivo. However, as a result of the intrinsically low sensitivity of MR imaging, high local concentrations of biological targets are required to generate discernable MR contrast. We hypothesize that the prostate‐specific membrane antigen (PSMA), an attractive target for imaging and therapy of prostate cancer, could serve as a suitable biomarker for MR‐based molecular imaging. We have synthesized three new high‐affinity, low‐molecular‐weight Gd^III‐based PSMA‐targeted contrast agents containing one to three Gd^III chelates per molecule. We evaluated the relaxometric properties of these agents in solution, in prostate cancer cells, and in an in vivo experimental model to demonstrate the feasibility of PSMA‐based MR molecular imaging.