An integrality theorem for subnormal operators

In a recent paper we conjectured that the principal function of a cyclic subnormal operator T is a.e. equal to the negative of a characteristic function. We showed that this was true in a variety of cases - including the general arc length Swiss Cheese.Now we prove stronger results. The conjecture is a consequence of:The principal function of a subnormal operator with trace class self-commutator assumes a.e. nonpositive integer values.It is an interesting fact that this integrality is a basic geometric property of subnormal operators and is not associated with any smoothness or "thinness" of the essential spectrum of T.This result is actually a simple corollary of a much more basic fact:The mosaic of a subnormal operator with trace class self-commutator is projection valued a.e.We have long known that the mosaic is a complete unitary invariant for T. Thus, this theorem establishes a map z Range B(z) which associates a subspace of Hilbert space with almost every point of the plane; and this generalized bundle completely characterizes the subnormal operator T. If T is cyclic then its mosaic B(·) is a.e. either the zero operator or a rank one projection.     

Induced representations,reproducing kernels and the conformal group

The properties of induced (or multiplier) representations of groups which act in Hilbert spaces with a reproducing kernel are investigated. A resumé of earlier work is followed by a discussion of criteria for the irreducibility of such representations. The notions of reproducing kernel and positive definite spherical function are found to overlap. As a result, functional equations (analogous to those of Godement for spherical functions) are found for the reproducing kernel. The abstract theory is illustrated by certain discrete series representations of the conformal group and by their limit points. In particular the so-called ladder representations (which give rise to the conformal symmetry of zero mass particles) are analysed from this viewpoint.     

A new family of water-swellable microgel particles

In this study a new family of microgel particles is investigated which contain methylmethacrylate (MMA), ethylacrylate (EA), acrylic acid (AA), glycerol propoxytriacrylate (GPTA), and Emulsogen (Em). GPTA is a trifunctional crosslinking monomer, whereas Em is a polymerisable alcohol ethoxylate surfactant. TEM and PCS data reveal that the extent of microgel swelling originates from a pH-independent contribution (due to Em) as well as a pH-dependent contribution (due to AA). The major contribution to swelling comes from pH-independent swelling. Consideration of the equations governing particle swelling allows the effective pK(a) of the incorporated AA groups to be estimated. There is evidence of a shift of the pK(a) for the AA groups from 4.5 to ca. 9.5 when the microgel particles containing AA also contain Em. This suggests intraparticle hydrogen bonding between AA and ethylene oxide segments at low pH.     

Fluorescence properties of fluorescein, tetramethylrhodamine and Texas Red linked to a DNA aptamer

We report the picosecond time-scale fluorescence dynamics of a dye-labeled DNA oligonucleotide or "aptamer" designed to bind specifically to Immunoglobulin E. Comparison of the photophysics of Texas Red (TR), fluorescein and 5'-carboxytetramethylrhodamine (TAMRA)-labeled aptamers reveals surprising differences with significant implications for measurements of oligonucleotide structure and dynamics. The fluorescence decay of the TR-aptamer is a simple single exponential with a weak temperature dependence. The fluorescence decay of the fluorescein-aptamer (fl-aptamer) is pH dependent and displays a complex temperature dependence with significant changes on melting of the aptamer tertiary structure. Despite its similarities to TR, TAMRA is strongly quenched when conjugated to the aptamer and displays complex fluorescence kinetics best described by a distributed rate model. Using the maximum entropy method, we have discovered two highly temperature-dependent fluorescence lifetimes for the TAMRA-aptamer. One of these lifetimes is similar to that of free TAMRA and displays the same temperature dependence. The other lifetime is quenched and displays a temperature dependence characteristic of a charge transfer reaction. These data set TR apart as an attractive alternative to TAMRA and fluorescein for studies such as fluorescence polarization and fluorescence resonance energy transfer, where environmental sensitivity of the probe is not desired.     

A vector-parallel scheme for Navier-Stokes computations at multi-gigaflop performance rates

A class of vector-parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out. The algorithms employ an artificial transient treatment that permits rapid integration to a steady state. In the present work a four-stage explicit Runge-Kutta scheme employing variable local step size is utilized for the ODE system integration. The RK-4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction-vorticity formulation of the flow problem. The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion. Four main procedures are considered which permit vector-parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss-Seidel method, red-black ordering and domain decomposition. Numerical performance studies are conducted with a representative viscous incompressible flow calculation. Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90.     

Impurity distribution and electrical characteristics of boron-doped Si1−x Ge x /Si p +/N heterojunction diodes produced using pulsed UV-laser-induced epitaxy and Gas-immersion laser doping

A two-step pulsed UV-laser process which independently controls the metallurgical and electrical junction depth of a Si_1–x Ge _x /Si heterojunction diode has been implemented. Pulsed Laser-Induced Epitaxy (PLIE) combined with Gas-immersion Laser Doping (GILD) are used to fabricate boron-doped heteroepitaxial p ⁺/N Si_1–x Ge _x /Si layers and diodes. Borontrifluoride is used as the gaseous dopant source in the GILD process step. Boron incorporation and activation are investigated as a function of laser energy fluence and the number of laser pulses using SIMS and Halleffect measurements. The dose of incorporated dopant is on the order of 10¹³ cm^–2 per pulse. The B profiles obtained are flat except for a peak at the interface resulting from segregation effects. The B and Ge distributions are compared with shifts in the turn-on voltage of p ⁺/N Si_1–x /Si heterojunction diodes produced by the process. The GILD/PLIE process is spatially selective with the resulting diodes fabricated being quasiplanar. Hole mobilities in the heavily doped Si_1–x Ge _x films are found to be slightly lower than in comparable Si films.Presently at the Oregon Graduate Institute, Beaverton, OR 97006, USA