Dilations and constrained algebras

It is well known that unital contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f whose first derivative vanishes at 0. We prove that there are unital contractive representations of A which are not completely contractive, and furthermore provide a Kaiser and Varopoulos inspired example for A and present a characterization of those contractive representations of A which are completely contractive. In the positive direction, for the algebra of rational functions with poles off the distinguished variety V in the bidisk determined by (z-w)(z+w)=0, unital contractive representations are completely contractive.Comment: New to version 2 is a proof of rational dilation for the distinguished variety in the bidisk determined by (z-w)(z+w)=

Optimal Calibration of PET Crystal Position Maps Using Gaussian Mixture Models

A method is developed for estimating optimal PET gamma-ray detector crystal position maps, for arbitrary crystal configurations, based on a binomial distribution model for scintillation photon arrival. The approach is based on maximum likelihood estimation of Gaussian mixture model parameters using crystal position histogram data, with determination of the position map taken from the posterior probability boundaries between mixtures. This leads to minimum probability of error crystal identification under the assumed model

Erratum: algebraic spin liquid as the mother of many competing orders

We correct an error in our paper Phys. Rev. B 72, 104404 (2005) [cond-mat/0502215]. We show that a particular fermion bilinear is not related to the other ``competing orders'' of the algebraic spin liquid, and does not possess their slowly decaying correlations. For the square lattice staggered flux spin liquid (equivalently, d-wave RVB state), this observable corresponds to the uniform spin chirality.Comment: 1.25 page

Optical and scratch resistant properties of diamondlike carbon films deposited with single and dual ion beams

Amorphous diamondlike carbon (DLC) films were deposited using both single and dual ion beam techniques utilizing filament and hollow cathode ion sources. Continuous DLC films up to 3000 A thick were deposited on fused quartz plates. Ion beam process parameters were varied in an effort to create hard, clear films. Total DLC film absorption over visible wavelengths was obtained using a Perkin-Elmer spectrophotometer. An ellipsometer, with an Ar-He laser (wavelength 6328 A) was used to determine index of refraction for the DLC films. Scratch resistance and frictional and adherence properties were determined for select films. Applications for these films range from military to the ophthalmic industries