Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

Surface tension of random copolymer melts

A mean-field theory is presented to describe the surface tension and interfacial profile of random A-B multiblock copolymer melts in contact with air or a solid substrate. The copolymer model accounts for variations in average composition and block sequence distribution, and reduces to a model for statistical copolymers as the block size approaches that of a monomer. Ideal copolymers lacking chemical correlations between successive segments are predicted to have a larger surface tension than “blocky” copolymers with a tendency for repeated segments of A or B. © 1992 John Wiley & Sons, Inc.     

Low temperature deposition of zinc oxide nanoparticles via zinc-rich vapor phase transport and condensation

ZnO nanoparticles as small as 80 nm were successfully synthesized using a modified vapor phase transport (VPT) process at substrate temperatures as low as 222 °C. Particle size distribution and morphology were characterized by scanning electron microscopy and atomic force microscopy. Energy dispersive X-ray spectroscopy and X-ray diffraction indicate the synthesis of high quality crystalline ZnO structures. Low temperature (4.2 K) photoluminescence (PL) spectroscopy was used to characterize the optical quality of the nanoparticles. Ultraviolet emission and a nanostructure specific feature at 3.366 eV are strong in the PL spectra. The 3.366 eV feature is observed to predominate the spectrum with decrease in particle size. This size effect corroborates the luminescence as a nanostructure-specific surface related exciton feature as previously speculated in the literature. In addition, self-assembled ZnO mesoparticles (>100 nm) were realized by increasing the growth time. Low growth temperatures of the particles allow for their potential utilization in flexible organic hybrid optoelectronics. However, this work focuses mainly on the modified synthesis and optical characterization of nanoparticles.     

Influence of conformational asymmetry on the surface enrichment of polymer blends II

We reexamine the influence of statistical segment length asymmetry on the surface segregation of homopolymer blends in a mean field thread model of polymer melts. By developing numerical self-consistent field solutions of the Edwards-Helfand equations, we demonstrate that the component with the smaller value of the parameter β² = a²/(6ν) (a is the statistical segment length and ν is the segment volume) is enriched at a neutral, impenetrable surface. Qualitatively, this finding is in agreement with our earlier analytical work and with experiment. However, in contrast to our earlier work, we find that the absolute magnitude of the segregation is a sensitive function of the chain lengths of the two species and of the compressibility of the system. © 1995 John Wiley & Sons, Inc.     

Microscopic dynamics in a strongly interacting Bose-Einstein condensate

An initially stable 85Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse near a Feshbach resonance. This pulse probed the strongly interacting regime for the BEC, with the diluteness parameter (na(3)) ranging from 0.01 to 0.5. Condensate number loss resulted from the pulse, and for triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until very short time scales (approximately 10 micros) were reached. The observed time dependence is very different from that expected in traditional inelastic loss processes, suggesting the presence of new microscopic BEC physics.     

Schur orthogonality relations and invariant sesquilinear forms

Important connections between the representation theory of a compact group and are summarized by the Schur orthogonality relations. The first part of this work is to generalize these relations to all finite-dimensional representations of a connected semisimple Lie group The second part establishes a general framework in the case of unitary representations of a separable locally compact group. The key step is to identify the matrix coefficient space with a dense subset of the Hilbert-Schmidt endomorphisms on .