A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators

A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator Cφ induced by a hyperbolic automorphism φ of the unit disc D acting on the classical Hardy space H² is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators

A hyperbolic universal operator commuting with a compact operator

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a non-trivial, quasinilpotent, injective, compact operator with dense range, but unlike other examples, it acts on the Bergman space instead of the Hardy space and this operator is associated with a `hyperbolic' composition operator

Muon Collider Overview: Progress and Future Plans

Besides continued work on the parameters of a 3-4 and 0.5 TeV CoM collider, many studies are now concentrating on a machine near 100 GeV that could be a factory for the s-channel production of Higgs particles. We mention the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay channel, muon cooling, acceleration, storage in a ring and the collider detector. We also mention theoretical and experimental R&D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This note is a summary of a report updating the progress on the R&D since the Feasibility Study of Muon Colliders presented at the Workshop Snowmass'96.Comment: 3 pages, 2 figures, LaTex EPAC format; to be published Proceedings of the EPAC98 Conference, Stockholm, Sweden, June 1998. Additional information and articles at http://www.cap.bnl.gov/mumu

The effect of diatomaceous earth in live, attenuated infectious bronchitis vaccine, immune responses, and protection against challenge.

Live virus vaccines are commonly used in poultry production, particularly in broilers. Massive application and generation of a protective local mucosal and humoral immunity with no adverse effects is the main goal for this strategy. Live virus vaccines can be improved by adding adjuvants to boost mucosal innate and adaptive responses. In a previous study we showed that diatomaceous earth (DE) can be used as adjuvant in inactivated vaccines. The aim of this study was to test DE as adjuvant in an Ark-DPI live infectious bronchitis virus (IBV) vaccine after ocular or spray application. Titrating the virus alone or after addition of DE showed that DE had no detrimental effect on the vaccine virus. However, adding DE to the vaccine did not induce higher IgG titers in the serum and IgA titers in tears. It also did not affect the frequency of CD4+ T cells, CD8+ T cells and monocytes/macrophages in the blood and the spleen determined by flow cytometry. In addition, protection generated against IBV homologous challenges, measured by viral load in tears, respiratory signs and histopathology in tracheas, did not vary when DE was present in the vaccine formulation. Finally, we confirmed through our observations that Ark vaccines administered by hatchery spray cabinet elicit weaker immune responses and protection against an IBV homologous challenge compared to the same vaccine delivered via ocular route

Simultaneous analysis of elastic scattering and transfer/breakup channels for the 6He+208Pb reaction at energies near the Coulomb barrier

The elastic and alpha-production channels for the 6He+208Pb reaction are investigated at energies around the Coulomb barrier (E_{lab}=14, 16, 18, 22, and 27 MeV). The effect of the two-neutron transfer channels on the elastic scattering has been studied within the Coupled-Reaction-Channels (CRC) method. We find that the explicit inclusion of these channels allows a simultaneous description of the elastic data and the inclusive alpha cross sections at backward angles. Three-body Continuum-Discretized Coupled-Channels (CDCC) calculations are found to reproduce the elastic data, but not the transfer/breakup data. The trivially-equivalent local polarization potential (TELP) derived from the CRC and CDCC calculations are found to explain the features found in previous phenomenological optical model calculations for this system.Comment: 7 pages, 6 figures (replaced with updated version

On the connected component of compact composition operators on the Hardy space

We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures.Comment: 16 page