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

The boundary field theory induced by the Chern-Simons theory

The Chern-Simons theory defined on a 3-dimensional manifold with boundary is written as a two-dimensional field theory defined only on the boundary of the three-manifold. The resulting theory is, essentially, the pullback to the boundary of a symplectic structure defined on the space of auxiliary fields in terms of which the connection one-form of the Chern-Simons theory is expressed when solving the condition of vanishing curvature. The counting of the physical degrees of freedom living in the boundary associated to the model is performed using Dirac's canonical analysis for the particular case of the gauge group SU(2). The result is that the specific model has one physical local degree of freedom. Moreover, the role of the boundary conditions on the original Chern- Simons theory is displayed and clarified in an example, which shows how the gauge content as well as the structure of the constraints of the induced boundary theory is affected.Comment: 10 page

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

Correction of diffraction effects in confocal raman microspectroscopy

A mathematical approach developed to correct depth profiles of wet-chemically modified polymer films obtained by confocal Raman microscopy is presented which takes into account scattered contributions originated from a diffraction-limited laser focal volume. It is demonstrated that the problem can be described using a linear Fredholm integral equation of the first kind which correlates apparent and true Raman intensities with the depth resolution curve of the instrument. The calculations of the corrected depth profiles show that considerable differences between apparent and corrected depth profiles exist at the surface, especially when profiles with strong concentration gradients are dealt with or an instrument with poor depth resolution is used. Degrees of modification at the surface obtained by calculation of the corrected depth profiles are compared with those measured by FTIR-ATR and show an excellent concordance.</p

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