Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Hematopoietic malignancies associated with viral and alcoholic hepatitis

Hepatitis C virus (HCV) and hepatitis B virus (HBV) have been associated with hematopoietic malignancies, but data for many subtypes are limited. From the U.S. Surveillance, Epidemiology, and End Results-Medicare database, we selected 61,464 cases (=67 years) with hematopoietic malignancies and 122,531 population-based controls, frequency-matched by gender, age, and year (1993-2002). Logistic regression was used to compare the prevalence of HCV, HBV, and alcoholic hepatitis in cases and controls, adjusted for matching factors, race, duration of Medicare coverage, and number of physician claims. HCV, HBV, and alcoholic hepatitis were reported in 195 (0.3%), 111 (0.2%), and 404 (0.7%) cases and 264 (0.2%), 242 (0.2%), and 798 (0.7%) controls, respectively. HCV was associated with increased risk of diffuse large B-cell lymphoma [odds ratio (OR) 1.52, 95% confidence interval (95% CI) 1.05-2.18], Burkitt lymphoma (OR 5.21, 95% CI 1.62-16.8), follicular lymphoma (OR 1.88, 95% CI 1.17-3.02), marginal zone lymphoma (OR 2.20, 95% CI 1.22-3.95), and acute myeloid leukemia (OR 1.54, 95% CI 1.00-2.37). In contrast, HBV was unrelated to any hematopoietic malignancies. Alcoholic hepatitis was associated with decreased risk of non-Hodgkin lymphoma overall, but increased risk of Burkitt lymphoma. In summary, HCV, but not other causes of hepatitis, was associated with the elevated risk of non-Hodgkin lymphoma and acute myeloid leukemia. HCV may induce lymphoproliferative malignancies through chronic immune stimulation. Copyright © 2008 American Association for Cancer Research.


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Self-consistent geometry in the computation of the vibrational spectra of molecules

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Electrical and Rheological Percolation of PMMA/MWCNT Nanocomposites as a Function of CNT Geometry and Functionality

The ability of carbon nanotubes (CNTs) to reinforce and enhance the electrical conductivity of polymer matrices is a function of both the aspect ratio and surface chemistry of the CNTs. Hitherto, due to the variability in MWCNT synthesis methods it has not been possible to study the effect of MWCNT aspect ratio and functionality on polymer composite properties. This paper was the first to report the correlation between MWCNT aspect ratio and functionality on the formation of electrical and rheological percolated networks. Furthermore, the fundamental ballistic conductance of MWCNTs made using arc discharge and chemical vapour deposition techniques was reported.

Modelling the Geometry of the Repeat Unit Cell of Three-Dimensional Weave Architectures,

The three-dimensional (3D) weaving process offers the ability to tailor the mechanical properties via design of the weave architecture. One repeat of the 3D woven fabric is represented by the unit cell. The model accepts basic weaver and material manufacturer data as inputs in order to calculate the geometric characteristics of the 3D woven unit cell. The specific weave architecture manufactured and subsequently modelled had an angle interlock type binding configuration. The modelled result was shown to have a close approximation compared to the experimentally measured values and highlighted the importance of the representation of the binder tow path.