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 .

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.

Optical coherence tomography is a valuable tool in the study of the effects of microneedle geometry on skin penetration characteristics and in-skin dissolution.

In this study, we used optical coherence tomography (OCT) to extensively investigate, for the first time, the effect that microneedle (MN) geometry (MN height, and MN interspacing) and force of application have upon penetration characteristics of soluble poly(methylvinylether-co-maleic anhydride, PMVE/MA) MN arrays into neonatal porcine skin in vitro. The results from OCT investigations were then used to design optimal and suboptimal MN-based drug delivery systems and evaluate their drug delivery profiles cross full thickness and dermatomed neonatal porcine skin in vitro. It was found that increasing the force used for MN application resulted in a significant increase in the depth of penetration achieved within neonatal porcine skin. For example, MN of 600 µm height penetrated to a depth of 330 µm when inserted at a force of 4.4 N/array, while the penetration increased significantly to a depth of 520 µm, when the force of application was increased to 16.4 N/array. At an application force of 11.0 N/array it was found that, in each case, increasing MN height from 350 to 600 µm to 900 µm led to a significant increase in the depth of MN penetration achieved. Moreover, alteration of MN interspacing had no effect upon depth of penetration achieved, at a constant MN height and force of application. With respect to MN dissolution, an approximate 34% reduction in MN height occurred in the first 15 min, with only 17% of the MN height remaining after a 3-hour period. Across both skin models, there was a significantly greater cumulative amount of theophylline delivered after 24 h from an MN array of 900 µm height (292.23 ± 16.77 µg), in comparison to an MN array of 350 µm height (242.62 ± 14.81 µg) (p < 0.001). Employing full thickness skin significantly reduced drug permeation in both cases. Importantly, this study has highlighted the effect that MN geometry and application force have upon the depth of penetration into skin. While it has been shown that MN height has an important role in the extent of drug delivered across neonatal porcine skin from a soluble MN array, further studies to evaluate the full significance of MN geometry on MN mediated drug delivery are now underway. The successful use of OCT in this study could prove to be a key development for polymeric MN research, accelerating their commercial exploitation.

Assessing software upgrades, plan properties and patient geometry using intensity modulated radiation therapy (IMRT) complexity metrics

Purpose: The aim of this study is to compare the sensitivity of different metrics to detect differences in complexity of intensity modulated radiation therapy (IMRT) plans following upgrades, changes to planning parameters, and patient geometry. Correlations between complexity metrics are also assessed.