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.

Solid-state analysis of low-melting 1,3-dialkylimidazolium hexafluorophosphate salts (ionic liquids) by combined x-ray crystallographic and computational analyses

The interactions of ions in the solid state for a series of representative 1,3-dialkylimidazolium hexafluorophosphate salts (either ionic liquids or closely related) have been examined by crystallographic analysis, combined with the theoretical estimation of crystal-packing densities and lattice-interaction energies. Efficient close-packing of the ions in the crystalline states is observed, but there was no compelling evidence for specific directional hydrogen-bonding to the hexafluorophosphate anions or the formation of interstitial voids. The close-packing efficiency is supported by the theoretical calculation of ion volumes, crystal lattice energies, and packing densities, which correlated well with experimental data. The crystal density of the salts can be predicted accurately from the summation of free ion volumes and lattice energies calculated. Of even more importance for future work, on these and related salts, the solid-state density of 1,3-dialkylimidazolium hexafluorophosphate salts can be predicted with reasonable accuracy purely on the basis of on ab initio free ion volumes, and this allows prediction of lattice energies without necessarily requiring the crystal structures.

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.

The absence of creativity in Feist and the computational process

The decision of the U.S. Supreme Court in 1991 in Feist Publications, Inc. v. Rural Tel. Service Co. affirmed originality as a constitutional requirement for copyright. Originality has a specific sense and is constituted by a minimal degree of creativity and independent creation. The not original is the more developed concept within the decision. It includes the absence of a minimal degree of creativity as a major constituent. Different levels of absence of creativity also are distinguished, from the extreme absence of creativity to insufficient creativity. There is a gestalt effect of analogy between the delineation of the not original and the concept of computability. More specific correlations can be found within the extreme absence of creativity. "[S]o mechanical" in the decision can be correlated with an automatic mechanical procedure and clauses with a historical resonance with understandings of computability as what would naturally be regarded as computable. The routine within the extreme absence of creativity can be regarded as the product of a computational process. The concern of this article is with rigorously establishing an understanding of the extreme absence of creativity, primarily through the correlations with aspects of computability. The understanding established is consistent with the other elements of the not original. It also revealed as testable under real-world conditions. The possibilities for understanding insufficient creativity, a minimal degree of creativity, and originality, from the understanding developed of the extreme absence of creativity, are indicated.