On minimal factorizations of rational matrix functions

The theory of factorization of rational matrix functions W() = = C(I-A)^–1B + D, as presented in the book Bart-Gohberg-Kaashoek [1], is extended here to the case where D = W() is not invertible, and applied to factorizations of monic matrix polynomials.     

Pulsed Electron-Nuclear Double Resonance in the Fourier Regime

Nuclear magnetic resonance (NMR) spectroscopy provides atomic-level molecular structural information. However, in molecules containing unpaired electron spins, NMR signals are difficult to measure directly. In such cases, data is obtained using the electron-nuclear double resonance (ENDOR) method, where nuclei are detected through their interaction with nearby unpaired electron spins. Unfortunately, electron spins spread the ENDOR signals, which challenges current acquisition techniques, often resulting in low spectral resolution that provides limited structural details. Here, we show that by using miniature microwave resonators to detect a small number of electron spins, integrated with miniature NMR coils, one can excite and detect a wide bandwidth of ENDOR data in a single pulse. This facilitates the measurement of ENDOR spectra with narrow lines spread over a large frequency range at much better spectral resolution than conventional approaches, which helps reveal details of the paramagnetic molecules’ chemical structure that were not accessible before.     

Breakdown of hydration repulsion between charged surfaces in aqueous Cs+ solutions

Using a surface force balance, we have measured the normal and shear forces between mica surfaces across aqueous caesium salt solutions (CsNO(3) and CsCl) up to 100 mM concentrations. In contrast to all other alkali metal ions at these concentrations, we find no evidence of hydration repulsion between the mica surfaces on close approach: the surfaces appear to be largely neutralized by condensation of the Cs ions onto the charged lattice sites, and are attracted on approach into adhesive contact. The contact separation at adhesion indicates that the condensed Cs ions protrude by 0.3 +/- 0.2 nm from each surface, an observation supported both by the relatively weak adhesion energies between the surfaces, and the relatively weak frictional yield stress when they are made to slide past each other. These observations show directly that the hydration shells about the Cs(+) ions are removed as the ions condense into the charged surface lattice. This effect is attributed to the low energies-resulting from their large ionic radius-required for dehydration of these ions.     

Interfacial characterization of chemical solution‐deposited thin films of PbSe on GaAs(100)

The microstructure and composition of the interfacial layer between chemically deposited PbSe and GaAs substrates were studied using high‐resolution transmission electron microscopy (HRTEM), Auger electron spectroscopy (AES), x‐ray photoelectron spectroscopy (XPS) and energy‐filtered TEM. The thickness of the interfacial layer varied significantly from direct contact of the film with the substrate to 5 nm in the thickest regions. The results established the presence of a discontinuous, amorphous intermediate layer of Ga₂O₃ at the PbSe/GaAs interface. Copyright © 2008 John Wiley & Sons, Ltd.     

Piatetski-Shapiro phenomenon in the uniqueness problem

We extend the phenomenon discovered by Piatetski-Shapiro (1954) to $l^q$ spaces. To be precise, for any $q>2$ we construct a compact K on the circle, which supports a distribution S with Fourier transform $\stackrel{?}{S}\in l^q$, but does not support such a measure. To cite this article: N. Lev, A. Olevskii, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Bonding in the superionic phase of water

The predicted superionic phase of water is investigated via ab initio molecular dynamics at densities of 2.0--3.0 g/cc (34-115 GPa) along the 2000 K isotherm. We find that extremely rapid (superionic) diffusion of protons occurs in a fluid phase at pressures between 34 and 58 GPa. A transition to a stable body-centered cubic O lattice with superionic proton conductivity is observed between 70 and 75 GPa, a much higher pressure than suggested in prior work. We find that all molecular species at pressures greater than 75 GPa are too short lived to be classified as bound states. Up to 95 GPa, we find a solid superionic phase characterized by covalent O-H bonding. Above 95 GPa, a transient network phase is found characterized by symmetric O-H hydrogen bonding with nearly 50% covalent character. In addition, we describe a metastable superionic phase with quenched O disorder.