Spatial design matrices and associated quadratic forms: structure and properties

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.     

Roughness reduction in submicron waveguides by low-molecular weight development

Roughness reduction of a submicron waveguide profile in chemically amplified negative resist is here performed by proper selection of an alkali-based developer, taking into account that its smaller molecules lead to smoother resist surface by altering the developing mechanism of aggregate extraction performed with standard quaternary ammonium hydroxide. Roughness is then analyzed by means of classical Atomic Force Microscope inspection; furthermore, a non-invasive line edge roughness analysis approach based on top-down scanning electron microscope acquisition gives comparable results, in terms of standard deviation and molecular aggregate periodicity.     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

Flow through a porous medium with mass removal and diffusion

A one-dimensional model of filtration through a saturated porous medium with a mutual action between the solid matrix and the flow is investigated. The substances removed from the porous soil are both particles transported by the liquid flow and substances which diffuse in the fluid. Received June 30, 1997     

The effect of the anion on the physical properties of trihalide-based N,N-dialkylimidazolium ionic liquids

Low viscosity, high density trihalide-based 1-n-butyl-3-methylimidazolium ionic liquids have been prepared and characterised. Key physical properties (density, conductivity, melting point, refractive index, surface tension and diffusion coefficient) of the ionic liquids have been determined and are compared with those of other 1,3-dialkylimidazolium molten salts. The relationship between anion identity and the physical properties of the ionic liquids under investigation is discussed.     

Evidence against the hopping mechanism as an important electron transfer pathway for conformationally constrained oligopeptides

The rate constant of intramolecular electron transfer through oligopeptides based on the alpha-aminoisobutyric acid residue was determined as a function of the peptide length and found to depend weakly on the donor-acceptor separation. By measuring the electron-transfer activation energy and estimating the energy gap between donor and bridge, we were able to discard the electron hopping mechanism.