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.     

Temperature Dependence of InSb Reflectivity in the Far Infrared: Determination of the Electron Effective Mass

We measured the dependence of the reflectivity of InSb crystals upon temperature in the submillimeter region using monochromatic radiation from an optically pumped far infrared (FIR) laser. The measures allowed us to determine the value of the electron effective mass at low temperatures with radiations of different frequencies. Our measurements extend the results obtained recently on pure crystals with magneto-optical methods to the low temperatures region where only old measures were available.     

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.     

New fir laser lines and frequency measurements from optically pumped13CD3OH3

We report the discovery of 57 new fir laser lines from¹³CD₃OH molecule optically pumped by a waveguide CO₂ laser of 300 MHz tunability. For all lines, precise frequency offset measurements between the CO₂ line center and the center of the absorbing¹³CD₃OH line were performed using the transferred Lamb-Dip technique. We have also measured directly the frequency of seven FIR laser lines by heterodyning with already known laser lines. We present a complete list of all known laser lines (134) and frequency measurements (24) for this molecule.Work supported by CNPq, FAPESP, FAEP-Brasil, and CNR-Italia     

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     

Assignments of methanol laser lines by frequency measurements and Fourier transform spectroscopy

We have measured the frequencies of four CH₃OH far-infrared laser lines that were previously known only by wavelength measurement. Two of these lines turned out to be doublets, bringing the total number of measured lines to six. We can now confirm the assignments of five of them and definitely disprove the assignments proposed for the sixth.In particular we confirm the assignments for the four strong laser lines at 205 and 208 µm pumped by the 9-P(34) CO₂ laser line. These lines share a common upper level in the first excited CO-stretch state, and terminate in the upper and lower levels of a hybrid state with J=5. Heterodyne frequency measurements and conventional microwave spectroscopy show that both lines are split into two components approximately 3.5 MHz apart. The origin of this further splitting is interpreted as a perturbed K-splitting.Work supported by Consiglio Nazionale delle Ricerche -Italia     

Frequency and efficiency measurements on FIR laser lines close to the N+ 3 P 2−3 P 1 transition

FIR laser lines close to the N^{+ 3} P ₂–³ P ₁ transition at 122 m can be used as a local oscillator for heterodyne detectors. The frequencies of some candidate laser lines from CH₂F₂,¹³CH₃OH, CD₃OD, and CD₃OH have been measured and the output power of the most interesting lines has been optimized.     

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.