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.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Time-resolved electron transport studies on InGaAs/GaAs-QWIPs

Due to the short internal response time, quantum-well infrared photodetectors (QWIPs) are interesting for high-speed applications such as heterodyne spectroscopy or laser pulse monitoring. We studied the photocurrent transients of InGaAs/GaAs-QWIPs after irradiation with infrared laser pulses of 250 fs duration. The excitation wavelength of about 9 μm matches the peak wavelength of the QWIP structure. The photocurrent transient consists of two different dynamical components, representing the fast photoionization in the quantum-wells and the slow injection current that compensates the remaining space charge. The investigations of the different components as a function of temperature and bias voltage were performed on a nanosecond time-scale. The experimental separation of the two photocurrent contributions allows us to determine the photoconductive gain. The Fourier transform of the photocurrent transient was compared with other experimental methods including heterodyne detection and microwave rectification. The quantitative agreement between these different measurement techniques is excellent.     

Cathodoluminescence study of extended defects in hydrothermal ZnO crystals

Understanding the luminescence of ZnO is very important for some applications. In spite of the many studies carried out, there are still some points concerning the origin of some of the luminescence emissions in ZnO crystals that require additional study; in particular, the role of extended defects remains to be a matter of controversy. We present here a cathodoluminescence analysis of the defects generated by Vickers indentation in hydrothermal HTT crystals. Special emphasis was paid to the luminescence band peaking around 3.3 eV. The origin of this band is a matter of controversy, since it has been related to different causes, extended defects being one of the candidates for this emission. The CL images were acquired around crystal defects. It is observed that the 3.3 eV emission is enhanced around the crystal defects; though it is also observed, but weaker, out of the defect regions, which suggests that there exist two luminescence emissions peaking very close to 3.3 eV. The two emissions, one related to structural defects and the other to the LO phonon replica of the free excitonic band, appear very close each other and their relative intensity should determine the shape of the spectrum.     

The preparation and structure of 1,4,5,6,7,7-hexachloro-2-endo-ferrocenylhydroxymethyl-3-endo-hydroxymethyl-5-norbornene

The crystal structure of a novel ferrocene derivative with potential flame-retardant/smoke-suppressant activity, 1,4,5,6,7,7-hexachloro-2-endo-ferrocenyl-hydroxymethyl-3-endo-hydroxymethyl-5-norbornene, has been determined. Some of the carbon–carbon bonds within the chlorendic residue are unusually long, and there is no interaction between the hydroxyl groups and the iron atom. There is evidence of intramolecular hydrogen bonding between the two hydroxyl groups.     

Importance of the Debye interaction in organic solutions: Henry's law constants for polar liquids in nonpolar solvents and vice versa

Henry's law constants have been determined for -butyrolactone (BL), ethyl acetate (EA), and 2-methyl-3-pentanol (MEP) in mixtures of iso-octane (ISO) and toluene (TOL), for BL, EA, TOL, and ISO in cinnamaldehyde (CIN) and for TOL and ISO in each other and in BL. From these data and published vapor pressures, the activity coefficients at infinite dilution and the standard molar Gibbs free energy of transfer, G ₂ ⁰ of the solutes from dilute solution in ISO to dilute solution in each solvent medium have been calculated. The different behavior patterns of BL and EA are attributed to differences in their abilities to exist in different conformations possessing different dipole moments. For polar solutes, G ₂ ⁰ decreases with increasing polarizability of the solvent and with increasing dipole moment of the solute, suggesting increased contributions from dipole-induced dipole (Debye) interactions. The sigmoidal plot of G ₂ ⁰ against the change in pair potential energy calculated from the classical expressions suggests that G ₂ ⁰ seriously underestimates the strength of the Debye interactions in comparison with the London interactions.     

N-labelling studies of the reaction of 2,6-di-t-butyl-4-methyl-4-nitrocyclohexa-2,5-dienone with nitrogen dioxide; A revised mechanism

Reaction of the ¹⁵N-4-nitrodienone (1) with excess nitrogen dioxide in benzene for 16 h gives the 4,5,6-trinitro ketone (2), labelled (¹⁵NO₂) at C6 but not at C4, and recovered 4-nitrodienone (1) in which extensive loss of ¹⁵NO₂ has occurred. The mechanistic implications of these and related results are discussed.     

Intermolecular multiple quantum coherences at high magnetic field: the nonlinear regime

Experiments have been carried at magnetic-field strengths of 9.4, 14.1, and 17.6 T to explore the evolution of intermolecular multiple quantum coherences in the nonlinear regime where the system evolves for times that are much greater than the characteristic time of action of the long-range dipolar field, tau(d). The results show the expected Bessel function form of the recorded signal as a function of time of evolution, with evident zeros and sign changes. As expected, the rate of signal evolution increases at higher-field strengths as a result of the increased equilibrium magnetization. A numerical method for calculating the evolution of magnetization under the action of the distant dipolar field, relaxation, and diffusion that is based on Fourier analysis of the magnetization distribution has been applied to the correlated two-dimensional spectroscopy revamped by asymmetric z-gradient echo detection sequence in the nonlinear regime and shown to produce results that are in good agreement with experimental data acquired at different magnetic fields and rates of spatial modulation. Experiments and simulations have also been used to explore the evolution of magnetization in a mixture of two interacting spin species in the nonlinear regime.