Adaptive nonparametric estimation of a multivariate regression function

We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of Krieger and Pickands (Ann. Statist.9 (1981) 1066–1078) and Abramson (J. Multivariate Anal.12 (1982), 562–567) in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.     

Heats of atomization and resonance energy of some ortho-substituted benzoic acids

An experimental determination of heats of atomization of some ortho-substituted benzoic acids has been performed by combustion and differential scanning calorimetry. Resonance energy was calculated by the difference between the heat of atomization in the gas phase and the sum of the bond energies of a fixed bond structure for a resonating molecule. As the van der Waals radii of the ortho-substituent increased a decrease in resonance energy was observed.     

Design of pi-conjugated organic materials for one-dimensional energy transport in nanochannels

Various end-substituted distyrylbenzenes have been synthesized to serve as guest molecules in inclusion compounds to promote efficient energy transport along one-dimensional channels. Their optical and photophysical properties have been characterized at both experimental and theoretical levels. All molecules display a large transition dipole moment between the ground state and lowest excited state and hence a short radiative lifetime (on the order of 1-2 ns). They also exhibit a large spectral overlap between the emission and absorption spectra, which enables efficient energy transport between molecules arranged in a head-to-tail configuration in nanochannels. Hopping rates on the order of 10(12) s(-1) are calculated at a full quantum-chemical level; this is much larger than the radiative lifetimes and opens the way for energy migration over large distances. Changes in the nature of the terminal substituents are found to modulate the optical properties weakly but to impact significantly the energy transfer rates.     

Large near resonance third order nonlinearity in GaN

We have studied third order nonlinearities, including two-photon absorption coefficient and nonlinear refractive index n ₂, of GaN in below bandgap ultraviolet (UV) wavelength regime by using UV femtosecond pulses. Two-photon absorption was investigated by demonstrating femtosecond UV pulsewidth autocorrelation in a GaN thin film while femtosecond Z-scan measurements revealed information for both n ₂ and . The distribution of n ₂ versus wavelength was found to be consistent with a model described by the quadratic Stark effect, which is the dominant factor contributed to the nonlinear refractive index near the bandgap. Large on the order of 10 cm/GW and large negative n ₂ with a magnitude on the order of several 10^–12 cm²/W were obtained. The at near mid-gap infrared (IR) wavelength was also found to be on the order of several cm/GW by using two-photon-type autocorrelations in a GaN thin film. Taking advantage of the large two-photon absorption at mid-gap wavelengths, we have demonstrated excellent image quality on two-photon confocal microscopy, including two-photon-scanning-photoluminescence imaging and two-photon optical-beam-induced current microscopy, on a GaN Hall measurement sample and an InGaN green light emitting diode.