Sharp Weighted Young's Inequalities and Moser–Trudinger Inequalities on Heisenberg Type Groups and Grushin Spaces

We obtain sharp weighted Moser–Trudinger inequalities for first-layer symmetric functions on groups of Heisenberg type, and for -symmetric functions on the Grushin plane. To this end, we establish weighted Young's inequalities in the form , for first-layer radial weights on a general Carnot group and functions with first-layer symmetric. The proofs use some sharp estimates for hypergeometric functions.Research supported by NSF grant DMS-0228807.     

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups

We solve Gromov's dimension comparison problem for Hausdorff and box counting dimension on Carnot groups equipped with a Carnot-Carathéodory metric and an adapted Euclidean metric. The proofs use sharp covering theorems relating optimal mutual coverings of Euclidean and Carnot-Carathéodory balls, and elements of sub-Riemannian fractal geometry associated to horizontal self-similar iterated function systems on Carnot groups. Inspired by Falconer's work on almost sure dimensions of Euclidean self-affine fractals we show that Carnot-Carathéodory self-similar fractals are almost surely horizontal. As a consequence we obtain explicit dimension formulae for invariant sets of Euclidean iterated function systems of polynomial type. Jet space Carnot groups provide a rich source of examples.     

The electronic spectrum of tantalum hydride and deuteride

The diatomic molecule tantalum hydride (TaH) and its isotopologue tantalum deuteride (TaD) have been detected for the first time by laser excitation spectroscopy. The gas-phase molecules were produced in a hollow cathode discharge. Two red-degraded bands, one arising from TaH at 636 nm and the other from TaD at 635 nm, have been recorded at sub-Doppler resolution by intermodulated fluorescence spectroscopy. A rotational analysis shows that both bands are Ω = 2←2 in character, with well-resolved Ω-doubling in the upper state of TaH. Analysis of the ¹⁸¹Ta magnetic dipole and electric quadrupole hyperfine structure reveals that the lower X³Φ₂ electronic state of the two transitions arises from a σ²πδ electronic configuration, in agreement with previous theoretical calculations. The bond length in the TaH X³Φ₂ (v = 0) level is found to be 1.756960(4) Å.     

Extraction of arsenic species from spiked soils and standard reference materials

The abilities of various extractants to recover four arsenic species [As(iii), As(v), dimethylarsinic acid (DMA), and monomethylarsonic acid (MMA)] from soils spiked with 20 micro g g(-1) As were investigated. The extractants were water, buffer solutions (citrate and ammonium dihydrogen phosphate), acidic solutions (phosphoric acid and acetic acid), a basic solution (sodium hydroxide) and household chemicals (vinegar and Coca Cola). Gentle shaking at room temperature with each extractant for 24 h gave different recoveries for the different arsenic species. With 0.1 M NaOH solution 46% As(iii), 53% DMA, 100% MMA and 84% As(v) were recovered. A rapid extraction procedure using a sonicator probe has been developed to obtain higher extraction efficiencies. Extracts of arsenic-spiked soil, SRM 2711 Montana soil and SRM 2709 San Joaquin soil were analyzed by HPLC-ICP-MS. In the SRM water extracts, DMA and MMA were identified in addition to inorganic arsenic. The solution detection limits (3s) were 0.1, 0.12, 0.13 and 0.15 ng mL(-1) for As(iii), DMA, MMA and As(v), respectively for HPLC-ICP-MS.     

Local Structure Analysis of Strontium Sorption to Hydrous Manganese Oxide

To develop mechanistic models of contaminant distribution processes, we conducted an X-ray absorption fine structure analysis of strontium sorption to hydrous manganese oxide (HMO). Sr K-edge measurements were performed at 298, 220, and 77 K, and at sample loadings from 10(-4) to 10(-2) mol Sr/g HMO. Results from fitting the first shell in the sorbed samples indicate that strontium is surrounded by 10-12 oxygen atoms at an average distance of 2.58 ?. This coordination environment is consistent with the strontium atom remaining hydrated upon sorption to the oxide, where in water hydrated strontium has approximately 9 atoms of oxygen at 2.62 ?. Furthermore, the temperature dependence of the strontium-oxygen bond also suggests physical adsorption due to the large contribution of the dynamic component of the Debye Waller factor. Although second-shell data are consistent with either 3 manganese atoms at 4.12 ? or 6 strontium atoms at 3.88 ?, both the near-edge and fine structure data for the manganese K-edge indicate that the local coordination environment of the manganese ion remains intact as a function of time or strontium sorption. Furthermore, the local structure of amorphous manganese oxide is highly ordered. Copyright 2000 Academic Press.     

Photodriven electron and energy transfer from a light-harvesting metallodendrimer

Intermolecular electron and energy transfer from a light-harvesting metallodendrimer [Ru[bpy(C-450)(4)](3)](2+), where bpy(C-450)(4) is a 2,2'-bipyridine derivative containing 4 coumarin-450 units connected together through aryl ether linkages, is observed in acetonitrile solutions at room temperature. The model complex [Ru(dmb)(3)](2+), where dmb is 4,4'-dimethyl-2,2'-bipyridine, is included for quantitative comparison. The excited states of both compounds are metal-to-ligand charge transfer in nature and participate in excited-state electron and triplet energy transfer processes. Quenching constants were determined from luminescence and time-resolved absorption experiments at constant ionic strength. [Ru[bpy(C-450)(4)](3)](2+) displays significantly slower quenching rates to molecular oxygen and methyl viologen relative to the other processes investigated. Triplet energy transfer from [Ru[bpy(C-450)(4)](3)](2+) to 9-methylanthracene is quantitatively indistinguishable from [Ru(dmb)(3)](2+) while reductive electron transfer from phenothiazine was slightly faster in the former. With the exception of dioxygen quenching, our results indicate that the current dendritic structure is ineffective in shielding the core from bimolecular electron and triplet energy transfer reactions. Electrochemical measurements of [Ru[bpy(C-450)(4)](3)](2+) reveal irreversible oxidative processes at potentials slightly negative to the Ru(III/II) potential that are assigned to oxidations in the dendritic structure. Excited-state oxidative electron-transfer reactions facilitate this process resulting in the reduction of ground-state Ru(III) to Ru(II) and the trapping of the methyl viologen radical cation (MV(*+)) when methyl viologen serves as the quencher. This process generates a minimum of 9 MV(*+)'s for every [Ru[bpy(C-450)(4)](3)](2+) molecule and disassembles the metallodendrimer, resulting in the production of a [Ru(dmb)(3)](2+)-like species and "free" C-450-like dyes.     

Determination of arsenic in gold by flow injection inductively coupled plasma mass spectrometry with matrix removal by reductive precipitation

Arsenic was determined in gold by flow injection hydride generation inductively coupled plasma-mass spectrometry following a batch mode reductive precipitation removal of the interfering gold matrix. A solution of potassium iodide, L-ascorbic acid, and hydrochloric acid was used as the reluctant. The recovery of gold by precipitation and filtration was 99 ± 3%. The detection limit for arsenic in gold was 55 ng g⁻¹ in the solid. The concentration of arsenic that was determined in the Royal Canadian Mint gold sample FAU-10 was 29.7 μg g⁻¹ in the solid; this value was indistinguishable, with 95% confidence, from values determined at the Royal Canadian Mint by graphite furnace atomic absorption spectrometry and by inductively coupled plasma-mass spectrometry. The standard deviation for four replicate determinations of the arsenic in FAU-10 was 0.972 μg g⁻¹ in the solid.     

Non-linear Doppler shift of the plasmon resonance in a grating-coupled drifting 2DEG

We report experimental measurements and computer calculations of the plasmon resonances of two dimensional electron gases in the far-infrared which show the effects of laterally drifting the 2DEG. Coupling to radiation is achieved using an overlaid metal grating of submicron period, and its periodic screening effect splits the plasmon into upper and lower energy modes. For a symmetric grating profile the higher energy mode is non-radiative for a stationary 2DEG and a splitting is not observable, but when the 2DEG is laterally drifted under the grating, coupling to both modes can occur, and their Doppler shifts produce an observable splitting which increases with drift velocity. These Doppler shifts are not linear with drift velocity for low velocities, but approach asymptotically the expected linear shift with increasing drift velocity. Experimental results on 2DEGs at GaAs/AlGaAs heterojunctions compare well with theoretical calculations.