High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser

We demonstrate the transfer of an ultrastable microwave frequency by transmitting a 30-nm-wide optical frequency comb from a mode-locked laser over 86?km of installed optical fiber. The pulse train is returned to the transmitter via the same fiber for compensation of environmentally induced optical path length changes. The fractional transfer stability measured at the remote end reaches 4×10(-17) after 1600?s, corresponding to a timing jitter of 64?fs.     

Two-letter group codes that preserve aperiodicity of inverse finite automata

We construct group codes over two letters (i.e., bases of subgroups of a two-generated free group) with special properties. Such group codes can be used for reducing algorithmic problems over large alphabets to algorithmic problems over a two-letter alphabet. Our group codes preserve aperiodicity of inverse finite automata. As an application we show that the following problems are PSpace-complete for two-letter alphabets (this was previously known for large enough finite alphabets): The intersection-emptiness problem for inverse finite automata, the aperiodicity problem for inverse finite automata, and the closure-under-radical problem for finitely generated subgroups of a free group. The membership problem for 3-generated inverse monoids is PSpace-complete. Both authors were supported in part by NSF grant DMS-9970471. The first author was also supported in part by NSF grant CCR-0310793. The second author acknowledges the support of the Excellency Center, “Group Theoretic Methods for the Study of Algebraic Varieties” of the Israeli Science Foundation.     

A 207Pb NMR study of the adducts of triphenyllead chloride and diphenyllead dichloride

²⁰⁷Pb NMR spectra were used to determine the structure of adducts of triphenyllead chloride and diphenyllead dichloride in CH₂Cl₂ and CH₃CN. The bases included several phosphorus donors, such as tributylphosphine, oxygen donors, such as tributylphosphine oxide, and nitrogen donors, such as pyridine. A number of bidentate bases were also studied. The ²⁰⁷Pb spectra indicate that rapid exchange occurs in the adducts, even at temperatures of ?90 °C. The magnitude of the shift relative to the lead acid indicates that all of the bases, including the bidentate bases, form five‐coordinate adducts with triphenyllead chloride. Diphenyllead dichloride forms six‐coordinate adducts, except for the adduct with tributylphosphine, which is five‐coordinate. This is the first report of a five‐coordinate adduct of diphenyllead dichloride. Copyright © 2003 John Wiley & Sons, Ltd.     

Laser spectroscopy of the 1s22s2p 3P2-3P1 transition in beryllium-like argon using the Oxford EBIT

A study of the 1s²2s2p ³P₂-³P₁ fine-structure transition in beryllium-like argon is planned on the Oxford electron beam ion trap (EBIT), using laser-induced resonance. This transition wavelength was measured previously as 594.373(4) nm, which is accessible using a dye laser. The ions are produced and excited in the EBIT and are confined during laser irradiation using the magnetic trapping mode. The ³P₂ level population is depleted by the laser and by subsequently monitoring the emitted fluorescence a laser resonance signal can be obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Line strength measurements of the 2ν3 band of methane

The line strengths of the manifolds of the 2ν₃ band of methane have been measured for the P, Q and R branches up to J = 10 (J = 9 for the R branch). The results are based on curves of growth using the assignments given by three different groups of investigators. They indicate that intensities deviate from the conventional factor given by Fox.(⁸) The deviation is descrived in terms of an empirical Herman-Wallis factor.