Author Index to Volumes 100 and 101: 1998

Through both analytical and numerical methods, we solve the eigenproblem u_zz >+(1/ z −λ−( z −1/ε)²) u =0 on the unbounded interval z ∈[−∞, ∞], where λ is the eigenvalue and u ( z )→0 as | z |→∞. This models an equatorially trapped Rossby wave in a shear flow in the ocean or atmosphere. It is the usual parabolic cylinder equation with Hermite functions as the eigenfunctions except for the addition of an extra term, which is a simple pole. The pole, which is on the interior of the interval, is interpreted as the limit δ→0 of 1/( z − i δ). The eigenfunction has a branch point of the form z  log( z ) at z =0, where the branch cut is on the upper imaginary axis. The eigenvalue is complex valued with an imaginary part, which we show, through matched asymptotics, to be approximately √ π exp(−1/ε²){1−2ε log ε+ε log 2+γε}. Because T ( λ ) is transcendentally small in the small parameter ε, it lies "beyond all orders" in the usual Rayleigh–Schrödinger power series in ε. Nonetheless, we develop special numerical algorithms that are effective in computing T ( λ ) for ε as small as 1/100.     

The modularity of some Q-curves

A Q-curve is an elliptic curve, defined over a number field, that is isogenous to each of its Galois conjugates. Ribet showed that Serre's conjectures imply that such curves should be modular. Let E be an elliptic curve defined over a quadratic field such that E is 3-isogenous to its Galois conjugate. We give an algorithm for proving any such E is modular and give an explicit example involving a quotient of J_o (169). As a by-product, we obtain a pair of 19-isogenous elliptic curves, and relate this to the existence of a rational point of order 19 on J₁ (13).     

High-efficiency fused-silica transmission gratings

We describe the design, fabrication, and performance of high-efficiency transmission gratings fabricated in bulk fused silica for use in high-power ultraviolet laser systems. The gratings exhibit a diffraction efficiency of 94% in order m=-1 and a damage threshold greater than 13>J/cm( 2) for 3-ns pulses at 351 nm. Model calculations and experimental measurements are in good agreement.     

Determination of trace level gamma-aminobutyric acid using an improved OPA pre-column derivatization and on-column preconcentration capillary liquid chromatography with electrochemical detection

An improved pre-column derivatization with o-phthalaldehyde/tert-butylthiol and on-column preconcentration are used with packed capillary liquid chromatography and electrochemical detection to obtain low concentration detection limits for gamma-aminobutyric acid (GABA). Using derivatization procedures from the literature, it was found that the detection limits for GABA were 380 amol in 50 microns i.d. packed capillaries, which is over 10-fold worse than the detection limit possible with the instrumentation. The higher detection limit was directly the result of electroactive interferences generated by the derivatization chemistry. Derivatization was improved by scavenging excess reagents with excess amine and iodoacetamide. With these improvements, the interfering peaks were eliminated and the detection limit was improved to 50 amol. With injection volumes of 0.5 microL, under conditions that permitted on-column preconcentration, the concentration detection limit, that is the concentration at which analytes could be derivatized and detected, was 100 pM. The technique was applied to determination of GABA release from islets of Langerhans.     

Incorporation of oxygen atoms into As+ implanted silicon during cw CO2 laser annealing in O2

By annealing Si layers amorphised by ion-implantation with a cw CO₂ laser beam in oxygen rich environments, it has been possible to incorporate O atoms into the recrystallized lattice. Absorption measurements on such regrown layers by infrared spectrometry have shown that the impurities are preferentially bonded into substitutional lattice sites, rather than existing interstitially. Supplementary RHEED studies have indicated thatβ-cristobalite, a crystalline form of SiO₂, has been formed. These investigations highlight the importance of the ambient during cw laser annealing.