Abstract. We study the Cauchy problem for the focusing nonlinear Schrödinger (NLS) equation. Using the ∂ generalization of the nonlinear steepest descent method we compute the long time asymptotic expansion of the solution ψ(x, t) in any fixed space-time cone x1 + v1t ≤ x ≤ x2 + v2t with v1 ≤ v2 up to an (optimal) residual error of order O t −3/4 . In each (x, t) cone the leading order term in this expansion is a multi-soliton whose parameters are modulated by soliton-soliton and soliton-radiation interactions as one moves through the cone. Our results only require that the initial data possess one L 2 (R) moment and (weak) derivative and that it not generate any spectral singularities (embedded eigenvalues).

The small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data, the family of square barriers, 0 .x/ D q OE L;L for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O.1/ maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.

We consider the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation for finite density type initial data. Using the ∂ generalization of the nonlinear steepest descent method of Deift and Zhou we derive the leading order approximation to the solution of NLS for large times in the solitonic region of space-time, |x| < 2t, and we provide bounds for the error which decay as t → ∞ for a general class of initial data whose difference from the non vanishing background possesses a fixed number of finite moments and derivatives. Using properties of the scattering map of NLS we derive, as a corollary, an asymptotic stability result for initial data which are sufficiently close to the N -dark soliton solutions of NLS.

Abstract-Olfactory epithelial structure and olfactory bulb neurophysiological responses were measured in chinook salmon and rainbow trout in response to 25 to 300 g copper (Cu)/L. Using confocal laser scanning microscopy, the number of olfactory receptors was significantly reduced in chinook salmon exposed to Ն50 g Cu/L and in rainbow trout exposed to Ն200 g Cu/L for 1 h. The number of receptors was significantly reduced in both species following exposure to 25 g Cu/L for 4 h. Transmission electron microscopy of olfactory epithelial tissue indicated that the loss of receptors was from cellular necrosis. Olfactory bulb electroencephalogram (EEG) responses to 10 Ϫ3 M L-serine were initially reduced by all Cu concentrations but were virtually eliminated in chinook salmon exposed to Ն50 g Cu/L and in rainbow trout exposed to Ն200 g Cu/L within 1 h of exposure. Following Cu exposure, EEG response recovery rates were slower in fish exposed to higher Cu concentrations. The higher sensitivity of the chinook salmon olfactory system to Cu-induced histological damage and neurophysiological impairment parallels the relative species sensitivity observed in behavioral avoidance experiments. This difference in species sensitivity may reduce the survival and reproductive potential of chinook salmon compared with that of rainbow trout in Cu-contaminated waters.

We have constructed an opal suppressor system in Escherichia coli to complement an existing amber suppressor system to study the structural basis of tRNA acceptor identity, particularly the role of middle anticodon nucleotide at position 35. The opal suppressor tRNA contains a UCA anticodon and the mRNA of the suppressed protein (which is easily purified and sequenced) contains a UGA nonsense triplet. Opal suppressor tRNAs of two tRNAAg isoacceptor sequences each gave arginine in the suppressed protein, while the corresponding amber suppressors with U35 in their CUA anticodons each gave arginine plus a second amino acid in the suppressed protein. Since C35 but not U35 is present in the anticodon of wild-type tRNAAg molecules, while the first anticodon position contains either C34 or U34, these results establish that C35 contributes to tRNAArg acceptor identity. Initial characterizations of opal suppressor tRNAArg mutants by suppression efficiency measurements suggest that the fourth nucleotide from the 3' end of tRNAArg (A73 or G73 in different isoacceptors) also contributes to tRNAArg acceptor identity. Wild-type and mutant versions of opal and amber tRNALYS suppressors were examined, revealing that U35 and A73 are important determinants of tRNALyS acceptor identity. The aminoacylation specificity of tRNA ("tRNA acceptor identity") is essential for protein synthesis. The structural features in tRNA that determine tRNA acceptor identity have been studied in several ways: by measuring in vitro aminoacylation of tRNAs that differ structurally from corresponding wild-type tRNAs (1-16); by determining the interacting surfaces in complexes of tRNAs and aminoacyl-tRNA synthetases (17-23); by comparing tRNA sequences (24-27); and by determining the in vivo amino acid specificities of suppressor tRNAs (28-44). The acceptor identity of tRNA results from the tRNA's productive interaction with the cognate aminoacyl-tRNA synthetase and nonproductive interactions with all other aminoacyl-tRNA synthetase enzymes. The net outcome of both types of interactions is obtained with a suppressor tRNA. For analysis, a suppressor tRNA gene present in a plasmid is inserted into a cell, and, because of its distinctive codon recognition properties, the acceptor identity of the transcribed suppressor tRNA is mirrored by the amino acid recovered in a suppressed protein. Mutants of a suppressor tRNA can pinpoint the specific nucleotides that determine tRNA acceptor identity when the amino acid recovered in the suppressed protein is altered.We previously reported (38) that the acceptor identity of Escherichia coli tRNAAr9 is partially determined by the adenosine residue at position 20 (A20) in the variable pocket (38). Our work was based on a computer analysis of tRNA sequences and subsequent sequencing of suppressed protein produced by mutants of amber suppressor tRNAs. We also suggested that the cytidine residue at position 35 (C35) in the wild-type anticodon contributes to tRNAAr9 acceptor identity because amber suppressor (U35) tR...