Almost commuting matrices

It is shown that if A and B are n x n complex matrices with A = A* and ||AB - BA||2/(n - 1), then there exist n x n matrices A' and B' with A' = A'* such that A'B' = B'A' and ||A - A'||[les] [epsilon], ||B - B'||[les] [epsilon].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23719/1/0000691.pd

Coastal and oceanic fish larvae in an area of upwelling off Yaquina Bay, Oregon

Reprinted from Fishery Bulletin, Vol. 75 (1), pages 125-145.A 1½-yr survey of planktonic fish larvae collected from 2 to 111 km off the mid-Oregon coast in 1971-72 yielded 287 samples which contained 23,578 individuals in 90 taxonomic groups, 78 identified at the species level. Two distinct faunal assemblages were founds a "coastal" assemblage 2 to 28 km offshore and an "offshore" assemblage 37 to 111 km from shore. The coastal group was dominated by Osmeridae, Parophrys vetulus, Isopsetta isolepis, and Microgadus proximus. The offshore group was dominated by Sebastes spp., Stenobrachius leucopsarus, Tarletonbeania crenularis, Lyopsetta exilis, and Engraulis mordax. Peak abundance in both assemblages occurred between February and July when >90% of all larvae were taken. Larval distribution patterns in each assemblage were similar in 1971 and 1972, but larval abundance was greater in 1971 than 1972. Ninety-nine percent of the larvae in 53 taxa designated as coastal and 96% of the larvae in 31 taxa designated as offshore were taken 2 to 28km or 37 to 111 km offshore respectively. This separation of coastal and offshore larvae may be explained, in part, by adult spawning locations and current circulation patterns. The species of larvae present in the coastal assemblage were similar to those in Yaquina Bay, but dominant species were quite different. The coastal zone is an important spawning area for P. vetulus, which utilizes Yaquina Bay estuary as a nursery during part of its early life

Swimbladder morphology and specific gravity of myctophids off Oregon

Three general types of swimbladders were found in the eight species of myctophids studied: gas-filled, fat-invested, and atrophied or reduced. Small specimens of all species had thin-walled, gas-filled swimbladders. Large specimens of Stenobrachius leucopsarus had fat-invested swim-bladders and large Diaphus theta had either gas-filled or atrophied swimbladders, as found by other workers. Large Tarletonbeania crenularis had either gas-filled or reduced swimbladders, large Lampanyctus ritteri and L. regalis had reduced swimbladders, and large Stenobrachius nannochir had fat-invested swimbladders. Protomyctophum thompsoni and P. crockeri retained gas-filled swimbladders.High body lipid content was found in S. leucopsarus, S. nannochir, L. ritteri and D. theta, and low lipid content was found in the other four species. Myctophids with high lipid content had specific gravities close to that of sea water (1.026–1.030). Tarletonbeania crenularis with a reduced swimbladder had a specific gravity of 1.088. Lampanyctus regalis had a lower specific gravity (1.040) due to high water content of the tissue.The swimbladder to body volumes in S. leucopsarus and D. theta were inversely related to body size and lipid content, indicating that lipids assume the primary buoyancy function as the gas-filled swimbladder regresses with age. This change may eliminate the physiological constraints imposed by a gas-filled swimbladder and permit the more extensive diel vertical migrations of adults

Detection of a Light Echo from the Otherwise Normal SN 2007af

We present the discovery of a light echo from SN 2007af, a normal Type Ia supernova (SN Ia) in NGC 5584. Hubble Space Telescope (HST) images taken three years post explosion reveal two separate echoes; an outer echo and extended central region, which we propose as an unresolved inner echo. Multiple images were obtained in the F160W, F350LP, F555W, and F814W using the Wide Field Camera 3. If the outer echo is produced by an interstellar dust sheet perpendicular to the line of sight, it is located ~800 pc in front of the SN. The dust for the inner echo is 0.45 pc < d < 90 pc away from the SN. The inner echo color is consistent with typical interstellar dust wavelength-dependent scattering cross-sections, while the outer echo color does not match the predictions. Both dust sheets, if in the foreground, are optically thin for scattering, with the outer echo sheet thickness consistent with the inferred extinction from peak brightness. Whether the inner echo is from interstellar or circumstellar dust is ambiguous. Overall, the echo characteristics are quite similar to previously observed SN Ia echoes.Comment: 15 pages, 6 figures, 7 table

Uniform semiclassical wave function for coherent 2D electron flow

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.Comment: 9 pages, 7 figure

Distribution and duration of pelagic life of larvae of dover sole, Microstomus pacificus; rex sole, Glyptocephalus zachirus; and petrale sole, Eopsetta jordani, in waters off Oregon

Dover and rex sole larvae attain an exceptionally large size and have a long pelagic life. Dover sole larvae (9-65 mm standard length) were collected in mid-water trawls and plankton nets during all months of the year. Judging from growth of larvae and occurrence in bottom trawls of recently metamorphosed juveniles, Dover sole are pelagic during their first year of life. Large larvae (50-65 mm standard length) are probably pelagic for over a year and few apparently are recruited to benthic populations. Dover sole larvae were most common in oceanic waters beyond the continental slope and in the upper 50 m of the water column. The rex sole larvae captured were 5-89 mm long. Average size and stage of development of larvae increased from March through February, and juveniles were common on the bottom during winter on the outer shelf. Thus the pelagic phase usually lasts about a year. Both rex and Dover sole may utilize the outer continental shelf-upper slope region for a nursery during early benthic life. Petrale sole larvae (10-22 mm standard length) were rare. They were collected only from March to June and appear to have a pelagic life of about 6 mo. Age-group 0 juveniles, uncommon in bottom trawl collections, were only captured on the inner continental shelf in the fall.Reprinted from Fishery bulletin, Vol. 75 (1), pages 173-183

Ecological and radioecological studies in the Columbia River Estuary and adjacent Pacific Ocean

This report represents the progress in "Ecological and Radioecological Studies in the Columbia River Estuary and Adjacent Pacific Ocean" for the period 1 April 1975 through 31 March 1976. This research has been supported with funds from the Division of Biomedical and Environmental Research, U.S. Energy Research and Development Administration through Contract AT(45-1)-2227, Task Agreement 12. Our current research activities are dealt with in a descriptive fashion in the section on Research in Progress. The Research Completed section of the report includes manuscripts which have been submitted for publication during the reporting period, as well as reprints of papers published during this same period

Submersible observations of deep-reef fishes of Heceta Bank, Oregon

Rockfishes, Sebastes spp.. were the most numerous and speciose fishes seen during 16 submersible dives from 64 to 305 m depth in the vicinity of Heceta Bank off the coast of Oregon. Dense schools of juvenile rockfishes and large yellowtail rockfish, S. flavidus, were observed only over rocky, high relief areas near the top of the bank, and highest densities of small benthic rockfishes (up to 5-10/m2) on the flanks of the bank. These observations suggest that shallow, rocky portions of Heceta Bank are a nursery area for juvenile rockfishes. Two species groups of nonschooling fishes were identified based on transects over the diverse seafloor habitats around the bank: one comprised primarily of rockfishes in shallow water on rock and cobble, and the other comprised of flatfishes, agonids, sablefish, and some rockfishes in deep water over mud and cobble. Species composition of fishes observed from submersible dives differed from species composition of fishes taken from trawl catches in the same general areas.This publication is associated with the document Fish Assemblages of Rocky Banks of the Pacific Northwest: Final Report by M.A. Hixon, B.N. Tissot, and W.G. Pearcy, and its accompanying data reports