Commutators on ℓ1\ell_1

The main result is that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17, 1513 - 1534) to obtain this result and use this generalization to obtain partial results about the commutators on spaces \X which can be represented as \displaystyle \X\simeq (\bigoplus_{i=0}^{\infty} \X)_{p} for some $1\leq p<\infty$ or $p=0$. In particular, it is shown that every compact operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus...\oplus\ell_{p_n}$ is given. We also show that strictly singular operators on $\ell_{\infty}$ are commutators.Comment: 17 pages. Submitted to the Journal of Functional Analysi

Measurements of ocean wave spectra and modulation transfer function with the airborne two frequency scatterometer

The directional spectrum and the microwave modulation transfer function of ocean waves can be measured with the airborne two frequency scatterometer technique. Similar to tower based observations, the aircraft measurements of the Modulation Transfer Function (MTF) show that it is strongly affected by both wind speed and sea state. Also detected are small differences in the magnitudes of the MTF between downwind and upwind radar look directions, and variations with ocean wavenumber. The MTF inferred from the two frequency radar is larger than that measured using single frequency, wave orbital velocity techniques such as tower based radars or ROWS measurements from low altitude aircraft. Possible reasons for this are discussed. The ability to measure the ocean directional spectrum with the two frequency scatterometer, with supporting MTF data, is demonstrated

E/V Nautilus EM302 Multibeam Echosounder System Review

Introduction The E/V Nautilus undertook leg NA040 to perform a review of the vessel’s Kongsberg EM302 multibeam echosounder in the vicinity of the continental shelf break offshore of St. Petersburg, Florida, from May 4-9, 2014 (Fig. 1). Paul Johnson and Kevin Jerram provided logistical and technical support for data collection and analysis. This report: • Describes the data collected. • Provides an overview of the processing methods used on the data • Presents the EM302 system performance for accuracy and coverage over the expected operational depth range. • Documents changes made to the system configuration prior to the 2014 field season. • Plots the EM302 transducer impedance data to document transducer health

Filled polymers for bearings and seals used in liquid hydrogen

Filled polytrifluorochloroethylene /PTFCE/ shows better thermal stability, less creep, and higher compressive moduli than filled polytetrafluoroethylene /PTFE/. Bearing and seal materials exhibiting the best characteristics contain a high percentage of PTFCE

Advanced 2-frequency ocean sensing radar using high resolution antenna beams

The opportunity to use a large space antenna system for remote sensing applications permits the creation of an advanced ocean sensing radar that combines the abilities of previously developed techniques. The 15 meter antenna will permit much higher angular and spatial resolution at the surface that will lead to techniques of observing ocean wave heights and the directional spectrum that had not previously been feasible from space. At the same time, sensors to measure ocean surface winds can be in operation and the data from both can be combined to increase the accuracy of each individual sensor. The existing capabilities and sensor techniques with typical data characteristics for the individual measurement of sea surface quantities are outlined

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte

Shear bands and cracking of metallic glass plates in bending

The thickness dependence of yielding and fracture of metallic glass plates subjected to bending is considered in terms of the shear band processes responsible for these properties. We argue that the shear band spacing (and length) scales with the thickness of the plate because of strain relaxation in the vicinity of the shear band at the surface. This is consistent with recent measurements of shear band spacing versus sample size. We also argue that the shear displacements in the shear band scale with the shear band length and plate thickness, thus causing cracks to be initiated in thicker plates at smaller bending strains. This leads to fracture bending strains that decrease markedly with increasing plate thickness, consistent with recent experiments. These results suggest that amorphous metals in the form of foams might have superior ductility and toughness