On strictly singular operators between separable Banach spaces

Let $X$ and $Y$ be separable Banach spaces and denote by \sss\sss(X,Y) the subset of \llll(X,Y) consisting of all strictly singular operators. We study various ordinal ranks on the set \sss\sss(X,Y). Our main results are summarized as follows. Firstly, we define a new rank \rs on \sss\sss(X,Y). We show that \rs is a co-analytic rank and that dominates the rank $\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\leq p<+\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that \sss\sss(\ell_p, Y_p) is a co-analytic non-Borel subset of \llll(\ell_p,Y_p) yet every strictly singular operator $T:\ell_p\to Y_p$ satisfies $\varrho(T)\leq 2$. This answers a question of Argyros.Comment: 20 pages, no figures; Mathematika, to appea

The pain of low status: the relationship between subjective socio-economic status and analgesic prescriptions in a Scottish community sample

There is a strong positive relationship between objective measures of socioeconomic status (OSS) and general health. However, there is an increasing interest in the relationship between health and subjective socioeconomic status (SSS), which describes one’s perceived rank in relation to the rest of society, based on factors such as income, occupation, and education. While the relationship between SSS and general health is well2established, the relationship between SSS and pain has received little attention. Gathering both self2report questionnaire data and General Practitioner medical data from a large representative community sample in Scotland between 2012 and 2013 ( N = 1824), we investigated the relationship between SSS and prescriptions for analgesic drugs. We found that higher levels of SSS significantly predicted lower odds of participants having been prescribed at least one analgesic drug in the previous six months. We obtained this result even after controlling for OSS2related variables (education, occupational status, and geographical location) and demographic variables (age and gender). This suggests that, just like the relationship between SSS and general health, SSS has important effects on pain that go beyond the influence of OSS

The Josephson Effect in Single Spin Superconductors

The Josephson Effect provides a primary signature of single spin superconductivity (SSS), the as yet unobserved superconducting state which was proposed recently as a low temperature phase of half-metallic antiferromagnets. These materials are insulating in the spin-down channel but are metallic in the spin-up channel. The SSS state is characterized by a unique form of p-wave pairing within a single spin channel. We develop the theory of a rich variety of Josephson effects that arise due to the form of the SSS order parameter. Tunneling is allowed at a SSS-SSS' junction but of course depends on the relative orientation of their order parameters. No current flows between an SSS and an s-wave BCS system due to their orthogonal symmetries, which potentially can be used to distinguish SSS from other superconducting states. Single spin superconductors also offer a means to probe other materials, where tunneling is a litmus test for any form of ``triplet'' order parameter.Comment: 4 pages, RevTeX, 2 PostScript figures included, to appear in J. Phys. and Chem. of Solid

Impact of Satellite Sea Surface Salinity Observations on ENSO Predictions from the NASA/GMAO Seasonal Forecast System

We assess the impact of satellite sea surface salinity (SSS) observations on dynamical ENSO forecasts. Assimilation of SSS improves the mixed layer depth (MLD) and modulates the Kelvin waves associated with ENSO. In column 2, the initialization differences between experiments that assimilate SSS minus those withholding SSS assimilation are presented. Column 3 shows examples of forecasts generated for the different phases of ENSO assimilating the different satellite SSS. In general, for all phases of ENSO, SSS assimilation improves forecasts. The far right column compares ensemble means for assimilation of individual and combined SMOS, Aquarius, and SMAP SSS forecasts. Finally, the latest forecasts are presented comparing assimilation versus no- assimilation of satellite SSS for single forecasts over the last year

Supersoft X-ray sources in M31: II. ROSAT-detected supersoft sources in the ROSAT, Chandra and XMM eras

We have performed Chandra observations during the past 3 years of 5 of the M31 supersoft X-ray sources (SSS) discovered with ROSAT. Surprisingly, only one of these sources has been detected, despite a predicted detection of about 20-80 counts. This has motivated a thorough check of the ROSAT M31 survey I data, including a relaxation of the hardness ratio requirement used to select SSS. This increases the number of SSS identified in survey I by 7. We then carried out a comparison with the ROSAT M31 survey II dataset which had hitherto not been explicitly investigated for SSS. We find that most of the ROSAT survey I sources are not detected, and only two new SSS are identified. The low detection rate in the ROSAT survey II and our Chandra observations implies that the variability time scale of SSS is a few months. If the majority of these sources are close-binary SSS with shell hydrogen burning, it further implies that half of these sources predominantly experience large mass transfer rates.Comment: accepted for publ. in ApJ; 2 ps-figures; high-quality figures available at http://www.mpe.mpg.de/~jcg/publis.htm

Complex group algebras of the double covers of the symmetric and alternating groups

We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\geq 5$ be an integer, $G$ a finite group, and let \AAA and \SSS^\pm denote the double covers of \Al_n and \Sy_n, respectively. We prove that \CC G\cong \CC \AAA if and only if G\cong \AAA, and \CC G\cong \CC \SSS^+\cong\CC\SSS^- if and only if G\cong \SSS^+ or \SSS^-. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.Comment: 27 pages, the previous version is revised slightly, to appear in Algebra & Number Theor