Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Australia Telescope Compact Array 1.2cm Observations of the Massive Star Forming Region G305.2+0.2

We report on Australia Telescope Compact Array observations of the massive star-forming region G305.2+0.2 at 1.2 cm. We detected emission in five molecules towards G305A, confirming its hot core nature. We determined a rotational temperature of 26 K for methanol. A non-local thermodynamic equilibrium excitation calculation suggests a kinematic temperature of the order of 200 K. A time-dependent chemical model is also used to model the gas-phase chemistry of the hot core associated with G305A. A comparison with the observations suggest an age of between 2 × 104 and 1.5 × 105 yr. We also report on a feature to the south-east of G305A which may show weak Class I methanol maser emission in the line at 24.933 GHz. The more evolved source G305B does not show emission in any of the line tracers, but strong Class I methanol maser emission at 24.933 GHz is found 3 arcsec to the east. Radio continuum emission at 18.496 GHz is detected towards two H ii regions. The implications of the non-detection of radio continuum emission towards G305A and G305B are also discussed.

The massive neutron star or low-mass black hole in 2S 0921-630

We report on the optical spectroscopy of the eclipsing halo low-mass X-ray binary 2S 0921-630, which reveals the absorption-line radial velocity curve of the K0 III secondary star with a semiamplitude K-2=92.89+/-3.84 km s(-1), a systemic velocity gamma=34.9+/-3.3 km s(-1), and an orbital period P-orb of 9.0035+/-0.0029 days (1 sigma). Given the quality of the data, we find no evidence for the effects of X-ray irradiation. Using the previously determined rotational broadening of the mass donor and applying conservative limits on the orbital inclination, we constrain the compact object mass to be 2.0-4.3 M-circle dot (1 sigma), ruling out a canonical neutron star at the 99% level. Since the nature of the compact object is unclear, this mass range implies that the compact object is either a low-mass black hole with a mass slightly higher than the maximum possible neutron star mass (2.9 M-circle dot) or a massive neutron star. If the compact object is a black hole, it confirms the prediction of the existence of low-mass black holes, while if the object is a massive neutron star, its high mass severely constrains the equation of state of nuclear matter.

Thermolyzable polymer networks and star polymers containing a novel, compact, degradable acylal-based dimethacrylate cross-linker: Synthesis, characterization, and thermolysis

A compact, cleavable acylal dimethacrylate cross-linker, 1,1-ethylenediol dimethacrylate (EDDMA), was synthesized from the anhydrous iron(III) chloride-catalyzed reaction between methacrylic anhydride and acetaldehyde. The ability of EDDMA to act as cross-linker was demonstrated by using it for the preparation of one neat cross-linker network, four star polymers of methyl methacrylate (MMA), and four randomly cross-linked MMA polymer networks using group transfer polymerization (GTP). For comparison, the corresponding polymer structures based on the commercially available ethylene glycol dimethacrylate (EGDMA) cross-linker (isomer of EDDMA) were also prepared via GTR The number of arms of the EDDMA-based star polymers was lower than that of the corresponding EGDMA polymers, whereas the degrees of swelling in tetrahydrofuran of the EDDMA-based MMA networks were higher than those of their EGDMA-based counterparts. Although none of the EDDMA-containing polymers could be cleanly hydrolyzed under basic or acidic conditions, they could be thermolyzed at 200 degrees C within 1 day giving lower molecular weight products.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

The rotational broadening of V395 Carinae. Implications on the compact object's mass

Context: The masses previously obtained for the X-ray binary 2S 0921-630 inferred a compact object that was either a high-mass neutron star or low-mass black-hole, but used a previously published value for the rotational broadening (v sin i) with large uncertainties. Aims: We aim to determine an accurate mass for the compact object through an improved measurement of the secondary star's projected equatorial rotational velocity. Methods: We have used UVES echelle spectroscopy to determine the v sin i of the secondary star (V395 Car) in the low-mass X-ray binary 2S 0921-630 by comparison to an artificially broadened spectral-type template star. In addition, we have also measured v sin i from a single high signal-to-noise ratio absorption line profile calculated using the method of Least-Squares Deconvolution (LSD). Results: We determine v sin i to lie between 31.3±0.5 km s-1 to 34.7±0.5 km s-1 (assuming zero and continuum limb darkening, respectively) in disagreement with previous results based on intermediate resolution spectroscopy obtained with the 3.6 m NTT. Using our revised v sin i value in combination with the secondary star's radial velocity gives a binary mass ratio of 0.281±0.034. Furthermore, assuming a binary inclination angle of 75° gives a compact object mass of 1.37±0.13 M_?. Conclusions: We find that using relatively low-resolution spectroscopy can result in systemic uncertainties in the measured v sin i values obtained using standard methods. We suggest the use of LSD as a secondary, reliable check of the results as LSD allows one to directly discern the shape of the absorption line profile. In the light of the new v sin i measurement, we have revised down the compact object's mass, such that it is now compatible with a canonical neutron star mass.

The death of massive stars - I. Observational constraints on the progenitors of Type II-P supernovae

We present the results of a 10.5-yr, volume-limited (28-Mpc) search for supernova (SN) progenitor stars. In doing so we compile all SNe discovered within this volume (132, of which 27 per cent are Type Ia) and determine the relative rates of each subtype from literature studies. The core-collapse SNe break down into 59 per cent II-P and 29 per cent Ib/c, with the remainder being IIb (5 per cent), IIn (4 per cent) and II-L (3 per cent). There have been 20 II-P SNe with high-quality optical or near-infrared pre-explosion images that allow a meaningful search for the progenitor stars. In five cases they are clearly red supergiants, one case is unconstrained, two fall on compact coeval star clusters and the other twelve have no progenitor detected. We review and update all the available data for the host galaxies and SN environments (distance, metallicity and extinction) and determine masses and upper mass estimates for these 20 progenitor stars using the STARS stellar evolutionary code and a single consistent homogeneous method. A maximum likelihood calculation suggests that the minimum stellar mass for a Type II-P to form is m(min) = 8.5(-1.5)(+1) M-circle dot and the maximum mass for II-P progenitors is m(max) = 16.5 +/- 1.5 M-circle dot, assuming a Salpeter initial mass function holds for the progenitor population (in the range Gamma = -1.35(-0.7)(+0.3)). The minimum mass is consistent with current estimates for the upper limit to white dwarf progenitor masses, but the maximum mass does not appear consistent with massive star populations in Local Group galaxies. Red supergiants in the Local Group have masses up to 25 M-circle dot and the minimum mass to produce a Wolf-Rayet star in single star evolution (between solar and LMC metallicity) is similarly 25-30 M-circle dot. The reason we have not detected any high-mass red supergiant progenitors above 17 M-circle dot is unclear, but we estimate that it is statistically significant at 2.4 sigma confidence. Two simple reasons for this could be that we have systematically underestimated the progenitor masses due to dust extinction or that stars between 17-25 M-circle dot produce other kinds of SNe which are not II-P. We discuss these possibilities and find that neither provides a satisfactory solution. We term this discrepancy the 'red supergiant problem' and speculate that these stars could have core masses high enough to form black holes and SNe which are too faint to have been detected. We compare the Ni-56 masses ejected in the SNe to the progenitor mass estimates and find that low-luminosity SNe with low Ni-56 production are most likely to arise from explosions of low-mass progenitors near the mass threshold that can produce a core-collapse.

Zooming In on the Progenitors of Superluminous Supernovae With the HST

We present Hubble Space Telescope (HST) rest-frame ultraviolet imaging of the host galaxies of 16 hydrogen-poor superluminous supernovae (SLSNe), including 11 events from the Pan-STARRS Medium Deep Survey. Taking advantage of the superb angular resolution of HST, we characterize the galaxies' morphological properties, sizes, and star formation rate (SFR) densities. We determine the supernova (SN) locations within the host galaxies through precise astrometric matching and measure physical and host-normalized offsets as well as the SN positions within the cumulative distribution of UV light pixel brightness. We find that the host galaxies of H-poor SLSNe are irregular, compact dwarf galaxies, with a median half-light radius of just 0.9 kpc. The UV-derived SFR densities are high ([Sigma(SFR)] similar or equal to 0.1M(circle dot) yr(-1) kpc(-1)), suggesting that SLSNe form in overdense environments. Their locations trace the UV light of their host galaxies, with a distribution intermediate between that of long-duration gamma-ray bursts (LGRBs; which are strongly clustered on the brightest regions of their hosts) and a uniform distribution (characteristic of normal core-collapse SNe), though cannot be statistically distinguished from either with the current sample size. Taken together, this strengthens the picture that SLSN progenitors require different conditions than those of ordinary core-collapse SNe to form and that they explode in broadly similar galaxies as do LGRBs. If the tendency for SLSNe to be less clustered on the brightest regions than are LGRBs is confirmed by a larger sample, this would indicate a different, potentially lower-mass progenitor for SLSNe than LRGBs.

SN 2011dh: DISCOVERY OF A TYPE IIb SUPERNOVA FROM A COMPACT PROGENITOR IN THE NEARBY GALAXY M51

On 2011 May 31 UT a supernova (SN) exploded in the nearby galaxy M51 (the Whirlpool Galaxy). We discovered this event using small telescopes equipped with CCD cameras and also detected it with the Palomar Transient Factory survey, rapidly confirming it to be a Type II SN. Here, we present multi-color ultraviolet through infrared photometry which is used to calculate the bolometric luminosity and a series of spectra. Our early-time observations indicate that SN 2011dh resulted from the explosion of a relatively compact progenitor star. Rapid shock-breakout cooling leads to relatively low temperatures in early-time spectra, compared to explosions of red supergiant stars, as well as a rapid early light curve decline. Optical spectra of SN 2011dh are dominated by H lines out to day 10 after explosion, after which He I lines develop. This SN is likely a member of the cIIb (compact IIb) class, with progenitor radius larger than that of SN 2008ax and smaller than the eIIb (extended IIb) SN 1993J progenitor. Our data imply that the object identified in pre-explosion Hubble Space Telescope images at the SN location is possibly a companion to the progenitor or a blended source, and not the progenitor star itself, as its radius (~1013 cm) would be highly inconsistent with constraints from our post-explosion spectra.

The fastest unbound star in our Galaxy ejected by a thermonuclear supernova

Hypervelocity stars (HVSs) travel with velocities so high that they exceed the escape velocity of the Galaxy. Several acceleration mechanisms have been discussed. Only one HVS (US 708, HVS 2) is a compact helium star. Here we present a spectroscopic and kinematic analysis of US 708. Traveling with a velocity of ∼1200 kilometers per second, it is the fastest unbound star in our Galaxy. In reconstructing its trajectory, the Galactic center becomes very unlikely as an origin, which is hardly consistent with the most favored ejection mechanism for the other HVSs. Furthermore, we detected that US 708 is a fast rotator. According to our binary evolution model, it was spun-up by tidal interaction in a close binary and is likely to be the ejected donor remnant of a thermonuclear supernova.

Entanglement distribution with global control in a star-shaped multi-splitter

Distributed quantum information processing (QIP) is a promising way to bypass problems due to unwanted interactions between elements. However, this strategy presupposes the engineering of protocols for remote processors. In many of them, pairwise entanglement is a key resource. We study a model which distributes entanglement among elements of a delocalized network without local control. The model is efficient both in finite- and infinite-dimensional Hilbert spaces. We suggest a setup of electromechanical systems to implement our proposal.