The partition algebra and the Kronecker product (Extended Abstract)

We propose a new approach to study the Kronecker coefficients by using the Schur–Weyl duality between the symmetric group and the partition algebra

The partition algebra and the Kronecker coefficients

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behaviour and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the reduced Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition

Optical Spectroscopy of X-Mega targets in the Carina Nebula - VI. FO 15: a new O-Type double-lined eclipsing binary

We report the discovery of a new O-type double-lined spectroscopic binary with a short orbital period of 1.4 days. We find the primary component of this binary, FO 15, to have an approximate spectral type O5.5Vz, i.e. a Zero-Age-Main-Sequence star. The secondary appears to be of spectral type O9.5V. We have performed a numerical model fit to the public ASAS photometry, which shows that FO 15 is also an eclipsing binary. We find an orbital inclination of ~ 80 deg. From a simultaneous light-curve and radial velocity solution we find the masses and radii of the two components to be 30 +/- 1 and 16 +/- 1 solar masses and 7.5 +/- 0.5 and 5.3 +/- 0.5 solar radii. These radii, and hence also the luminosities, are smaller than those of normal O-type stars, but similar to recently born ZAMS O-type stars. The absolute magnitudes derived from our analysis locate FO 15 at the same distance as Eta Carinae. From Chandra and XMM X-ray images we also find that there are two close X-ray sources, one coincident with FO 15 and another one without optical counterpart. This latter seems to be a highly variable source, presumably due to a pre-main-sequence stellar neighbour of FO 15.Comment: 11 pages, 9 figures, 3 tables. Accepted for publication in MNRAS. Higher resolution version available at http://lilen.fcaglp.unlp.edu.ar/papers2006.htm

Mapping the extent and spread of multiple plant invasions can help prioritise management in Galapagos National Park

Mapping is an important tool for the management of plant invasions. If landscapes are mapped in an appropriate way, results can help managers decide when and where to prioritize their efforts. We mapped vegetation with the aim of providing key information for managers on the extent, density and rates of spread of multiple invasive species across the landscape. Our case study focused on an area of Galapagos National Park that is faced with the challenge of managing multiple plant invasions. We used satellite imagery to produce a spatially-explicit database of plant species densities in the canopy, finding that 92% of the humid highlands had some degree of invasion and 41% of the canopy was comprised of invasive plants. We also calculated the rate of spread of eight invasive species using known introduction dates, finding that species with the most limited dispersal ability had the slowest spread rates while those able to disperse long distances had a range of spread rates. Our results on spread rate fall at the lower end of the range of published spread rates of invasive plants. This is probably because most studies are based on the entire geographic extent, whereas our estimates took plant density into account. A spatial database of plant species densities, such as the one developed in our case study, can be used by managers to decide where to apply management actions and thereby help curtail the spread of current plant invasions. For example, it can be used to identify sites containing several invasive plant species, to find the density of a particular species across the landscape or to locate where native species make up the majority of the canopy. Similar databases could be developed elsewhere to help inform the management of multiple plant invasions over the landscape

A mesoscopic ring as a XNOR gate: An exact result

We describe XNOR gate response in a mesoscopic ring threaded by a magnetic flux $\phi$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the inputs of the XNOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strength, magnetic flux and gate voltages. Our theoretical study shows that, for a particular value of $\phi$ ($=\phi_0/2$) ($\phi_0=ch/e$, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the two inputs to the gate are the same, while if one but not both inputs are high (1), a low output current (0) results. It clearly exhibits the XNOR gate behavior and this aspect may be utilized in designing an electronic logic gate.Comment: 8 pages, 5 figure

Correlation Effects in Side-Coupled Quantum Dots

Using Wilson's numerical renormalization group (NRG) technique we compute zero-bias conductance and various correlation functions of a double quantum dot (DQD) system. We present different regimes within a phase diagram of the DQD system. By introducing a negative Hubbard U on one of the quantum dots, we simulate the effect of electron-phonon coupling and explore the properties of the coexisting spin and charge Kondo state. In a triple quantum dot (TQD) system a multi-stage Kondo effect appears where localized moments on quantum dots are screened successively at exponentially distinct Kondo temperatures.Comment: 13 pages, 10 figure

Molecular Gas, Dust and Star Formation in Galaxies: II. Dust properties and scalings in \sim\ 1600 nearby galaxies

We aim to characterize the relationship between dust properties. We also aim to provide equations to estimate accurate dust properties from limited observational datasets. We assemble a sample of 1,630 nearby (z<0.1) galaxies-over a large range of Mstar, SFR - with multi-wavelength observations available from wise, iras, planck and/or SCUBA. The characterization of dust emission comes from SED fitting using Draine & Li dust models, which we parametrize using two components (warm and cold ). The subsample of these galaxies with global measurements of CO and/or HI are used to explore the molecular and/or atomic gas content of the galaxies. The total Lir, Mdust and dust temperature of the cold component (Tc) form a plane that we refer to as the dust plane. A galaxy's sSFR drives its position on the dust plane: starburst galaxies show higher Lir, Mdust and Tc compared to Main Sequence and passive galaxies. Starburst galaxies also show higher specific Mdust (Mdust/Mstar) and specific Mgas (Mgas/Mstar). The Mdust is more closely correlated with the total Mgas (atomic plus molecular) than with the individual components. Our multi wavelength data allows us to define several equations to estimate Lir, Mdust and Tc from one or two monochromatic luminosities in the infrared and/or sub-millimeter. We estimate the dust mass and infrared luminosity from a single monochromatic luminosity within the R-J tail of the dust emission, with errors of 0.12 and 0.20dex, respectively. These errors are reduced to 0.05 and 0.10 dex, respectively, if the Tc is used. The Mdust is correlated with the total Mism (Mism \propto Mdust^0.7). For galaxies with Mstar 8.5<log(Mstar/Msun) < 11.9, the conversion factor \alpha_850mum shows a large scatter (rms=0.29dex). The SF mode of a galaxy shows a correlation with both the Mgass and Mdust: high Mdust/Mstar galaxies are gas-rich and show the highest SFRs.Comment: 24 pages, 28 figures, 6 tables, Accepted for publication in A&

Time Dependent Current Oscillations Through a Quantum Dot

Time dependent phenomena associated to charge transport along a quantum dot in the charge quantization regime is studied. Superimposed to the Coulomb blockade behaviour the current has novel non-linear properties. Together with static multistabilities in the negative resistance region of the I-V characteristic curve, strong correlations at the dot give rise to self-sustained current and charge oscillations. Their properties depend upon the parameters of the quantum dot and the external applied voltages.Comment: 4 pages, 3 figures; to appear in PR