Geometry of Banach spaces and biorthogonal systems

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system

Clump stars in the Solar Neighbourhood

Hipparcos data has allowed the identification of a large number of clump stars in the Solar Neighbourhood. We discuss our present knowledge about their distributions of masses, ages, colours, magnitudes, and metallicities. We point out that the age distribution of clump stars is ``biased'' towards intermediate-ages. Therefore, the metallicity information they contain is different from that provided by the local G dwarfs. Since accurate abundance determinations are about to become available, these may provide useful constraints to chemical evolution models of the local disc.Comment: 6 pages, proc. of the Sept. 20-24, 1999 Vulcano Workshop "The chemical evolution of the Milky Way: stars vs. clusters", eds. F. Matteucci, F. Giovanell

Dynamic Transitions in a Two Dimensional Associating Lattice Gas Model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical $\lambda$-line. The high density liquid phase and the fluid phases are separated by a second $\tau$ critical line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong trans ition when the critical $\lambda$-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the $\tau$-critical line is crossed by decreasing the temperature at a constant chemical potential.Comment: 22 page

Liquid polymorphism and density anomaly in a three-dimensional associating lattice gas

We investigate the phase diagram of a three-dimensional associating gas $(ALG)$ model. This model combines orientational ice-like interactions and ``van der Waals'' that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances making the connection between this model and continuous isotropic soft-core potentials. We present Monte Carlo studies of the $ALG$ model showing the presence of two liquid phase, two critical points and A density anomaly

Evolution of stellar structure in the Small Magellanic Cloud

The projected distribution of stars in the Small Magellanic Cloud (SMC) from the Magellanic Clouds Photometric Survey is analysed. Stars of different ages are selected via criteria based on V magnitude and V-I colour, and the degree of `grouping' as a function of age is studied. We quantify the degree of structure using the two-point correlation function and a method based on the Minimum Spanning Tree and find that the overall structure of the SMC is evolving from a high degree of sub-structure at young ages (~10 Myr) to a smooth radial density profile. This transition is gradual and at ~75 Myr the distribution is statistically indistinguishable from the background SMC distribution. This time-scale corresponds to approximately the dynamical crossing time of stars in the SMC. The spatial positions of the star clusters in the SMC show a similar evolution of spatial distribution with age. Our analysis suggests that stars form with a high degree of (fractal) sub-structure, probably imprinted by the turbulent nature of the gas from which they form, which is erased by random motions in the galactic potential on a time-scale of a galactic crossing time.Comment: Updated to match final journal styl

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

The Asymptotic Giant Branch and the Tip of the Red Giant Branch as Probes of Star Formation History: The Nearby Dwarf Irregular Galaxy KKH 98

We investigate the utility of the asymptotic giant branch (AGB) and the red giant branch (RGB) as probes of the star formation history (SFH) of the nearby (D=2.5 Mpc) dwarf irregular galaxy, KKH 98. Near-infrared (IR) Keck Laser Guide Star Adaptive Optics (AO) images resolve 592 IR bright stars reaching over 1 magnitude below the Tip of the Red Giant Branch. Significantly deeper optical (F475W and F814W) Hubble Space Telescope images of the same field contain over 2500 stars, reaching to the Red Clump and the Main Sequence turn-off for 0.5 Gyr old populations. Compared to the optical color magnitude diagram (CMD), the near-IR CMD shows significantly tighter AGB sequences, providing a good probe of the intermediate age (0.5 - 5 Gyr) populations. We match observed CMDs with stellar evolution models to recover the SFH of KKH 98. On average, the galaxy has experienced relatively constant low-level star formation (5 x 10^-4 Mo yr^-1) for much of cosmic time. Except for the youngest main sequence populations (age < 0.1 Gyr), which are typically fainter than the AO data flux limit, the SFH estimated from the the 592 IR bright stars is a reasonable match to that derived from the much larger optical data set. Differences between the optical and IR derived SFHs for 0.1 - 1 Gyr populations suggest that current stellar evolution models may be over-producing the AGB by as much as a factor of three in this galaxy. At the depth of the AO data, the IR luminous stars are not crowded. Therefore these techniques can potentially be used to determine the stellar populations of galaxies at significantly further distances.Comment: 15 pages, 14 figs, accepted for publication in Ap