Uniform algebras and approximation on manifolds

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we show that the only obstruction to $\mathcal{A} = \mathcal{C}(\bar{\Omega})$ is that there is a holomorphic disk $D \subset \bar{\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk

A lattice model for the kinetics of rupture of fluid bilayer membranes

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion), the thickness of the hydrophobic part of the bilayer, the hydrophobicity and a parameter characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium ``phase diagram'' is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first order rupture line is found with increasing tension, and a continuous increase in proto-pore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated PC lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.Comment: 15 pages, 8 figure

Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z

The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account mainly in the atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin already shown by the authors for harmonic oscillator potential and called the 'spin-orbit pendulum'. However this effect has not the exact periodicity of the simpler model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title changed, one reference adde

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Optical Spectra of SNR Candidates in NGC 300

We present moderate-resolution (<5A) long-slit optical spectra of 51 nebular objects in the nearby Sculptor Group galaxy NGC 300 obtained with the 2.3 meter Advanced Technology Telescope at Siding Spring Observatory, Australia. Adopting the criterion of [SII]/Ha>=0.4 to confirm supernova remnants (SNRs) from optical spectra, we find that of 28 objects previously proposed as SNRs from optical observations, 22 meet this criterion with six showing [SII]/Ha of less than 0.4. Of 27 objects suggested as SNRs from radio data, four are associated with the 28 previously proposed SNRs. Of these four, three (included in the 22 above) meet the criterion. In all, 22 of the 51 nebular objects meet the [SII]/Ha criterion as SNRs while the nature of the remaining 29 objects remains undetermined by these observations.Comment: Accepted for publication in Astrophysics & Space Scienc

Ascomycetous yeast species recovered from grapes damaged by honeydew and sour rot

Aims: To identify ascomycetous yeasts recovered from sound and damaged grapes by the presence of honeydew or sour rot. Methods and Results: In sound grapes, the mean yeast counts ranged from 3.20 ± 1.04 log CFU g-1 to 5.87 ± 0.64 log CFU g-1. In honeydew grapes, the mean counts ranged from 3.88 ± 0.80 log CFU g-1 to 6.64 ± 0.77 log CFU g-1. In sour rot grapes counts varied between 6.34 ± 1.03 and 7.68 ± 0.38 log CFU g-1. Hanseniaspora uvarum was the most frequent species from sound samples. In both types of damage, the most frequent species were Candida vanderwaltii, H. uvarum and Zygoascus hellenicus. The latter species was recovered in high frequency because of the utilization of the selective medium DBDM (Dekkera ⁄ Brettanomyces differential medium). The scarce isolation frequency of the wine spoilage species Zygosaccharomyces bailii (in sour rotten grapes) and Zygosaccharomyces bisporus (in honeydew affected grapes) could only be demonstrated by the use of the selective medium ZDM (Zygosaccharomyces differential medium). Conclusions: The isolation of several species only from damaged grapes indicates that damage constituted the main factor determining yeast diversity. The utilization of selective media is required for eliciting the recovery of potentially wine spoilage species. Significance and Impact of the Study: The impact of damaged grapes in the yeast ecology of grapes has been underestimate

HI in the Outskirts of Nearby Galaxies

The HI in disk galaxies frequently extends beyond the optical image, and can trace the dark matter there. I briefly highlight the history of high spatial resolution HI imaging, the contribution it made to the dark matter problem, and the current tension between several dynamical methods to break the disk-halo degeneracy. I then turn to the flaring problem, which could in principle probe the shape of the dark halo. Instead, however, a lot of attention is now devoted to understanding the role of gas accretion via galactic fountains. The current $\rm \Lambda$ cold dark matter theory has problems on galactic scales, such as the core-cusp problem, which can be addressed with HI observations of dwarf galaxies. For a similar range in rotation velocities, galaxies of type Sd have thin disks, while those of type Im are much thicker. After a few comments on modified Newtonian dynamics and on irregular galaxies, I close with statistics on the HI extent of galaxies.Comment: 38 pages, 17 figures, invited review, book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

The Milky Way Bulge: Observed properties and a comparison to external galaxies

The Milky Way bulge offers a unique opportunity to investigate in detail the role that different processes such as dynamical instabilities, hierarchical merging, and dissipational collapse may have played in the history of the Galaxy formation and evolution based on its resolved stellar population properties. Large observation programmes and surveys of the bulge are providing for the first time a look into the global view of the Milky Way bulge that can be compared with the bulges of other galaxies, and be used as a template for detailed comparison with models. The Milky Way has been shown to have a box/peanut (B/P) bulge and recent evidence seems to suggest the presence of an additional spheroidal component. In this review we summarise the global chemical abundances, kinematics and structural properties that allow us to disentangle these multiple components and provide constraints to understand their origin. The investigation of both detailed and global properties of the bulge now provide us with the opportunity to characterise the bulge as observed in models, and to place the mixed component bulge scenario in the general context of external galaxies. When writing this review, we considered the perspectives of researchers working with the Milky Way and researchers working with external galaxies. It is an attempt to approach both communities for a fruitful exchange of ideas.Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 36 pages, 10 figure