Resolutions of Subsets of Finite Sets of Points in Projective Space

Given a finite set, $X$, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is ``as big as possible'' inside $X$. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution is not always achieved, by incorporating an example of Eisenbud and Popescu. However, we show that it {\em is} achieved for sets of points in projective two space: given any finite set of points in projective two space for which the minimal free resolution is known, there must exist a subset having the predicted resolution.Comment: 17 page

New methodology to measure the dynamics of ocular wave front aberrations during small amplitude changes of accommodation

We present a methodology to measure the systematic changes of aberrations induced by small changes in amplitude of accommodation. We use a method similar the one used in electrophysiology, where a periodic stimulus is presented to the eye and many periods (epochs) of the stimulus are averaged. Using this technique we have measured changes in higher order aberrations from 0.006μm to 0.02μm and correlated them with amplitude changes of accommodation as small as 0.14D. These small changes would have been undetectable without epoch averaging. The correlation coefficients of Zernike terms with defocus were calculated, demonstrating higher values of correlation for epoch averaging. The accurate monitoring of defocus at the start of the accommodation response has shown some interesting trends that may be related with the mechanisms behind accommodation

Internal kinematic and physical properties in a BCD galaxy: Haro 15 in detail

We present a detailed study of the kinematic and physical properties of the ionized gas in multiple knots of the blue compact dwarf galaxy Haro 15. Using echelle and long slit spectroscopy data, obtained with different instruments at Las Campanas Observatory, we study the internal kinematic and physical conditions (electron density and temperature), ionic and total chemical abundances of several atoms, reddening and ionization structure. Applying direct and empirical methods for abundance determination, we perform a comparative analysis between these regions and in their different components. On the other hand, our echelle spectra show complex kinematics in several conspicuous knots within the galaxy. To perform an in-depth 2D spectroscopic study we complete this work with high spatial and spectral resolution spectroscopy using the Integral Field Unit mode on the Gemini Multi-Object Spectrograph instrument at the Gemini South telescope. With these data we are able to resolve the complex kinematical structure within star forming knots in Haro 15 galaxy.Comment: 6 pages, 2 figures, IX Scientific Meeting of the Spanish Astronomical Society held on September 13-17, 2010, in Madrid, Spai

The Nature of Deeply Buried Ultraluminous Infrared Galaxies: A Unified Model for Highly Obscured Dusty Galaxy Emission

We present models of deeply buried ultraluminous infrared galaxy (ULIRG) spectral energy distributions (SEDs) and use them to construct a three-dimensional diagram for diagnosing the nature of observed ULIRGs. Our goal is to construct a suite of SEDs for a very simple model ULIRG structure, and to explore how well this simple model can (by itself) explain the full range of observed ULIRG properties. We use our diagnostic to analyze archival Spitzer Space Telescope IRS spectra of ULIRGs and find that: (1) In general, our model does provide a comprehensive explanation of the distribution of mid-IR ULIRG properties; (2) >75% (in some cases 100%) of the bolometric luminosities of the most deeply buried ULIRGs must be powered by a dust-enshrouded active galactic nucleus; (3) an unobscured "keyhole" view through <~10% of the obscuring medium surrounding a deeply buried ULIRG is sufficient to make it appear nearly unobscured in the mid-IR; and (4) the observed absence of deeply buried ULIRGs with large PAH equivalent widths is naturally explained by our models showing that deep absorption features are "filled-in" by small quantities of foreground unobscured PAH emission (e.g., from the host galaxy disk) at the level of ~1% the bolometric nuclear luminosity. The modeling and analysis we present will also serve as a powerful tool for interpreting the high angular resolution spectra of high-redshift sources to be obtained with the James Webb Space Telescope.Comment: 20 pages, 14 figures. Accepted for publication in the Ap

Solving the two-center nuclear shell-model problem with arbitrarily-orientated deformed potentials

A general new technique to solve the two-center problem with arbitrarily-orientated deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle spectra for $^{12}$C + $^{12}$C $\to$ $^{24}$Mg are calculated using deformed Woods-Saxon potentials. These clearly show that non-axial symmetric configurations play a crucial role in molecular resonances observed in reaction processes for this system at low energy

A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models

We study Schwinger-Dyson equation for fermions in Yukawa and Wess-Zumino models, in terms of dynamical mass generation and the wavefunction renormalization function. In the Yukawa model with $\gamma_5$-type interaction between scalars and fermions, we find a critical coupling in the quenched approximation above which fermions acquire dynamical mass. This is shown to be true beyond the bare 3-point vertex approximation. In the Wess-Zumino model, there is a neat cancellation of terms leading to no dynamical mass for fermions. We comment on the conditions under which these results are general beyond the rainbow approximation and also on the ones under which supersymmetry is preserved and the scalars as well do not acquire mass. The results are in accordance with the non-renormalization theorem at least to order $\alpha$ in perturbation theory. In both the models, we also evaluate the wavefunction renormalization function, analytically in the neighbourhood of the critical coupling and numerically, away from it.Comment: 12 pages and 7 Postscript figures, accepted for publication in Journal of Physics G: Nuclear and Particle Physic