Tame and wild theorem for the category of filtered by standard modules for a quasi-hereditary algebra

We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove the tame-wild dichotomy for the category ${\cal F}(\Delta)$ of filtered by standard modules for a quasi-hereditary algebra. Moreover, in the tame case, we show that given a fixed dimension $d$, for every $d$-dimensional indecomposable module $M \in {\cal F}(\Delta)$, with the only possible exception of those lying in a finite number of isomorphism classes, the module $M$ coincides with its Auslander-Reiten translate in ${\cal F}(\Delta)$. Our results are based on a theorem by Koenig, K\"ulshammer, and Ovsienko relating ${\cal F}(\Delta)$ with the module category of some special type of ditalgebra.Comment: 51 page

Implementing TOPbase/Iron Project: Continuous Absorption from Fe II

We discuss implementation of TOPbase and Iron Project opacities for stellar spectral codes. We use a technique employed by Peach, where a Boltzmann-averaged cross section is calculated for selected temperatures, and the opacity obtained from double interpolation in temperature and wavelength. It is straightforward to include {\it all} levels for which cross sections have been calculated. Boltzmann-averaged cross sections for Fe II show a local maximum between 1700 and 2000[A]. We suggest this feature arises from 3d^5 4snl to 3d^5 4pnl transitions within Fe II. IUE spectra of iron-rich CP stars show local minima in this region. Theoretical calculations of a representative stellar continuum demonstrate that Fe II photoionization contributes significantly to the observed minima.Comment: 6 pages, 5 figures. See http://www.astro.lsa.umich.edu/users/cowley/paper2r for better definition figure

A Simple Dynamic Model of Credit and Aggregate Demand

The purpose of the paper is to present a tractable model of an old topic which is becoming more important in macroeconomics: the link between financial structure and economic activity.Aggregate Demand, Fiscal Policy, Monetary Policy, moral hazard, adverse selection, suuply of credit, reserves.

Atomic data from the Iron Project. LXIV. Radiative transition rates and collision strengths for Ca II

This work reports radiative transition rates and electron impact excitation rate coefficients for levels of the n= 3, 4, 5, 6, 7, 8 configurations of Ca II. The radiative data were computed using the Thomas-Fermi-Dirac central potential method in the frozen core approximation and includes the polarization interaction between the valence electron and the core using a model potential. This method allows for configuration interactions (CI) and relativistic effects in the Breit-Pauli formalism. Collision strengths in LS-coupling were calculated in the close coupling approximation with the R-matrix method. Then, fine structure collision strengths were obtained by means of the intermediate-coupling frame transformation (ICFT) method which accounts for spin-orbit coupling effects. We present extensive comparisons with the most recent calculations and measurements for Ca II as well as a comparison between the core polarization results and the "unpolarized" values. We find that core polarization affects the computed lifetimes by up to 20%. Our results are in very close agreement with recent measurements for the lifetimes of metastable levels. The present collision strengths were integrated over a Maxwellian distribution of electron energies and the resulting effective collision strengths are given for a wide range of temperatures. Our effective collision strengths for the resonance transitions are within ~11% from previous values derived from experimental measurements, but disagree with latter computations using the distorted wave approximation.Comment: 8 pages, 4 figures. The atomic data from this work, including energy levels, A-values, and effective collision strengths, is available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A

Existence of a multiplicative basis for a finitely spaced module over an aggregate

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable representations admits a multiplicative basis. In Sections 4.10-4.12 of [P. Gabriel, A. V. Roiter, Representations of finite-dimensional algebras. Encyclopaedia of Math. Sci., vol. 73, Algebra 8, Springer-Verlag, 1992] an analogous hypothesis was formulated for finitely spaced modules over an aggregate. We prove this conjecture.Comment: 17 page

Time-dependent Photoionization of Gaseous Nebulae: the Pure Hydrogen Case

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full time-dependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionization/thermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and non-linearly from the illuminated face of the cloud to the ionization front (IF). Ionization/thermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solutions. Moreover, even the time average ionization and temperature is different from any steady-state case. This time average is characterized by over-ionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of non-linear propagation times for thermal/ionization fronts and equilibration times.Comment: Accepted for publication in ApJ. 36 pages, 12 figure

[TiII] and [NiII] emission from the strontium filament of eta Carinae

We study the nature of the [TiII] and [NiII] emission from the so-called strontium filament found in the ejecta of eta Carinae. To this purpose we employ multilevel models of the TiII and NiII systems which are used to investigate the physical condition of the filament and the excitation mechanisms of the observed lines. For the TiII ion, for which no atomic data was previously available, we carry out ab initio calculations of radiative transition rates and electron impact excitation rate coefficients. It is found that the observed spectrum is consistent with the lines being excited in a mostly neutral region with an electron density of the order of $10^7$ cm$^{-3}$ and a temperature around 6000 K. In analyzing three observations with different slit orientations recorded between March~2000 and November~2001 we find line ratios that change among various observations, in a way consistent with changes of up to an order of magnitude in the strength of the continuum radiation field. These changes result from different samplings of the extended filament, due to the different slit orientations used for each observation, and yield clues on the spatial extent and optical depth of the filament. The observed emission indicates a large Ti/Ni abundance ratio relative to solar abundances. It is suggested that the observed high Ti/Ni ratio in gas is caused by dust-gas fractionation processes and does not reflect the absolute Ti/Ni ratio in the ejecta of \etacar. We study the condensation chemistry of Ti, Ni and Fe within the filament and suggest that the observed gas phase overabundance of TiComment: 14 paginas, 12 figure