Optimization of Nordsieck's Method for the Numerical Integration of Ordinary Differential Equations

Stability and accuracy of Nordsieck's integration method can be improved by choosing the zero-positions of the extraneous roots of the characteristic equation in a suitable way. Optimum zero-positions have been found by minimizing the lower bound of the interval of absolute stability and the coefficient of the truncation error. Various properties of the improved methods have been analysed, such as the behaviour of the high-order terms, the equivalence with multistep methods and the damping of perturbations

Public Opinion in Germany on the Papacy and the Hierarchy During the Fourteenth Century and the Early Conciliar Period

A thorough understanding of public opinion on the medieval ecclesiastical system is of great importance for the proper interpretation of the events leading up to the Reformation. The necessity of this becomes more apparent when we consider the vital position of the Church in the medieval system and the direct and immediate bearing it had on the daily pursuits, welfare, and happiness of the peoples of Western Europe not only as members of the Church, the Alleinseligmachende, but also as subjects of actual or, at least, theoretical feudal fiefs of the Apostolic See

How the Professional Judgment Standard Could Undermine the Validity of Sexually Violent Predator Laws

The Article presents common features of the statutory schemes for the involuntary dedication of sexually violent predators in the U.S. in 2011. It examines several cases in the Supreme Court that shed some light on how the treatment that is offered to sexually violent predators might impact the constitutionality of their confinement. It discusses the consequences and proprietary of the professional judgment standard as a way to evaluate challenges to treatment

Stellar Polarimetry: Where Are We and Where Are We Going?

On the final day of the Stellar Polarimetry conference, participants split up into three "breakout sessions" to discuss the future of the field in the areas of instrumentation, upcoming opportunities, and community priorities. This contribution compiles the major recommendations arising from each breakout session. We hope that the polarimetric community will find these ideas useful as we consider how to maintain the vitality of polarimetry in the coming years.Comment: 7 pages, published in proceedings of "Stellar Polarimetry: From Birth to Death" (Madison, WI, June 2011

Ultraviolet Imaging Polarimetry of the Large Magellanic Cloud. II. Models

Motivated by new sounding-rocket wide-field polarimetric images of the Large Magellanic Cloud, we have used a three-dimensional Monte Carlo radiation transfer code to investigate the escape of near-ultraviolet photons from young stellar associations embedded within a disk of dusty material (i.e. a galaxy). As photons propagate through the disk, they may be scattered or absorbed by dust. Scattered photons are polarized and tracked until they escape to be observed; absorbed photons heat the dust, which radiates isotropically in the far-infrared, where the galaxy is optically thin. The code produces four output images: near- UV and far-IR flux, and near-UV images in the linear Stokes parameters Q and U. From these images we construct simulated UV polarization maps of the LMC. We use these maps to place constraints on the star + dust geometry of the LMC and the optical properties of its dust grains. By tuning the model input parameters to produce maps that match the observed polarization maps, we derive information about the inclination of the LMC disk to the plane of the sky, and about the scattering phase function g. We compute a grid of models with i = 28 deg., 36 deg., and 45 deg., and g = 0.64, 0.70, 0.77, 0.83, and 0.90. The model which best reproduces the observed polarization maps has i = 36 +2/-5 degrees and g ~0.7. Because of the low signal-to-noise in the data, we cannot place firm constraints on the value of g. The highly inclined models do not match the observed centro-symmetric polarization patterns around bright OB associations, or the distribution of polarization values. Our models approximately reproduce the observed ultraviolet photopolarimetry of the western side of the LMC; however, the output images depend on many input parameters and are nonunique.Comment: Accepted to AJ. 20 pages, 7 figure

Recombination Ghosts in Littrow Configuration: Implications for Spectrographs Using Volume Phase Holographic Gratings

We report the discovery of optical ghosts generated when using Volume Phase Holographic (VPH) gratings in spectrographs employing the Littrow configuration. The ghost is caused by light reflected off the detector surface, recollimated by the camera, recombined by, and reflected from, the grating and reimaged by the camera onto the detector. This recombination can occur in two different ways. We observe this ghost in two spectrographs being developed by the University of Wisconsin - Madison: the Robert Stobie Spectrograph for the Southern African Large Telescope and the Bench Spectrograph for the WIYN 3.5m telescope. The typical ratio of the brightness of the ghost relative to the integrated flux of the spectrum is of order 10^-4, implying a recombination efficiency of the VPH gratings of order 10^-3 or higher, consistent with the output of rigorous coupled wave analysis. Any spectrograph employing VPH gratings, including grisms, in Littrow configuration will suffer from this ghost, though the general effect is not intrinsic to VPH gratings themselves and has been observed in systems with conventional gratings in non-Littrow configurations. We explain the geometric configurations that can result in the ghost as well as a more general prescription for predicting its position and brightness on the detector. We make recommendations for mitigating the ghost effects for spectrographs and gratings currently built. We further suggest design modifications for future VPH gratings to eliminate the problem entirely, including tilted fringes and/or prismatic substrates. We discuss the resultant implications on the spectrograph performance metrics.Comment: 13 pages, 8 figures, emulateapj style, accepted for publication in PAS