Explicit generating functional for pions and virtual photons

We construct the explicit one-loop functional of chiral perturbation theory for two light flavours, including virtual photons. We stick to contributions where 1 or 2 mesons and at most one photon are running in the loops. With the explicit functional at hand, the evaluation of the relevant Green functions boils down to performing traces over the flavour matrices. For illustration, we work out the pi+ pi- -> pi0 pi0 scattering amplitude at threshold at order p^4, e^2p^2.Comment: 20 pages, 2 figures; version accepted for publication, minor typographical changes, acknowledgments adde

Quality Control in Online Courses: Using a Social Constructivist Framework

There has recently been increased interest in the quality of online courses. Faculty from the School of Education at Marquette University suggest using social constructivist theories in the design and development of online courses and in the training and pedagogy of online instructors to ensure quality in online courses. Quality can be designed into online courses by focusing on complex tasks, using multiple perspectives, establishing a learning community, encouraging the social negotiation of meaning and providing assistance for learners at various levels. While good design can go a long way to ensure quality in online courses, the quality of the instructor is equally critical. Training instructors to establish a supportive climate, provide constructive feedback, and ask critical and probing questions leads to high quality online instruction

Globular Cluster Populations in Four Early-Type Poststarburst Galaxies

We present a study of the globular cluster systems of four early-type poststarburst galaxies using deep g and I-band images from the ACS camera aboard the Hubble Space Telescope (HST). All the galaxies feature shells distributed around their main bodies and are thus likely merger remnants. The color distribution of the globular clusters in all four galaxies shows a broad peak centered on g-I ~ 1.4, while PGC 6240 and PGC 42871 show a significant number of globular clusters with g-I ~ 1.0. The latter globular clusters are interpreted as being of age ~ 500 Myr and likely having been formed in the merger. The color of the redder peak is consistent with that expected for an old metal-poor population that is very commonly found around normal galaxies. However, all galaxies except PGC 10922 contain several globular clusters that are significantly brighter than the maximum luminosity expected of a single old metal-poor population. To test for multiple-age populations of overlapping g-I color, we model the luminosity functions of the globular clusters as composites of an old metal-poor subpopulation with a range of plausible specific frequencies and an intermediate-age subpopulation of solar metallicity. We find that three of the four sample galaxies show evidence for the presence of an intermediate-age (~ 1 Gyr) globular cluster population, in addition to the old metal-poor GC population seen in normal early-type galaxies. None of the galaxies show a significant population of clusters consistent with an old, metal-rich red cluster population that is typically seen in early-type galaxies.Comment: 41 pages, 13 figures, accepted for publication in AJ. Some figues have been downgraded to reduce their size

A Radio Perspective on the Wet Merger Remnant NGC 34

We present VLA observations of the neutral hydrogen and radio continuum of NGC 34 (= NGC 17 = Mrk 938). This object is an ideal candidate to study the fate of gas in mergers, since, as shown by an optical study done by Schweizer & Seitzer (2007), it is a gas-rich ("wet") merger remnant of two disk galaxies of unequal mass hosting a strong central starburst and a weak AGN. We detect HI emission from both tidal tails and from nearby galaxies, suggesting that NGC 34 is actually part of a gas-rich group and might have recently interacted with one of its companions. The kinematics of the gas suggests this remnant is forming an outer disk of neutral hydrogen from the gas of the northern tail. We also detect broad HI absorption (514 +/- 21 km/s wide) at both negative and positive velocities with respect to the systemic velocity. This absorption could be explained by the motions of the tidal tails or by the presence of a circumnuclear disk. In addition, we present radio-continuum images that show both nuclear (62.4 +/- 0.3 mJy) and extra-nuclear emission (26.5 +/- 3.0 mJy). The extra-nuclear component is very diffuse and in the shape of two radio lobes, spanning 390 kpc overall. This emission could be a signature of an AGN that has turned off, or it could originate from a starburst-driven superwind. We discuss the possible scenarios that explain our observations, and what they tell us about the location of the gas and the future evolution of NGC 34.Comment: 29 pages, 12 figures, 2 tables. Accepted for publication in the Astronomical Journal. Figs. 1, 2 & 6 degraded to reduce file size

Discovery of a Small Central Disk of CO and HI in the Merger Remnant NGC 34

We present CO(1-0) and HI(21-cm) observations of the central region of the wet merger remnant NGC 34. The Combined Array for Research in Millimeter-wave Astronomy (CARMA) observations detect a regularly rotating disk in CO with a diameter of 2.1 kpc and a total molecular hydrogen mass of ($2.1 \pm 0.2) \times10^9~M_\odot$. The rotation curve of this gas disk rises steeply, reaching maximum velocities at 1" (410 pc) from the center. Interestingly, HI observations done with the Karl G. Jansky Very Large Array show that the absorption against the central continuum has the exact same velocity range as the CO in emission. This strongly suggests that the absorbing HI also lies within 1" from the center, is mixed in and corotates with the molecular gas. A comparison of HI absorption profiles taken at different resolutions (5"-45") shows that the spectra at lower resolutions are less deep at the systemic velocity. This provides evidence for HI emission in the larger beams, covering the region from 1 kpc to 9 kpc from the center. The central rapidly rotating disk was likely formed either during the merger or from fall-back material. Lastly, the radio continuum flux of the central source at mm wavelengths ($5.4\pm1.8$ mJy) is significantly higher than expected from an extrapolation of the synchrotron spectrum, indicating the contribution of thermal free-free emission from the central starburst.Comment: Accepted for publication in A

Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading

It is widely acknowledge that there has been a major breakthrough in the mathematical theory of option trading. This breakthrough, which is usually summarized by the Black-Scholes formula, has generated a lot of excitement and a certain mystique. On the mathematical side, it involves advanced probabilistic techniques from martingale theory and stochastic calculus which are accessible only to a small group of experts with a high degree of mathematical sophistication; hence the mystique. In its practical implications it offers exciting prospects. Its promise is that, by a suitable choice of a trading strategy, the risk involved in handling an option can be eliminated completely. Since October 1987, the mood has become more sober. But there are also mathematical reasons which suggest that expectations should be lowered. This will be the main point of the present expository account. We argue that, typically, the risk involved in handling an option has an irreducible intrinsic part. This intrinsic risk may be much smaller than the a priori risk, but in general one should not expect it to vanish completely. In this more sober perspective, the mathematical technique behind the Black-Scholes formula does not lose any of its importance. In fact, it should be seen as a sequential regression scheme whose purpose is to reduce the a priori risk to its intrinsic core. We begin with a short introduction to the Black-Scholes formula in terms of currency options. Then we develop a general regression scheme in discrete time, first in an elementary two-period model, and then in a multiperiod model which involves martingale considerations and sets the stage for extensions to continuous time. Our method is based on the interpretation and extension of the Black-Scholes formula in terms of martingale theory. This was initiated by Kreps and Harrison; see, e.g. the excellent survey of Harrison and Pliska (1981,1983). The idea of embedding the Black-Scholes approach into a sequential regression scheme goes back to joint work of the first author with D. Sondermann. In continuous time and under martingale assumptions, this was worked out in Schweizer (1984) and Föllmer and Sondermann (1986). Schweizer (1988) deals with these problems in a general semimartingale mode

Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading

It is widely acknowledge that there has been a major breakthrough in the mathematical theory of option trading. This breakthrough, which is usually summarized by the Black-Scholes formula, has generated a lot of excitement and a certain mystique. On the mathematical side, it involves advanced probabilistic techniques from martingale theory and stochastic calculus which are accessible only to a small group of experts with a high degree of mathematical sophistication; hence the mystique. In its practical implications it offers exciting prospects. Its promise is that, by a suitable choice of a trading strategy, the risk involved in handling an option can be eliminated completely. Since October 1987, the mood has become more sober. But there are also mathematical reasons which suggest that expectations should be lowered. This will be the main point of the present expository account. We argue that, typically, the risk involved in handling an option has an irreducible intrinsic part. This intrinsic risk may be much smaller than the a priori risk, but in general one should not expect it to vanish completely. In this more sober perspective, the mathematical technique behind the Black-Scholes formula does not lose any of its importance. In fact, it should be seen as a sequential regression scheme whose purpose is to reduce the a priori risk to its intrinsic core. We begin with a short introduction to the Black-Scholes formula in terms of currency options. Then we develop a general regression scheme in discrete time, first in an elementary two-period model, and then in a multiperiod model which involves martingale considerations and sets the stage for extensions to continuous time. Our method is based on the interpretation and extension of the Black-Scholes formula in terms of martingale theory. This was initiated by Kreps and Harrison; see, e.g. the excellent survey of Harrison and Pliska (1981,1983). The idea of embedding the Black-Scholes approach into a sequential regression scheme goes back to joint work of the first author with D. Sondermann. In continuous time and under martingale assumptions, this was worked out in Schweizer (1984) and Föllmer and Sondermann (1986). Schweizer (1988) deals with these problems in a general semimartingale mode

Mode-coupling theory for structural and conformational dynamics of polymer melts

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.Comment: 4 pages, 3 figures, Phys. Rev. Lett. in pres