Compact weighted composition operators and fixed points in convex domains

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward the boundary of D, and p is a holomorphic self-map of D such that the weighted composition operator W assigning the product of m and the composition of f and p to a given function f is compact on a holomorphic functional Hilbert space (containing the polynomial functions densely) on D with reproducing kernel K blowing up along the diagonal of D toward its boundary, then p has a unique fixed point in D. We apply this result by making a reasonable conjecture about the spectrum of W based on previous one-variable and multivariable results concerning compact weighted and unweighted composition operators.Comment: 10 pages. Corrected a few typographical errors and an error in one step of the main result's proof. This paper was presented in September 2005 at the Wabash Extramural Modern Analysis Mini-conference in Indianapoli

Why Do They (Still) Sing Stories? Singing Narratives in Tanjung Bunga (Eastern Flores, Lamaholot, Indonesia)

In eastern Flores, on the Tanjung Bunga peninsula (among Western Lamaholot speakers), several times a year, ritual narratives (opak) are performed on a square dancing area, where all the clans of the same ceremonial land meet. Three types of narrative are sung, according to three kinds of rituals. The article explains the context, content and performance details of these stories, performed all night long. Why do the various clans continue to sing all these narrative? What values do these long poems have for people who sing them? Until now, studies on this subject have been remarkably few, and not even a partial transcription or translation of these narratives is available. This article offers a preliminary insight into these sung narratives, to show how vital they still are in eastern Flores

Product Variety and Demand Uncertainty

We show that demand uncertainty leads to vertical product differentiation even when consumers are homogeneous. When a firm anticipates that its inventory or capacity may not be fully utilized, product variety can reduce its expected costs of excess capacity. When the firm offers a continuum of product varieties, the highest quality product has the highest profit margins but the lowest percentage margin, while the lowest quality product has the highest percentage margin but the lowest absolute margin. We derive these results in both a monopoly model and a variety of different competitive models. We conclude with a discussion of empirical predictions together with a brief discussion of supporting evidence available from marketing studies.

Energy in Yang-Mills on a Riemann Surface

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang-Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on Atiyah and Bott's conjecture concerning Morse theory for the space of connections modulo gauge transformations.Comment: 7 pages, 2 figures, Latex2e with epsfig, submitted to Journal of Mathematical Physic

SEC Enforcement Heuristics: An Empirical Inquiry

This Article examines the overlap between SEC securities enforcement actions and private securities fraud class actions. We begin with an overview of data concerning all SEC enforcement actions from 1997 to 2002. We find that the volume of SEC enforcement proceedings is relatively modest. We next examine the scope of the recently enacted Fair Fund provision that authorizes the SEC to designate civil penalties it recovers from defendants to benefit defrauded private investors. We conclude that this provision offers only limited potential relief for private investors. We complete this Part of the Article with an analysis of the serious resource limitations faced by the SEC. The second portion of the Article contains an empirical analysis of the determinants of SEC enforcement actions and the overlap of private fraud suits and SEC enforcement proceedings. Using bivariate analysis, we find that (1) private suits with parallel SEC actions settle for significantly more than private suits without such proceedings; (2) SEC enforcement actions target significantly smaller companies than private actions alone; (3) private cases with parallel SEC actions take substantially less time to settle than other private cases; and (4) private cases with parallel SEC actions have significantly longer class periods than other private actions. Finally, we create a model for estimating damages to compare settlement ratios in cases with parallel SEC actions to those in private actions. We find that one-fourth of all the private class action settlements occurring in suits that yield less than 10 percent of provable losses are settled for less than 2 percent of provable losses, but that there are no private actions with parallel SEC suits with such small settlements. In the final Part of the Article, we conduct a multivariate regression analysis of the determinants of when SEC enforcement actions are filed. We find that the most highly significant determinant of SEC actions is financial distress. Estimated losses do not appear to be a statistically significant factor in the SEC\u27s decision to file these suits

SUSTAINABILITY: OBSERVATIONS, EXPECTATIONS AND POLICY IMPLICATIONS

Agricultural and Food Policy,

The Arecibo HII Region Discovery Survey

We report the detection of radio recombination line emission (RRL) using the Arecibo Observatory at X-band (9GHz, 3cm) from 37 previously unknown HII regions in the Galactic zone 66 deg. > l > 31 deg. and |b| < 1 deg. This Arecibo HII Region Discovery Survey (Arecibo HRDS) is a continuation of the Green Bank Telescope (GBT) HRDS. The targets for the Arecibo HRDS have spatially coincident 24 micron and 20 cm emission of a similar angular morphology and extent. To take advantage of Arecibo's sensitivity and small beam size, sources in this sample are fainter, smaller in angle, or in more crowded fields compared to those of the GBT HRDS. These Arecibo nebulae are some of the faintest HII regions ever detected in RRL emission. Our detection rate is 58%, which is low compared to the 95% detection rate for GBT HRDS targets. We derive kinematic distances to 23 of the Arecibo HRDS detections. Four nebulae have negative LSR velocities and are thus unambiguously in the outer Galaxy. The remaining sources are at the tangent point distance or farther. We identify a large, diffuse HII region complex that has an associated HI and 13CO shell. The ~90 pc diameter of the G52L nebula in this complex may be the largest Galactic HII region known, and yet it has escaped previous detection.Comment: Accepted to ApJ Data can be found here: http://go.nrao.edu/hrd

Styrene-terminated polysulfone oligomers as matrix material for graphite reinforced composites: An initial study

Styrene terminated polysulfone oligomers are part of an oligomeric class of compounds with end groups capable of thermal polymerization. These materials can be used as matrices for graphite reinforced composites. The initial evaluation of styrene terminated polysulfone oligomer based composites are summarized in terms of fabrication methods, and mechanical and environmental properties. In addition, a description and evaluation is provided of the NASA/Industry Fellowship Program for Technology Transfer