On the Analytic Structure of Commutative Nilmanifolds

In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases, the nilpotent group $N$ has irreducible unitary representations whose coefficients are square integrable modulo the center $Z$ of $N$. Here we show that, in those three "exceptional" cases, the group $N$ is a semidirect product $N_1 \rtimes \mathbb{R}$ or $N_1 \rtimes \mathbb{C}$ where the normal subgroup $N_1$ contains the center $Z$ of $N$ and has irreducible unitary representations whose coefficients are square integrable modulo $Z$. This leads directly to explicit harmonic analysis and Fourier inversion formulae for commutative nilmanifolds

Applying Problem Based Learning to Improve Student Engagement in an Engineering Economics Course

Maintaining high levels of student engagement and interest is a widespread challenge in teaching Engineering Economics courses. To address this challenge at Baylor’s School of Engineering and Computer Science, a series of problem-based homework assignments focused on personal investing and tax return preparation have been developed and integrated into the Global Business Economics and Communication course. This transition in course structure has resulted in significant improvements in student engagement as measured by class attendance, homework completion rates, and course evaluation statistics. This transition also increased polarization of students’ academic performance which may be addressed through further development of the problem-based learning course content.Cockrell School of Engineerin

Roscoe Pound, Melvin Belli, and the Personal-Injury Bar: The Tale of an Odd Coupling

In the fourth chapter of Patriots and Cosmopolitans: Hidden Histories of American Law, legal historian John Fabian Witt tells the story of a collaboration between storied scholar Roscoe Pound and trial virtuoso Melvin M. Belli, which he calls among the most startling and yet unremarked-upon relationships in the annals of American law. Witt argues that it both shaped and energized the efforts of personal-injury lawyers to oppose proposals that would shift to the administrative branch of government responsibility for compensating auto-accident victims. Entitled The King and the Dean, in reference to the media\u27s coronation of Belli as the King of Torts , and Pound\u27s lengthy term (1916-1936) at the helm of the Harvard Law School, the chapter advances the claim that the two men came together synergistically in the early 1950s and mobilized a campaign by personal-injury lawyers to resist the enactment of automobile no-fault plans and other proposals that would have replaced common-law tort suits with alternative compensation mechanisms. This Article will first take issue with Witt\u27s story of the Pound-Belli relationship and then offer a different version of the interaction between the Dean and the plaintiffs\u27 trial bar

A Midrash On Water

(Excerpt) Jews and Christians share a common foundation of Scripture. It is within this common, sacred text that we shall find the source of Grace upon Grace: Living Water. It requires little religious imagination to link the use of water as a purification rite in the Biblical world to the use of the mikveh in the early rabbinic period, and ultimately to the transformative ritual of Baptism as an essential sacramental rite in Christianity. My task this evening is not to trace that course of ritual development, but rather to consider the many and varied texts of Scripture from within which we find water, Mayim, as a central metaphor for God\u27s presence and human struggle. I offer a midrash-an open interpretation of Biblical texts on water, a Jewish understanding of the religious significance of water, for our ongoing interfaith conversation on ritual and liturgy. Midrash is a form of rabbinic literature in which the text is used liked a prism and understanding, like light from many different sources, allowed to shine through the angles of glass, and if we are both lucky and skillful we shall see the bright colors of the spectrum suspended like a rainbow in front of our eyes. Midrash is a discipline of reading and rereading classic sacred texts, always allowing for our reality as readers and the overflowing surplus meaning of scripture to find their own new horizons of understanding

Rolling the tachyon in super BSFT

We investigate the rolling of the tachyon on the unstable D9 brane in Type IIA string theory by studying the BSFT action. The action is known for linear profiles of the tachyon, which is the expected asymptotic behavior of the tachyon as it approaches the closed string vacuum, as recently described by Sen. We find that the action does indeed seem consistent with the general Sen description, in that it implies a constant energy density with diminishing pressure. However, the details are somewhat different from an effective field theory of Born-Infeld type. For instance, the BSFT action implies there are poles for certain rolling velocities, while a Born-Infeld action would have a cut. We also find that solutions with pressure diminishing from either the positive or negative side are possible.Comment: 8 pages LaTeX; v2, references adde

Quark-Monopole Potentials in Large N Super Yang-Mills

We compute the quark-monopole potential for ${\cal N}=4$ super Yang-Mills in the large $N$ limit. We find an attractive potential that falls off as 1/L and is manifestly invariant under $g\to 1/g$. The strength of the potential is less than the quark-antiquark and monopole-antimonopole potentials.Comment: 10 pages (harvmac), 2 figures; v.2 typos corrected, one paragraph rewritte

Book Review: Deforming Tort Reform

The storms buffeting the tort system over the past two decades have come in three distinct waves. In the late 1960s, steep increases in the insurance costs incurred by health care providers protecting against negligence claims by patients triggered what came to be known as the medical malpractice crisis. In the mid-1970s, manufacturers whose liability insurance premiums suddenly soared raised obstreperous complaints that called public attention to the existence of a product liability crisis. Finally, other groups whose activities created risks exposing them to lawsuits found that their liability insurance rates had also risen precipitously. A full-blown torts crisis was at hand. The common law of torts attracted a major share of the blame for each of the three crises. Observers blamed the medical malpractice crisis on judicial decisions that expanded the doctrine of res ipsa loquitur by permitting juries to infer negligence from the mere occurrence of an untoward result following medical treatment, and that recognized a duty of due care by physicians to disclose the risk of treatment to patients. Members of Congress, among others, blamed the product liability crisis on state-by-state variations in rules governing the obligations of manufacturers and sellers. Working groups formed to study the issue found the across-the-board torts crisis attributable to the erosion of fault as the basis for liability and the adoption of rules and practices that were allegedly responsible for undue increases in compensatory as well as punitive damage awards. As a consequence, those adversely affected by rising insurance costs demanded, and often achieved, what they called tort reform. Responding to pressure, states enacted pro-defendant legislative adjustments to common law rules of medical malpractice, products liability, and general tort law. By equating tort reform with unidirectional statutory modification of the common law, its advocates succeeded in investing the term with a politically useful, if skewed, meaning. Until the dawn of the present age of tort-related crises, the notion of tort reform was likely to evoke images of a movement to change pro-defendant common law rules so that injured plaintiffs could more easily win judgments or recover full damages. Indeed, through the first half of the twentieth century, the tort system tended to protect the interests of defendants in general as well as particular categories of defendants. What might be called the old tort reform was partly an effort to rectify these imbalances

Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable Subgroups

In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that nilradicals of minimal parabolic subgroups of real reductive Lie groups are stepwise square integrable. Here, in Part I, we prove stepwise square integrability for nilradicals of arbitrary parabolic subgroups of real reductive Lie groups. This is technically more delicate than the case of minimal parabolics. We further discuss applications to Plancherel formulae and Fourier inversion formulae for maximal exponential solvable subgroups of parabolics and maximal amenable subgroups of real reductive Lie groups. Finally, in Part II, we extend a number of those results to (infinite dimensional) direct limit parabolics. These extensions involve an infinite dimensional version of the Peter-Weyl Theorem, construction of a direct limit Schwartz space, and realization of that Schwartz space as a dense subspace of the corresponding $L^2$ space.Comment: The proof of Theorem 5.9 is improved, several statements are clarified, and a certain number of typographical errors are correcte