Integrable systems from the classical reflection equation

We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection equation. In the case that $G$ is factorizable, we show that the time evolution of these systems is described by a Lax equation, and present its solution in terms of a factorization problem in $G$. Our construction is closely related to the semiclassical limit of Sklyanin's integrable quantum spin chains with reflecting boundaries.Comment: 23 pages, published versio

Current Status of VHE Astronomy

Very-high-energy astronomy studies the Universe at energies between 30 GeV and 100 TeV. The past decade has seen enormous progress in this field. There are now at least seven known sources of VHE photons. By studying these objects in the VHE regime one can begin to understand the environments surrounding these objects, and how particle acceleration is realized in nature. In addition the photon beams from the extragalactic gamma-ray sources can be used to study the electromagnetic fields in the intervening space. This recent progress can be traced to the development of a new class of detector with the ability to differentiate between air showers produced by gamma rays and those produced by the much more numerous hadronic cosmic-ray background. Much more sensitive instruments are currently in the design phase and two new types of instruments are beginning to take data. In this paper we will discuss the physics of these sources and describe the existing and planned detectors.Comment: 7 pages, 3 figure

\u3ci\u3eAmEx\u3c/i\u3e and Post-Cartesian Antitrust

I. Introduction II. Situating American Express ... A. Different Sides of the American Express Opinion ... 1. Two-Sided Markets ... 2. The American Express Opinion ... B. The Real Issue Is Messy, Not Two-Sided, Markets … C. The Many Messes of Modern Markets III. Competition in Messy Markets ... A. Simple Competition in Simple Markets ... B. More Complex Competition in Messier Markets ... C. American Express: The Competition Is in the Pudding IV. The Many Sides of AmEx’s Rightness ... A. A Burden Best Born by Plaintiffs ... B. Economic Theory as a Question of Law or of Fact? V. Conclusio

Busing did not fail. We did. : Doublespeak, Whiteness, and the Contradictions of Liberalism in Public Schooling

Using an interdisciplinary approach and a gear metaphor, I look at why an early 2000s school desegregation program in the Twin Cities was praised as revolutionary, but ended up resulting in greater segregation in the cities. This dissonance serves as an entry point for my greater project, in which I attempt to understand how doublespeak functions as a tool of white resistance to desegregation efforts in the North, and by extension, as a tool of white supremacy. Zooming out, I look at how the contradictions of liberalism harness the manipulation of language and the construction of whiteness to ensure that public schools serve as a site for the reproduction of white supremacy