Hidden Beneath: Watermarks in the Early American Document Collection

This summer, as the Smith Intern at Special Collections, I was tasked with working on a hodge-podge of assembled documents, previously referred to as the “18th Century Document” collection. The box’s contents had been around for just about as long as anyone could remember, and really only got exposure for the Revolutionary War classes that had class sessions through Special Collections. Yet, as I browsed through the collection (which was really a small assemblage of papers), the box was much more than a Revolution collection. [excerpt

Modeling CO, CO2_2 and H2_2O ice abundances in the envelopes of young stellar objects in the Magellanic Clouds

Massive young stellar objects in the Magellanic Clouds show infrared absorption features corresponding to significant abundances of CO, CO$_2$ and H$_2$O ice along the line of sight, with the relative abundances of these ices differing between the Magellanic Clouds and the Milky Way. CO ice is not detected towards sources in the Small Magellanic Cloud, and upper limits put its relative abundance well below sources in the Large Magellanic Cloud and the Milky Way. We use our gas-grain chemical code MAGICKAL, with multiple grain sizes and grain temperatures, and further expand it with a treatment for increased interstellar radiation field intensity to model the elevated dust temperatures observed in the MCs. We also adjust the elemental abundances used in the chemical models, guided by observations of HII regions in these metal-poor satellite galaxies. With a grid of models, we are able to reproduce the relative ice fractions observed in MC massive young stellar objects (MYSOs), indicating that metal depletion and elevated grain temperature are important drivers of the MYSO envelope ice composition. Magellanic Cloud elemental abundances have a sub-galactic C/O ratio, increasing H$_2$O ice abundances relative to the other ices; elevated grain temperatures favor CO$_2$ production over H$_2$O and CO. The observed shortfall in CO in the Small Magellanic Cloud can be explained by a combination of reduced carbon abundance and increased grain temperatures. The models indicate that a large variation in radiation field strength is required to match the range of observed LMC abundances. CH$_3$OH abundance is found to be enhanced in low-metallicity models, providing seed material for complex organic molecule formation in the Magellanic Clouds.Comment: Accepted in ApJ 20 pages, 8 figures, 6 table

Sequences of reflection functors and the preprojective component of a valued quiver

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix

The Auslander-Reiten Components in the Rhombic Picture

For an indecomposable module $M$ over a path algebra of a quiver of type $\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts. We describe how these invariants for $M$ and for its dual specify the position of $M$ in the Auslander-Reiten quiver of the algebra.Comment: 29 pages; 6 figures; references added to Section 1 as per the referee's suggestions; to appear in Communications in Algebr

Intrinsic Valuing and the Limits of Justice: Why the Ring of Gyges Matters

Commentators such as Terence Irwin (1999) and Christopher Shields (2006) claim that the Ring of Gyges argument in Republic II cannot demonstrate that justice is chosen only for its consequences. This is because valuing justice for its own sake is compatible with judging its value to be overridable. Through examination of the rational commitments involved in valuing normative ideals such as justice, we aim to show that this analysis is mistaken. If Glaucon is right that everyone would endorse Gyges’ behavior, it follows that nobody values justice intrinsically. Hence, the Gyges story constitutes a more serious challenge than critics maintain

Optimal periodic binary codes of lengths 28 to 64

Results from computer searches performed to find repeated binary phase coded waveforms with optimal periodic autocorrelation functions are discussed. The best results for lengths 28 to 64 are given. The code features of major concern are where (1) the peak sidelobe in the autocorrelation function is small and (2) the sum of the squares of the sidelobes in the autocorrelation function is small

A Recipe for State Dependent Distributed Delay Differential Equations

We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that the resulting delay differential equation preserves non-negativity of initial conditions and we characterise local stability of equilibria. By specifying the distribution of maturation age, we recover state dependent discrete, uniform and gamma distributed delay differential equations. We show how to reduce the uniform case to a system of state dependent discrete delay equations and the gamma distributed case to a system of ordinary differential equations. To illustrate the benefits of these reductions, we convert previously published transit compartment models into equivalent distributed delay differential equations.Comment: 28 page