Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Providential Tides: the Double Low Water of Narragansett Bay

We investigate a mechanism for producing double-lows and double-highs in the semi-diurnal tide by selective amplification of higher harmonics in a resonant gulf. A double low water is observed at Providence, RI, near the head of Narragansett Bay on days when there is a flattening of the low water tidal curve at Newport, at the mouth of the bay. The flattening is caused by an unusually large quarter-diurnal component to the tide at Newport. The quarter diurnal component has the right phase (a maximum close to the time of the minimum in the semi-diurnal tide) to produce a prolonged flattening of the tidal curve around low water. The natural period of Narragansett Bay (for quarter-wavelength resonance) is close to 4 h and the quarter diurnal tide is amplified, relative to the semi-diurnal tide, within the bay. The selective amplification of the higher harmonic further prolongs the flattening effect at Providence and, occasionally, is sufficient to create a double low water at the head of the bay from quarter and semi-diurnal tides alone. More often, though, a sixth-diurnal harmonic produced within the bay, added to the flattened low water at Providence, creates the double low water. This mechanism of selective amplification of tidal harmonics could be relevant to double tides elsewhere

Data report : hypoxia in the York River, 1988-1989

As part of the hypoxia program of the Virginia Chesapeake Bay Initiatives, the Division of Physical Oceanography of the Virginia Institute of Marine Science (VIMS) conducted a series of measurements in the York River estuary. The measurements were made in summer, 1988 and 1989. Two types of measurements were conducted in each year: measurements at moored stations and measurements by slackwater surveys. The former collected data for investigation of dissolved oxygen (DO) variation, and associated physical parameters, in an intratidal time scale, as well as for studying the vertical distributions of the measured parameters. The latter collected data for spatial distributions of DO, temperature, and salinity, and for investigation of temporal variation over the summer. This data report describes the field measurements and provides graphical presentation of the data. The numerical values of the data are archived and stored on magnetic tapes, which may be retrieved through the VIMS computer system

Climate change and health effects in Northwest Alaska

This article provides examples of adverse health effects, including weather-related injury, food insecurity, mental health issues, and water infrastructure damage, and the responses to these effects that are currently being applied in two Northwest Alaska communities

Hypoxia in the York River, 1991

This data report describes field studies conducted during the summer of 1991 by the Virginia Institute of Marine Science (VIMS) when both the physical environment and the dissolved oxygen regime were monitored, with the objective of better understanding how physical transport processes affect DO. The 1991 data sets will be presented here. Analysis and interpretation of the data is the subject of other scientific reports

Corporate Panel—Chapter 11 Cramdown Interest Rates: Till, Momentive, and the Proper Valuation Method

The Corporate Panel debated the appropriate way to determine chapter 11 cramdown interest rates

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation