The Hasse-Minkowski Theorem

The Hasse-Minkowski theorem concerns the classification of quadratic forms over global fields (i.e., finite extensions of Q and rational function fields with a finite constant field). Hasse proved the theorem over the rational numbers in his Ph.D. thesis in 1921. He extended the research of his thesis to quadratic forms over all number fields in 1924. Historically, the Hasse-Minkowski theorem was the first notable application of p-adic fields that caught the attention of a wide mathematical audience. The goal of this thesis is to discuss the Hasse-Minkowski theorem over the rational numbers and over the rational function fields with a finite constant field of odd characteristic. Our treatments of quadratic forms and local fields, though, are more general than what is strictly necessary for our proofs of the Hasse-Minkowski theorem over Q and its analogue over rational function fields (of odd characteristic). Our discussion concludes with some applications of the Hasse-Minkowski theorem.

Community Series Administrator Guide

A technical guide for managing community series in DigitalCommons@UConn.

Relationship of Turfgrass Growth and Quality to Soil Nitrate Desorbed from Anion Exchange Membranes

Anion exchange membranes (AEMs) are a potential method for determining the plant available N status of soils; however, their capacity for use with turfgrass has not been researched extensively. The main objective of this experiment was to determine the relationship between soil nitrate desorbed from AEMs and growth response and quality of turfgrass managed as a residential lawn. Two field experiments were conducted with a bluegrass-ryegrass-fescue mixture receiving four rates of N fertilizer (0, 98, 196, and 392 kg N ha(-1) yr(-1)) with clippings returned or removed. The soils at the two sites were a Paxton fine sandy loam (coarse-loamy, mixed, active, mesic Oxyaquic Dystrudepts) and a variant of a Hinckley gravelly sandy loam (sandy-skeletal, mixed, mesic Typic Udorthents). Anion exchange membranes were inserted into plots and exchanged weekly during the growing seasons of 1998 and 1999. Nitrate-N was desorbed from AEMs and quantified. As N fertilization rates increased, desorbed NO3-N increased. The relationship of desorbed NO3-N from AEMs to clipping yield and turfgrass quality was characterized using quadratic response plateau (QRP) and Cate-Nelson models (C-Ns). Critical levels of desorbed NO3-N ranged from 0.86 to 8.0 microgram cm(-2) d(-1) for relative dry matter yield (DMY) and from 2.3 to 12 microgram cm(-2) d(-1) for turfgrass quality depending upon experimental treatment. Anion exchange membranes show promise of indicating the critical levels of soil NO3-N desorbed from AEMs necessary to achieve maximum turfgrass quality and yield without overapplication of N.

Kentucky Bluegrass Response to Potassium and Nitrogen Fertilization

The response of Kentucky bluegrass (Poa pratensis L.) to potassium (K) fertilization has been inconsistent. The objective of this research was to determine the effects of K fertilization across varying nitrogen (N) rates and clipping management on Kentucky bluegrass clipping yields, quality, tissue K concentrations, apparent N recovery, and N use efficiency. A 2 x 4 x 4 factorial was arranged in a splitplot design and repeated across two years. Main plots were clipping treatments (returned vs. removed) and subplots were N rates (0, 98, 196, and 294 kg ha(-1) yr(-1)) in combination with K rates (0, 81, 162, and 243 kg ha(-1) yr(-1)). There was no positive effect of K on clipping yields and quality even though soil extractable K levels tested low. Higher K rates, however, increased N recovery and use efficiency for all but the highest N rate. Tissue K response to K fertilization was nonlinear. Yield and quality responses were not correlated to tissue K concentration. Nonexchangeable K levels were high in the native soil, and may have provided an additional source of K for bluegrass. The results suggest that extractable K values alone may not adequately predict available K to Kentucky bluegrass in this sandy loam soil.

Crossing the Chasm: from Cutting Edge to Practical Application

Presentation to the Capital District Library Council, Albany New York. Audience was public, school, academic, and special librarians. Topics covered: * Trends & buzzwords - Based on LITA's recent Top Tech Trends * Blogging - What is it? Who's using it? See examples of cool library blogs! * RSS - What is it? Why do we care? See examples of how to use it * Wikis - What the heck is a wiki? Why should you care (again)? See examples of how to use wikis * Information Overload - How can I keep up?! Wiki for presentation is available at http://crossingchasm.pbwiki.com/ ; this includes links to all sites shown in presentation.