CM points and weight 3/2 modular forms.

The theta correspondence has been an important tool in the theory of automorphic forms with plentiful applications to arithmetic questions. In this paper, we consider a specific theta lift for an isotropic quadratic space V over Q of signature (1, 2). The theta kernel we employ associated to the lift has been constructed by Kudla-Millson (e.g., [29, 30]) in much greater generality for O(p, q) (U(p, q)) to realize generating series of cohomo-logical intersection numbers of certain, ’special ’ cycles in locally symmetric spaces of orthogonal (unitary) type as holomorphic Siegel (Hermitian) mod-ular forms. In our case for O(1, 2), the underlying locally symmetric space M is a modular curve, and the special cycles, parametrized by positive in-tegers N, are the classical CM points Z(N); i.e., quadratic irrationalities of discriminant −N in the upper half plane. We survey the results of [16] and of our joint work with Bruinier [12] on using this particular theta kernel to define lifts of various kinds of functions F on the underlying modular curve M. The theta lift is given b

ALMOST A CENTURY OF ANSWERING THE QUESTION: WHAT IS A MOCK THETA FUNCTION?

Quite a few famous and extraordinarily gifted mathematicians led lives that were tragically cut short. Ramanujan is certainly among them. While suffering from a fatal disease, he discovered what he called mock theta functions. Three months before his death in 1920 at the age of 32, he described them in a letter to Hardy that was written under difficultie

Negotiating Contract Language on Health & Safety: A Union Guide to Planning, with Sample Clauses

[Excerpt] Rather than representing the final word on the subject, we hope this manual will represent the first step in an evolutionary process of increasingly effective and comprehensive health and safety contract language guidance. This can only succeed if labor leaders communicate with us concerning critical failures and successes in utilizing or obtaining contract language related to the work environment. We look forward to hearing about your experiences

Real-time application of knowledge-based systems

The Rapid Prototyping Facility (RPF) was developed to meet a need for a facility which allows flight systems concepts to be prototyped in a manner which allows for real-time flight test experience with a prototype system. This need was focused during the development and demonstration of the expert system flight status monitor (ESFSM). The ESFSM was a prototype system developed on a LISP machine, but lack of a method for progressive testing and problem identification led to an impractical system. The RPF concept was developed, and the ATMS designed to exercise its capabilities. The ATMS Phase 1 demonstration provided a practical vehicle for testing the RPF, as well as a useful tool. ATMS Phase 2 development continues. A dedicated F-18 is expected to be assigned for facility use in late 1988, with RAV modifications. A knowledge-based autopilot is being developed using the RPF. This is a system which provides elementary autopilot functions and is intended as a vehicle for testing expert system verification and validation methods. An expert system propulsion monitor is being prototyped. This system provides real-time assistance to an engineer monitoring a propulsion system during a flight

A Conjoint Analysis of Public Preferences for Agricultural Land Preservation

Public preferences for the nonmarket services of permanently preserved agricultural land are measured and compared using conjoint analysis. The results from a survey of 199 Delawareans suggest environmental and nonmarket-agricultural services are the most important preserved-land attributes. Results also suggest that open space associated with wetlands on farms is neither an amenity nor a disamenity. On the margin, preserved parcels with agricultural and environmental attributes provide net benefits, which may exceed $1,000,000 for a 1,000-acre parcel. Preserved forestland provides benefits per acre that are statistically equivalent to cropland, though forestland may be less expensive to preserve.Land Economics/Use,

Handbook for Computerized Reliability Analysis Method /CRAM/

Method for analyzing reliability by use of computer

The distribution of the eigenvalues of Hecke operators

For each prime $p$, we determine the distribution of the $p^{th}$ Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As $p\to\infty$, this distribution tends to the Sato--Tate distribution

Ultrasonic stress wave characterization of composite materials

The work reported covers three simultaneous projects. The first project was concerned with: (1) establishing the sensitivity of the acousto-ultrasonic method for evaluating subtle forms of damage development in cyclically loaded composite materials, (2) establishing the ability of the acousto-ultrasonic method for detecting initial material imperfections that lead to localized damage growth and final specimen failure, and (3) characteristics of the NBS/Proctor sensor/receiver for acousto-ultrasonic evaluation of laminated composite materials. The second project was concerned with examining the nature of the wave propagation that occurs during acoustic-ultrasonic evaluation of composite laminates and demonstrating the role of Lamb or plate wave modes and their utilization for characterizing composite laminates. The third project was concerned with the replacement of contact-type receiving piezotransducers with noncontacting laser-optical sensors for acousto-ultrasonic signal acquisition