Castelnuovo-Mumford Regularity in Biprojective Spaces

We define the concept of regularity for bigraded modules and bigraded polynomial ring. In this setting we prove analogs of some of the classical results on $m$-regularity for graded modules over polynomial algebras.Comment: 17 Pages, 2 figure

Curvilinear Base Points, Local Complete Intersection and Kozsul Syzygies in Biprojective Spaces

We prove analogs of results of Cox/Schenck on the structure of certain ideals in the bigraded polynomial ring k[s,u;t,v].Comment: 12 page

On ℓ-adic representations for a space of noncongruence cuspforms

This paper is concerned with a compatible family of 4-dimensional ℓ-adic representations ρℓ of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that: 1. It is automorphic: the L-function L(s,ρℓ∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρℓ∨ is the dual of ρℓ. 2. For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12. The key point is that the representation ρℓ admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long

Environmental exposure effects on composite materials for commercial aircraft

A study was conducted to determine the effects of long term flight and ground exposure on three commercially available graphite-epoxy material systems: T300/5208, T300/5209, and T300/934. Sets of specimens were exposed on commercial aircraft and ground racks for 1, 2, 3, 5, and 10 years. Inflight specimen sites included both the interior and exterior of aircraft based in Hawaii, Texas, and New Zealand. Ground racks were located at NASA-Dryden and the above mentioned states. Similar specimens were exposed to controlled lab conditions for up to 2 years. After each exposure, specimens were tested for residual strength and a dryout procedure was used to measure moisture content. Both room and high temperature residual strengths were measured and expressed as a pct. of the unexposed strength. Lab exposures included the effects of time alone, moisture, time on moist specimens, weatherometer, and simulated ground-air-ground cycling. Residual strengths of the long term specimens were compared with residual strengths of the lab specimens. Strength retention depended on the exposure condition and the material system. Results showed that composite materials can be successfully used on commercial aircraft if environmental effects are considered

Degradation mechanisms of materials for large space systems in low Earth orbit

Degradation was explored of various materials used in aerospace vehicles after severe loss of polymeric material coatings (Kapton) was observed on an early shuttle flight in low Earth orbit. Since atomic oxygen is the major component of the atmosphere at 300 km, and the shuttle's orbital velocity produced relative motion corresponding to approx. 5 eV of oxygen energy, it was natural to attribute much of this degradation to oxygen interaction. This assumption was tested using large volume vacuum systems and ion beam sources, in an exploratory effort to produce atomic oxygen of the appropriate energy, and to observe mass loss from various samples as well as optical radiation. Several investigations were initiated and the results of these investigations are presented in four papers. These papers are summarized. They are entitled: (1) The Space Shuttle Glow; (2) Laboratory Degradation of Kapton in a Low Energy Oxygen Ion Beam; (3) The Energy Dependence and Surface Morphology of Kapton Degradation Under Atomic Oxygen Bombardment; and (4) Surface Analysis of STS 8 Samples