Maximal quadratic modules on *-rings

We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example of a maximal proper quadratic module is the cone of all positive semidefinite complex matrices of a fixed dimension. We show that the support of a maximal proper quadratic module is the symmetric part of a prime $\ast$-ideal, that every maximal proper quadratic module in a Noetherian $\ast$-ring comes from a maximal proper quadratic module in a simple artinian ring with involution and that maximal proper quadratic modules satisfy an intersection theorem. As an application we obtain the following extension of Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let $c$ be an element of the Weyl algebra $\mathcal{W}(d)$ which is not negative semidefinite in the Schr\" odinger representation. It is shown that under some conditions there exists an integer $k$ and elements $r_1,...,r_k \in \mathcal{W}(d)$ such that $\sum_{j=1}^k r_j c r_j^\ast$ is a finite sum of hermitian squares. This result is not a proper generalization however because we don't have the bound $k \le d$.Comment: 11 page

Stress Rupture Life Reliability Measures for Composite Overwrapped Pressure Vessels

Composite Overwrapped Pressure Vessels (COPVs) are often used for storing pressurant gases onboard spacecraft. Kevlar (DuPont), glass, carbon and other more recent fibers have all been used as overwraps. Due to the fact that overwraps are subjected to sustained loads for an extended period during a mission, stress rupture failure is a major concern. It is therefore important to ascertain the reliability of these vessels by analysis, since the testing of each flight design cannot be completed on a practical time scale. The present paper examines specifically a Weibull statistics based stress rupture model and considers the various uncertainties associated with the model parameters. The paper also examines several reliability estimate measures that would be of use for the purpose of recertification and for qualifying flight worthiness of these vessels. Specifically, deterministic values for a point estimate, mean estimate and 90/95 percent confidence estimates of the reliability are all examined for a typical flight quality vessel under constant stress. The mean and the 90/95 percent confidence estimates are computed using Monte-Carlo simulation techniques by assuming distribution statistics of model parameters based also on simulation and on the available data, especially the sample sizes represented in the data. The data for the stress rupture model are obtained from the Lawrence Livermore National Laboratories (LLNL) stress rupture testing program, carried out for the past 35 years. Deterministic as well as probabilistic sensitivities are examined

Control room operators’ cue utilization predicts cognitive resource consumption during regular operational tasks

This study was designed to examine whether qualified practitioners' cue utilization is predictive of their sustained attention performance during regular operational tasks. Simulated laboratory studies have demonstrated that cue utilization differentiates cognitive load during process control tasks. However, it was previously unclear whether similar results would be demonstrated with qualified practitioners during familiar operational tasks. Australian distribution network service provider (DNSP) operators were classified with either higher or lower cue utilization based on an assessment of cue utilization within the context of electrical power distribution. During two, 20-min periods of operators' regular workdays, physiological measures of workload were assessed through changes in cerebral oxygenation in the prefrontal cortex compared to baseline, and through eye behavior metrics (fixation rates, saccade amplitude, and fixation dispersion). The results indicated that there were no statistically significant differences in eye behavior metrics, based on levels of cue utilization. However, as hypothesized, during both sessions, operators with higher cue utilization demonstrated smaller increases in cerebral oxygenation in the prefrontal cortex from baseline, compared to operators with lower cue utilization. The results are consistent with the proposition that operators with higher cue utilization experience lower cognitive load during periods of regular activity during their workday, compared to operators with lower cue utilization. Assessments of cue utilization could help identify operators who are better able to sustain attention during regular operational tasks, as well as those who may benefit from cue-based training interventions.Daniel Sturman, Mark W. Wiggins, Jaime C. Auton, Shayne Loft, William S. Helton, Johanna I. Westbrook and Jeffrey Braithwait

A review of techniques for parameter sensitivity analysis of environmental models

Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42691/1/10661_2004_Article_BF00547132.pd