Proof of the Umbral Moonshine Conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.Comment: 56 pages, to appear in Research in the Mathematical Science

Shear Behavior of High-Strength Self-Consolidating Concrete in Nebraska University Bridge Girders

Current reinforced and prestressed concrete design equations were developed for conventional concrete elements. Self-consolidating concrete (SCC) typically contains a lower coarse aggregate content and size than conventional concrete, which potentially hinders the aggregate interlock contribution to a concrete\u27s shear strength. Thus, shear design equations must be verified with SCC mixtures. Two full-scale precast, prestressed concrete Nebraska University girders were tested to assess the shear behavior of high-strength SCC. Both girders were designed to permit two tests on each girder, both with and without shear reinforcement. Ultimate shear loads and crack patterns were documented and compared with code estimates, finite element models, and a collected prestressed concrete shear database. The girders exceeded the predicted factored concrete shear resistance from current U.S. design standards. However, additional test data are required to identify any distinguishable trends of the shear strength of SCC mixtures

Assessing Post-ADA Employment: Some Econometric Evidence and Policy Considerations

This article explores the relationship between the Americans with Disabilities Act (“ADA”) and the relative labor market outcomes for people with disabilities. Using individual-level longitudinal data from 1981 to 1996 derived from the previously unexploited Panel Study of Income Dynamics (“PSID”), we examine the possible effect of the ADA on (1) annual weeks worked; (2) annual earnings; and (3) hourly wages for a sample of 7120 unique male household heads between the ages of 21 and 65 as well as a subset of 1437 individuals appearing every year from 1981 to 1996. Our analysis of the larger sample suggests the ADA had a negative impact on the employment levels of disabled persons relative to non-disabled persons but no impact on relative earnings. However, our evaluation of the restricted sample raises questions about these findings. Using these data, we find little evidence of adverse effects on weeks worked but strong evidence of wage declines for the disabled, albeit declines beginning in 1986, well before the ADA’s passage. These results therefore cast doubt on the adverse ADA-related impacts found in previous studies, particularly Acemoglu and Angrist (2001). The conflicting narratives that emerge from our analysis shed new light on, but also counsel caution in reaching final conclusions about, the impact of the ADA on employment outcomes for people with disabilities

Assessing Post-ADA Employment: Some Econometric Evidence and Policy Considerations

This article explores the relationship between the Americans with Disabilities Act (“ADA”) and the relative labor market outcomes for people with disabilities. Using individual-level longitudinal data from 1981 to 1996 derived from the previously unexploited Panel Study of Income Dynamics (“PSID”), we examine the possible effect of the ADA on (1) annual weeks worked; (2) annual earnings; and (3) hourly wages for a sample of 7120 unique male household heads between the ages of 21 and 65 as well as a subset of 1437 individuals appearing every year from 1981 to 1996. Our analysis of the larger sample suggests the ADA had a negative impact on the employment levels of disabled persons relative to non-disabled persons but no impact on relative earnings. However, our evaluation of the restricted sample raises questions about these findings. Using these data, we find little evidence of adverse effects on weeks worked but strong evidence of wage declines for the disabled, albeit declines beginning in 1986, well before the ADA’s passage. These results therefore cast doubt on the adverse ADA-related impacts found in previous studies, particularly Acemoglu and Angrist (2001). The conflicting narratives that emerge from our analysis shed new light on, but also counsel caution in reaching final conclusions about, the impact of the ADA on employment outcomes for people with disabilities

Effects of prostaglandin E(2 )on the electrical properties of thermally classified neurons in the ventromedial preoptic area of the rat hypothalamus

BACKGROUND: Physiological and morphological evidence suggests that activation of the ventromedial preoptic area of the hypothalamus (VMPO) is an essential component of an intravenous LPS-dependent fever. In response to the endogenous pyrogen prostaglandin E(2 )(PGE(2)), the majority of temperature insensitive neurons in the VMPO show an increase in firing rate, while warm sensitive neurons are inhibited. We have hypothesized that these PGE(2 )dependent effects on firing rate are due to changes in the inherent electrical properties of VMPO neurons, which are regulated by the activity of specific ionic currents. RESULTS: To characterize the electrical properties of VMPO neurons, whole-cell recordings were made in tissue slices from male Sprague-Dawley rats. Our results indicate that PGE(2 )dependent firing rate responses were not the result of changes in resting membrane potential, action potential amplitude and duration, or local synaptic input. However, PGE(2 )reduced the input resistance of all VMPO neurons, while increasing the excitability of temperature insensitive neurons and decreasing the excitability of warm sensitive neurons. In addition, the majority of temperature insensitive neurons responded to PGE(2 )with an increase in the rate of rise of the depolarizing prepotential that precedes each action potential. This response to PGE(2 )was reversed for warm sensitive neurons, in which the prepotential rate of rise decreased. CONCLUSION: We would therefore suggest that PGE(2 )is having an effect on the ionic currents that regulate firing rate by controlling how fast membrane potential rises to threshold during the prepotential phase of the action potential

Adaptive Flight Control Design with Optimal Control Modification on an F-18 Aircraft Model

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to as the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly; however, a large adaptive gain can lead to high-frequency oscillations which can adversely affect the robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient robustness. A damping term (v) is added in the modification to increase damping as needed. Simulations were conducted on a damaged F-18 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) with both the standard baseline dynamic inversion controller and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model