On isoperimetric inequalities with respect to infinite measures

We study isoperimetric problems with respect to infinite measures on $R ^n$. In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$, we prove that, among all sets with given $\mu-$measure, the ball centered at the origin has the smallest (weighted) $\mu-$perimeter. Our results are then applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems and a comparison result for elliptic boundary value problems.Comment: 25 page

The Kindergarten Rule of Sustainable Growth

The relationship between economic growth and the environment is not well understood: we have only limited understanding of the basic science involved and very limited data. Because of these difficulties it is especially important to develop a series of relatively simple theoretical models that generate stark predictions. This paper presents one such model where societies implement the Kindergarten rule of sustainable growth.' Following the Kindergarten rule means implementing zero emission technologies in either finite time or asymptotically. The underlying simplicity of the model allows us to provide new predictions linking the path of environmental quality to pollutant characteristics (stocks vs. flows; toxics vs. irritants) and primitives of the economic system. It also provides a novel Environmental Catch-up Hypothesis.

Economic Growth and the Environment: A Review of Theory and Empirics

This paper reviews both theory and empirical work on economic growth and the environment. We develop four simple growth models to help us identify key features generating sustainable growth. We show how some combination of technological progress in abatement, intensified abatement, shifts in the composition of national output and induced innovation are necessary for sustainable growth, and then demonstrate how growth models employing any one of these mechanisms generate other potentially refutable predictions on abatement costs, pollution levels, or emission intensities.

Simple versus optimal rules as guides to policy

This paper contributes to the policy evaluation literature by developing new strategies to study alternative policy rules. We compare optimal rules to simple rules within canonical monetary policy models. In our context, an optimal rule represents the solution to an intertemporal optimization problem in which a loss function for the policymaker and an explicit model of the macroeconomy are specified. We define a simple rule to be a summary of the intuition policymakers and economists have about how a central bank should react to aggregate disturbances. The policy rules are evaluated under minimax and minimax regret criteria. These criteria force the policymaker to guard against a worst-case scenario, but in different ways. Minimax makes the worst possible model the benchmark for the policymaker, while minimax regret confronts the policymaker with uncertainty about the true model. Our results indicate that the case for a model-specific optimal rule can break down when uncertainty exists about which of several models is true. Further, we show that the assumption that the policymaker’s loss function is known can obscure policy trade-offs that exist in the short, medium, and long run. Thus, policy evaluation is more difficult once it is recognized that model and preference uncertainty can interact.

Determining the Probability of Violating Upper-Level Wind Constraints for the Launch of Minuteman Ill Ballistic Missiles At Vandenberg Air Force Base

The 30th Operational Support Squadron Weather Flight (30 OSSWF) provides comprehensive weather services to the space program at Vandenberg Air Force Base (VAFB) in California. One of their responsibilities is to monitor upper-level winds to ensure safe launch operations of the Minuteman Ill ballistic missile. The 30 OSSWF requested the Applied Meteorology Unit (AMU) analyze VAFB sounding data to determine the probability of violating (PoV) upper-level thresholds for wind speed and shear constraints specific to this launch vehicle, and to develop a graphical user interface (GUI) that will calculate the PoV of each constraint on the day of launch. The AMU suggested also including forecast sounding data from the Rapid Refresh (RAP) model. This would provide further insight for the launch weather officers (LWOs) when determining if a wind constraint violation will occur over the next few hours, and help to improve the overall upper winds forecast on launch day

Time Dependent Clustering Analysis of the Second BATSE Gamma-Ray Burst Catalog

A time dependent two-point correlation-function analysis of the BATSE 2B catalog finds no evidence of burst repetition. As part of this analysis, we discuss the effects of sky exposure on the observability of burst repetition and present the equation describing the signature of burst repetition in the data. For a model of all burst repetition from a source occurring in less than five days we derive upper limits on the number of bursts in the catalog from repeaters and model-dependent upper limits on the fraction of burst sources that produce multiple outbursts.Comment: To appear in the Astrophysical Journal Letters, uuencoded compressed PostScript, 11 pages with 4 embedded figure

Transport in Transitory, Three-Dimensional, Liouville Flows

We derive an action-flux formula to compute the volumes of lobes quantifying transport between past- and future-invariant Lagrangian coherent structures of n-dimensional, transitory, globally Liouville flows. A transitory system is one that is nonautonomous only on a compact time interval. This method requires relatively little Lagrangian information about the codimension-one surfaces bounding the lobes, relying only on the generalized actions of loops on the lobe boundaries. These are easily computed since the vector fields are autonomous before and after the time-dependent transition. Two examples in three-dimensions are studied: a transitory ABC flow and a model of a microdroplet moving through a microfluidic channel mixer. In both cases the action-flux computations of transport are compared to those obtained using Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy

Studying Attractor Symmetries by Means of Cross Correlation Sums

We use the cross correlation sum introduced recently by H. Kantz to study symmetry properties of chaotic attractors. In particular, we apply it to a system of six coupled nonlinear oscillators which was shown by Kroon et al. to have attractors with several different symmetries, and compare our results with those obtained by ``detectives" in the sense of Golubitsky et al.Comment: LaTeX file, 16 pages and 16 postscript figures; tarred, gzipped and uuencoded; submitted to 'Nonlinearity