Riesz s-Equilibrium Measures on d-Dimensional Fractal Sets as s Approaches d

Let $A$ be a compact set in \Rp of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $\mu^{s,A}$ is the unique Borel probability measure with support in $A$ that minimizes \Is(\mu):=\iint\Rk{x}{y}{s}d\mu(y)d\mu(x) over all such probability measures. In this paper we show that if $A$ is a strictly self-similar $d$-fractal, then $\mu^{s,A}$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below

The Allure of Technology: How France and California Promoted Electric Vehicles to Reduce Urban Air Pollution

All advanced industrialized societies face the problem of air pollution produced by motor vehicles. In spite of striking improvements in internal combustion engine technology, air pollution in most urban areas is still measured at levels determined to be harmful to human health. Throughout the 1990s and beyond, California and France both chose to improve air quality by means of technological innovation, adopting legislation that promoted clean vehicles, prominently among them, electric vehicles (EVs). In California, policymakers chose a technology-forcing approach, setting ambitious goals (e.g., zero emission vehicles), establishing strict deadlines and issuing penalties for non-compliance. The policy process in California called for substantial participation from the public, the media, the academic community and the interest groups affected by the regulation. The automobile and oil industries bitterly contested the regulation, in public and in the courts. In contrast, in France the policy process was non-adversarial, with minimal public participation and negligible debate in academic circles. We argue that California's stringent regulation spurred the development of innovative hybrid and fuel cell vehicles more effectively than the French approach. However, in spite of the differences, both California and France have been unable to put a substantial number of EVs on the road. Our comparison offers some broad lessons about how policy developments within a culture influence both the development of technology and the impact of humans on the environment.Environmental policy, Electric vehicles, Air pollution, Technology policy, Sustainable transport

Estimating the Number of Stable Configurations for the Generalized Thomson Problem

Given a natural number N, one may ask what configuration of N points on the two-sphere minimizes the discrete generalized Coulomb energy. If one applies a gradient-based numerical optimization to this problem, one encounters many configurations that are stable but not globally minimal. This led the authors of this manuscript to the question, how many stable configurations are there? In this manuscript we report methods for identifying and counting observed stable configurations, and estimating the actual number of stable configurations. These estimates indicate that for N approaching two hundred, there are at least tens of thousands of stable configurations.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-015-1245-

A sequence of discrete minimal energy configurations that does not converge in the weak-star topology

We demonstrate a set A and a value of s for which the sequence of N-point discrete minimal Riesz s-energy configurations on A does not have an asymptotic distribution in the weak-star sense as N tends to infinity

Portland presbyopia onset delay study

The Portland Presbyopia Onset Delay Study (PPODS), was designed to ascertain if nearpoint visual abilities responsible for comfortable, clear nearpoint vision can be improved through vision therapy (VT) for 35+ year old pre-presbyopes. Subjects were divided into two groups: a control group and a VT group. Four months of home based VT were prescribed. Procedures used were accommodative push-ups, loose lens tromboning , monocular lens rocks, binocular lens flips, distance rocks, eye stretches, and vergence stimulation. Improvement was seen in the vision therapy group as compared to the control group in increased vergence ranges, increased AC/A ratio, and increased accommodative facility. Accommodative amplitude was resistant to the therapeutic intervention, as was accommodative posture as measured by subjective cross grid techniques. Anecdotal comments from the VT subjects supported improved near point ability. Suggestions for further study are provided

Investigating The Retention Of Bright And Dark Ejecta From Small Rayed Craters On Mars

Thesis (Ph.D.) University of Alaska Fairbanks, 2010Impact cratering is one of the principal geologic processes operating throughout the solar system. On Mars, small rayed impact craters (SRC) form continuously and randomly on the surface. Ejecta retention, the timespan and ability of excavated ejecta to remain in place around a crater rim, records a lineage of recent surface processes. However, the timescales under which small rayed craters are produced and their origin, whether terrestrial or cosmic, plays an important role in further investigating surface processes and possible recent climate variations. By examining thousands of randomly chosen panchromatic images from the Mars Orbiter Camera Narrow Angle (MOCNA) camera, a population of 630 SRC was catalogued across three equatorial and two polar regions on Mars. The survey of MOCNA images also revealed intriguing Enigmatic Linear Features (ELFs) in the northern hemisphere of Mars, which a short side study revealed to be a unique form of dust-devil track. From statistically examining several physical parameters, dust deposition and periglacial erosion were found to be the major factors affecting ejecta retention for the SRC. SRC morphology revealed ejecta retention sequences that followed four stages of ejecta retention from the initial impact to eventual erasure from the surface. By reconstructing the current cratering rate from estimates of atmospheric filtering, it was possible to calculate the ejecta retention age across Mars. In general, SRC ejecta are retained on the surface for <100 ka. Based on ejecta morphology and retention age estimates, a possible shift from depositional to erosional processes just south of the Martian equator is suspected to have occurred within this timeframe

The Allure of Technology: How France and California Promoted Electric and Hybrid Vehicles to Reduce Urban Air Pollution

All advanced industrialized societies face the problem of air pollution produced by motor vehicles. In spite of striking improvements in internal combustion engine technology, air pollution in most urban areas is still measured at levels determined to be harmful to human health. Throughout the 1990s and beyond, California and France both chose to improve air quality by means of technological innovation, adopting legislation that promoted clean vehicles, prominently among them, electric vehicles (EVs). In California, policymakers chose a technology-forcing approach, setting ambitious goals (e.g., zero emission vehicles), establishing strict deadlines and issuing penalties for non-compliance. The policy process in California called for substantial participation from the public, the media, the academic community and the interest groups affected by the regulation. The automobile and oil industries bitterly contested the regulation, in public and in the courts. In contrast, in France the policy process was non-adversarial, with minimal public participation and negligible debate in academic circles. We argue that California\u27s stringent regulation spurred the development of innovative hybrid and fuel cell vehicles more effectively than the French approach. However, in spite of the differences, both California and France have been unable to put a substantial number of EVs on the road. Our comparison offers some broad lessons about how policy developments within a culture influence both the development of technology and the impact of humans on the environment. © Springer Science+Business Media, LLP 2007