Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Technology Transfer in Forest Pest Management: A Case History

The current approach being used in the spruce budworm technology transfer program for the Lake States is described. During 1981-1982, we concentrated on needs assessment surveys and the development and packaging of materials in five areas: general manual, chemical control handbook, silviculture handbook, instruction manual for remote sensing workshops, and technical reports on budworm impact on spruce-fir stands. We present a list of factors that researchers and technology transfer specialists should consider when plan- ning a research and technology transfer program in forest pest management

The Economics of Spruce Budworm Outbreaks in the Lake States: An Overview

Economic effects of spruce budworm outbreaks in the Lake States were examined. The recent outbreak caused spruce and fir mortality on 420 thousand ha (I.OS million acres) of commercial forest land in the Lake States. Two models of Lake States spruce-fir markets were developed. A Static Economic Model established the nature of the Lake States spruce-fir market and a Comparative Static Model examined changes brought about by spruce budworm outbreaks. Outbreaks result in short-run supply shifts which probably decrease total revenue to stumpage owners but do not affect demand. The magnitude of long-run impacts were dependent on developing Lake States markets and forest management techniques. Further research is necessary on the value of short-run losses to stumpage owners so that the costs of forest management can be compared with outbreak losses. Long-run shifts in demand can be facilitated by attracting new industry to the area, developing new markets for the spruce-fir resource, and demonstrating that the spruce-fir resource can provide a continuous fiber source in the future. These shifts would provide the price incentives that land managers require to undertake intensive forest management. Research on the development of new markets for the spruce-fir resource is needed. As markets develop, the long-run impacts become less severe. Technology transfer programs already exist to aid land managers in developing management strategies to increase yields of spruce-fir and minimize outbreak impact

Letter dated from G. A. Montgomery to W. S. Featherston. 26 January 1888

Letter sent from Rosedale, Mississippi; regarding lands claimed by children, lands bought by the railroads. Envelope.https://egrove.olemiss.edu/ciwar_corresp/1286/thumbnail.jp

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Maternal smoking during pregnancy and appetite control in offspring

Aims: Intrauterine exposure to tobacco smoke products has been associated with long-term neurobehavioral effects. Modified appetite control might explain the recently observed association between maternal smoking during pregnancy and obesity in offspring. Methods: Some 10,557 British adults aged 42 years born between 3-9 March 1958 were followed up in a birth cohort study (NCDS). The main outcome measure was self-reported poor appetite at age 42 years and main exposure was maternal smoking during pregnancy. Results: The proportion of offspring with poor appetite increased with maternal smoking during pregnancy: nonsmoking 4.5%; (4.0% - 5.0%), medium smoking 5.6%; (4.5 % - 6.8 %), variable smoking 6.8 %; (4.9 % - 9.1 %) and heavy smoking 7.7 %; (6.3 % - 9.4 %). The unadjusted odds ratios for maternal smoking during pregnancy (ever/never) and poor appetite is 1.49 (1.25 - 1.77) and after adjustment for BMI at 42 years and other potential confounding factors it is 1.22 (1.07 - 1.48). Conclusions: Offspring of mothers who smoked during pregnancy were more likely to report a poor appetite independent of a number of potential confounding factors. Although not in the expected direction, the results suggest maternal smoking during pregnancy may influence appetite perception through a developmental influence or through confounding by social factors

Lipid droplet detection by the cavity perturbation method

There are currently no point-of-care diagnosis strategies available to indicate the presence of neoplasmic growth. This research aims to develop a novel diagnostic strategy based on detecting TAG accumulation in cells. This element of the research is a preliminary experiment to prove the concept of detecting TAG lipid droplets in YEPD media. It was found that a change in mono-unsaturated concentration can be detected by the frequency shift in a resonant cavity. The dielectric constant of TAG vegetable oils was calculated at 2.34-2.39. It was also found that concentrations of lipid droplet can be differentiated up to 5% (v/v)

Spontaneous creation of non-zero angular momentum modes in tunnel-coupled two-dimensional degenerate Bose gases

We investigate the dynamics of two tunnel-coupled two-dimensional degenerate Bose gases. The reduced dimensionality of the clouds enables us to excite specific angular momentum modes by tuning the coupling strength, thereby creating striking patterns in the atom density profile. The extreme sensitivity of the system to the coupling and initial phase difference results in a rich variety of subsequent dynamics, including vortex production, complex oscillations in relative atom number and chiral symmetry breaking due to counter-rotation of the two clouds.Comment: 7 pages, 5 figure

On multiplicative functions which are small on average

Let $f$ be a completely multiplicative function that assumes values inside the unit disc. We show that if \sum_{n2, for some $A>2$, then either $f(p)$ is small on average or $f$ pretends to be $\mu(n)n^{it}$ for some $t$.Comment: 51 pages. Slightly strengthened Theorem 1.2 and simplified its statement. Removed Remark 1.3. Other minor changes and corrections. To appear in Geom. Funct. Ana