Tur\`an numbers of Multiple Paths and Equibipartite Trees

The Tur\'an number of a graph H, ex(n;H), is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. Let P_l denote a path on l vertices, and kP_l denote k vertex-disjoint copies of P_l. We determine ex(n, kP_3) for n appropriately large, answering in the positive a conjecture of Gorgol. Further, we determine ex (n, kP_l) for arbitrary l, and n appropriately large relative to k and l. We provide some background on the famous Erd\H{o}s-S\'os conjecture, and conditional on its truth we determine ex(n;H) when H is an equibipartite forest, for appropriately large n.Comment: 17 pages, 13 figures; Updated to incorporate referee's suggestions; minor structural change

Urban water management: optimal price and investment policy under uncertainty

Australian urban water utilities face a significant challenge in designing appropriate demand management and supply augmentation policies in the presence of increasing water scarcity and uncertainty over future dam inflows. This paper considers the design of optimal demand management and supply augmentation policies for urban water. In particular, scarcity pricing is considered as a potential alternative to the predominant demand management policy of water restrictions. A stochastic dynamic programming model of an urban water market is developed based on data from the Australian Capital Territory. The model involves an explicit consideration of uncertainty via a probability distribution over dam inflows. Given a specification of the demand and supply for urban water, state dependent optimal price and investment policies are estimated. The results illustrate how the optimal urban water price varies inversely with the prevailing storage level and how the optimal timing of investment differs significantly between rain dependent and rain independent augmentation options.Public Economics, Resource /Energy Economics and Policy, Risk and Uncertainty,

Modeling the Mechanisms of the Photomechanical Response of a Nematic Liquid Crystal Elastomer

Recent studies of azo-dye doped liquid crystal elastomers show a strong photomechanical response. We report on models that predict experimental results that suggest photothermal heating is the dominant mechanism in a planar constrained geometry. We compare our models with experiments to determine key material parameters, which are used to predict the dynamical response as a function of intensity. We show that a local strain from photothermal heating and a nonlocal strain from thermal diffusion is responsible for the observed length changes over time. This work both elucidates the fundamental mechanisms and provides input for the design of photomechanical optical devices, which have been shown to have the appropriate properties for making smart materials.Comment: 7 Figures, 1 Tabl

Cascading of Liquid Crystal Elastomer Photomechanical Optical Devices

Photomechanical actuation is demonstrated in two coupled liquid crystal elastomer photomechanical optical devices (PODs) acting in series. The response function of an individual POD is characterized and used to predict the temporal response of the coupled system. The predicted coupled-system response agrees with the experiment for several waveforms and frequencies, suggesting that large-scale integration of photomechanical devices is possible.Comment: 4 pages, 4 figures, 1 tabl

Comparison of Aquatic-Insect Habitat and Diversity Above and Below Road Crossings in Low-Order Streams

The effects of road crossings on fish communities have been extensively studied; yet little attention has been given to macroinvertebrate communities. This study evaluated physical stream characteristics, water quality, and aquatic-insect richness from above and below road crossings of low-order streams in the Ouachita National Forest in Arkansas. Fifteen road crossings were sampled during October and November 2005. Erosion was significantly higher below road crossings than above. Sites downstream of road crossings had significantly lower pH and significantly higher turbidity than sites upstream of road crossings. Despite differences in water quality and habitat, there was no apparent difference in aquatic-insect richness from above and below road crossings based on the EPT index, suggesting that road crossings did not act as barriers to insect movement. The water-quality differences observed were well within acceptable limits and likely not biologically important

Thresholds for Pebbling on Grids

Given a connected graph $G$ and a configuration of $t$ pebbles on the vertices of G, a $q$-pebbling step consists of removing $q$ pebbles from a vertex, and adding a single pebble to one of its neighbors. Given a vector $\bf{q}=(q_1,\ldots,q_d)$, $\bf{q}$-pebbling consists of allowing $q_i$-pebbling in coordinate $i$. A distribution of pebbles is called solvable if it is possible to transfer at least one pebble to any specified vertex of $G$ via a finite sequence of pebbling steps. In this paper, we determine the weak threshold for $\bf{q}$-pebbling on the sequence of grids $[n]^d$ for fixed $d$ and $\bf{q}$, as $n\to\infty$. Further, we determine the strong threshold for $q$-pebbling on the sequence of paths of increasing length. A fundamental tool in these proofs is a new notion of centrality, and a sufficient condition for solvability based on the well used pebbling weight functions; we believe this weight lemma to be the first result of its kind, and may be of independent interest. These theorems improve recent results of Czygrinow and Hurlbert, and Godbole, Jablonski, Salzman, and Wierman. They are the generalizations to the random setting of much earlier results of Chung. In addition, we give a short counterexample showing that the threshold version of a well known conjecture of Graham does not hold. This uses a result for hypercubes due to Czygrinow and Wagner.Comment: 16 pages; comments are welcom

Multiple Points of Contact: Promoting Rural Postsecondary Preparation through School-Community Partnerships

Formal and informal partnerships between rural schools and their communities can provide a wide range of supports for all students, but particularly those from low-income families. In this analysis of six small rural school districts in Virginia we show how the broad participation of community groups and individuals supports academic achievement as well as preparation and aspirations for postsecondary education. Results demonstrate that school-community partnerships provide multiple points of contact for students that buttress the efforts of school personnel by extended educational opportunities outside the classroom and by meeting the needs of low-income students when parents and teachers are unable to do so

Therapeutic Phlebotomy Related to Polycythemia Vera and Hemochromatosis

This study looks at therapeutic phlebotomy as first-line treatment of blood disorders, including polycythemia vera and hemochromatosis. Some professionals prefer alternative treatments to phlebotomy