The Camassa-Holm Equation: Conserved Quantities and the Initial Value Problem

Using a Miura-Gardner-Kruskal type construction, we show that the Camassa-Holm equation has an infinite number of local conserved quantities. We explore the implications of these conserved quantities for global well-posedness.Comment: 8 pages, LaTe

Examining the Contributions of Glacial Till Water to Storm Runoff using Two- and Three-Component Hydrograph Separations

Two- and three-component hydrograph separations based on 18O and dissolved silica are used to investigate the contributions of glacial till water to the storm runoff of a headwater stream on the Canadian Shield. Two-component isotopic hydrograph separations based on 18O indicate that the volume and flux of event water could be accounted for by direct precipitation onto saturated areas. Three-component hydrograph separations distinguish between event water, preevent soil water, and preevent till water. These results show that groundwater flow through coarse-textured glacial tills can make a significant contribution to stream discharge during runoff events (29 and 62% in this study) despite the lower hydraulic conductivities of the tills compared to the overlying soils. The three-component hydrograph separations also demonstrate that the relative contributions of preevent soil water and preevent till water changed during one runoff event such that the average water chemistry of the preevent component varied during the event. Two-component hydrograph separations using dissolved silica indicate that seasonal changes in the till water contributions also occur and are related to groundwater levels. Measurements of vertical hydraulic gradients during runoff events indicate that the increase in flow from the tills to the soils is minimal and cannot account for the large and rapid increase in till water flow into the stream. Till water that has discharged to the soils prior to the event is probably being flushed from the soils into the stream during events

Optimal Design Of English Auctions With Discrete Bid Levels

This paper considers a form of ascending price English auction widely used in both live and online auctions. This discrete bid auction requires that the bidders submit bids at predetermined discrete bid levels, and thus, there exists a minimal increment by which the bid price may be raised. In contrast, the academic literature of optimal auction design deals almost solely with continuous bid auctions. As a result, there is little practical guidance as to how an auctioneer, seeking to maximize its revenue, should determine the number and value of these discrete bid levels, and it is this omission that is addressed here. To this end, a model of a discrete bid auction from the literature is considered, and an expression for the expected revenue of this auction is derived. This expression is used to determine both numerical and analytical solutions for the optimal bid levels, and uniform and exponential bidder’s valuation distributions are compared. Finally, the limiting case where the number of discrete bid levels is large is considered. An analytical expression for the distribution of the optimal discrete bid levels is derived, and an intuitive understanding of how this distribution maximizes the revenue of the auction is developed

P58IPK, a Plant Ortholog of Double-Stranded RNA-Dependent Protein Kinase PKR Inhibitor, Functions in Viral Pathogenesis

AbstractP58IPK is a cellular inhibitor of the mammalian double-stranded RNA-activated protein kinase (PKR). Here we provide evidence for the existence of its homolog in plants and its role in viral infection at the organism level. Viral infection of P58IPK-silenced Nicotiana benthamiana and Arabidopsis knockouts leads to host death. This host cell death is associated with phosphorylation of the α subunit of eukaryotic translation initiation factor (eIF-2α). Loss of P58IPK leads to reduced virus titer, suggesting that wild-type P58IPK protein plays an important role in viral pathogenesis. Although our complementation results using mammalian P58IPK suggest conservation of the P58IPK pathway in plants and animals, its biological significance seems to be different in these two systems. In animals, P58IPK is recruited by the influenza virus to limit PKR-mediated innate antiviral response. In plants, P58IPK is required by viruses for virulence and therefore functions as a susceptibility factor