A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions

We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectral parameter. We further illustrate our approach by developing the basic algebro-geometric setting for the sGmKdV hierarchy, including Baker-Akhiezer functions, trace formulas, Dubrovin-type equations, and theta function representations for its algebro-geometric solutions. Although we mainly focus on sG-type equations, our formalism also yields the sinh-Gordon, elliptic sine-Gordon, elliptic sinh-Gordon, and Liouville-type equations combined with the mKdV hierarchy.Comment: LaTeX; emphasis put on the mKdV hierarch

STOCK MARKET VALUATIONS AND FOREIGN DIRECT INVESTMENT

We outline and test two theories of foreign direct investment based on capital market mispricing. The “cheap assets” or “fire-sale” theory considers FDI inflows as the purchase of undervalued host country assets, while the “cheap financial capital” theory views FDI outflows as a natural use of the relatively low-cost capital available to overvalued firms in the source country. The results are consistent with the cheap financial capital theory: FDI flows are unrelated to host country stock market valuations, as measured by the aggregate market-to-book-value ratio, but are strongly positively related to source country valuations and negatively related to future source country stock returns, especially when capital account restrictions limit cross-country arbitrage

Waves and patterning in developmental biology: vertebrate segmentation and feather bud formation as case studies

In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming cues and generate spatially heterogeneous patterns. We base our discussion around two well known patterning events that take place in the early embryo: somitogenesis and feather bud formation. We outline mathematical models to describe each patterning mechanism, present the results of numerical simulations and discuss the validity of each model in relation to our example patterning processes

Synchronous Online Philosophy Courses: An Experiment in Progress

There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class

February 7, 1945

Who\u27s Who of Enlisted Men spotlights CPL Archie Silver, base baker of General Mess; CPL Silver contributes a column himself about the recent doings in General Mess; pages 4 and 5 are (almost) full pages telling the steps taken in the production of the Observer, showing LT A.G. Thompson, PFC Pasquale Grosso, SGT Fritz Snyder, Jim Coghill, J.M. McLeod, Edward Goodin, CPL James Burns, and SGT Stanley Mikelk in action; and we meet WAC corporals & sisters Phyllis and Stella Stappler.https://digicom.bpl.lib.me.us/dowfieldobserver/1028/thumbnail.jp

Density and temperature of energetic electrons in the Earth's magnetotail derived from high-latitude GPS observations during the declining phase of the solar cycle

Single relativistic-Maxwellian fits are made to high-latitude GPS-satellite observations of energetic electrons for the period January 2006-November 2010; a constellation of 12 GPS space vehicles provides the observations. The derived fit parameters (for energies similar to 0.1-1.0 MeV), in combination with field-line mapping on the nightside of the magnetosphere, provide a survey of the energetic electron density and temperature distribution in the magnetotail between McIlwain L-values of L = 6 and L = 22. Analysis reveals the characteristics of the density-temperature distribution of energetic electrons and its variation as a function of solar wind speed and the Kp index. The density-temperature characteristics of the magnetotail energetic electrons are very similar to those found in the outer electron radiation belt as measured at geosynchronous orbit. The energetic electron density in the magnetotail is much greater during increased geomagnetic activity and during fast solar wind. The total electron density in the magnetotail is found to be strongly correlated with solar wind speed and is at least a factor of two greater for high-speed solar wind (V-SW = 500-1000 km s(-1)) compared to low-speed solar wind (V-SW = 100-400 km s(-1)). These results have important implications for understanding (a) how the solar wind may modulate entry into the magnetosphere during fast and slow solar wind, and (b) if the magnetotail is a source or a sink for the outer electron radiation belt

Climate-Mediated Nitrogen and Carbon Dynamics in a Tropical Watershed

Climate variability affects the capacity of the biosphere to assimilate and store important elements, such as nitrogen and carbon. Here we present biogeochemical evidence from the sediments of tropical Lake Titicaca indicating that large hydrologic changes in response to global glacial cycles during the Quaternary were accompanied by major shifts in ecosystem state. During prolonged glacial intervals, lake level was high and the lake was in a stable nitrogen-limited state. In contrast, during warm dry interglacials lake level fell and rates of nitrogen concentrations increased by a factor of 4–12, resulting in a fivefold to 24-fold increase in organic carbon concentrations in the sediments due to increased primary productivity. Observed periods of increased primary productivity were also associated with an apparent increase in denitrification. However, the net accumulation of nitrogen during interglacial intervals indicates that increased nitrogen supply exceeded nitrogen losses due to denitrification, thereby causing increases in primary productivity. Although primary productivity in tropical ecosystems, especially freshwater ecosystems, tends to be nitrogen limited, our results indicate that climate variability may lead to changes in nitrogen availability and thus changes in primary productivity. Therefore some tropical ecosystems may shift between a stable state of nitrogen limitation and a stable state of nitrogen saturation in response to varying climatic conditions