Principal Solutions Revisited

The main objective of this paper is to identify principal solutions associated with Sturm-Liouville operators on arbitrary open intervals $(a,b) \subseteq \mathbb{R}$, as introduced by Leighton and Morse in the scalar context in 1936 and by Hartman in the matrix-valued situation in 1957, with Weyl-Titchmarsh solutions, as long as the underlying Sturm-Liouville differential expression is nonoscillatory (resp., disconjugate or bounded from below near an endpoint) and in the limit point case at the endpoint in question. In addition, we derive an explicit formula for Weyl-Titchmarsh functions in this case (the latter appears to be new in the matrix-valued context).Comment: 27 pages, expanded Sect. 2, added reference

Studies of the scattering/absorption of minerals

Reflectance spectra were computed for water ice and ammonia ice mixtures as functions of weight fraction, grain size, and viewing geometry to simulate possible outer solar system satellite surfaces. Reflectance spectra of planetary surfaces are most affected by the weight fraction and grain sizes of the minerals in the surface. The reflectance can range from 1.0 to about 0.01 by changing the grain size or weight fraction, a factor of 100. Viewing geometry changes the reflectance by about 25 percent or less

Causes of spurious features in spectral reflectance data

Several techniques are becoming common in the analysis of imaging spectrometer data that can lead to spurious absorption features or to changes in the position, width, and shape of actual absorption features. It is a common practice to calibrate AIS or other imaging spectrometer data by averaging each pixel along the flight line. The average is used to calibrate the spectral data by dividing the spectrum at each pixel by the average. If some pixels in the data set contain an absorption, then the average will also show an absorption. Some AIS data has had problems with wavelength stability from one scan line to the next which can produce spurious features with some analysis methods. If a pixel has a spectrum with an absorption having a different position or width than the spectrum used in a ratio, then the ratio can produce a spurious absorption at a different position and width than the true absorption feature. An average spectrum ratioed to each pixel will produce band shifts, and changes in width or shape. If continuum removal is performed by substraction rather than division, band positions can also be shifted

ASSESSING THE RISKS OF A FUTURE RAPID LARGE SEA LEVEL RISE: A REVIEW

Our aim is to make an appropriate characterization and interpretation of the risk problem of rapid large sea level rise that reflects the very large uncertainty in present day knowledge concerning this possibility, and that will be useful in informing discussion about risk management approaches. We consider mainly the potential collapse of the West Antarctic ice sheet as the source of such a sea level rise. Our review, characterization and interpretation of the risk makes us conclude that the risk of a rapid large sea level rise is characterized by potentially catastrophic consequences and high epistemic uncertainty; effective risk management must involve highly adaptive management regimes, vulnerability reduction, and prompt development of capabilities for precautionary reduction of climate change forcings.sea level rise, West Antarctic ice sheet, climate change, adaptive management, epistemic uncertainty, risk management arenas, vulnerability