Acoustic Scattering and the Extended Korteweg deVries hierarchy

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa-Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.Comment: 18 page

Digital land use mapping in Oakland County, Michigan

ERTS-1 data for a portion of Oakland County, Michigan was computer processed to produce a map of water, urban areas, wooded areas, and other vegetation. Comparison with RB-57 photography of the area shows a good correspondence of the two sources of data. Preliminary evaluation indicates that this type of four-category map derived from ERTS data will be useful for conceptual studies of large geographic areas in recreational planning

Action-Angle variables for the Gel'fand-Dikii flows

Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side. Action-angle variables are then constructed. Using this, complete integrability is demonstrated in the strong sense. Real action-angle variables are constructed in the self-adjoint case

Analysis of recreational land and open space using ERTS-1 data

There are no author-identified significant results in this report

Some economic benefits of a synchronous earth observatory satellite

An analysis was made of the economic benefits which might be derived from reduced forecasting errors made possible by data obtained from a synchronous satellite system which can collect earth observation and meteorological data continuously and on demand. User costs directly associated with achieving benefits are included. In the analysis, benefits were evaluated which might be obtained as a result of improved thunderstorm forecasting, frost warning, and grain harvest forecasting capabilities. The anticipated system capabilities were used to arrive at realistic estimates of system performance on which to base the benefit analysis. Emphasis was placed on the benefits which result from system forecasting accuracies. Benefits from improved thunderstorm forecasts are indicated for the construction, air transportation, and agricultural industries. The effects of improved frost warning capability on the citrus crop are determined. The benefits from improved grain forecasting capability are evaluated in terms of both U.S. benefits resulting from domestic grain distribution and U.S. benefits from international grain distribution

Remote sensing in Michigan for land resource management

An extensive program was conducted to establish practical uses of NASA earth resource survey technology in meeting resource management problems throughout Michigan. As a result, a broad interest in and understanding of the usefulness of remote sensing methods was developed and a wide variety of applications was undertaken to provide information needed for informed decision making and effective action

Multipeakons and a theorem of Stieltjes

A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scattering shifts.Comment: 6 page