Causal and Stable Input/Output Structures on Multidimensional Behaviours

In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable called "time". We define in a natural way causality and stability on input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the Pc operator defining the behaviour (Bc)0,y We also quote results which in effect characterise time autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix. We prove this result for the 2D case and for the case of a single equation; for the general case it requires solution of an open problem concerning the geometry of a particular set in Cn. In order to characterize input/output stability we also develop new results on inclusions of kernels, freeness of variables, and closure with respect to S,S' and associated spaces, which are of independent interest. We also discuss stability of autonomous behaviours, which we beleive to be governed by a corresponding condition

Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

Production of a water quality map of Saginaw Bay by computer processing of LANDSAT-2 data

Surface truth and LANDSAT measurements collected July 31, 1975, for Saginaw Bay were used to demonstrate a technique for producing a color coded water quality map. On this map, color was used as a code to quantify five discrete ranges in the following water quality parameters: (1) temperature, (2) Secchi depth, (3) chloride, (4) conductivity, (5) total Kjeldahl nitrogen, (6) total phosphorous, (7)chlorophyll a, (8) total solids and (9) suspended solids. The LANDSAT and water quality relationship was established through the use of a set of linear regression equations where the water quality parameters are the dependent variables and LANDSAT measurements are the independent variables. Although the procedure is scene and surface truth dependent, it provides both a basis for extrapolating water quality parameters from point samples to unsampled areas and a synoptic view of water mass boundaries over the 3000 sq. km bay area made from one day's ship data that is superior, in many ways, to the traditional machine contoured maps made from three day's ship data

Computer Mapping of Water Quality in Saginaw Bay with LANDSAT Digital Data

The author has identified the following significant results. LANDSAT digital data and ground truth measurements for Saginaw Bay (Lake Huron), Michigan, for 31 July 1975 were correlated by stepwise linear regression and the resulting equations used to estimate invisible water quality parameters in nonsampled areas. Chloride, conductivity, total Kjeldahl nitrogen, total phosphorus, and chlorophyll a were best correlated with the ratio of LANDSAT Band 4 to Band 5. Temperature and Secchi depth correlate best with Band 5

Automatic classification of eutrophication of inland lakes from spacecraft data

The author has identified the following significant results. Spacecraft data and computer techniques can be used to rapidly map and store onto digital tapes watershed land use information. Software is now available by which this land use information can be rapidly and economically extracted from the tapes and related to coliform counts and other lake contaminants (e.g. phosphorus). These tools are basic elements for determining those land use factors and sources of nutrients that accelerate eutrophication in lakes and reservoirs

The super-oscillating superlens

We demonstrate a lens that creates a sub-wavelength focal spot beyond the near-field by exploiting the phenomenon of super-oscillation

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Application of LANDSAT to the surveillance of lake eutrophication in the Great Lakes basin

The author has identified the following significant results. A step-by-step procedure for establishing and monitoring the trophic status of inland lakes with the use of LANDSAT data, surface sampling, laboratory analysis, and aerial observations were demonstrated. The biomass was related to chlorophyll-a concentrations, water clarity, and trophic state. A procedure was developed for using surface sampling, LANDSAT data, and linear regression equations to produce a color-coded image of large lakes showing the distribution and concentrations of water quality parameters, causing eutrophication as well as parameters which indicate its effects. Cover categories readily derived from LANDSAT were those for which loading rates were available and were known to have major effects on the quality and quantity of runoff and lake eutrophication. Urban, barren land, cropland, grassland, forest, wetlands, and water were included