Properties Of Such Maps Research Articles

On the solvability of nonlinear noncompact operator equations

AbstractThe notion of (p, k)-epi mappings is introduced. The properties of such mappings are studied and the results obtained are applied to some differential equations.

On stability preserving mappings

We view systems as mappings which connect a set of inputs (input functions) with a set of outputs (output functions). Such systems are said to be stability preserving if a stable (asymptotically stable) reference input results in an output with the same stability properties. In the present paper we study the properties of such mappings, we establish a block diagram algebra for such mappings, and we relate the properties of such mappings to BIBO stability and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I/O</tex> continuity (in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_{\infty</tex> sense). We show how stability preserving mappings arise in some applications in a natural way.

Recent Sedimentation and the Search for Petroleum

The thesis of this paper is that sedimentary characteristics will become increasingly important in the search for oil. Emphasis is placed on the increase in quantification of sedimentary data; new and more complete studies of sedimentary environments; application of the techniques to ancient sediments; and the development and improvement of methods for recording the quantitative data in map form. A brief review is given of some trends in modern sedimentation, illustrated by particle roundness and sphericity, as an introduction to quantitative sedimentary studies. The viewpoint is extended to environments of sedimentation, approached as closed systems with boundary conditions, materials, and energy sources as the basic subjects of study. The data of quantitative environm ntal studies lend themselves to presentation on contour-type maps and surfaces, and some of the geometrical properties of such maps and surfaces are reviewed. A classification of maps is given, to indicate the wide range of sedimentary data both recent and ancient, suitable for presentation in this manner.