Organisational niche boundaries in the n-space

The paper investigates organizational boundary spanning from the point of view of neighborhood relations. Neighborhood is defined with the closeness of organizations' resource utilization patterns. The key resource is the clientele's demand for organizational outputs (products, party programs, membership, etc.). Demand is characterized qualitatively by n taste descriptors that span an n-dimensional resource space. Organizational niche boundaries may take different forms and size. To avoid niche overlap over boundaries, organizations can configure in the resource space in different clusterings. Which are the densest arrangements that allow for the coexistence of maximal number of organizations? How can these coexisting neighborhoods build up? How do competition, new entry and the number of immediate neighbors change around the niche boundary with space dimension? The paper applies results of the sphere packing problem in n-dimensional geometry to answer these questions.

Plastic deformation mechanisms in polyimide resins and their semi-interpenetrating networks

High-performance thermoset resins and composites are critical to the future growth of space, aircraft, and defense industries in the USA. However, the processing-structure-property relationships in these materials remain poorly understood. In the present ASEE/NASA Summer Research Program, the plastic deformation modes and toughening mechanisms in single-phase and multiphase thermoset resins were investigated. Both thermoplastic and thermoset polyimide resins and their interpenetrating networks (IPNs and semi-IPNs) were included. The fundamental tendency to undergo strain localization (crazing and shear banding) as opposed to a more diffuse (or homogeneous) deformation in these polymers were evaluated. Other possible toughening mechanisms in multiphase thermoset resins were also examined. The topological features of network chain configuration/conformation and the multiplicity of phase morphology in INPs and semi-IPNs provide unprecedented opportunities for studying the toughening mechanisms in multiphase thermoset polymers and their fiber composites

Space environmental effects on polymers and composites

The response of polymers and polymer-based composites to the space environment is being investigated. A wide range of materials are covered in this study, including elastometer seals for Space Station Freedom, polymer films for thermal control, and composites for space structural elements. Space environmental agents of concern include atomic oxygen, thermal cycling, space debris impacts, UV, charged particles and other forms of high-energy radiation. This ambitious project is potentially a multi-year research effort and the success of such a project could be expected to have a profound impact on the design of future space-based structures. The research goal of this first Summer is to identify the priority areas of research and to carry out the initial phase task so that a collaborative research can proceed smoothly and fruitfully in the near future

Roots of bivariate polynomial systems via determinantal representations

We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-parameter eigenvalue problem. The first determinantal representation is suitable for polynomials with scalar or matrix coefficients, and consists of matrices with asymptotic order $n^2/4$, where $n$ is the degree of the polynomial. The second representation is useful for scalar polynomials and has asymptotic order $n^2/6$. The resulting method to compute the roots of a system of two bivariate polynomials is competitive with some existing methods for polynomials up to degree 10, as well as for polynomials with a small number of terms.Comment: 22 pages, 9 figure