Selection and Scheduling of Advanced Missions for NASA Using 0-1 Integer Linear Programming

A 0-1 integer linear programme for the selection and scheduling of US National Aeronautics and Space Administration (NASA) missions over a long planning horizon is presented. This model was formulated to allow a higher-level user-interaction with an advanced missions database currently being developed. The model implicitly considers the multi-objective nature of the problem, which results from the desire to maximize benefits in several categories as well as from the desire to minimize cost. In addition, the model allows the planner much flexibility in the selection process. This is accomplished by allowing the planner the ability to specify long- or short-term budget constraints, precursor/follow-on mission requirements, or any number of other idiosyncratic constraints which might be of importance in the decision process. Small example problems are solved in order to illustrate the approach, and areas for further research are discussed.     

The influence of the oxygen exposure on the thermal faceting of W[1 1 1] tip

The oxygen induced faceting of the macroscopic W[1 1 1] tip has been studied for oxygen exposures in the range 0.5-31 L and annealing temperatures 800-1800 K using the field ion microscopy (FIM) technique. After annealing at temperatures lower than 800 K, higher than 1850 K or for exposures lower than 0.5 L faceting was not observed. For exposures 0.5-1.9 L and annealing temperatures 800-1600 K well developed {1 1 2} facets with sharp edges formed. For exposures higher than 2.0 L edges of the {1 1 2} facets were broadening and disappearing, what has been attributed to the formation of three-dimensional tungsten oxides. The oxides could be easily removed by annealing the tip at 1700 K, what leads to formation of sharp facet edges. On the basis of these results a modified procedure of the ultrasharp tip fabrication has been proposed.     

On false branch points of incompressible branched immersions

We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.Work done while the first author was a visiting member of the Max-Planck-Institut für Mathematik at Bonn. Both authors acknowledge the support of Max-Planck-Institut für Mathematik, Bonn and Schwerpunkt Geometrie at Mathematisches Institut, University of Heidelberg     

Differential form methods in the theory of variational systems and Lagrangian field theories

This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation.     

Asymptotic expansions for renewal measures in the plane

Summary Let P be a distribution in the plane and define the renewal measure R=P ^*nwhere * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.Research supported by NSF grants MCS-8102080 and DMS-8504708