<p>Let X be a smooth projective variety over C equipped with a C*-action whose fixed points are isolated. Let Y and Z be subvarieties of complementary dimentions in X which intersect properly. In this thesis we present an algorithm for computing the points of intersection between Y and Z based on homotopy continuation and the Bialynicki-Birula decompositions of X into locally closed invariant subsets. As an application we present a new solution to the inverse kinematic problem of a general six-revolute serial-link manipulator.</p>

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 154-157). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 154-157). Also available on the Internet.

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Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains vi, 77 p. Includes abstract. Includes bibliographical references (p. 75-77). WVU users: Also available in print for a fee.

Thesis (M.A. in Education)--University of Calif., May 1920. / Bibliography: p. 122-124.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 76-79). Also available on the Internet.

In this thesis, applications of a numerical continuation method to two- and three-dimensional bifurcation problems are presented. The 2D problems are motivated by solar applications. In particular, it is shown that the bifurcation properties of a previously studied model for magnetic arcades depend strongly on the pressure function used in the model. The bifurcation properties of a straight flux model for coronal loops are investigated and compared with the results of linear ideal MHD stability analysis. It is shown that for line-tied boundary conditions, the method for the calculation of the equilibrium sequence determines whether the first or the second bifurcation point coincides with the linear stability threshold. Also, in this thesis, the 3D version of the continuation code is applied for the first time. The problems treated with the 3D code are therefore chosen with the intention to demonstrate the general capabilities of the code and to see where its limitations are. Whereas the code performs as expected for relatively simple albeit nonlinear bifurcation problems, a clear need for further development is shown by more involved problems.

Abstract This thesis describes part of the work that has been done in the Chemical Process Engineering Laboratory of the University of Oulu to systematize conceptual process design. The aim has been to develop a design methodology, i.e. how process design is done, based on a carefully elaborated concept analysis. The starting point has been that all the knowledge related to process design, i.e. not only the procedural knowledge related to the design activity itself, but also the declarative knowledge related to the design target (process) and the environment (project) in which the design is done, should be systematized. The process design methodology can be represented within a single formalism by treating the activity, target and resources as structural parts of the project object. In that case, each design decision becomes properly constrained by the goal and the resources available, and is also stored together with the domain knowledge on which the decision was based. This holistic approach was adopted when the phenomenon driven process design methodology was built to systematize chemical process development while simultaneously supporting creativity. This thesis concentrates on knowledge generation activity as part of the phenomenon driven process design methodology. A brief description of the generic chemical process object model is presented, after which the focus is on the design activity and the strategy of design. The phenomenon driven process design of an MTBE production process is described as an illustration of the methodology. It is shown how combinations of reaction and separation, such as reactive distillation, evolve naturally during a design project. For the evaluation of attainable state distributions, which is an important design task implied by the methodology, a robust method was developed to solve the modified MESH equations of reactive distillation. The method was also applied when developing a rigorous calculation method for the determination of minimum energy demand of multicomponent distillation.