<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>

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.

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. / QC 20101108

A computational tool that uses an automated and reliable procedure for systematic generation of global phase equilibrium diagram (GPED) is developed for binary system using equation of state and its extension to the ternary system is discussed. The proposed algorithm can handle solid phase and also can predict all major six types of phase diagrams. The procedure enables automatic generation of GPED which incorporates calculations of all important landmarks such as critical endpoints, quadruple point (if any), critical line, liquid-liquid-vapor line (if any), solid-liquid-liquid line (if any) and solid-liquid-vapor line. The method is also capable of locating all azeotropic phenomena such as azeotropic endpoint, critical azeotrope, pure azeotropic point and azeotropic lines. Although, we demonstrated the methodology for cubic equation of state, the proposed strategy is completely general that doesn't require any knowledge about the type of phase diagram and can be applied to any pressure explicit equation of state model. Newton homotopy based global method has been applied for phase stability test and critical point calculations to ensure reliability. Having computed the binary phase diagrams, the methodology to generate global phase diagrams for ternary system is discussed that can locate all important thermodynamic landmarks such as tricritical point, quadruple critical endpoint, quadruple azeotropic endpoint, quintuple point and critical azeotropic endpoint. The procedure to trace ternary phenomena having two degree of freedom such as critical surface, solid-liquid-vapor surface and liquid-liquid-vapor surface has been discussed. Finally, applications of reliable global methods to solve the fluid-fluid phase equilibrium problem using SAFT equation for binary system and the solid-fluid phase equilibrium problem for binary and ternary systems have been demonstrated through representative computations.