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Quadratically Constrained Convex Quadratic Programmes., Wieslawa Teresa. Obuchowska
Quadratically Constrained Convex Quadratic Programmes., Wieslawa Teresa. Obuchowska
Electronic Theses and Dissertations
In this thesis we consider four problems arising from our study of quadratically constrained convex quadratic programmes (QCQP). The first problem concerns the representation of a quadratically constrained convex feasible region. We define the term "minimal representation" and give necessary and sufficient conditions for a representation to be minimal. The second problem deals with boundedness of quadratically constrained convex feasible regions. In particular, we provide necessary and sufficient conditions for unboundedness which are in the form of an algorithm which requires the identification of implicit equality constraints in homogeneous linear systems. The third problem is concerned with feasible regions which …
Simple Torsion Free C(,2)-Modules Having A 2-Dimensional Weight Space., Ling Chen
Simple Torsion Free C(,2)-Modules Having A 2-Dimensional Weight Space., Ling Chen
Electronic Theses and Dissertations
Let L denote a finite dimensional simple Lie algebra over the complex numbers $\doubc$ having a Cartan subalgebra ${\cal H}$. The classification of all simple ${\cal H}$-diagonalizable L-modules having all finite dimensional weight spaces is known to depend on determining the simple torsion free L-modules of finite degree. It is further known that the only simple Lie algebras which admit simple torsion free modules of finite degree are those of types A and C. For the case of $C\sb2$ we prove that every indecomposable torsion free $C\sb2$-module of degree 2 is simple and it is equivalent to a submodule of …