In Part I of this thesis, we locate a (conjecturally complete) set of unitary representations in the admissible dual of U(p, q). In a little more detail, Barbasch and Vogan have used the theory of Kazhdan-Lusztig cells to parametrize the irreducible Harish-Chandra modules with integral infinitesimal character in terms of their annihilators and associated varieties. Vogan has conjectured that th...

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise versa. Investigation of this phenomenon leads to a family of pairings involving standard, costandard and tilting modules. In the graded case, under some ”Kos...

The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...

This study proposes a vision-based intelligent nighttime driver assistance and surveillance system (VIDASS system) implemented by a set of embedded software components and modules, and integrates these modules to accomplish a component-based system framework on an embedded heterogamous dual-core platform. Therefore, this study develops and implements computer vision and sensing techniques of ni...

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise versa. Investigation of this phenomenon leads to a family of pairings involving standard, costandard and tilting modules. In the graded case, under some ”Kos...

Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valua...

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified...