Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.

No description available.

by Kin-Ming Liu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 66-67. / Chapter §0 --- Introduction / Chapter §1 --- Preliminaries and notations / Chapter §2 --- A summary on ultra-(DF)-spaces and order-ultra-（DF)-spaces / Chapter §3 --- " ""Dual"" properties between projective and inductive topologies in topological vector spaces" / Chapter §4 --- Application of barrelledness on continuity of bilinear mappings and projective tensor product / Chapter §5 --- Countably order-quasiultrabarrelled spaces

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf. 29.

Chan Ka Wo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 114-118). / Abstracts in English and Chinese. / Introduction --- p.iii / Conventions of This Thesis --- p.vi / Prerequisites --- p.xiii / Chapter 1 --- Cones in Real Vector Spaces --- p.1 / Chapter 1.1 --- The Fundamentals of Cones --- p.2 / Chapter 1.2 --- Enlargements of a Cone --- p.22 / Chapter 1.3 --- Special Cones in Real Vector Spaces --- p.29 / Chapter 1.3.1 --- Positive Cones --- p.29 / Chapter 1.3.2 --- Bishop-Phelps Cones --- p.36 / Chapter 1.3.3 --- Quasi-Bishop-Phelps Cones --- p.42 / Chapter 1.3.4 --- Quasi*-Bishop-Phelps Cones --- p.45 / Chapter 1.3.5 --- Gallagher-Saleh D-cones --- p.47 / Chapter 2 --- Generalizations in Topological Vector Spaces --- p.52 / Chapter 2.1 --- Efficiency and Positive Proper Efficiency --- p.54 / Chapter 2.2 --- Type I Generalizations --- p.71 / Chapter 2.3 --- Type II Generalizations --- p.82 / Chapter 2.4 --- Type III Generalizations --- p.92 / Chapter 3 --- Generalizations in Dual Spaces --- p.97 / Chapter 3.1 --- Weak*-Support Points of a Set --- p.98 / Chapter 3.2 --- Generalizations in the Dual Space of a General Normed Space --- p.100 / Chapter 3.3 --- Generalizations in the Dual Space of a Banach Space --- p.104 / Epilogue: Glimpses Beyond --- p.112 / Bibliography --- p.114

Chee Shiu Chung = 阻尼振子的線空間結構與哈密頓理論 / 朱兆中. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 88). / Text in English; abstracts in English and Chinese. / Chee Shiu Chung = Zu ni zhen zi de xian kong jian jie gou yu ha mi dun li lun / Zhu Zhaozhong. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Conservative Systems --- p.4 / Chapter 2.1 --- General Formalism --- p.4 / Chapter 2.2 --- One Simple Harmonic Oscillator --- p.7 / Chapter 2.3 --- Two Coupled Harmonic Oscillators --- p.9 / Chapter 3 --- Dissipative Systems --- p.12 / Chapter 3.1 --- Elimination of Bath --- p.12 / Chapter 3.2 --- One Oscillator with Dissipation --- p.16 / Chapter 3.3 --- Two Oscillators with Dissipation --- p.19 / Chapter 4 --- Eigenvector Expansion and Bilinear Map --- p.21 / Chapter 4.1 --- Formalism --- p.21 / Chapter 4.2 --- Inner Product and Bilinear Map --- p.23 / Chapter 4.3 --- Normalization and Phase --- p.25 / Chapter 4.4 --- Matrix Representation --- p.25 / Chapter 4.5 --- Duality --- p.28 / Chapter 5 --- Applications and Examples of Eigenvector Expansion --- p.31 / Chapter 5.1 --- Single Oscillator --- p.31 / Chapter 5.2 --- Two Oscillators --- p.32 / Chapter 5.3 --- Uneven Damping --- p.33 / Chapter 6 --- Time Evolution --- p.36 / Chapter 6.1 --- Initial-Value Problem --- p.36 / Chapter 6.1.1 --- Green's Function --- p.37 / Chapter 6.2 --- Sum Rules --- p.39 / Chapter 7 --- Time-Independent Perturbation Theory --- p.41 / Chapter 7.1 --- Non-degenerate Perturbation --- p.41 / Chapter 7.2 --- Degenerate Perturbation Theory --- p.46 / Chapter 8 --- Jordan Block --- p.48 / Chapter 8.1 --- Jordan Normal Basis --- p.48 / Chapter 8.1.1 --- Construction of Basis Vectors --- p.48 / Chapter 8.1.2 --- Bilinear Map --- p.50 / Chapter 8.1.3 --- Example of Jordan Normal Basis --- p.55 / Chapter 8.2 --- Time Evolution --- p.56 / Chapter 8.2.1 --- Time Dependence of Basis Vectors --- p.56 / Chapter 8.2.2 --- Initial-Value Problem --- p.58 / Chapter 8.2.3 --- Green's Function --- p.59 / Chapter 8.2.4 --- Sum Rules --- p.60 / Chapter 8.3 --- Jordan Block Perturbation Theory --- p.61 / Chapter 8.3.1 --- Lowest Order Perturbation --- p.61 / Chapter 8.3.2 --- Higher-Order Perturbation --- p.65 / Chapter 8.3.3 --- Non-generic Perturbations --- p.66 / Chapter 8.4 --- Examples of High-Order Criticality --- p.66 / Chapter 8.4.1 --- Fourth-order JB --- p.67 / Chapter 8.4.2 --- Third-order JB --- p.74 / Chapter 8.4.3 --- Two Second-order JB --- p.79 / Chapter 9 --- Conclusion --- p.81 / Chapter A --- Appendix --- p.83 / Chapter A.l --- Fourier Transform and Contour Integration --- p.83 / Chapter B --- Degeneracy and Criticality --- p.86 / Bibliography --- p.88

Fan, Sin Tsun Edward. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 85-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Motivation --- p.5 / Chapter 1.2 --- Main results --- p.10 / Chapter 2 --- Preliminaries --- p.14 / Chapter 2.1 --- Z-gradations of Semisimple Lie Algebras --- p.14 / Chapter 2.2 --- Basic Facts about Algebraic Groups --- p.15 / Chapter 3 --- Weight Multiplicity Free Representations and Pre- homogeneous Vector Spaces --- p.18 / Chapter 3.1 --- Weight Multiplicity Free Representations --- p.18 / Chapter 3.2 --- Prehomogeneous Vector Spaces --- p.22 / Chapter 4 --- Augmentations of Dynkin Diagrams --- p.25 / Chapter 5 --- Orbit Finiteness and Prehomogeneity --- p.32 / Chapter 6 --- Termination of Z-grading --- p.36 / Chapter 7 --- Explicit Construction of Generic Elements in Simply- laced Cases --- p.42 / Chapter 8 --- The Ambient Lie Algebras of Parabolic PVS's --- p.47 / Chapter 9 --- PVS's of Twisted Affine Type --- p.52 / Chapter 10 --- "Orbit Structure of (GL2 x SL2m+1,C2 x A2C2m+1)" --- p.55 / Chapter 11 --- Nilvarieties and Generalisation of Open Orbits --- p.59 / Chapter 11.1 --- Nilvarieties and Visible Representations --- p.59 / Chapter 11.2 --- Augmeantations of Affine Dynkin Diagrams --- p.62 / Chapter 11.3 --- Classification of Irreducible Visible Representations --- p.67 / Chapter 12 --- Real Forms of PVS of Parabolic Type --- p.70 / Chapter 12.1 --- Representations of Real Reductive Lie Algebras and Satake Diagrams --- p.70 / Chapter 12.2 --- Real Forms of PVS of Parabolic Type --- p.77 / Chapter 13 --- Tables --- p.81 / Bibliography --- p.85

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 103-107). Available also in a digital version from Dissertation Abstracts.

No description available.

Typescript. / Thesis (Ph. D.)--University of Hawaii, 1971. / Bibliography: leaves 73-74. / vi, 74 l