Thesis (Ph.D.)--York University, 2008. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 102-108). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR51694

published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Wong Chun Wai Carto. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-80). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- The Probabilistic Approach --- p.9 / Chapter 2.1 --- Diffusion on the Sierpinski gasket --- p.9 / Chapter 2.2 --- A Laplacian from the diffusion process --- p.18 / Chapter 2.3 --- Other ramifications --- p.24 / Chapter 3 --- The Analytic Approach --- p.28 / Chapter 3.1 --- Discrete Laplacians on finite sets --- p.28 / Chapter 3.2 --- Laplacian from a compatible sequence --- p.33 / Chapter 3.3 --- Compatible sequence from a harmonic structures --- p.40 / Chapter 3.4 --- Existence theorem for harmonic structures --- p.50 / Chapter 4 --- On Two Related Classes of Symmetric Polytopes --- p.55 / Chapter 4.1 --- Symmetries and regular polytopes --- p.56 / Chapter 4.2 --- Classification of highly symmetric polytopes --- p.62 / Chapter 4.3 --- Classification of strongly symmetric polytopes --- p.66 / Bibliography --- p.78

Wu, Xiaoming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 30-34). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.4 / Chapter 2.1 --- Kernel Learning Theory --- p.4 / Chapter 2.1.1 --- Positive Semidefinite Kernel --- p.4 / Chapter 2.1.2 --- The Reproducing Kernel Map --- p.6 / Chapter 2.1.3 --- Kernel Tricks --- p.7 / Chapter 2.2 --- Spectral Graph Theory --- p.8 / Chapter 2.2.1 --- Graph Laplacian --- p.8 / Chapter 2.2.2 --- Eigenvectors of Graph Laplacian --- p.9 / Chapter 2.3 --- Convex Optimization --- p.10 / Chapter 2.3.1 --- From Linear to Conic Programming --- p.11 / Chapter 2.3.2 --- Second-Order Cone Programming --- p.12 / Chapter 2.3.3 --- Semidefinite Programming --- p.12 / Chapter 3 --- Fast Graph Laplacian Regularized Kernel Learning --- p.14 / Chapter 3.1 --- The Problems --- p.14 / Chapter 3.1.1 --- MVU --- p.16 / Chapter 3.1.2 --- PCP --- p.17 / Chapter 3.1.3 --- Low-Rank Approximation: from SDP to QSDP --- p.18 / Chapter 3.2 --- Previous Approach: from QSDP to SDP --- p.20 / Chapter 3.3 --- Our Formulation: from QSDP to SQLP --- p.21 / Chapter 3.4 --- Experimental Results --- p.23 / Chapter 3.4.1 --- The Results --- p.25 / Chapter 4 --- Conclusion --- p.28 / Bibliography --- p.30

published_or_final_version / Mathematics / Master / Master of Philosophy

Bibliography: leaves 103-105. / xii, 105 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1997

Thesis (Ph. D.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Ph. D.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 80-91). Also available in print.

by He Zhaokui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 81-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminaries --- p.8 / Chapter 2.1 --- The Laplacian of a compact manifold --- p.8 / Chapter 2.2 --- The Laplacian of a graph --- p.9 / Chapter 2.3 --- Some basic facts about the eigenvalues of a graph --- p.13 / Chapter 3 --- Bound of the first non-zero eigenvalue in terms of Cheeger constant --- p.18 / Chapter 3.1 --- The Cheeger constant --- p.18 / Chapter 3.2 --- The Cheeger inequality of a compact manifold --- p.19 / Chapter 3.3 --- The Cheeger inequality of a graph --- p.23 / Chapter 4 --- Diameters and eigenvalues --- p.27 / Chapter 4.1 --- Some facts --- p.27 / Chapter 4.2 --- Estimate the eigenvalues of graphs --- p.29 / Chapter 4.3 --- The heat kernel of compact manifolds --- p.34 / Chapter 4.4 --- Estimate the eigenvalues of manifolds --- p.35 / Chapter 5 --- Harnack inequality and eigenvalues on homogeneous graphs --- p.40 / Chapter 5.1 --- Preliminaries --- p.40 / Chapter 5.2 --- The Neumann eigenvalue of a subgraph --- p.41 / Chapter 5.3 --- The Harnack inequality --- p.44 / Chapter 5.4 --- A lower bound of the first non-zero eigenvalue --- p.52 / Chapter 6 --- Harnack inequality and eigenvalues on compact man- ifolds --- p.54 / Chapter 6.1 --- Gradient estimate --- p.54 / Chapter 6.2 --- Lower bounds for the first non-zero eigenvalue --- p.59 / Chapter 7 --- Heat kernel and eigenvalues of graphs --- p.63 / Chapter 7.1 --- The heat kernel of a graph --- p.54 / Chapter 7.2 --- Lower bounds for eigenvalues --- p.70 / Chapter 8 --- Estimate the eigenvalues of a compact manifold --- p.73 / Chapter 8.1 --- An isoperimetric constant --- p.75 / Chapter 8.2 --- A lower estimate for the (m + l)-st eigenvalue --- p.77