by Tsoi, Man. / Thesis submitted in: July 1999. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 56-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.12 / Chapter 2.1 --- Lie Group and Lie Algebra --- p.12 / Chapter 2.2 --- Harmonic Maps --- p.15 / Chapter 2.3 --- Some Factorization theorems --- p.17 / Chapter 3 --- A Survey on Unlenbeck's Results --- p.22 / Chapter 3.1 --- Preliminary --- p.24 / Chapter 3.2 --- Extended Solutions --- p.26 / Chapter 3.3 --- The Variational Formulas for the Extended Solutions --- p.30 / Chapter 3.4 --- "The Representation of A(S2, G) on holomorphic maps C* → G" --- p.33 / Chapter 3.5 --- An Action of G) on extended solutions and Backlund Transformations --- p.39 / Chapter 3.6 --- The Additional S1 Action --- p.42 / Chapter 3.7 --- Harmonic Maps into Grassmannians --- p.43 / Chapter 4 --- Harmonic Maps into Compact Lie Groups --- p.47 / Chapter 4.1 --- Symmetry group of the harmonic map equation --- p.48 / Chapter 4.2 --- A New Formulation --- p.49 / Chapter 4.3 --- "Harmonic Maps into Grassmannian, Another Point of View" --- p.53 / Bibliography

This qualitative study, carried out in an early learning center in an international school in Japan, aims to examine the place, meaning, and practice of assessment of young children’s learning through the methodology of documentation as defined and developed by the educators of the Reggio Emilia Approach. Whereas most aspects of instruction and assessment practices focus on individual performances and achievements, this study looks at the learning strategies of young children within the group and the learning of the group and the complexities of assessment practices assigned to socio-cultural theory. The focus of this study, therefore, is framed within socio-cultural theory to look at the intersection of the two, that of group learning and documentation, where the systematic and purposeful documentation of the ways in which groups develop ideas, theories and understanding is given space as being critical to learning of individuals as well as of groups towards building an understanding of assessment from a socio-cultural perspective. Learning is viewed as relevant to experience where the relations between the social and personal (cultural) are shared and that each person learns autonomously and through the ways of learning of others. The study was carried out in the form of action research in the course of one academic year, with the researcher acting as an active participant observer to a group of 4 children and a teacher who formed a learning group through a yearlong project on the concept of color. The teacher was asked to document the process of the salient paths of learning of the children through the project, becoming the ‘documentor’ of the project, and the researcher ‘documenting the documentor’. The main findings suggest to view learning of young children as a web of reciprocal expectations and possibilities of engagement built upon children’s constant mediation between scientific and everyday concepts with and through others.

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Lun Miu-chi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 37-42). / Abstracts in English and Chinese. / Acknowledgment --- p.i / Table of contents --- p.ii / Abstract --- p.iv / Chapter Chapter 1: --- Introduction / Relationship Harmony --- p.1 / Previous Research on Relationship Harmony --- p.1 / Relationship Harmony in Groups --- p.3 / The Five-Factor Model of Personality and Relationship Harmony --- p.5 / "Relationship Harmony, Interpersonal Attraction, and Group Cohesiveness" --- p.8 / "Relational Experiences, Group Cohesiveness, and Group Performance" --- p.11 / The Nonindependence Issue --- p.12 / Chapter Chapter 2: --- Method / Participants --- p.14 / Measures --- p.14 / Analytical Strategy --- p.17 / Chapter Chapter 3: --- Results / Table 1: Descriptive statistics of the variables Self-report RH --- p.18 / Table 2: Correlation matrix of the variables --- p.19 / Table 3: Results regarding self-report RH Other-given RH --- p.20 / Table 4: Results regarding other-given RH Self-report Liking --- p.22 / Table 5: Results regarding self-report liking Other-given Liking --- p.24 / Table 6: Results regarding other-given liking Individual's Attraction to Group --- p.24 / Table 7: Results regarding individual's attraction to the group Perception of Group Integration --- p.26 / Table 8: Results regarding perception of group integration Group Performance Outcome --- p.27 / Table 9: Results regarding the mediating role of group integration between group relationship harmony and group performance --- p.29 / Chapter Chapter 4: --- Discussion / Personality Correlates of Relationship Harmony and Interpersonal Attraction --- p.30 / "Relationship Harmony, Interpersonal Attraction, and Group Cohesiveness" --- p.33 / "Relational Constructs, Group Cohesiveness, and Group Performance" --- p.34 / Future Research Direction --- p.35 / Reference --- p.37 / Appendixes / Chapter Appendix 1: --- The Interpersonal Liking Scale --- p.43 / Chapter Appendix 2: --- The Group Interaction Measure --- p.44

Chan, Wai-Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 52-53). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iii / Introduction --- p.iv / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- C*-algebras --- p.1 / Chapter 1.2 --- Topological groups --- p.8 / Chapter 2 --- Property T for topological groups --- p.18 / Chapter 2.1 --- Definitions and some basic properties --- p.18 / Chapter 2.2 --- Hereditary properties --- p.23 / Chapter 2.3 --- A characterization for property T --- p.26 / Chapter 2.4 --- Examples --- p.32 / Chapter 3 --- Property T for C*-algebras --- p.34 / Chapter 3.1 --- Countable discrete groups and their group C*- algebras --- p.34 / Chapter 3.2 --- Property T and nuclearity --- p.46 / Bibliography --- p.52

Given a function (more generally, a measure) on a locally compact Abelian group, one can define the Toeplitz operators as certain integral transforms of functions on the dual group, where the kernel is the Fourier transform of the original function or measure. In the case of the unit circle, this corresponds to forming a matrix out of the Fourier coefficients in a particular way. We will study the asymptotic eigenvalue distributions of these Toeplitz operators.

This thesis contains methods of finding new presentations of finite groups, particularly nonabelian simple groups. We have presented several progenitors such as 2^{*8}:Z_4 wr Z_2, 3^{*3}:_m L(2,7), 2^{*4}:[2:2^2], 2^{*11}:D_{11} and many more on which we've found the mathieu group M12 and 2*[M21:2^2] among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of PGL(2,7), [3 x A_5]:2, 3:[A_6:2], and 2 x [(3 x L(2,11)):2] using the process of double coset enumeration.

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