Pseudo-differential operators, heat calculus and index theory of groupoids satisfying the Lauter-Nistor condition

In this thesis, we study singular pseudo-differential operators defined by groupoids satisfying the Lauter-Nistor condition, by a method parallel to that of manifolds with boundary and edge differential operators. The example of the Bruhat sphere is studied in detail. In particular, we construct an extension to the calculus of uniformly supported pseudo-differential operators that is analogous to the calculus with bounds defined on manifolds with boundary. We derive a Fredholmness criterion for operators on the Bruhat sphere, and prove that their parametrices up to compact operators lie inside the extended calculus; we construct the heat kernel of perturbed Laplacian operators; and prove an Atiyah-Singer type renormalized index formula for perturbed Dirac operators on the Bruhat sphere using the heat kernel method.Comment: Warwick PhD Thesi

The relationship between attributional style and destructive responses to job dissatisfaction: an exploratory study of internal migrant workers in China

published_or_final_versio

Environmental learning using a problem-based approach in the field: A case study of a Hong Kong school

This study investigated the environmental learning of a group of senior geography students through a problem-based learning (PBL) field programme to see if the goals of education for the environment could be accomplished. In the PBL field programme, the students were given a problem statement concerning a real-life scenario of an old lady living in a remote village of Hong Kong. During the PBL field programme which also has adopted an action research framework, the students were observed to have identified the problem statement, set hypotheses, constructed the research methods and collected empirical data in an authentic environment all by themselves. This paper reports on the first cycle of this piece of action research. Data were collected both quantitatively and qualitatively via questionnaires, students' reflective journals, field observation notes and group interviews. The initial finding of this PBL field programme reveals that students had acquired more in-depth knowledge and extended their comfort zones in learning. They were able to develop and practice their critical thinking and problem-solving skills while they were working on the problem in the field. Although there was no evidence of sustained self-directed learning among the students, the PBL field programme offered them a framework for developing self-directed learning. An initial conclusion is that PBL in the field can provide a useful framework and direction for EE to accomplish the goals of education for the environment. ©. 2008 T. Kwan & M. So.published_or_final_versio

Pseudo-differential operators, heat calculus and index theory of groupoids satisfying the Lauter-Nistor condition

In this thesis, we study singular pseudo-differential operators defined by groupoids satisfying the Lauter-Nistor condition, by a method parallel to that of manifolds with boundary and edge differential operators. The example of the Bruhat sphere is studied in detail. In particular, we construct an extension to the calculus of uniformly supported pseudo-differential operators that is analogous to the calculus with bounds defined on manifolds with boundary. We derive a Fredholmness criterion for operators on the Bruhat sphere, and prove that their parametrices up to compact operators lie inside the extended calculus; we construct the heat kernel of perturbed Laplacian operators; and prove an Atiyah-Singer type renormalized index formula for perturbed Dirac operators on the Bruhat sphere using the heat kernel method

Deformation and KK-theoretic Index Formulae on Boundary Groupoids

Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from the pair groupoid}.Under the assumption that a deformation from the pair groupoid $M \times M$ exists for Lie groupoid $\mathcal{G}\rightrightarrows M$, we construct explicitly a deformation index map relating the analytic index on $\mathcal{G}$ and the index on the pair groupoid. We apply this map to boundary groupoids of the form $\mathcal{G} = M_0 \times M_0 \sqcup G \times M_1 \times M_1 \rightrightarrows M=M_0\sqcup M_1$, where $G$ is an exponential Lie group, to obtain index formulae for (fully) elliptic (pseudo)-differential operators on $\mathcal{G}$, with the aid of the index formula by M. J. Pflaum, H. Posthuma, and X. Tang. These results recover and generalize our previous results for renormalizable boundary groupoids via the method of renormalized trace

Trust relationship between client's project manager and contractor

Thesis (B.Sc)--University of Hong Kong, 2007.Includes bibliographical references (p. 113-120).published_or_final_versio

ANALYSIS AND ESTIMATION ON KOREA-SAARC PARTNERSHIP SEMINAR

SAARC was formed in 1985 with the objective of exploiting “accelerated economic growth, social progress and cultural development in the region” for the welfare of the peoples of South Asia. In 1995, its corresponding RTA (SAPTA) came into force. South Asian Free Trade Agreement (SAFTA) has been ratified and entered into force in mid-2006. As its importance echoes around the world over the time, there has been a growing interest among many countries and organizations to be associated with SAARC as Observers and to engage with SAARC in collaborative endeavours. Especially, Korea, as an observer, has opened “Korea –SAARC Partnership Seminar” in Seoul, Korea every year since 2010. For preparing 6th Seminar agenda to be opened on December this year, the authors analyzed its activity during last 5 years and estimated to draw the concrete strategies for co-prospects mutually. As a result, the authors proposed to conclude “Korea-SAARC FTA” linking Korea’s ODA, KSP and FT