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Sustainable development related design and research has shown a focus shift from new building projects to existing ones; from the building scale to the regional and the urban scale; from construct and assessing the energy performance of buildings to participating at an earlier design stage. Taipei has been selected as the subject of this research due to its extremely high urbanization and huge pressure from the existing built environment. In order to achieve the national goal for reducing CO2 emissions, appropriate localized guidelines for buildings are urgently needed. Therefore, this research aims to understand, analyze and predict the energy performance of the architectures in Taipei, and offers a series of design strategies to help reduce the energy demand at building and urban scales. This will be achieved through the application of modelling, integrating SketchUp (@Last Software 2000), HTB2 v2.10 (WSA 2008; Alexander 2008), and Virvil Plugins (WSA 2012; Jones et al. 2011). The whole research process is a two-phase study. The first phase is to create models at different scales based on observation of the practical building environment, analysis of architecture related data and practical situations in Taipei, and then simulate them in a bottom-up method to understand the fundamental energy performance of different buildings, groups, blocks and districts. In the second phase, the model is extended to examine important variables and related strategies at both building and urban scales. This research finds that lighting, equipment efficiency, temperature settings of AC systems, orientation, glazing ratio, shading devices, and wall-to-volume ratio are important variables for architectures at building scale. Furthermore, development intensity, block usage type, wall-to-volume ratio, volume rate, building coverage ratio, average building height, surrounding road width, over-shading, insulation and outdoor environment are comparatively critical at urban scale. Additional interesting findings showed that the impacts brought by orientation, shading device, and insulation are not consistent at different scales. Lastly, some guidelines are presented to be used as a reference for new and existing buildings.

This thesis investigates and compares the development and characteristics of the pension systems in China, Hong Kong, Singapore and Taiwan. It uses a policy index to compare the inputs of these four pension systems as well as their social outputs. The thesis starts by reviewing the ancient Chinese welfare and political ideologies and practices and the Western welfare ideologies and regimes to discover the core values behind the Chinese Community pensions. Four country case studies examine the development and performance of these state pension schemes in the context of the family support system and demographic trends. They explore the sustainability of pension provisions, the adequacy of public pensions, personal and private sources of retirement income. The problems of these four pension provisions are thus revealed. The policy index constructed through the radar chart and Surface Measure of Overall Performance (SMOP) approaches is used to compare the performances of these four pension systems on policy inputs and social outputs. The conclusion of the research is that Confucianism and capitalism integrate into a new paternalism through the patriarchal values they share and which dominate the Chinese Community nowadays. But the features of these four pension systems vary due to the different political, historical, economic and social contexts of each state. The findings show that none of these pension provisions can effectively prevent elderly people from poverty in old age. They all rely on personal social security responsibility and the continuation of the family support system. This thesis concludes that all these states lack a needs-based basic pension system to secure retirees’ income level.

This thesis outlines a formalism to study various physical phenomena based on a generalized concept of quaternions. It is shown that there is a total of 64 possible multiplication rules which can be defined starting with the generalized imaginary units first introduced by Hamilton. Of these 64 choices, only 8 lead to non-commutative division algebras, two of which are associated to the left- and right-chirality quaternions while the other six are generalizations of the split-quaternion, a concept first introduced by Cockle. Next, we show that both the left- and right- chirality versions of the generalized split-quaternions in their 4 × 4 matrix forms are algebraically isomorphic and can be related to each other by 4 × 4 permutation matrices of the C2 × C2 group. We first show that the left- and right-chirality quaternions can be used (1) to generate clockwise and anti-clockwise rotations in our three-dimensional space, (2) to describe Lorentz boosts with constant velocity in an arbitrary direction, (3) to introduce a new approach to calculate the probability of spin components, as well as the mean and standard deviation of a Hermitian operator in quantum mechanics, and (4) to reformulate quantum gates and qubits in quantum computing. We then use the quaternion formalism to study noise in quantum circuits and calculate the qubit fidelity after applications of many noisy gates on an initial qubit state. Next, it is shown how each of the generalized split-quaternion algebras can be used to solve the problem of quantum-mechanical tunneling through an arbitrary one-dimensional conduction band energy profile. This demonstrates that six different spinors (4 × 4 matrices) can be used to represent the amplitudes of the left and right propagating waves in a device. Finally, we point out an interesting connection between the non-commutative split-quaternion division algebras and the uniqueness of our four-dimensional space-time by introducing a super split-quaternion formed of a superposition of either the left- or right-chirality versions of split-quaternions. It is shown that the norm of this super split-quaternion has a form identical to the space-time interval. This opens the door for an interpretation of the special and general theories of relativity based on a quaternionic viewpoint of the universe.