A Three-Dimensional Voting System in Hong Kong

The voting system in the Legislative Council of Hong Kong (Legco) is sometimes unicameral and sometimes bicameral, depending on whether the bill is proposed by the Hong Kong government. Therefore, although without any representative within Legco, the Hong Kong government has certain degree of legislative power --- as if there is a virtual representative of the Hong Kong government within the Legco. By introducing such a virtual representative of the Hong Kong government, we show that Legco is a three-dimensional voting system. We also calculate two power indices of the Hong Kong government through this virtual representative and consider the $C$-dimension and the $W$-dimension of Legco. Finally, some implications of this Legco model to the current constitutional reform in Hong Kong will be given

On the boundary of weighted numerical ranges

In this article, we are going to introduce the weighted numerical range which is a further generalization both the c-numerical range and the rank k numerical range. If the boundaries of weighted numerical ranges of two matrices (possibly of different sizes) overlap at sufficiently many points, then the two matrices share common generalized eigenvalues

Light Gluino, Light Bottom Squark Scenario, and LEP Predictions

The scenario of light gluinos and light sbottoms was advocated to explain the discrepancy between the measured and theoretical production of $b$ quarks at the Tevatron. This scenario will have model-independent predictions for $Z\to q\bar q \tilde{g} \tilde{g}$ at the $Z^0$-pole, and $e^+ e^- \to q\bar q \tilde{g} \tilde{g}$ at LEPII. We show that the data for $Z\to q \bar q g^* \to q\bar q b \bar b$ at LEPI cannot constrain the scenario, because the ratio $\Gamma(Z \to q\bar q \tilde{g} \tilde{g})/ \Gamma(Z \to q \bar q g^* \to q\bar q b \bar b) = 0.15 - 0.04$ for $m_{\tilde{g}}= 12-16$ GeV is smaller than the uncertainty of the data. However, at LEPII the ratio $\sigma(e^+ e^- \to q\bar q \tilde{g} \tilde{g})/ \sigma(e^+ e^- \to q \bar q g^* \to q\bar q b \bar b) \simeq 0.4 - 0.2$ for $m_{\tilde{g}}= 12-16$ GeV, which may give an observable excess in $q\bar q b\bar b$ events; especially, the $4b$ events.Comment: to match the published version in PR

A review of life cycle assessments of renewable energy systems

A review of life cycle assessments (LCAs) of wind energy published in the past few years are presented in this paper. The aim is to identify the differences of the developed methodologies, in particular, the factors such as methods used, energy performance and influence of uncertainty. Each of the factors is addressed to highlight the shortcomings and strengths of various approaches. Potential issues were identified regarding the way LCA is used for assessing environmental impact and energy performance of wind energy. It is found that the potential of incorporating the quantification of uncertainty in the manufacturing phase has not been studied elaborately. A framework methodology has been proposed in this paper to address this issue