Welfare Recipients and Workforce Laws

CRS_June_2004_Welfare_Recipients_and_Workforce_Laws.pdf: 1325 downloads, before Oct. 1, 2020

Bondi mass with a cosmological constant

The mass loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant $\Lambda\in\R$ was recently worked out, using the Newman-Penrose-Unti approach. In that same article, an expression for the Bondi mass of the isolated system, $M_\Lambda$, for the $\Lambda>0$ case was proposed. The stipulated mass $M_\Lambda$ would ensure that in the absence of any incoming gravitational radiation from elsewhere, the emitted gravitational waves must carry away a positive-definite energy. That suggested quantity however, introduced a $\Lambda$-correction term to the Bondi mass $M_B$ (where $M_B$ is the usual Bondi mass for asymptotically flat spacetimes) which would involve not just information on the state of the system at that moment, but ostensibly also its past history. In this paper, we derive the identical mass-loss equation using an integral formula on a hypersurface formulated by Frauendiener based on the Nester-Witten identity, and argue that one may adopt a generalisation of the Bondi mass with $\Lambda\in\R$ \emph{without any correction}, viz. $M_\Lambda=M_B$ for any $\Lambda\in\R$. Furthermore with $M_\Lambda=M_B$, we show that for \emph{purely quadrupole gravitational waves} given off by the isolated system (i.e. when the "Bondi news" $\sigma^o$ comprises only the $l=2$ components of the "spherical harmonics with spin-weight 2"), the energy carried away is \emph{manifestly positive-definite} for the $\Lambda>0$ case. For a general $\sigma^o$ having higher multipole moments, this perspicuous property in the $\Lambda>0$ case still holds if those $l>2$ contributions are weak --- more precisely, if they satisfy any of the inequalities given in this paper.Comment: 29 pages, accepted for publication by Physical Review

Professional Ethics in the Construction Industry

The results are provided of a small, but reprersentative, questionnaire survey of typical project managers, architects and building contractors concerning their views and experiences on a range of ethical issues surrounding construction industry activities. Most (90%) subscribed to a professional Code of Ethics and many (45%) had an Ethical Code of Conduct in their employing organisations, with the majority (84%) considering good ethical practice to be an important organisational goal. 93% of the respondents agreed that "Business Ethics" should be driven or governed by "Personal Ethics", with 84% of respondents stating that a balance of both the requirements of the client and the impact on the public should be maintained. No respondents were aware of any cases of employers attempting to force their employees to initiate, or participate in, unethical conduct. Despite this, all the respondents had witnessed or experienced some degree of unethical conduct, in the form of unfair conduct (81%), negligence (67%), conflict of interest (48%), collusive tendering (44%), fraud (35%), confidentiality and propriety breach (32%), bribery (26%) and violation of environmental ethics (20%)

Welfare Reform: An Issue Overview

CRS ReportCRSWelfareReform101403.pdf: 866 downloads, before Oct. 1, 2020

No-boarding buses: Synchronisation for efficiency

We investigate a no-boarding policy in a system of $N$ buses serving $M$ bus stops in a loop, which is an entrainment mechanism to keep buses synchronised in a reasonably staggered configuration. Buses always allow alighting, but would disallow boarding if certain criteria are met. For an analytically tractable theory, buses move with the same natural speed (applicable to programmable self-driving buses), where the average waiting time experienced by passengers waiting at the bus stop for a bus to arrive can be calculated. The analytical results show that a no-boarding policy can dramatically reduce the average waiting time, as compared to the usual situation without the no-boarding policy. Subsequently, we carry out simulations to verify these theoretical analyses, also extending the simulations to typical human-driven buses with different natural speeds based on real data. Finally, a simple general adaptive algorithm is implemented to dynamically determine when to implement no-boarding in a simulation for a real university shuttle bus service.Comment: 49 pages, 9 figures. Video available here: https://www.youtube.com/watch?v=SBNqvTr1Aj

Helicalised fractals

We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line and circle, showing that it takes the form of the self-similar dimension for a self-similar fractal, with lower bound of 1. Upper bounds to the Hausdorff dimension as functions of $\omega$ have been determined for the linear helical fractal, curved helical fractal and circular fractal, based on the no-self-intersection constraint. For large number of windings $\omega\rightarrow\infty$, the upper bounds all have the limit of 2. This would suggest that carrying out a topological analysis on the structure of chromosomes by modelling it as a two-dimensional surface may be beneficial towards further understanding on the dynamics of DNA packaging.Comment: 25 pages, 10 figures. v3: Detailed derivation of the Hausdorff dimension included. Accepted by Chaos, Solitons & Fractal