Using Different Approaches to Evaluate Individual Social Equity in Transport

Inequalities not only exist in the field of economics in relation to income and wealth, but also in other areas, such as the transport sector, where access to and use of different transport modes varies markedly across population groups, and which provides the means to access everyday living activities. A key concern within the transport sector is that inequality has extended beyond the traditional measures of travel, and now covers a wide range of effects relating to social exclusion, freedom, well-being and being able to access reasonable opportunities and resources. In order to address the aforementioned issues, an important question to resolve is what type of methods can be used to measure inequalities in transport most effectively. Therefore, this study aims to apply different approaches, including the Capabilities Approach (CA) and a further six inequality indices, namely the Gini coefficient, the Atkinson index, the Palma ratio, the Pietra ratio, the Schutz coefficient and the Theil index, to the case study using the relatively migrant-rich lower-income neighbourhood of Tuqiao, in Beijing, in order to assess individual transport-related social inequity issues. The findings suggest that the CA is useful in assessing transport-related inequalities where there are significant barriers to the take up of accessibility, for example where there are high levels of disadvantaged groups and disaggregated analysis can be undertaken. The Palma ratio appears to have a larger effect than the Gini coefficient and the other inequality indices when measuring transport-related social inequity. In addition, we also found that most income inequality methods adapted from econometrics may be better suited to measuring transport-related social inequity between different regions, cities or countries, or within the same area, but at different points in time, rather than to measuring a single neighbourhood as a whole. Finally, we argue that to what extent politicians or transport planners can use appropriate management tools to measure transport-related social inequalities may be significant in terms of the progress that can be made in the fight against social inequity in the transport field

A covariant entropy bound conjecture on the dynamical horizon

As a compelling pattern for the holographic principle, our covariant entropy bound conjecture is proposed for more general dynamical horizons. Then we apply our conjecture to $\Lambda$CDM cosmological models, where we find it imposes a novel upper bound $10^{-90}$ on the cosmological constant for our own universe by taking into account the dominant entropy contribution from super-massive black holes, which thus provides an alternative macroscopic perspective to understand the longstanding cosmological constant problem. As an intriguing implication of this conjecture, we also discuss the possible profound relation between the present cosmological constant, the origin of mass, and the anthropic principle.Comment: JHEP style, 9 pages, 1 figure, honorable mention award received from Gravity Research Foundation for 2008 Essay Competitio

Note on the thermal history of decoupled massive particles

This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in Ref.\cite{Weinberg}, the strategies employed here are simpler, and the results obtained here are more general.Comment: JHEP style, 4 pages, to appear in CQ

The Picard group of the loop space of the Riemann sphere

The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p} maps from the circle S^1 to the sphere is an infinite dimensional complex manifold. We compute the Picard group of holomorphic line bundles on this loop space as an infinite dimensional complex Lie group with Lie algebra the first Dolbeault group. The group of Mobius transformations G and its loop group LG act on this loop space. We prove that an element of the Picard group is LG-fixed if it is G-fixed; thus completely answer the question by Millson and Zombro about G-equivariant projective embedding of the loop space of the Riemann sphere.Comment: International Journal of Mathematic

Oscillation-free method for semilinear diffusion equations under noisy initial conditions

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.Comment: 19 pages, 9 figure