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

Non-Abrikosov Vortex and Topological Knot in Two-gap Superconductor

We establish the existence of topologically stable knot in two-gap superconductor whose topology $\pi_3(S^2)$ is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in Ginzburg-Landau theory of two-gap superconductor which has a non-vanishing condensate at the core, and identify the knot as a twisted magnetic vortex ring made of the helical vortex. We discuss how the knot can be constructed in the recent two-gap $\rm MgB_2$ superconductor.Comment: 4 pages, 3 figure

Witnessing a Poincar\'e recurrence with Mathematica

The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers. The latter problem then can be somewhat satisfactorily solved by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is implemented in the Mathematica built-in function \verb"LatticeReduce". The procedure is illustrated with a harmonic chain. The incredibly large recurrence times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure