to achieve sustainable urban development and values from social justice; it is essential that all citizens enjoy resources, facilities and life opportunities equally. due to lack of a stable or systematic approach of measuring urban problems, disparity in environmental conditions or access to social and physical infrastructures is more obvious, especially in the cities of developing countries. ...

We have examined, repeated and extended earlier numerical calculations of Berger and Moncrief for the evolution of unpolarized Gowdy T 3 cosmological models. Our results are consistent with theirs and we support their claim that the models exhibit AVTD behaviour, even though spatial derivatives cannot be neglected. The behaviour of the curvature invariants and the formation of structure through...

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phasemodulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results re...

The transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We develop a projector operator method able to derive, in this case, a generalized Smoluchowski equation for the position variable. We show that this explicitly non-markovian equation can be written as a systematic expansion involving higher-order derivatives. We use the latter t...

A straightforward discretisation of problems in high dimensions often leads to an exponential growth in the number of degrees of freedom. Sparse grid approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives and the fast Fourier transform (FFT) has been adapted to this thin discretisation. We show that this so cal...

We show that the renormalized self-intersection local time γt(x) for both the Brownian motion and symmetric stable process in R is differentiable in the spatial variable and that γ′ t(0) can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random Schwartz distribution. Analogo...

A bstract We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders derivatives. Working perturbation theory, we construct cubic interactions that can contribute tree-level bispectra, showing they come from EFToI operators containing two or three powers extrinsic curvature and its covariant derivatives: other be removed by field redefinitions star...

This paper presents the first step in establishing a link between the heavy-tailed nature of terrain and a new terrain modeling technique, L1 splines, that is, splines based on minimizing the L1 norm rather than the square of the L2 norm. To establish this link, we focus on the heavy-tailed nature of the second derivatives that occur in the L1 spline minimization principles. For one urbanterrai...