Group analysis of differential equations and generalized functions

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau's theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions remain symmetries for generalized solutions. Moreover, we introduce a generalization of the infinitesimal methods of group analysis that allows to compute symmetries of linear and nonlinear differential equations containing generalized function terms. Thereby, the group generators and group actions may be given by generalized functions themselves.Comment: 27 pages, LaTe

The geography of creative people in Germany

It has been argued that creativity is an important source of regional growth. This paper investigates the geography of people in creative occupation in Germany. The population share of the Creative Class as well as of bohemians and artists is relatively high in larger cities, but smaller places and rural regions may also have a considerable proportion of people with a creative job. While ethnical and cultural diversity and a high level of public supply in health care and education can explain the distribution of creative people, employment opportunities seem to play only a minor role. A high share of creative occupations seems to be conducive to regional growth; however, the exact nature of this relationship is still unclear

Asymmetric response of a jammed plastic bead raft

Fluctuation-dissipation relations have received significant attention as a potential method for defining an effective temperature in nonequilibrium systems. The successful development of an effective temperature would be an important step in the application of statistical mechanics principles to systems driven far from equilibrium. Many of the systems of interest are sufficiently dense that they are close to the jamming transition, a point at which interesting correlations develop. Here we study the response function in a driven system of plastic beads as a function of the density in order to elucidate the impact of the jamming transition on the use of fluctuation-dissipation relations. The focus is on measuring the response function for applied shear stress. We find that even when the amplitude of the applied stress leads to a linear response in the strain, the time scale of the response is dependent on the direction of the applied stress

Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models

We construct an edge-weight distribution for i.i.d. first-passage percolation on $\mathbb{Z}^2$ whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.Comment: Published in at http://dx.doi.org/10.1214/12-AAP864 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Credit card debt puzzles

Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper' framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework can actually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers. Klassifikation: E210, G11