Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Schooling, Nation Building, and Industrialization: a Gellnerian Approach (new version)

We model a two-region country where value is created through bilateral production between masses and elites (bourgeois and landowners). Industrialization requires the elites to finance schools and the masses to attend them. Schooling raises productivity, particularly for matches between masses and bourgeois. At the same time, only country-wide education ("unified schooling") renders the masses mobile across regions. Alternatively, schools can be implemented in one region alone ("regional education") or the regionally dominant group can choose to implement schooling in its own region but refuse to share the costs/proceeds within the wider country-level group ("secession"). We show that schools are more likely to be set-up when the bourgeoisie dominates, but that this is not necessarily socially efficient. Unified schooling is always chosen if the identity of the dominant elite at the regional and country level is the same and/or the industrialization shock is sufficiently high. If instead the bourgeoisie is dominant in one region and landowners are dominant country-wise, the bourgeoisie of that region may promote the secession of the region, and this can be socially efficient. The model is shown to be consistent with evidence for 19th century France and Spain

Detecting Determinism in High Dimensional Chaotic Systems

A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from deterministic systems even if the dimension of the latter is as high as 13. The method is shown to succeed in identifying determinism in electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E (25 apr 2001