A dynamical systems model of unorganized segregation

We consider Schelling’s bounded neighborhood model (BNM) of unorganized segregation, from the perspective of modern dynamical systems theory. We carry out a complete quantitative analysis of the system for linear tolerance schedules. We derive a fully predictive model and associate each term with a social meaning. We recover and generalize Schelling’s qualitative results.

For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur, and show how neighborhood tipping can be explained in terms of basins of attraction.

When population movement is limited, we derive exact criteria for the occurrence of new population mixes.

For nonlinear tolerance schedules, we illustrate our approach with numerical simulations.     

Des extensions plus petites que leurs groupes de Galois

In this article we construct some Galois extensions L∕K with finite Galois groups and such that |Gal(L∕K)|>[L:K]. Using an analog of the Noether method, we explain how to obtain, with a fixed center, such a Galois curiosity with a Galois group as large as we want.

Résumé : Dans cet article, nous construisons une extension galoisienne L∕K à groupe de Galois fini et telle que |Gal(L∕K)|>[L:K]. En utilisant un analogue non commutatif de la méthode de Noether, nous expliquons ensuite comment, à centre fixé, l’on peut construire une telle curiosité galoisienne avec un groupe aussi gros que l’on veut.

Mots clés : Corps gauches; théorie de Galois.     

Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data

We consider semidiscrete approximations of parabolic boundary value problems based on an elliptic approximation by J. Nitsche, in which the approximating subspaces are not subject to any boundary conditions. Optimal L_p (L ₂) error estimates are derived for both smooth and nonsmooth boundary data. The approach is

based on semigroup theory combined with the theory of singular integrals.