We analyze a model of optimal gerrymandering where two parties receive a noisy signal about voter preferences from a continuous distribution and simultaneously design districts in di¤erent states and in which the median voter in a district determines the winner. The form of the optimal gerrymander involves “slices”of extreme right-wing voters that are paired with “slices” of left-wing voters, a...

The earthquakelike model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth-sliding regimes of tribological systems within a framework which separates the calculation of the friction force from...

and some self-adjoint boundary condition at the origin. We assume that U is some bounded function for which HU has absolutely continuous spectrum. The presence of the absolutely continuous spectrum has direct consequences for the physical properties of the quantum particle described by the operator HU (see, e.g. [23, 2]). If we perturb this operator by some decaying potential V (x), the Weyl cr...