We establish an uncertainty principle over arbitrary finite groups, generalizing those of Donoho, Stark and Meshulam. Specifically, we show that if Π is a projection operator on the group algebra C[G] that commutes with projection onto each group element, and Π̂ is a projection operator that commutes with the right G-action on C[G], then ‖Π Π̂‖2 ≤ rk Π× rk Π̂/|G|.

We consider a FETI-DP formulation for the Stokes problem on nonmatching grids in 2D. The FETI-DP method is a domain decomposition method that uses Lagrange multipliers to match the solutions continuously across the subdomain boundaries in the sense of dual-primal variables. We use the mortar matching condition as the continuity constraints for the FETI-DP formulation. Moreover, to satisfy the c...

ly, we may think of a differential operator ~ on M as a mapping on the smooth functions on M. That is, let C~(M) denote the space of smooth real-valued functions on M. Then 3' : C~(M) ~ C~(M). Bifurcations on Hemispheres 215 In our extension theory we consider only those operators that respect the symmetries on M and N. We define these operators as follows. There is a natural action of ISO(M) o...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.