On a product of universal hyperalgebras
Abstract We introduce and study a new operation of product of universal hyperalgebras which lies, with respect to set inclusion, between the cartesian product of the hyperalgebras and the cartesian product of their idempotent hulls. We give sufficient conditions for the validity of the first exponential law and a weak form of the second exponential law for the direct power of universal hyperalgebras with respect to the product introduced.
DIAGONAL -ALGEBRAS
. Let G be a locally compact group with C (cid:3) ( G ) and C (cid:3) r ( G ) its enveloping and reduced C (cid:3) -algebras respectively. We show that if C (cid:3) ( G ) is residually (cid:12)nite dimensional, then G is maximally almost periodic, and C (cid:3) r ( G ) is residually (cid:12)nite dimensional if and only if G is both amenable and maximally almost periodic. Letting (cid:21) G be the left regular representation of G , we show that a certain quasidiagonality condition on f (cid:21) G ( s ) : s 2 G g implies that G is amenable.
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...