A family of linear homogeneous 4th order elliptic differential operators with real constant coefficients, and bounded nonsmooth convex domains are constructed in so that the have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces .
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...
In this paper, we determine all the normal forms of Hermitian matrices over finite group rings , where , is a commutative -group with order . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.