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An extension of the Kadison-Dubois representation theorem is proved. This extends both the classical version  and the preordering version given by Jacobi in . It is then shown how this can be used to sharpen the results on representations of strictly positive polynomials given by Jacobi...
We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in...
We examine the conditions for two algebraic function fields over real closed fields to be Witt equivalent. We show that there are only two Witt classes of algebraic function fields with a fixed real closed field of constants: real and non-real ones. The first of them splits further into...
A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight
, its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge...
of a finite group G whose restriction to any Sylow subgroup equals the restriction of some inner automorphism of G shall be called Coleman automorphism, named for D. B. Coleman, who's important observation from  especially shows that such automorphisms occur...
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