A rational function belongs to the Hardy space, H 2 H^2 , of square-summable power serie...

Given a collection P = {p1(x1, . . . , x2k2), . . . , pk2(x1, . . . , x2k2)} of k commutative polynomials in 2k variables, the objective is to find a condensed representation for these polynomials in terms of a single non-commutative polynomial p(X,Y ) in two k × k matrix variables X and Y . Algorithms that will generically determine whether the given family P has a non-commutative representati...

We compute the Grothendieck group K0 of non-commutative analogues of projective space bundles. Our results specialize to give the K0-groups of non-commutative analogues of projective spaces, and specialize to recover the K0-group of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection theory for quantum ruled surfaces.

Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SUq(2), the Green function and the Kernel on the q-homogeneous space M = SU(2)q/U(1) are derived. A path integration is formulated. Green function for the free massive scalar field on the non-commutative Einstein space R ×M is presented.

The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasi-equivariant maps from the space of metrics on the worldsheet to the space of n-tuples of oneand two-dimensional loops. The two-dimensional case is based on the cylinders interacted with a path space connection. The special 2-gauge string model is formulated using two 1-connections, nonabelia...

We generalize recent results by G.A. Freiman, M. Herzog and coauthors on the structure theory of product-sets from the context of linearly (i.e., strictly and totally) ordered groups to linearly ordered semigroups. In particular, we find that if S is a finite subset of a linearly ordered semigroup generating a nonabelian subsemigroup, then |S2| ≥ 3 |S| − 2. On the road to this goal, we also pro...