Computation of the Cartan Spaces of Affine Homogeneous Spaces

Computation of Weyl Groups of G-varieties

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We establish algorithms for computing Weyl groups for homogeneous spaces and affine homogeneous vector bundles. For some special classes of G-varieties (affine...

Computation of Weight Lattices of G-varieties

Let G be a connected reductive group. To any irreducible G-variety X one assigns the lattice generated by all weights of B-semiinvariant rational functions on X , where B is a Borel subgroup of G. This lattice is called the weight lattice of X . We establish algorithms for computing weight lattices for homogeneous spaces and affine homogeneous vector bundles. For affine homogeneous spaces of ra...

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

State spaces of $K_0$ groups of some rings

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...