For Γ a relatively hyperbolic group, we construct a model for the universal space among Γ-spaces with isotropy on the family VC of virtually cyclic subgroups of Γ. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in O+(n, 1) = Isom(Hn). We use the information we obtain to explicitly compute the lower algebraic K-theory of t...

We study the Lüroth problem for partial differential fields. The main result is following analog of generalized Lüroth's theorem: Let F be a field characteristic 0 with m commuting derivation operators, u=u1,…,un set indeterminates over F. prove that an intermediate G between and F〈u〉 simple extension if only dimension polynomial u form ωu/G(t)=n(t+mm)−(t+m−sm) some s∈N. This generalizes classi...

Abstract We consider a family of quasilinear second order elliptic differential operators which are not coercive and defined by functions in Marcinkiewicz spaces. prove the existence solution to corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability when datum more regular.