The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C^*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero. Dedicated to the memory of Peter Slodowy     

On the Relationship Between Entropy and Enthalpy of Grain Boundary Segregation

An extensive study of anisotropy of grain boundary segregation in -iron, performed in the last decade, confirmed the existence of a linear relationship between entropy and enthalpy of solute segregation at individual grain boundaries. A thermodynamic analysis of this relationship is performed in the present work. It is shown that this dependence defines a compensation temperature and an entropy-like parameter. The compensation temperature is not necessarily connected with a phase transformation, but it represents exclusively a mean temperature at which all boundaries approach to a mean value of the Gibbs free energy of segregation. The most important consequences of this dependence are outlined: a reversed anisotropy of grain boundary segregation at temperatures above the compensation temperature, and a new method for the prediction of the enthalpy and entropy of solute segregation at individual grain boundaries.