Twisted Equivariant KK-Theory and the Baum–Connes Conjecture for Group Extensions

In this paper we study the stability of the Baum–Connes conjecture with coefficients undertaking group extensions. For this, it is necessary to extend Kasparov's equivariant KK-theory to an equivariant theory for twisted actions of groups on C ^*-algebras. As a consequence of our stability results, we are able to reduce the problem of whether closed subgroups of connected groups satisfy the Baum–Connes conjecture, with coefficients to the special case of center-free semi-simple Lie groups.     

The costly process of creating a cavity in <Emphasis Type="Italic">n</Emphasis>-octanol

Free-energy perturbation calculations are used to evaluate the free energy of cavity formation in n-octanol. A detailed theoretical analysis of the procedure is given and some limiting value phenomena are discussed. The data become subject to a three-parameter fit and a revised formulation of the popular approach due to Pierotti of calculating cavitation free energies is given. Pierottis approach is based on the equation derived from scaled particle theory (SPT) by Reiss et al. [(2000) J. Chem. Phys. 31:369–380]. The revision of Pierottis approach has the important advantage of being completely independent of the solvent hard-sphere radius, an empirical parameter in the standard procedure, which is hard to define in a uniformly valid way.Acknowledgments. S.H. gratefully acknowledges supercomputing support from the University of Linz, GUP, Professor Volkert and Dr. Kranzlmüller, and the University of Salzburg, RIST⁺⁺, Professor Zinterhof.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions

We consider the Dirichlet boundary value problem for quasilinear elliptic systems in a bounded domain \(\Omega \subset \mathbb {R}^N\) with a diagonal \((p_1, p_2)\)-Laplacian as leading differential operator of the form

$$\begin{aligned} -\Delta _{p_i} u_i=f_i(x, u_1,u_2,\nabla u_1,\nabla u_2)\ \ \text {in }\Omega ,\ \ u_i=0\ \ \text {on }\partial \Omega , \end{aligned}$$

where the component functions \(f_i\) (\(i=1,2\)) of the lower order vector field may also depend on the gradient of the solution \(u=(u_1,u_2)\). The main goal of this paper is twofold. First, we establish an enclosure and existence result by means of the trapping region which is formed by pairs of appropriately defined sub-supersolutions. Second, by a suitable construction of sequences of expanding trapping regions we are able to prove the existence of extremal positive and negative solutions of the system. The theory of pseudomonotone operators, regularity results due to Cianchi-Maz’ya, as well as a strong maximum principle due to Pucci-Serrin are essential tools in the proofs.