An explicit characterization of Calogero-Moser systems

Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.

     

The Inverse Resonance Problem for Jacobi Operators

It is proved in this paper that super-exponentially decaying,possibly non-selfadjoint perturbations of the free Jacobi operatorare uniquely determined by the location of all their eigenvaluesand resonances. 2000 Mathematics Subject Classification 39A70,34K29.     

Common pool resources with support

We examine the role of support for coalition stability in common pool resource games such as fisheries games. Some players may not want to join a coalition that jointly manages a resource. Still, because they benefit from spillovers, they may want to support the coalition with a transfer payment to set incentives for others to join. We find that the impact of support on equilibria of this game is limited to games with three or five players. Recommendations for Resource Managers

• Coalitions may be able to effectively manage common pool resources such as fisheries but such coalitions are often not stable due to free-rider incentives.
• We explore the impact of a transfer scheme that can improve this coalition stability which would lead to larger and more effective coalitions.
• Our results show that this new transfer scheme works only for cases where the number of players is small.

     

On the Inverse Resonance Problem

A new technique is presented which gives conditions under whichperturbations of certain base potentials are uniquely determinedfrom the location of eigenvalues and resonances in the contextof a Schrödinger operator on a half line. The method extendsto complex-valued potentials and certain potentials whose firstmoment is not integrable.     

On the leading energy correction for the statistical model of the atom: Interacting case

Introducing the Hellmann-Weizsäcker functional for large angular momenta and the orbitals of the Bohr atom for small angular momenta we obtain an upper bound on the quantum mechanical ground state energy of atoms that proves Scott's conjecture.Supported by the Deutsche Forschungsgemeinschaft     

Numerical approximation of the Cahn-Larché equation

Summary Spinodal decomposition, i.e., the separation of a homogeneous mixture into different phases, can be modeled by the Cahn-Hilliard equation - a fourth order semilinear parabolic equation. If elastic stresses due to a lattice misfit become important, the Cahn-Hilliard equation has to be coupled to an elasticity system to take this into account. Here, we present a discretization based on finite elements and an implicit Euler scheme. We first show solvability and uniqueness of solutions. Based on an energy decay property we then prove convergence of the scheme. Finally we present numerical experiments showing the impact of elasticity on the morphology of the microstructure.Research supported by DFG Priority Program Analysis, Modeling and Simulation of Multiscale Problems under AR234/5-2 and GA695/2-2     

Nuclear structure effects in the mass region aroundA=100, derived from experimentalQ β -values

The endpoint energies ofβ-transitions in 15 neuron-rich nuclei with mass numbers 101≦A≦106 have been measured with a plastic scintillator telescope in coincidence with a large Ge(Li)-detector at the on-line mass separator LOHENGRIN. From theQ _β -values obtained in these experiments, nuclear structure effects in this region of the nuclear chart are deduced. Finally, nuclear masses derived from theseQ _β -values are compared with the predictions of different theoretical mass calculations.