Volume growth and parabolicity

We characterize -parabolicity of a noncompact complete Riemannian manifold in terms of the volume growth of under very weak assumptions on . Some of the results also apply to the setting of metric measure spaces.

     

Theoretical chemistry of gold

Gold is an element whose unique properties are strongly influenced by relativistic effects. A large body of appropriate calculations now exist and their main conclusions are summarized. The theoretical interpretation of the aurophilic attraction is discussed in detail.     

Possible high-pressure structures of sulfur trioxide

Calculations with the linearized augmented plane wave method indicate that several high-density forms of sulfur trioxide should be accessible at pressures above 29 GPa, with densities up to 1.7 times larger than the presently known forms of solid SO3.     

Relativity,gold, closed-shell interactions,and CsAu.NH3

The chemical properties of gold are strongly influenced by relativistic effects. One example is the large electronegativity of Au, which qualitatively explains the stability of (solid or liquid) cesium auride, Cs(+)Au(-), and other systems with Au(-) ions. An especially impressive compound is CsAu.NH(3), the structure and bonding of which are discussed. Future possibilities for finding further aurides are outlined.     

Comparing Nonsmooth Nonconvex Bundle Methods in Solving Hemivariational Inequalities

Hemivariational inequalities can be considered as a generalization of variational inequalities. Their origin is in nonsmooth mechanics of solid, especially in nonmonotone contact problems. The solution of a hemivariational inequality proves to be a substationary point of some functional, and thus can be found by the nonsmooth and nonconvex optimization methods. We consider two type of bundle methods in order to solve hemivariational inequalities numerically: proximal bundle and bundle-Newton methods. Proximal bundle method is based on first order polyhedral approximation of the locally Lipschitz continuous objective function. To obtain better convergence rate bundle-Newton method contains also some second order information of the objective function in the form of approximate Hessian. Since the optimization problem arising in the hemivariational inequalities has a dominated quadratic part the second order method should be a good choice. The main question in the functioning of the methods is how remarkable is the advantage of the possible better convergence rate of bundle-Newton method when compared to the increased calculation demand.     

Simultaneous measurement of 2 and 3 spins in proton proton elastic scattering at 6 GeVc

The elastic cross section for proton proton scattering at 6 $\text{GeV}\text{c}$ was measured using a 70% polarized beam and a 75% polarized target at the Argonne ZGS. In the range $\text{P}{}_{\mathrm{\perp }}{}^2\text{= 0.5 → 2.0(}\text{GeV}\text{c}\text{)}{}^2$ we obtained small error measurements for the ↑↑, ↓↓ and ↑↓ initial spin states perpendicular to the scattering plane. At P_⊥² = 0.5 we also measured the recoil spin and found that the 5 different cross sections were very unequal.     

Formation of cracks under deformations with finite energy

With a map , , that belongs to the John Ball class where n-1 < p < n and one can associate a set valued map F whose values are subsets of describing the topological character of the singularity of f at . verak conjectured that , where S is the set of points at which f is not continuous and is the Hausdorff measure. The purpose of our paper is to confirm this expectation.Received: 3 March 2003, Accepted: 15 April 2003, Published online: 1 July 2003Mathematics Subject Classification (2000): 74B20Piotr Hajasz: Hajasz was supported by KBN grant 2 PO3A 028 22 and Koskela by the Academy of Finland,SA-34082. Part of this research was done while Hajasz was at the Department of Mathematics of the University of Michigan. He wishes to thank UM for the support and hospitality.     

Geometric Interpretations of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">P</Emphasis></Superscript>-Poincaré Inequalities on Graphs with Polynomial Volume Growth

On graphs with polynomial volume growth of exponent Q, we characterize L^p-Poincaré inequalities in the range Q – 1 < p < + in terms of capacity estimates, depending on the position of p with respect to Q.Research partially supported by the European Commission (IHP Network Harmonic Analysis and Related Problems 2002–2006, Contract HPRN-CT-2001-00273-HARP).Lecture held by Th. Coulhon in the Seminario Matematico e Fisico on January 19, 2004Received: May, 2004     

Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1,1 data

We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C ^1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case.