Ungleichungen für elementare Mittelwerte

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The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.     

Adsorption of dicarboxylates on nano-sized gibbsite particles: effects of ligand structure on bonding mechanisms

The adsorption of the dicarboxylates o-phthalate, maleate, fumarate, malonate, and oxalate (representing ligands with the general composition ⁻O₂C---C_n---CO₂⁻; n=0, 1, or 2) on gibbsite were studied by means of quantitative batch adsorption experiments and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. The interpretations of ATR-FTIR spectra were aided by comparison with IR spectra of solution species and by results from theoretical frequency calculations. The main objectives of the study were to identify the molecular level bonding mechanisms of the dicarboxylates to gibbsite, and to investigate how these were influenced by the composition and structure of the ligands. Carboxylates with n=2 formed predominantly outer sphere complexes, whereas the importance of inner sphere complexes progressively increased for n=1 and 0. The inner sphere structures were identified as mononuclear chelates with one oxygen from each carboxylate group bonded to Al(III) at the surface. This showed the importance of chelate ring structure for the formation of inner sphere surface complexes, with stabilities of the complexes increasing in the order seven-membered ring less than six-membered ring less than five-membered ring. For ligands with n=2 only small variations in surface speciation were observed as a function of steric factors; irrespective of the relative positions of the carboxylate groups and bulkiness of the ligands outer sphere bonding is the dominating adsorption mode. Adsorption experiments were also conducted with gibbsite particles exhibiting differences in shape and surface roughness. These experiments showed that inner sphere complexes were favored on the less well-developed and more irregular gibbsite particles.     

Equation of motion of small bodies in relativity

There is proven a theorem, to the effect that a material body in general relativity, in a certain limit of sufficiently small size and mass, moves along a geodesic.