On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

Rationalisation of weak ferromagnetism in manganese(III) chains: the relation between structure and ordering phenomena

The synthesis, structure and magnetic properties of the one-dimensional chain compounds [Mn(cyclam)(SO4)]ClO4.H2O (1) and [Mn(cyclam)(HCOO)](CF3SO3)(ClO4) (2) are reported. Cyclam is the cyclic tetradentate ligand 1,4,7,11-tetraazacyclotetradecane. Both chain compounds exhibit antiferromagnetic interactions within the chains. A magnetic ordering phase transition at 5.5 K in (1) is investigated by magnetisation measurements along the three principal crystallographic axes of a single crystal and the results show unambiguously that the ferromagnetic ordering is only taking place along one crystallographic axis. The spin structure of the magnetic ordered phase and the magnitude of the ferromagnetic moment are correlated with the crystal structure and symmetry of the compound.     

Chemistry of λ-2H-azaphosphirene metal complexes

In this review, important aspects of λ³-2H-azaphosphirene metal complexes are discussed in relation to synthesis, physical properties and synthetic applications; ab-initio calculations on relative energies of CH₂NP isomers and of λ³-2H-azaphosphirene metal complexes (Cr, Mo, W) are also presented. Currently, there are three routes to this unsaturated three-membered ring system, which are discussed in detail: two of them use a rearrangement of metal carbene complexes, whereas the other relies on [2+1] cycloaddition reactions of electrophilic terminal phosphanediyl complexes and carbonitriles. The structural data show characteristics of a very strained heterocyclic ring system, which partially helps to understand the reactivity of this heterocycle complex in solution. The synthetic potential of λ³-2H-azaphosphirene metal complexes is illustrated by selected examples, which demonstrate their ability to serve, under very mild conditions as precursor for various new building blocks, i.e. nitrilium phosphanylide complexes, electrophilic terminal phosphanediyl complexes and phosphavinyl-nitrene complexes.     

Magnetic and Electrical Properties, Eu Mössbauer Spectroscopy, and Chemical Bonding of REAgMg (RE=La, Ce, Eu, Yb) and EuAuMg

Single-phase samples of REAgMg (RE=La, Ce, Eu, Yb) and EuAuMg were prepared by reacting the elements in sealed tantalum tubes in a high-frequency furnace. LaAgMg and CeAgMg adopt the hexagonal ZrNiAl-type structure, while EuAgMg, YbAgMg, and EuAuMg crystallize with the orthorhombic TiNiSi type. Chemical bonding was exemplarily investigatedfor EuAgMg and EuAuMg on the basis of TB-LMTO-ASAcalculations. Magnetic susceptibility measurements indicatePauli paramagnetism for LaAgMg and YbAgMg with room-temperature susceptibilities of 2.4(1)×10⁻⁹ and 1.5(1)×10⁻⁹ m³/mol, respectively. CeAgMg remains paramagnetic down to 2 K. The experimental magnetic moment of 2.52(2) μ_B/Ce above 50 K is compatible with trivalent cerium. EuAgMg and EuAuMg are paramagnetic above 50 K with experimentalmagnetic moments of 7.99(5) μ_B/Eu for the silver and 7.80(5) μ_B/Eu for the gold compound, indicating divalent europium. Ferromagnetic ordering is detected at T_C=22.0(3) K (EuAgMg) and T_C=36.5(5) K (EuAuMg). At 4.2 K and 5 T the saturation magnetizations are 7.1(1) and 7.3(1) μ_B/Eu for EuAgMg and EuAuMg, respectively. According to the very small hysteresis, EuAgMg and EuAuMg may be classified as soft ferromagnets. All compounds are metallic conductors. For EuAgMg and EuAuMg freezing of spin-disorder scattering is observed below T_C. At 78 K ¹⁵¹Eu Mössbauer spectra show isomer shifts of −9.00(4) and −8.72(8) mm/s for EuAgMg and EuAuMg, respectively. Full magnetic hyperfine field splitting is detected at 4.2 K with hyperfine fields of 17.4(1) and 18.3(2) T at the europium nuclei of EuAgMg and EuAuMg.