Bounds for bounded motion around a perturbed fixed point

We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the bound on the perturbation. This method yields a value _c such that for< _c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of basin and attractor respectively).The analysis is based on the Lyapunov function which exists for the unperturbed map.     

Weighted Banzhaf values

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.     

Reduced and excited states of the intermediates (alpha-diimine)(C5R5)Rh in hydride transfer catalysis schemes: EPR and resonance Raman spectroscopy, and comparative DFT calculations of Co, Rh and Ir analogues

The electronic structures of the highly air-sensitive intermediates (N[caret]N) (C(5)Me(5))Rh, (N[caret]N = 2,2'-bipyridine (bpy), 2,2'-bipyrimidine (bpym), 2,2'-bipyrazine (bpz) and 3,3'-bipyridazine (bpdz)) of hydride transfer catalysis schemes were studied through resonance Raman (rR) spectroscopy and through EPR of the reduced forms [(N[caret]N) (C(5)Me(5))Rh](.-). The rR results are compatible with a predominant MLCT character of the lowest excited states [ (N[caret]N) (C(5)Me(5))Rh]*, and the EPR spectra of the reduced states reveal the presence of anion radical ligands, (N[caret]N) (.-), coordinated by unusually electron rich rhodium(i) centres. The experimental results, including the assignments of electronic transitions, are supported by DFT calculations for the model compounds [(N[caret]N)(C(5)H(5))Rh](o)/(.-), (N[caret]N) = bpy or bpym. The calculations confirm a significant but not complete mixing of metal and ligand orbitals in the lowest unoccupied MO which still retains about 3/4 pi* (N[caret]N) character. DFT calculations on (bpy)(C(5)H(5))M and [(bpy)(C(5)H(5))ClM](+), M = Co, Rh, Ir, agree with the experimental results such as the differences between the homologues, especially the different LUMO characters of the precursor cations in the case of Co-->d(M)) and Rh or Ir (-->pi*(bpy)).     

Thermal decomposition of hydrotalcitewith hexacyanoferrate(II) and hexacyanoferrate(III) anions in the interlayer

The thermal decompositions of hydrotalcites with hexacyanoferrate(II) and hexacyanoferrate(III) in the interlayer have been studied using thermogravimetry combined with mass spectrometry. X-ray diffraction shows the hydrotalcites have a d(003) spacing of 11.1 and 10.9 Å which compares with a d-spacing of 7.9 and 7.98 Å for the hydrotalcite with carbonate or sulphate in the interlayer. XRD was also used to determine the products of the thermal decomposition. For the hydrotalcite decomposition the products were MgO, Fe₂O₃ and a spinel MgAl₂O₄. Dehydration and dehydroxylation take place in three steps each and the loss of cyanide ions in two steps.     

Thermal decomposition of the vivianite arsenates—implications for soil remediation

The presence of arsenate compounds in soils and mineral dump leachates is common. One potential method for the removal of the arsenates from soils is through thermal treatment. High-resolution thermogravimetric analysis has been used to follow this thermal decomposition of selected vivianite arsenates. This decomposition occurs as a series of steps. The first two steps involve dehydration with 6 mol of water lost in the first step and two in the second. The third major weight loss step occurs in the 750-800 °C temperature range with de-arsenation. The application of infrared emission spectroscopy confirms the loss of water by around 250 °C and the loss of arsenic as arsenic pentoxide is observed by the loss of AsO stretching bands at around 826 cm⁻¹. Thermal activation of arsenic contaminated soils may provide a method of decontamination.     

Projektivitätengruppen von ovoidalen Möbius-und Laguerreebenen

Zusammenfassung Die Untersuchungen über Projektivitätengruppen in Möbius- und Laguerreebenen von Freudenthal-Strambach [7], Kroll [16] und Funk [9] zeigten, daß die Schärfe der dreifachen Transitivität dieser Gruppen gerade die miquelschen Ebenen charakterisiert. Die vorliegende Arbeit zielt vor allem darauf, für endliche nichtmiquelsche Möbius- und Laguerreebene die Projektivitätengruppe anzugeben. Dazu identifizieren wir zunächst einige Untergruppen (P) der Projektivitätengruppe, und untersuchen dann im zweiten Abschnitt die Beziehungen dieser Gruppen zueinander, wobei sich Zusammenhänge mit der Steinerschen Erzeugung von Kegelschnitten ergeben. Nach diesen Vorbereitungen ergibt sich dann Satz 3.1, der besagt, daß die Projektivitätengruppe jeder endlichen ovoidalen Möbius- oder Laguerreebene, welche nicht miquelsch ist, die alternierende Gruppe enthält. Abschnitt 4 liefert schließlich Methoden zur Beantwortung der Frage, ob eine solche Projektivitätengruppe ungerade Permutationen enthält. Damit kann man z.B. die genauen Projektivitätengruppen der Möbiusebenen vom Suzuki-Tits-Typ angeben (Korollar 4.9).     

Population of the states in collisions of mixed-state (1s21S,1s2s3S) B3+ and C4+ ion beams with He and H2 targets

Auger KLn lines are observed in high-resolution electron spectra obtained in collisions of mixed-state (1s²¹S,1s2s³S) He-like beams of 4 MeV B³⁺ with H₂ and 6 MeV C⁴⁺ with He targets. Supporting atomic structure calculations show these lines to correspond to doubly excited states, which can be readily populated by electron transfer to the component of the mixed-state beam. They thus provide indirect evidence for the existence of the corresponding KLn quartet states, similarly produced, even though their weak Auger decay does not allow for their direct observation in the electron spectra. These KLn quartet states mostly decay in a cascade chain of strong radiative E1 transitions, eventually terminating at the state, which is thus additionally enhanced. An upper limit on the state population due to cascades is obtained by assuming a statistical production of KLn quartet to doublet states followed by a 100% cascade feeding of the state. Our estimated upper limit is supported by our absolute cross section measurements and corresponding three-electron atomic orbital close coupling calculations in progress. Results to date are presented and discussed.