Mössbauer studies on the series La1-xSrxFeO3

Mössbauer spectra have been recorded at 4.2 and 300 K on the series La_1–x Sr _x FeO₃, wherex varies from 0 to 1.0 in steps of 0.1. Neutron diffraction experiments have shown that the crystal structure is orthorhombic for 0x<0.3, rhombohedral for 0.4x0.7, and cubic for 0.8<x1.0. Mössbauer spectra at 4.2 K are composed of magnetic sextet components arising from different charge states of iron ions. In the orthorhombic and rhombohedral phases, the charge states Fe³⁺ and Fe⁵⁺ coexist. In the cubic phase, iron is present as Fe³⁺ and Fe⁴⁺ states. At 300 K, the samples are magnetically ordered in the range 0 x0.3 and the coexistence of Fe³⁺ and Fe⁵⁺ remains. For samples 0.4x1.0, the samples are paramagnetic. Fits to these spectra require two components, one corresponding to an Fe⁴⁺ state, the other being best described as an Fe³⁺ ion forx0.7 but forx>0.7 having a mean charge state which increases to 3.5 forx=1.0.     

Enlarged scaling ranges for the KS-entropy and the information dimension

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data. (c) 1996 American Institute of Physics.     

Phenyldimethylsilyl-Substituted Ketenes and Bisketenes

The phenyldimethylsilyl-substituted monoketene PhMe(2)SiCH=C=O (1) and bisketene (PhMe(2)SiC=C=O)(2) (3) have been prepared and compared to the corresponding Me(3)Si- and t-BuMe(2)Si-substituted species. The (13)C, (17)O, and (29)Si NMR spectra fit the pattern shown by other silylketenes and provide no evidence for transmission of a substituent effect of the Ph group through the silicon to the ketenyl group, as has been proposed for PhMe(2)Si-substituted radicals. The UV spectrum of 1 does show a longer lambda and greater epsilon than for t-BuMe(2)SiCH=C=O, and this may indicate some interaction of the phenyl group with the ketene chromophore, while the greater reactivity of 1 in hydration compared to t-BuMe(2)SiCH=C=O is ascribed to the inductive effect of the phenyl. The very similar ring-opening reactivity of the bis(phenyldimethylsilyl)cyclobutenedione (6) to form 3 compared to the bis(Me(3)Si) analogues also provides no evidence of a significant interaction of the phenyl with the ketene. A new type of stabilized 1,8-bisketene based on the arylbis(dimethylsilyl) grouping, namely, 1,4-bis(ketenyldimethylsilyl)benzene (12), has been prepared for the first time.     

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.     

Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.