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.     

Selective mixed coupling of carboxylic acids (II). — photolysis of unsymmetrical diacylperoxides with alkenyl-, halo-, keto-, carboxyl-groups and a chiral α-carbon. Comparison with the mixed kolbe electrolysis

Alkenoyl and functionalized alkanoyl dodecanoyl peroxides are prepared in 70 to 97 % yield and photolyzed at ?78° C. Thereby 4- to 10-alkenoyl and 4-alkanoyl peroxides afford good yields (56 – 68 %) of unsymmetrical coupling products. Similarly α- to σ-haloalkanoyl, cholanoyl or 3- and 4-carboxyalkanoyl peroxides can be coupled (40 – 70 %). The α-chiral diacyl peroxide ls undergoes the photochemical coupling reaction with 80 % retention of its configuration. The photolysis of diacyl peroxides at ?78° C proves to be a favorable supplement of the Kolbe-electrolysis in cases, where the electrolysis fails or produces low yields.     

On the formation of the [M ? OH]+ ion in m-nitrobenzaldoxime. evidence for a cyclohexadiene-type intermediate ion

In m-nitrobenzaldoxime a strongly enhanced loss of OH? is observed as compared with the p-nitro compound. Evidence is presented for a fragmentation mechanism involving the formation of a cyclohexadiene-type intermediate ion formed by a rearrangement of the hydroxyl hydrogen to the phenyl ring.     

High-Resolution,Higher-Order UV/VIS Derivative Spectrophotometry

Derivative spectrophotometry has gained increasing importance in the past two years and is currently experiencing vigorous development. Following and introduction the present article provides a review of this extremely effective method. In particular, the advantages of higher-order derivative spectrophotometry (HODS method, n > 2) are discussed on the basis of practical examples from a wide range of analytical fields. The results are achieved with the aid of a newly developed analog computer unit, whereby for the first time readily reproducible, low-noise, on-line spectra can be obtained up to the 7th order and even, in favorable cases, up to the 9th order. In practice it has proved valuable to work with spectra of the 3rd to 5th order; but even higher derivations could be profitable for the separation of strongly superposed signals or for “fingerprinting”.     

Zdanovskii’s Rule and Isopiestic Measurements Applied to Synthetic Bayer Liquors

Isopiestic measurements of mixed electrolyte solutions involving sodium hydroxide and other components of Bayer liquors were performed at 50?°C and 100?°C. Most of the systems studied obey Zdanovskii’s rule exactly or very closely. However, those with sodium chloride as one of their components show deviations from Zdanovskii’s rule, which are well predicted by our thermodynamic modelling software based on Pitzer’s equations.     

Approximate molecular orbital theory: the ese mo formalism.: III. Parametrization for all- or valence-electron calculation using accurate STF bases for molecules containing 1st, 2nd,and 3rd row atoms. SO2 results

The key components of a completely theoretical parametrization of the essential-structural-elements molecular orbital (ESE MO) formalism using Slater-type AO basis in the LCAO SCF procedure are discussed. Special attention is paid to the problem of separability into core and valence parts of the total molecular wavefunction, including the case where valence functions strongly overlap neighbouring core orbitals. The use of Huzinaga and Cantu effective hamiltonian is proposed. The parametrization is tested in relation to the SO₂ molecules. The role of sulphur 3d functions in bonding as predicted by the present ESE MO calculations and ab initio calculations are compared. The present parametrization appears to adequately handle both the core/valence separation, and the diffuse higher valence sulphur 3d functions in this system.     

Isolierung von (−)-Dunnion aus Calceolaria integrifolia MURR. (Scrophulariaceae)

Isolation of (?)-dunnione from the leaves of Calceolaria integrifolia, MURR . (fam. Scrophulariaceae) From the leaves of Calceolaria integrifolia, a plant often used in horticulture. partially racemic (?)-dunnione (1) has been isolated. This seems to be the first record of its occurrence outside the family Gesneriaceae, where it previously has been found in two species as the (+)-enantiomer.     

Hexacyanopalladium(IV)-säure und Hexacyanopalladate(IV)

The preparation and the properties of the hexacyanopalladium(IV) acid (H₃O)₂[Pd(CN)₆] and of a number of metal hexacyanopalladates(IV) are described. UV, IR and Raman spectra are reported, force constants have been calculated and the bonding properties are discussed. K₂[Pd(CN)₆] crystallizes in a hexagonal lattice; a = 7.42, c = 6.65 Å, Z = 1.     

Reactions of 6-diazopenicillanates with allylic sulphides,selenides, and bromides

6-Diazopenicillanates react with allylic sulphides, selenides and bromides, to give 6,6-disubstituted penicillanates $\text{via}$ [2,3]-sigmatropic rearrangements.