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.     

Determination of platinum and palladium in strongly acid solution by means of flow injection analysis

Microamounts of Pt(II/IV) (0.25–800 μg/ml) and Pd(II) (5–600 μg/ml) in> 0.5 M hydrochloric acid can readily be determined by means of a simple FIA method based on the selective reaction of tin(II)chloride with these metals. The FIA method has a high linear dynamic range, and is relatively free from interferences of many transition metals, with the exception of Au and Rh; small amounts of other PGMs can be tolerated. Determination of Pt on a hydrogenation catalyst by this method compares well with that found by flame atomic absorption spectroscopy. By monitoring at two or more wavelengths, Pt and Pd can be determined in mixtures by this means, to yield a simple, cost-effective FIA method for possible on-line determinations and quality control of, in particular, Pt containing acidic refinery and other process streams.     

Total synthesis and properties of prostaglandins. 36. Condensation of (+)2-oxabicyclo[3.3.0]-6-octen-3-one with furylacrolein and furylpropionic aldehyde

A study was made of the condensation of bicyclic -lactone I with furylacrolein and furylpropionic aldehyde. Significant differences were observed in the reactivity of the aldols obtained, and in the stereochemical trend of their dehydration reaction.For Communication 35, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1035–1039, August, 1993.     

Polyfunctional macroheterocycles. 7. Synthetic enzyme analogs. synthesis of 16- and 22-membered nitrogen and sulfur crown compounds containing exocyclic histamine and histidine fragments and carboxyl groups

The acid hydrolysis of 9,14-bis(2-methoxycarbonylethyl)-11-12-benzo-3,4-(4,5-dimethylbenzo)-10,13-dioxo-1,6-dithia-9,14-diazacyclohexadeca-3,11-diene leads to the corresponding 9,14-biscarboxy derivative. The reaction of 4,9,15,20-tetrakis-(2-methoxycarbonylethyl)-6,7,17,18-dibenzo-5,8,16,19-tetraoxo-1,12-dithia-4,9,15,20-tetraazacyclodocosa-6,17-diene with hydrazine hydrate and subsequent treatment with NaNO₂ gave the corresponding tetraazide. The reaction of this tetraazide with histamine and histidine leads to macroheterocycles, containing exocyclic histamine and histidine fragments.For Communication 6, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 130–133, January, 1993.     

Derivatives of isoquinoline. 30. Synthesis of 4-spirosubstituted dioxenoisoquinolines

Methods have been developed for the synthesis of 1,4-benzodioxanyl-6-ethylamine with cyclopentyl and tetrahydropyranyl substituents in the -position. These compounds have been used as starting materials for the synthesis of new heterocyclic systems, the 4-spirocyclosubstituted dioxinoisoquinolines.For Communication 29, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 677–680, May, 1993.     

Characterisation of chlorinated hydrocarbons in a third generation candidate fish reference material (Limanda limanda) prepared under cryogenic conditions

Summary This paper describes the cryogenic preparation of 50 individual specimens of dab (Limanda limanda) from the Baltic Sea to produce a homogeneous fish material. 950 subsamples (8 g each) are stored in the gaseous phase over liquid nitrogen. Five series of analyses were randomly selected out of store. The results show that the obtained precision of 8 to 9% could be used as an indication unit for the deviation of the mean values of CHC concentrations from true values. If the analytical variability is 5%, the maximum inhomogeneity in the subsamples is 3–4%. It may be concluded that the subsamples of the candidate fish reference material (RM) are homogeneous enough for analytical purposes. Thus ESB (German Environmental Specimen Bank) material prepared in accordance with the standard operating procedure (SOP) [1] are valuable and appropriate reference materials. The prepared fish RM is suitable for the analysis of chlorinated hydrocarbons in fat containing marine samples.     

Synthesis of derivatives of ketocarboxylic acids by the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide

The decomposition of 1,4-dihydroxy-1,4-dihydroperoxycyclohexane under the action of FeSO₄ and the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide under the action of Fe^II salts in the presence of various ligands or under the action of Cu^II sulfate have been studied. A preparative method for the synthesis of derivatives of diketodicarboxylic or -functionally substituted ketocarboxylic acids from 1,4-cyclohexanedione monoethyleneketal has been developed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1231–1235, July, 1993.     

Algebraic version of extension theory for a quantum system with internal structure

An explicit two-channel matrix representation is obtained for the Hamiltonians of systems with internal structure in the framework of the theory of extensions of symmetric operators. Generalized potentials that are equivalent to zero-range interactions with internal structure and automatically reproduce the boundary conditions that correspond to them asx0 are constructed.St. Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 163–181, November, 1993.     

A note on the illumination of convex bodies

LetKE ^d be a convex body and letl _r(K) denote the minimum number ofr-dimensional affine subspaces ofE ^d lying outsideK with which it is possible to illuminateK, where 0rd–1. We give a new proof of the theorem thatl _r(K)(d+1)/(r+1) with equality for smoothK.The work was supported by Hung. Nat. Found. for Sci . Research No. 326-0213 and 326-0113.     

Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.