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Factorization of Operators in Krein Spaces and Linear-Fractional Relations of Operator Balls

Advances in Pure Mathematics 2013年第1期3卷 29-33页

作者： Victor anatoly Khatskevich valery anatoly senderov Department of Mathematics ORT Braude Academic College Karmiel Israel Pyatnitskoe Highway 23-2-156 Moscow Russia

We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.

关键词： Krein Space Linear Fractional Relation Plus-Operator Factorization

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The Research of Fractal Characteristics of the Electrocardiogram in a Real Time Mode

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Journal of Mathematics and System Science 2012年第3期2卷 191-195页

作者： valery Antonov anatoly Kovalenko Artem Zagaynov Vu Van Quang St. Petersburg State Polytehnical University St. Petersburg 195251 Russia loffe Physical-Technical Institute of the Russian Academy of Sciences St. Petersburg 194021 Russia

The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric （and probabilistic） properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.

关键词： Holter monitoring ECG correlation dimension fractal analysis of time series non-linear dynamics of heart rate

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AFM Height Measurements of Molecular Layers of a Carbocyanine Dye

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World Journal of Nano Science and Engineering 2011年第3期1卷 67-72页

作者： valery V. Prokhorov Sergey I. Pozin Dmitry A. Lypenko Olga M. Perelygina Eugene I. Mal’tsev anatoly V. Vannikov Frumkin Institute of Electrochemistry of the Russian Academy of Sciences

Atomic force microscopy (AFM) was used for the morphological characterization and precise height meas-urements of two-dimensional molecular layers of carbocyanine dye 3,3’-di(r-sulfopropyl)-4,4’,5,5’-dibenzo-9-ethylthiacarbocyanine betaine pyridinium salt. The AFM measurements reveal three morphological types of molecular aggregates: leaves, stripes and spots. The leaves are stripes have same monolayer height ~1.4 nm and different crystal shapes: the leaves are monoloyers with the lens shape and the stripes are bilay-ers with the shape of extended rectangles. The monolayer height ~1.4 nm was interpreted as indicating the symmetrical packing arrangement of dye molecules. In the symmetrical monolayer, the sulfopropyl groups of all-trans monomer units are located on both monolayer sides whereas the adjacent stacked dye molecules have a lateral slippage providing the J-aggregate optical properties. The lower height of spots ~1 nm was explained by the model of an asymmetric monolayer with sulfopropyl groups of all-trans monomers occupy-ing the same position with respect to the monolayer plane. The packing arrangement of all-trans monomers in the asymmetric monolayer corresponds to H-aggregate. The alternative models of the packing arrange-ment in monolayers with mono-cis1 monomer configuration are discussed.

关键词： Atomic Force Microscopy J-Aggregates H-Aggregates Monolayers

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Change in the Pore Structure of Carbon-Carbon Composites during Successive Stages of High-Pressure Impregnation and Heat Treatment

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Journal of Chemistry and Chemical Engineering 2012年第12期6卷 1056-1060页

作者： Ekaterina V. Koganl Yury M. Volfkovich Artem P. Malakho valery V. Kulakov anatoly M. Kenigfest Valentin E. Sosenkin Chemistry Department Moscow State University Moscow 119991 Russia Frumkin Institute of Physical Chemistry and Electrochemistry Russian Academy of Science Moscow 119071 Russia OAO Rubin Aircraft Corporation Balashikha 143900 Russia

Pore structure of C/C （Carbon-Carbon） composite after several stages of pitch impregnation under the high pressure and heat treatment was investigated by means of low temperature nitrogen adsorption and the standard contact porosimetry. Total pore volume, pore size distribution and specific surface area were calculated for samples of composite after several successive stages of treatment. The radius of pores presented in the material changes from 1 nm to 90 tam. Total pore volume and specific surface area both decrease after successive stages of pitch impregnation under the pressure, whereas heat treatment up to 1,750 ℃ and 2,000 ℃ leads to creation of some porous space and pore volume expansion. The bulk porosity of C/C composite comes down from 33.7% to 13.7% after the serial stages of treatment and the specific surface area is reduced by half compared to the initial material.

关键词： Carbon-carbon composite pore structure total pore volume specific surface area high-pressure impregnation heattreatment.

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