High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.     

A new antifriction and sealing material based on radiation-modified polytetrafluoroethylene

The current situation with research into the effect of ionizing radiation exposure on the structure and properties of polytetrafluoroethylene was analyzed. New methods of radiation-induced modification, that improve the performance characteristics of polytetrafluoroethylene, were discussed. The results of research into properties of polytetrafluoroethylene irradiated at temperatures exceeding the melting point of its crystalline phase in media with different compositions were presented. It is shown that, under certain irradiation conditions, an extremely strong increase (up to 10 000-fold) in the wear resistance of polytetrafluoroethylene can be achieved, with the creepage decreased up to 100-fold. A conclusion was made that high-temperature radiation-induced modification can yield new modifications of the polymer, in which the advantages offered by untreated polytetrafluoroethylene are combined with high mechanical and triboengineering characteristics.     

Synthesis of triterpene acids α-monoglycerides and their citrates

α-Monoglycerides of triterpene acids, glycyrrhetic and 18-dehydroglycyrrhetic, and their citrates are synthesized. The structures are confirmed using IR, UV, and¹H and¹³C NMR spectroscopies. A. B. Bekturov Institute of Chemical Sciences, Ministry of Science, Academy of Sciences of the Republic of Kazakhstan, Almaty, fax (3272) 61 57 65. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 746–750, November–December, 1999.     

Raman spectroscopic studies of planar gettering effects

Raman scattering spectroscopy is used to study the elastic stress distribution in the epitaxial silicon operating areas in the vicinity of planar getter areas, the latter being created by previous ion implantation of the substrate. Data concerning the effect of the operating element size and the dose of implantation into the getter area are obtained. The results are compared with those of X-ray topographic analysis of the structures.     

Actions of Pointed Hopf Algebras on Quantum Torus

Actions of finite dimensional pointed Hopf algebras on generic quantum torus are classified.

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Sunto Vengono classificate le azioni delle algebre di Hopf puntate di dimensione finita sul toro quantico generico.

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Research partially supported by grants RFBR 03-01-00167, NSh-1910.2003.1 and INTAS00-566     

On symmetry groups of quasicrystals

A relationship between two types of symmetry groups of quasicrystals in the cut-andproject model is studied.     

Influence of a magnetic field on the thermoacoustic stability of a high-temperature heat releasing gas

The conditions of thermoacoustic stability are found for a high-temperature electrically conducting gas with internal heat release in a constant magnetic field which transforms acoustic waves into fast and slow magnetoacoustic oscillations, and also introduces Joule dissipation. The investigation is by means of the energy balance method, and also by direct solution of the equations for small perturbations in the special case of wavelengths of the acoustic oscillations that are short compared with the inhomogeneity scales in the region of heat release. The limits of stability with respect to fast and slow magnetoacoustic oscillations are found.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1979.     

Diazotization of 6-amino-2-phenyl-7-chloro-2H-benzotriazole-4-carboxylic acid and transformations of the resulting diazo compounds

6-Amino-2-phenyl-7-chloro-2H-benzotriazole-4-carboxylic acid was prepared by oxidation of 2,5-diamino-4-chloro-2-phenylazobenzoic acid, and its diazotization and subsequent transformations of the diazo compounds were studied. 7-Hydroxy-2-phenyl-2H-benzotriazole-4-carboxylic acid was prepared.Translated from Zhurnal Obshchei Khimii, Vol. 74, No. 11, 2004, pp. 1894–1897.Original Russian Text Copyright © 2004 by Artamonov, Perevalov.This revised version was published online in April 2005 with a corrected cover date.     

Synthesis of 2-azaanthraquinone and its derivatives

The acylation of benzene, toluene, and chlorobenzene with cinchomeronic acid anhydride in the presence of AlCl₃ has given in each case both possible isomers of the corresponding aroylpyridinecarboxylic acid. It was found that the yields of reaction products and their isomeric compositions depend on the conditions of performing the reaction. The intramolecular cyclization of the isomeric keto acids in the presence of 2% oleum has given 2-azaanthraquinone and chlorine derivatives of it.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 514–518, April, 1980.