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71.
Belov V. V. Dobrokhotov S. Yu. Maksimov V. A. 《Theoretical and Mathematical Physics》2003,135(3):765-791
Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics. 相似文献
72.
In a recent paper to this journal (Whitman A M et al 2003 Waves Random Media 13 269-86) we derived a set of coupled equations that describe the intermodal scattering of acoustic radiation in a duct whose speed of sound varies randomly in space and time. In the paper we were mainly interested in modes that were not near cutoff. Here we study the solution of these equations in the vicinity of the cutoff. We find that near cutoff almost all the energy is reflected back independent of the other duct parameters. In addition to presenting these results, we analyse the mathematical structure of the equations in these regions in order to elucidate the reason for this behaviour. 相似文献
73.
The rate constants k1 for the reaction of CF3CF2CF2CF2CF2CHF2 with OH radicals were determined by using both absolute and relative rate methods. The absolute rate constants were measured at 250–430 K using the flash photolysis–laser‐induced fluorescence (FP‐LIF) technique and the laser photolysis–laser‐induced fluorescence (LP‐LIF) technique to monitor the OH radical concentration. The relative rate constants were measured at 253–328 K in an 11.5‐dm3 reaction chamber with either CHF2Cl or CH2FCF3 as a reference compound. OH radicals were produced by UV photolysis of an O3–H2O–He mixture at an initial pressure of 200 Torr. Ozone was continuously introduced into the reaction chamber during the UV irradiation. The k1 (298 K) values determined by the absolute method were (1.69 ± 0.07) × 10?15 cm3 molecule?1 s?1 (FP‐LIF method) and (1.72 ± 0.07) × 10?15 cm3 molecule?1 s?1 (LP‐LIF method), whereas the K1 (298 K) values determined by the relative method were (1.87 ± 0.11) × 10?15 cm3 molecule?1 s?1 (CHF2Cl reference) and (2.12 ± 0.11) × 10?15 cm3 molecule?1 s?1 (CH2FCF3 reference). These data are in agreement with each other within the estimated experimental uncertainties. The Arrhenius rate constant determined from the kinetic data was K1 = (4.71 ± 0.94) × 10?13 exp[?(1630 ± 80)/T] cm3 molecule?1 s?1. Using kinetic data for the reaction of tropospheric CH3CCl3 with OH radicals [k1 (272 K) = 6.0 × 10?15 cm3 molecule?1 s?1, tropospheric lifetime of CH3CCl3 = 6.0 years], we estimated the tropospheric lifetime of CF3CF2CF2CF2CF2CHF2 through reaction with OH radicals to be 31 years. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 26–33, 2004 相似文献
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D. N. Karimov E. A. Krivandina Z. I. Zhmurova B. P. Sobolev V. A. Bezhanov S. P. Chernov G. M. Shapochkin 《Crystallography Reports》2006,51(6):1009-1015
Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca1?x R xF2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region. 相似文献
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We present here a methodology for searching a robust pore size distribution (PSD) for adsorbent materials. The method is based on a combination of individual adsorption isotherms, obtained from Grand Canonical Monte Carlo simulations, a regularization procedure to invert the adsorption integral equation (Tikhonov regularization solved by singular value decomposition), and the needed experimental adsorption isotherm. The selection of several parameters from the available choices to start the procedure are discussed here: the size of the kernel (number of individual pores and number of experimental adsorption points to be included), the fulfillment of the Discrete Picard condition, and the L-curve criteria, all leading to find a reliable and robust PSD. The procedure is applied to plugged hexagonal templated silicas (PHTS), synthesized, and characterized in our laboratory. 相似文献
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