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21.
This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. 相似文献
22.
S. A. Gurevich T. A. Zaraiskaya S. G. Konnikov V. M. Mikushkin S. Yu. Nikonov A. A. Sitnikova S. E. Sysoev V. V. Khorenko V. V. Shnitov Yu. S. Gordeev 《Physics of the Solid State》1997,39(10):1691-1695
The concentration and chemical state of copper in the subsurface region of Cu/SiO2 composite films obtained by simultaneous magnetron sputtering from two sources (Cu and SiO2) are determined by x-ray photoelectron spectroscopy (XPS). It is established that copper in the as-grown film is primarily in the form of unoxidized atoms dispersed in a SiO2 matrix. Annealing of the film results in practically no oxidation, but about 70% of the copper atoms condense into metallic clusters with sizes below 10 Å in the subsurface region and about 50 Å in the bulk of the film. The changes in the binding energy of core electrons, and especially in the energies of Auger electrons, are so large in this situation that photoelectron and Auger spectroscopy are efficient methods for monitoring the chemical state of this composite material. 相似文献
23.
L. K. Aminov I. N. Kurkin D. A. Lukoyanov K. P. Chernov 《Physics of the Solid State》1997,39(8):1184-1186
Results are reported for measurements of the spin-lattice relaxation times of E′1 centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz
over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of
the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm−1. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency
dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation
of irradiation centers in crystalline quartz and quartz glass.
Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997) 相似文献
24.
The effect of iodine sorption on the free volume of polycarbonate is investigated by Positron Annihilation Lifetime method.
The observed results are interpreted in terms of the Charge Transfer Complex formation and precipitation of iodine at the
initial and final stages of sorption, respectively. At higher levels of sorption, changes in the second lifetime and its intensity
seem to suggest a conformational transformation, probably due to the net change in the amorphous-crystalline boundary regions
of the polymer matrix. The free volume cavities have been predominantly occupied by I-
3 species and the diffusion process obeys Fick’s law. An exponential type correlation has been observed between fractional
free volume and the diffusion coefficient.
Received: 13 June 1996/Accepted: 20 September 1996 相似文献
25.
We provide a characterization of the limit periodic sets for analytic families of vector fields under the hypothesis that the first jet is non-vanishing at any singular point. Also, applying the family desingularization method, we reduce the complexity of some of these sets. 相似文献
26.
Daniel L. Feldheim Del R. Lawson Charles R. Martin 《Journal of Polymer Science.Polymer Physics》1993,31(8):953-957
We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc. 相似文献
27.
J. E. Fischer E. Werwa P. A. Heiney 《Applied Physics A: Materials Science & Processing》1993,56(3):193-196
We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C60 evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C60 planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C60 is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy. 相似文献
28.
29.
30.
Using an integral theory of grating diffraction we calculate efficiencies greater than 100% if a coating with gain is taken into account. A connection with guided modes is conjectured. The application in optical computing seems to be possible. 相似文献