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991.
Nikolaií N. Nekhoroshev Dmitrií A. Sadovskií Boris I. Zhilinskií 《Annales Henri Poincare》2006,7(6):1099-1211
We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map
of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal
mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors
before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss
manifestations of this monodromy in quantum systems.
Communicated by Eduard Zehnder
Submitted: February 25, 2005; Accepted: November 17, 2005 相似文献
992.
993.
994.
I. N. Medvedev G. A. Mikhailov 《Computational Mathematics and Mathematical Physics》2006,46(8):1442-1458
The efficiency of the “value” and “partial value” modeling related to the construction of a modeling distribution for an auxiliary random variable by multiplying the initial density by a value function is investigated. The value function usually corresponds to a solution of the adjoint equation. Conditions under which the value modeling of the initial distribution reduces the variance compared to the direct simulation are obtained. It is proved that the variance of the weighted estimate is bounded in the case of the partial value modeling. This proposition provides a basis for a method for determining whether or not the variance of the weighted estimate is bounded. This method uses the majorizing adjoint equation. Using a practically important problem in transport theory as an example, the asymptotic optimization of the distribution of the mean free path is presented. The application of the proposed method of the investigation of the variance boundedness for the analysis of the classical exponential transformation method of simulating the mean free path of a particle in the one-dimensional and the spherical variants is discussed. 相似文献
995.
996.
997.
Characterization of spherical particles using high-order neural networks and scanning flow cytometry
Vladimir V. Berdnik Alexander Shvalov Valeri Maltsev Valery A. Loiko 《Journal of Quantitative Spectroscopy & Radiative Transfer》2006,102(1):62-72
We retrieve the radius R, real n and imaginary k parts of the refractive index of homogeneous spherical particles using angular distribution of the light-scattering intensity. To solve the inverse light-scattering problem we use a high-order neural-network technique. The effect of network parameters on optimization is examined. The technique is evaluated for noise-corrupted input data at 0.6 μm<R<10.6 μm, 1.02<n<1.38, and 0<k<0.03. The errors of retrieval for nonabsorbing particles do not exceed 0.05 μm for radius and 0.015 for refractive index. The experimental verification is fulfilled by experimental data retrieved by means of a scanning flow cytometer. The light-scattering profiles of polystyrene beads and spherized red blood cells are processed with the high-order neural networks and a non-linear regression at Mie theory. The parameters retrieved by the high-order neural networks correlate well with the parameters retrieved by the least-square method. 相似文献
998.
Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe2B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αxβ, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe2B in 1045 steel, 15.8% for FeB and 3.4% for Fe2B in M2 steel. 相似文献
999.
We study experimentally the frequency dependences of the refractive index n and the absorption coefficient k of distilled,
sea, and river water. The measurements were performed using a quasioptical device with a backward-wave oscillator as the radiation
source and OAP-7 optical-acoustic receivers at a water temperature of 27°C in the cell. The quantities n and k were determined
from the measured transmission and reflection coefficients of the cell with water by means of joint numerical solution of
the equations for these quantities. For distilled water in the frequency range f = 75–120 GHz, we obtained n = 6.142–3.926
· 10–2f[GHz] + 1.307 · 10–4(f[GHz])2 and k = 3.607–2.101 · 10−2 f[GHz] + 5.252 · 10–5(f[GHz])2. On the whole, these data are in good agreement with the measurement results obtained by other authors at several frequencies
of the indicated range and coincide with the calculation data based on the models by Meissner and Wentz and by Liebe et al.
within the limits of the rms determination errors 0.05 and 0.02 for the parameters n and k, respectively. The values of n
and k for different seawater samples and river water containing insoluble admixtures coincide with the values of these quantities
for distilled water within the limits of the experimental measurement errors 3–5% and 1–2%, respectively. The dependences
n(f) and k(f) obtained experimentally for seawater are compared with those calculated on the basis of the developed models.
Measurements of the transmission spectrum of a cell with double distilled water were performed for low power density of radiation
(less than μW/cm2) to reproduce the effect of water resonant transparency reported many times in the literature. Our measurements did not reveal
any resonant features in the spectral behavior of the refractive index n and the absorption coefficient k of water and gave
the same result as for a power density exceeding the threshold of appearance of this effect.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 489–501, June 2006. 相似文献
1000.