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We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ0?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ0. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Trukhin D. V. Rogozhnikova O. Yu. Troitskaya T. I. Kuzhelev A. A. Amosov E. V. Halpern H. J. Koval’ V. V. Tormyshev V. M. 《Russian Journal of Organic Chemistry》2019,55(3):296-301
Russian Journal of Organic Chemistry - The reaction of Finland trityl with tertiary aliphatic alcohols containing a terminal tertiary amino group, followed by quaternization of the amino groups,... 相似文献
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We study a problem with rapidly oscillating coefficients which arises in describing the process of thermo-chemical formation
of a composite material. We homogenize this problem and study the existence and uniqueness of solutions to the original and
homogenized problems, as well as properties of the solutions. We estimate an error in homogenization with order O( ?{e} ) O\left( {\sqrt {\varepsilon } } \right) in the energy norm and with order O(ε) in the L
∞-norm. Bibliography: 10 titles. 相似文献
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It is shown that the class of perturbations of the semigroup of shifts on by unitary cocycles with the property (where is the Hilbert-Schmidt class) contains strongly continuous semigroups of isometric operators, whose unitary parts possess spectral decompositions with the measure being singular with respect to the Lebesgue measure. Thus, we describe also the subclass of strongly continuous groups of unitary operators that are perturbations of the group of shifts on by Markovian cocycles with the property .
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We study a class of $E_0$ -semigroups of endomorphisms of a von Neumann factor $\mathcal{M}$ possessing the following property: an $e_0$ -semigroup of endomorphisms of $\mathcal{B}\left( \mathcal{H} \right)$ , where $\mathcal{H}$ is the standard representation space for $\mathcal{M}$ , and a product system of Hilbert spaces can be associated with each of these $E_0$ -semigroups. 相似文献
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We derive the evolution equation for probability distributions and characteristic functions of the quantum tomograms associated with the linear and nonlinear evolutions of quantum states.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 365–370, February, 2005. 相似文献