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991.
Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc. 相似文献
992.
In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions. 相似文献
993.
994.
This work deals with the polymer latexes synthesized using zinc-containing monomers. The effect of the ligand environment of the zinc-containing monomers on the colloidal and rheological properties of the latexes, as well as on mechanical properties of their films is studied. Mixed zinc salts containing the residues of saturated and unsaturated carboxylic acids are shown to be more efficient cross-linking agents than the symmetric salts of this metal. 相似文献
995.
E. V. Ermanyuk 《Experiments in fluids》2002,32(2):242-251
This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly
stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating
in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional
similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by
vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids
having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients
is based on Fourier analysis of the time-history of damped oscillation tests.
Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001 相似文献
996.
997.
This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced. 相似文献
998.
A modernized conception of hierarchical structure of reality is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–6, December, 1980. 相似文献
999.
1000.
V. I. Bliznikas A. P. Norden B. N. Shapukov A. P. Shirokov 《Journal of Mathematical Sciences》1991,55(6):2091-2100
Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989. 相似文献