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41.
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
42.
Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()α≤≤ ()
n
−ω. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour
number μ(G) of G: n− (n−ω)()
n
−ω≤μ(G)≤n−α() α.
Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002 相似文献
43.
The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal. 相似文献
44.
Onofrio Mario Di Vincenzo Plamen Koshlukov Roberto La Scala 《Advances in Applied Mathematics》2006,37(4):541
In this paper we describe completely the involutions of the first kind of the algebra UTn(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UTn(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT2(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT3(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UTn(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities. 相似文献
45.
R. Martínez-Snchez J. A. Matutes-Aquino O. Ayala-Valenzuela S. D. De la Torre 《Physica B: Condensed Matter》2002,320(1-4):285-287
An amorphous phase containing traces of non-transformed Co and Ti powders was obtained by mechanical alloying nominal compositions of Co67Ti33 and Co50Ti50 in a high-energy ball-mill. These alloys were prepared from elemental powders of Co and Ti. The heat treatment of Co67Ti33 at 573, 873 and 1173 K crystallized nanoparticles of Co2Ti and Co3Ti compounds, while the same treatments conducted on Co50Ti50 resulted in the formation of Co2Ti and CoTi nanoparticles. The saturation magnetizations reached a maximum value in the amorphous state and they decreased when the temperatures of the heat treatment rose. Demagnetizing interparticle interaction effects were estimated through hysteresis loops and initial magnetization curves using the Fourier technique. 相似文献
46.
We study the propagation of the light mesons σ,ω,ρ, and a0(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible
to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric
nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation
of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated.
Received: 16 October 2001 / Accepted: 10 January 2002 相似文献
47.
Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the ql-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as ql-integrable f with q(|f|) < ∞, and of ql-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most
finitely additive integration theories. 相似文献
48.
49.
In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure,
over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative
measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique
of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained
quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely
different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms
of cyclic coarse-grained quantum logics. 相似文献
50.