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 application As an application we produce complete hyperbolic 5-manifolds that are nontrivial plane bundles over closed hyperbolic 3-manifolds and conformally flat 4-manifolds that are nontrivial circle bundles over closed hyperbolic 3-manifolds. As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras. The proof is an application of a recent result by W. The application arises because of a very strong homological property enjoyed by certain cell filtrations forq-permutation modules. We give as an application a family of singular Schubert varieties. As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups. As an application, under the same assumption on the transitive group, we show that weakly symmetric spaces are precisely the homogeneous Riemannian manifolds with commutative algebra of invariant differential operators. As an application, we derive the Kazhdan-Lusztig conjecture for nonintegral blocks from the integral case for finite or affine Weyl groups. As the first application, we present the first and second fundamental theorems for ${\rm SO}_n(K)$-actions. As the third application, we describe a K-basis for the ring of invariants for the adjoint action of ${\rm SL}_2(K)$ on m copies of $sl_2(K)$ in terms of traces. As an application, we determine the conjugacy classes of automorphisms of the plane for which n(Φ) = 1. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials that are not Riesz bases for $L^2[-R,R].$ A signal processing application in which such sampling sets arise naturally is described in detail. As an application we prove new theorems concerning stability offrames (and frame-like decompositions) under perturbation in both Hilbert spaces and Banach spaces. As an application, starting from the Monge-Ampère setting introduced in [3], we get a space of homogeneous type modeling the real analysis for such an equation. As an application of these techniques, we prove that the set of MRA wavelets is arcwise connected in L2(R). As an application we give lower bounds for convolutions ? ? f, where ? is a radially decreasing function. As an application we construct statistically selfsimilar Salem sets. The estimates then follow from a simple application of Gershgorin's theorem to each matrix. As an application of this abstract formulation, a constructive procedure is developed, which produces all wavelet sets in ?nrelative to an integral expansive matrix. Application to estimating the initial heat distribution is analyzed.

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2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社