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 standard The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [GPS] and to groups generated by reflections. A new approach to standard monomial theory for classical groups As an immediate application we obtain a new proof of the main theorem of standard monomial theory for classical groups. There are two well known combinatorial tools in the representation theory ofSLn, the semi-standard Young tableaux and the Gelfand-Tsetlin patterns. Fr?nsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebraUq(g). For a smooth oriented surface Σ, denote byM(Σ) the set of all ways to represent Σ as a result of gluing together standard spheres with holes ("the Lego game"). We give the classification of all finite dimensional Levi-Tanaka algebras of CR codimension two and construct the corresponding standard homogeneous CR manifolds. In addition to the standard cohomological tools in algebraic geometry, the proof crucially relies on the nonvanishing of certain 3j-symbols from the quantum theory of Standard monomial bases, Moduli spaces of vector bundles, and Invariant theory This does not, however, give rise to vanishing identities for the standard nonsymmetric Macdonald and Koornwinder polynomials; we discuss the required modification to these polynomials to support such results. This paper presents an expansion for radial tempered distributions on ${\bf R}^n$ in terms of smooth, radial analyzing and synthesizing functions with space-frequency localization properties similar to standard wavelets. This paper proves that every standard digit set D gives a setT (A, D) that tiles?n with a lattice tiling. Let ? denote the standard (i.e., Levi-Civita) Laplacian for some non-compact, connected, complete, separable Riemannian manifild M. This problem does not arise if f is continuous, and can be removed by using the standard summability methods. The definitions of the ?∞,qα spaces are extended in a natural way to ?∞,∞α and it is proven that this is the same space as ?∞,∞α, which justifies the standard convention in which the two spaces are defined to be equal. The use of time-frequency methods (phase space methods) allows the use of rough symbols of ultra-rapid growth in place of smooth symbols in the standard classes. We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at The CoMFA model developed using most common structure based alignment and tripos standard field demonstrated high predictive ability (q2 = 0.573, r2 = 0.711).

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2008 CNKI－中国知网

2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社