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 degree As a corollary we obtain that the moduli space of rank 3 and degree 0 bundles on a smooth projective curve of genusg is C-M. Lower degree bounds for modular invariants and a question of I. In particular, we prove an integral formula for the degree of an ample divisor on a variety of complexity 1, and apply this formula to computing the degree of a closed 3-dimensional orbit in any SL2-module. Given integers n,d,e with $1 \leqslant e >amp;lt; \frac{d}{2},$ let $X \subseteq {\Bbb P}^{\binom{d+n}{d}-1}$ denote the locus of degree d hypersurfaces in ${\Bbb P}^n$ which are supported on two hyperplanes with multiplicities d-e and e. This paper studies intersection theory on the compactified moduli space ${\mbox{$\cal M$}} (n,d)$ of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface $\Sigma$ of genus $g \geq 2$ where n and d may have common factors. We consider free affine actions of unipotent complex algebraic groups on Cn and prove that such actions admit an analytic geometric quotient if their degree is at most 2. Moreover, we classify free affine C2-actions on Cn of degree n - 1 and n - 2. For every n >amp;gt; 4, an action of degree n - 2 appears in the classification whose quotient topology is not Hausdorff. Let n(Φ) be the transcendence degree of k(X)Φ over k. Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K) Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree Hence, we are able to approximate (in the L2-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Hence, we are able to approximate (in the L2-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Schr?dinger equation and oscillatory Hilbert transforms of second degree We assume that Ω∈L logL(Sn-1) is homogeneous of degree zero and ∫Sn-1Ω=0. The accuracy of f is the highest degree p such that all multivariate polynomials q with degree(q)>amp;lt;p are exactly reproduced from linear combinations of translates of f1,...,fr along the lattice Γ. These coefficients are multivariate polynomials yα,i(x) of degree |α| evaluated at lattice points k∈Γ. Let P be a non-negative, self-adjoint differential operator of degree d on ?n. The notions of localization and related approximation properties are a spectrum of ideas that quantify the degree to which elements of one frame can be approximated by elements of another frame. may be expressed simply with the help of higher degree Poisson wavelets.

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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