共查询到20条相似文献,搜索用时 31 毫秒
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Let H:Cn→Cn be a polynomial map, JH the Jacobian matrix of H , and VH the linear subspace of Mn(C) spanned by {JH(α)|α∈Cn}, the set of evaluated Jacobian matrices of H . We describe the dimension of VH through a power-linear Gorni–Zampieri mate of H, and give a numerical algorithm for computing this dimension and determining whether JH is additive-nilpotent, i.e., whether VH is a nilpotent subspace. 相似文献
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Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
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In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider n discrete time observations with step Δ. The asymptotic framework is: n tends to infinity, Δ=Δn tends to zero while nΔn tends to infinity. First, we use a Fourier approach (“frequency domain”): this allows us to construct an adaptive nonparametric estimator and to provide a bound for the global L2-risk. Second, we use a direct approach (“time domain”) which allows us to construct an estimator on a given compact interval. We provide a bound for L2-risk restricted to the compact interval. We discuss rates of convergence and give examples and simulation results for processes fitting in our framework. 相似文献
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The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg [11] proved that the C?-algebra C?(F∞) of the free group F∞ on countably many generators characterises relative weak injectivity for pairs of C?-algebras by means of the maximal tensor product. One of the main results of this paper shows that C?(F∞) also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products and . 相似文献
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Hadwiger’s Theorem states that En-invariant convex-continuous valuations of definable sets in Rn are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable R-valued functions on Rn. This generalizes intrinsic volumes to (dual pairs of) non-linear valuations on functions and provides a dual pair of Hadwiger classification theorems. 相似文献
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In this article, we construct simply connected symplectic Calabi–Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along T4. Using our method, we also construct symplectic non-Kähler Calabi–Yau 6-manifolds with fundamental group Z. This paper also produces the first examples of simply connected and non-simply connected symplectic Calabi–Yau 6-manifolds with fundamental groups Zp×Zq, and Z×Zq for any p≥1 and q≥2via co-isotropic Luttinger surgery. 相似文献
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Based on [19], we develop a global correspondence between immersed hypersurfaces ?:Mn→Hn+1 satisfying an exterior horosphere condition, also called here horospherically concave hypersurfaces, and complete conformal metrics e2ρgSn on domains Ω in the boundary Sn at infinity of Hn+1, where ρ is the horospherical support function, ∂∞?(Mn)=∂Ω, and Ω is the image of the Gauss map G:Mn→Sn. To do so we first establish results on when the Gauss map G:Mn→Sn is injective. We also discuss when an immersed horospherically concave hypersurface can be unfolded along the normal flow into an embedded one. These results allow us to establish general Alexandrov reflection principles for elliptic problems of both immersed hypersurfaces in Hn+1 and conformal metrics on domains in Sn. Consequently, we are able to obtain, for instance, a strong Bernstein theorem for a complete, immersed, horospherically concave hypersurface in Hn+1 of constant mean curvature. 相似文献
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In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q∈L1[0,1] and qn=0 for n=0,−1,−2,..., where qn are the Fourier coefficients of q with respect to the system {ei2πnx}. We prove that the Bloch eigenvalues are (2πn+t)2 for n∈Z, t∈C and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator. 相似文献