共查询到20条相似文献,搜索用时 0 毫秒
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Pierre Apkarian Dominikus Noll Laleh Ravanbod 《Set-Valued and Variational Analysis》2016,24(1):115-148
We propose a bundle trust-region algorithm to minimize locally Lipschitz functions which are potentially nonsmooth and nonconvex. We prove global convergence of our method and show by way of an example that the classical convergence argument in trust-region methods based on the Cauchy point fails in the nonsmooth setting. Our method is tested experimentally on three problems in automatic control. 相似文献
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Fix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g?2, and also fix an integer r such that degree(ξ)>r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles over X of rank r and determinant ξ. The Fourier-Mukai transform, with respect to a Poincaré line bundle on X×J(X), of any F∈Mξ(r) is a stable vector bundle on J(X). This gives an injective map of Mξ(r) in a moduli space associated to J(X). If g=2, then Mξ(r) becomes a Lagrangian subscheme. 相似文献
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Helmut A. Hamm 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):131-138
In his book SGA2, A. Grothendieck developed Lefschetz theorems for the Picard group, the aim being to compare the Picard group
of a projective variety with the one of a hyperplane section. An intermediate object is the Picard group of the formal completion
along the hyperplane section. Here we proceed similarly but in the local complex analytic context. The use of the exponential
sequence leads to analytic as well as topological depth conditions. 相似文献
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I. Biswas 《Topology》2006,45(2):403-419
Let X be a nonsingular algebraic curve of genus g?3, and let Mξ denote the moduli space of stable vector bundles of rank n?2 and degree d with fixed determinant ξ over X such that n and d are coprime. We assume that if g=3 then n?4 and if g=4 then n?3, and suppose further that n0, d0 are integers such that n0?1 and nd0+n0d>nn0(2g-2). Let E be a semistable vector bundle over X of rank n0 and degree d0. The generalised Picard bundle Wξ(E) is by definition the vector bundle over Mξ defined by the direct image where Uξ is a universal vector bundle over X×Mξ. We obtain an inversion formula allowing us to recover E from Wξ(E) and show that the space of infinitesimal deformations of Wξ(E) is isomorphic to H1(X,End(E)). This construction gives a locally complete family of vector bundles over Mξ parametrised by the moduli space M(n0,d0) of stable bundles of rank n0 and degree d0 over X. If (n0,d0)=1 and Wξ(E) is stable for all E∈M(n0,d0), the construction determines an isomorphism from M(n0,d0) to a connected component M0 of a moduli space of stable sheaves over Mξ. This applies in particular when n0=1, in which case M0 is isomorphic to the Jacobian J of X as a polarised variety. The paper as a whole is a generalisation of results of Kempf and Mukai on Picard bundles over J, and is also related to a paper of Tyurin on the geometry of moduli of vector bundles. 相似文献
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Michael Skeide 《Proceedings Mathematical Sciences》2006,116(4):429-442
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra ℬa(E) of adjointable operators on a HilbertB-moduleE to show that the quotient of the group of generalized unitaries onE and its normal subgroup of unitaries onE is a subgroup of the group of automorphisms of the range idealB
E
ofE inB. We determine the kernel of the canonical mapping into the Picard group ofB
E
in terms of the group of quasi inner automorphisms ofB
E
. As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators onE modulo inner automorphisms as a subgroup of the (opposite of the) Picard group. 相似文献
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Elliptic points of the Picard modular group 总被引:1,自引:0,他引:1
Dan Yasaki 《Monatshefte für Mathematik》2009,156(4):391-396
We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian
integers on 2-dimensional complex hyperbolic space.
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Yukinobu Adachi 《Journal of Mathematical Analysis and Applications》2009,354(1):96-98
We show the little Picard theorem for a map of a quasicompact manifold to a relatively compact domain of Pn whose degeneracy locus of the Kobayashi pseudodistance is contained in some algebraic hypersurface. 相似文献
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O. B. Skaskiv 《Journal of Mathematical Sciences》1990,48(5):570-578
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 46, pp. 90–100, 1986. 相似文献
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Francois R. Cossec 《Mathematische Annalen》1985,271(4):577-600
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R.-P. Holzapfel 《Mathematische Nachrichten》1988,139(1):115-137
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Answering a question of [BV] it is proved that the Picard bundle on the moduli space of stable vector bundles of rank two,
on a Riemann surface of genus at least three, with fixed determinant of odd degree is stable. 相似文献
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Bernhard Runge 《Mathematische Nachrichten》1997,184(1):259-273
We study moduli spaces of principally polarized abelian varieties with an automorphism of finite order. After some examples (e. g. hermitian modular forms) we compute the ring of Picard modular forms in the case considered by Picard. 相似文献
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Ali Aral Hatice Gül İnce İlarslan Gülen Başcanbaz Tunca 《Mathematical Methods in the Applied Sciences》2016,39(18):5140-5148
The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya‐type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in 1 . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous -order scalar ordinary differential equations with coefficients being elliptic functions (associated with a common period lattice) to linear homogeneous first-order systems. In particular, the qualitative Floquet-type structure of fundamental systems of solutions in terms of elliptic and exponential functions, polynomials, and Weierstrass zeta functions of the independent variable is determined. Connections with completely integrable systems are mentioned.