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81.
RANDOMITERATIONOFHOLOMORPHICSELF-MAPSOVERBOUNDEDDOMAINSINC~N¥ZHANGWENJUN;RENFUYAO(DeparatmentofMathematics,HenalUniversitytKa?.. 相似文献
82.
D. Castro M. Giusti J. Heintz G. Matera L.M. Pardo 《Foundations of Computational Mathematics》2003,3(4):347-420
Elimination theory was at the origin of algebraic geometry in the nineteenth century and now deals with the algorithmic solving of multivariate polynomial equation systems over the complex numbers or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e., polynomial equation systems) and admitting the representation of certain limit objects. Our main result is the following: let there be given such a data structure and together with this data structure a universal elimination algorithm, say P, solving arbitrary
parametric polynomial equation systems. Suppose that the algorithm P avoids unnecessary branchings and that
P admits the efficient computation of certain natural limit objects (as, e.g., the Zariski closure of a given constructible algebraic set or the parametric greatest common divisor of two given algebraic families of univariate polynomials). Then P$ cannot be a polynomial time algorithm. The paper contains different variants of this result and discusses their practical implications. 相似文献
83.
钟同德 《数学物理学报(B辑英文版)》1998,(4)
1IntroductionTheauthorhasobtainedaKoppelman-Leray-Norguetformulaforaiccafq-coneavewedgeinndimensionalSteinmanifoldsX[11,inthispaperbasedonthisformulaweobtainahomotopyformulaforalocalq-concavewedge,byusingthisformulaweobtainthesolutionformulafor0-equationonlocalq-concavewedges,anddiscussanextensionproblemonlocalq-concavewedges.Inviewofsavespareweusethenotationsdefinitionsandresultsdirectlywithoutspreadout.airlateruseweonlyintroducetwonewdefinitions[2]:Definition1.1Acolloction(U,pl,''tPN)wi… 相似文献
84.
Atsushi Atsuji 《Potential Analysis》2008,29(2):119-138
We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in C
n
. This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete
computation of the remainder term in the case of nonsingular algebraic submanifolds.
Partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science. 相似文献
85.
Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to Cn ? {0}. The authors show that there exists a line bundle L over X such that E ? L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π?(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E. 相似文献
86.
For an open subset U of a locally convex space E, let (H(U),τ0) denote the vector space of all holomorphic functions on U, with the compact-open topology. If E is a separable Fréchet space with the bounded approximation property, or if E is a (DFC)-space with the approximation property, we show that (H(U),τ0) has the approximation property for every open subset U of E. These theorems extend classical results of Aron and Schottenloher. As applications of these approximation theorems we characterize the spectra of certain topological algebras of holomorphic mappings with values in a Banach algebra. 相似文献
87.
Chunlin Lei Degui Yang Xueqin Wang 《Journal of Mathematical Analysis and Applications》2008,341(1):224-234
Let k be a positive integer with k?2; let h(?0) be a holomorphic function which has no simple zeros in D; and let F be a family of meromorphic functions defined in D, all of whose poles are multiple, and all of whose zeros have multiplicity at least k+1. If, for each function f∈F, f(k)(z)≠h(z), then F is normal in D. 相似文献
88.
Jouko S. Arponen 《Theoretical chemistry accounts》1991,80(2-3):149-179
Summary The algebraic structures of theconfiguration interaction, normal coupled cluster, andextended coupled cluster methods are reviewed and developed. These methods are pointed out to perform a mapping of the quantum mechanical problem into a classical phase space, where in each case the classical canonical coordinates have characteristically different cluster and locality properties. Special focus is given to the extended coupled cluster method (ECCM), which alone is based on an entirely additively separable coordinate system. The general principles are formulated for systems with both bosonic and fermionic degrees of freedom, allowing both commutative and anticommutative (Grassmann) cluster amplitudes. The properties of the classical images are briefly discussed. It is proposed that phase spaces may exist which are fixed points of quantization.Based on a talk given at theWorkshop on Coupled-Cluster Theory at the Interface of Atomic Physics and Quantum Chemistry, Harvard-Smithsonian Institute for Theoretical Atomic and Molecular Physics, Cambridge, MA, August 7–11, 1990 相似文献
89.
In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold . Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an -algebra that controls the deformations of Y. This -algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y. 相似文献
90.
In this paper, the authors establish distortion theorems for various subfamilies Hk(B) of holomorphic mappings defined in the unit ball in Cn with critical points, where k is any positive integer. In particular, the distortion theorem for locally biholomorphic mappings is obtained when k tends to oo. These distortion theorems give lower bound son det f(z) and Redet f'(z). As an application of these distortion theorems, the authors give lower and upper bounds of Bloch constants for the subfamilies βk (M) of holomorphic mappings. Moreover, these distortion theorems are sharp. When B is the unit disk in C, these theorems reduce to the results of Liu and Minda. A new distortion result of Re det f'(z) for locally biholomorphic mappings is also obtained. 相似文献