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131.
Kazuo Kobayasi 《Proceedings of the American Mathematical Society》1999,127(4):1143-1150
We construct an inertial manifold for the evolution equation as a limit of the inertial manifolds for the difference approximations of the Trotter-Kato type and show that this limit is taken in a topology.
132.
133.
The asymptotic properties of maximum likelihood estimates of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous variables and innovations to the output vector. The exogenous variables are assumed to be such that the sample serial covariances converge to limits. The innovations are assumed to be martingale differences and to be nondeterministic in a fairly weak sense. Stronger conditions ensure that the asymptotic distribution of the estimates has the same covariance matrix as for Gaussian innovations but these stronger conditions are somewhat implausible. With each ARMAX structure may be associated an integer (the McMillan degree) and all structures for a given value of this integer may be topologised as an analytic manifold. Other parameterizations and topologisations of spaces of structures as analytic manifolds may also be considered and the presentation is sufficiently general to cover a wide range of these. Greater generality is also achieved by allowing for general forms of constraints. 相似文献
134.
Bob Hoogenboom 《Arkiv f?r Matematik》1982,20(1):69-85
Proofs are given of two theorems of Berezin and Karpelevič, which as far as we know never have been proved correctly. By using
eigenfunctions of the Laplace-Beltrami operator it is shown that the spherical functions on a complex Grassmann manifold are
given by a determinant of certain hypergeometric functions. By application of this result, it is proved that a certain system
of operators, fow which explicit expressions are given, generates the algebra of radial parts of invariant differential operators. 相似文献
135.
In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP2.
Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99. 相似文献
136.
137.
GAO Hongzhu GUO Ren Department of Mathematics Beijing Normal University Beijing China 《中国科学A辑(英文版)》2004,47(3):431-439
The problem of embedding spheres in rational surfaces CP~2#nCP~2 is studied.For homology classes u=(b_1+k, b_2,…, b_n) with positive self-intersection numbers, anecessary and sufficient condition to detect its representability is given when k≤5. 相似文献
138.
Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces 总被引:1,自引:1,他引:0
This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds
M with singularities x
1
, ..., x
n
locally modelled on specialLagrangian cones
C
1, ..., C
n
in
m
with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space
X
of deformations of X in M, and construct a natural topology on it. Then we show that
X
is locally homeomorphic to the zeroes of a smooth map :
X
X between finite-dimensional vector spaces.Here the infinitesimal deformation space
X depends only on the topology of X, and the obstruction space
X only on the cones C
1, ..., C
n
at x
1, ..., x
n
. If the cones C
i
are stable then
X is zero, and
X
is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M. 相似文献
139.
We prove that a compact almost Kähler manifold satisfying that a certain part of thedivergence W of the Weyl conformal tensor W vanishes isKähler. 相似文献
140.
ZHANG Zhenyue & ZHA Hongyuan Department of Mathematics Zhejiang University Yuquan Campus Hangzhou China Department of Computer Science Engineering The Pennsylvania State University University Park PA U.S.A. 《中国科学A辑(英文版)》2004,47(6):908-920
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning. 相似文献