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991.
Hlronobu Ishihara 《代数通讯》2013,41(9):4327-4335
A new genus g = g (X, ?) is defined for the pairs (X, ?S)that consist of n-dimensional compact complex manifolds X and ample vector bundles ? of rank r less than n on X. In case r = n-1g is equal to curve genus. Above pairs (X,?) with g less than two are classified. For spanned ? it is shown that g is greater than or equal to the irregularity of X, and its equality condition is given. 相似文献
992.
It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the
bifurcation set has singularities at the corresponding energy level.We formulate certain genericity assumptions for two degrees
of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy
levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under
our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing
the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate
integrable two degrees of freedom systems.
相似文献
993.
Danny Fundinger 《Journal of Nonlinear Science》2008,18(4):391-413
This paper presents a new numerical method for computing global stable manifolds and global stable sets of nonlinear discrete
dynamical systems. For a given map f:ℝ
d
→ℝ
d
, the proposed method is capable of yielding large parts of stable manifolds and sets within a certain compact region M⊂ℝ
d
. The algorithm divides the region M in sets and uses an adaptive subdivision technique to approximate an outer covering of the manifolds. In contrast to similar
approaches, the method requires neither the system’s inverse nor its Jacobian. Hence, it can also be applied to noninvertible
and piecewise-smooth maps. The successful application of the method is illustrated by computation of one- and two-dimensional
stable manifolds and global stable sets. 相似文献
994.
李珍珠 《数学的实践与认识》2011,41(11)
研究线性流形上广义次对称矩阵的左右逆特征值问题及其最佳逼近问题.利用广义次对称矩阵的性质及矩阵的奇异值分解得到问题的通解表达式.同时,给出其有唯一的最佳逼近解以及求最佳逼近解的算法. 相似文献
995.
利用Hamel关于射影平坦的基本方程,我们导出了Randers度量的λ形变保持射影平坦的充分条件.特别,对一类具有特殊旗曲率性质的Randers度量我们证明了这类度量一定存在保持射影平坦性的λ形变. 相似文献
996.
We use the homology groups of the path space of an arbitrary Riemannian manifold to define some analogs of the distance function and study their main properties. For the natural systems with gyroscopic forces we prove an existence theorem for solutions to the two-point boundary value problem, which complements the results of [1]. We apply the geodesic modeling method of [1, 2], using the generalized distance functions. 相似文献
997.
Simon Gindikin 《中国科学A辑(英文版)》2008,51(4):562-567
We discuss the horospherical duality as a geometrical background of harmonic analysis on semisimple symmetric spaces. 相似文献
998.
Andrew Hassell 《Advances in Mathematics》2008,217(2):586-682
Consider a compact manifold with boundary M with a scattering metric g or, equivalently, an asymptotically conic manifold (M○,g). (Euclidean Rn, with a compactly supported metric perturbation, is an example of such a space.) Let Δ be the positive Laplacian on (M,g), and V a smooth potential on M which decays to second order at infinity. In this paper we construct the kernel of the operator −1(h2Δ+V−2(λ0±i0)), at a non-trapping energy λ0>0, uniformly for h∈(0,h0), h0>0 small, within a class of Legendre distributions on manifolds with codimension three corners. Using this we construct the kernel of the propagator, e−it(Δ/2+V), t∈(0,t0) as a quadratic Legendre distribution. We also determine the global semiclassical structure of the spectral projector, Poisson operator and scattering matrix. 相似文献
999.
1000.
We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L 2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincaré inequality. 相似文献