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排序方式: 共有381条查询结果,搜索用时 15 毫秒
1.
本文使用变分方法证明了三维标准切触球的标准勒让德扭结,至少存在一个弦连结适应于标准切触结构的任何选定切触形式,这部分证明了著名的阿诺德弦猜想。 相似文献
2.
Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b0(M) − b2(M) + b4(M) − b6(M) + … where σ (M) is the signature of M and bi(M) is the ith Betti number of M. 相似文献
3.
Yi Lin 《Advances in Mathematics》2007,208(2):699-709
In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces. 相似文献
4.
A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups. 相似文献
5.
Martin Gruebele 《Theoretical chemistry accounts》2003,109(2):53-63
Vibrational energy flow in organic molecules occurs by a multiple-time-scale mechanism that can be modeled by a single exponential
only in its initial stages. The mechanism is a consequence of the hierarchical structure of the vibrational Hamiltonian, which
leads to diffusion of vibrational wavepackets on a manifold with far fewer than the 3N−6 dimensions of the full vibrational state space. The dynamics are controlled by a local density of states, which does not
keep increasing with molecular size. In addition, the number of vibrational coordinates severely perturbed during chemical
reaction is small, leading to preservation of the hierarchical structure at chemically interesting energies. This regularity
opens up the possibility of controlling chemical reactions by controlling the vibrational energy flow. Computationally, laser
control of intramolecular vibrational energy redistribution can be modeled by quantum-classical, or by purely quantum-mechanical
models of the molecule and control field.
Received: 26 July 2002 / Accepted: 30 September 2002 / Published online: 2 December 2002
Electronic Supplementary Material to this paper can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00214-002-0394-2.
Acknowledgements. This work was supported by NSF grant CHE 9986670.
Correspondence to: M. Gruebele e-mail: gruebele@scs.uiuc.edu 相似文献
6.
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination. 相似文献
7.
For a closed symplectic manifold with compatible Riemannian metric g we study the Sobolev geometry of the group of all diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the metric carries conjugate points via some simple examples. 相似文献
8.
For a scalar evolution equation ut = K(t, x, u, ux, . . . , u2m+1) with m ≥ 1, the cohomology space H1,2() is shown to be isomorphic to the space of variational operators and an explicit isomorphism is given. The space of symplectic operators for ut = K for which the equation is Hamiltonian is also shown to be isomorphic to the space H1,2() and subsequently can be naturally identified with the space of variational operators. Third order scalar evolution equations admitting a first order symplectic (or variational) operator are characterized. The variational operator (or symplectic) nature of the potential form of a bi-Hamiltonian evolution equation is also presented in order to generate examples of interest. 相似文献
9.
该文讨论一个新的离散特征值问题,导出了相应的离散的Hamilton系统的保谱族,并且证明了它们是Liouville可积系。通过谱问题的双非线性化,导出一个新的可积的辛映射 。
相似文献
10.
Plasmas confined in tokamaks with non-symmetric perturbations are surrounded by a chaotic layer of magnetic field lines that guide charged particles to the tokamak wall. We use an analytical two-dimensional symplectic mapping to study the resulting fractal patterns of field line escape. However, particles may experience several collisions before escaping toward the tokamaks wall. We add a random collisional term to the field line mapping to investigate how the particle collisions modify their escape patterns. 相似文献