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排序方式: 共有470条查询结果,搜索用时 15 毫秒
1.
M. A. Bertolim M. P. Mello K. A. de Rezende 《Transactions of the American Mathematical Society》2005,357(10):4091-4129
In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.
2.
Pingan Zeng Jiaquan Liu Yuxia Guo 《Journal of Mathematical Analysis and Applications》2004,300(1):102-128
In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero. 相似文献
3.
Duan-zhi ZHANG School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2007,50(6):761-772
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems. 相似文献
4.
For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically
solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four
different intensities,I = 1 × 108, 1 × 1013, 5 × 1016, and 5 × 1018 W cm−2 respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation
probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold
dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent
elevation to the vibrational continuum, have been obtained and analysed.
Dedicated to Professor C N R Rao on his 70th birthday
An erratum to this article is available at . 相似文献
5.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
6.
Zhihong Xia 《Journal of Differential Equations》2004,200(2):185-190
We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases. 相似文献
7.
研究了在均匀分层介质中构成标准矢量波函数的必要条件。研究结果表明在均匀分层介质中构成标准矢量波函数一般需遵循Morse-Feshbach判据外,领示矢量只能选取与折射率变化方向一致的那根坐标轴单位矢量。但在某些特定的条件下,对领示矢量的选取条件可以放宽为只需遵循Morse-Feshbach判据即可。 相似文献
8.
S. David Morley Raymond J. Abraham Ian S. Haworth David E. Jackson Martin R. Saunders Jeremy G. Vinter 《Journal of computer-aided molecular design》1991,5(5):475-496
Summary Four modifications to the COSMIC molecular mechanics force field are described, which greatly increase both its versatility and the accuracy of calculated conformational energies. The Hill non-bonded van der Waals potential function has been replaced by a two-parameter Morse curve and a new H-H potential, similar to that in MM3, incorporated. Hydrocarbon energies in particular are much improved.A simple iterative Hückel pi-electron molecular orbital calculation allows modelling of conjugated systems. Calculated bond lengths and rotational barriers for a series of conjugated hydrocarbons and nitrogen heterocycles are shown to be as accurate as those determined by the MM2 SCF method.Explicit hydrogen-bonding potentials for H-bond acceptor-donor atom pairs have been included to give better hydrogen bond energies and lengths. The van der Waals radii of protonic hydrogens are reduced to 0.5 Å and the energy well depth is increased to 1.0 kcal mol-1.Two new general atom types, N+
sp
2
and O-
sp
3
, have been introduced which allow a wide variety of charged conjugated systems to be studied. A minimum of parameterisation is required, as the new types are easily included in the Hückel scheme which automatically adjusts bond and torsional parameters according to the defined bond-order relationships. 相似文献
9.
Martin van Gemmeren 《Transactions of the American Mathematical Society》1996,348(6):2413-2426
In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.
10.
J. C. Lpez V. A. L. Rivera Yu. F. Smirnov A. Frank 《International journal of quantum chemistry》2002,88(2):280-295
The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002 相似文献