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A rounding error analysis of the symplectic Lanczos method is given for the Hamiltonian eigenvalue problem.

给出了求解大规模、稀疏Hamilton矩阵特征问题的辛Lanczos算法的舍入误差分析。

Moreover, a rounding error analysis of the symplectic Lanczos method is given for the Hamiltonian eigenvalue problem.

寻找一个稳定的有效的保结构的求解Hamilton特征问题的算法以及如何稳定有效地求解大规模Hamilton矩阵特征问题的辛Lanczos算法一直是数值界迫切需要研究的课题。

In this paper,it will be shown that by replacing the time integral of the Hamiltonian by another appropriate functional,and by substituting the scalar product by a semi-scalar product,an appropriate function space can be found in which classically non- conservative systems,i.e.,systems which are non-...

本文将指出用另一个适当的泛函代替啥密顿的时间积分以及用一个拟标量积代替标量积，可以建立一个适当的函数空间，在那个函数空间中，传统的非保守系统——即关于能量是非保守的系统具有保守系统的性质。

The framework of the spectral theory for infinite dimensional Hamiltonian operators is construted in this project, and the relationship between semigroups of the operators and the spectral properties of the operators is found out, which is the basis of extending the separation of the variables method.

中文摘要：本项目建立了无穷维Hamilton算子的谱理论框架，揭示了其谱分布情况以及算子半群的联系，为拓宽分离变量法的应用范围提供了理论基础。

This dissertation studies some topics in soliton and integrable system,which mainly include as follows:exact solutions especially travelling wave solu-tions and solitary wave solutions,Painlevēproperty,transformation,similarity reduction,symmetries and their Lie algebra structure,generation ofsoliton hierarchy and their zero curvature representation,Hamiltonian struc-ture,Lax or Liouville integrability,nonlinearization of Lax pairs,applications ofWu's method and symbolic computation.

本文研究内容涉及到孤立子和可积系统的多个方面：精确解特别是行波解和孤波解，Painlevē性质、变换、相似约化、对称及其Lie代数结构、孤子族的生成及其零曲率表示，Hamilton结构，Lax和Liouville可积性、Lax组的非线性化以及吴方法和符号计算在上述研究中的应用。

Employed the Hamiltonian system theories of elastic mechanics, a series of crack singular analytical elements satisfying different boundary conditions along crack surfaces in the vicinity of crack tip are constructed. These hyper-elements can describe the crack tip fields accurately for different simplified fracture models.

应用弹性力学哈密顿体系理论，在裂纹尖端构造出满足不同裂纹表面边界条件的一类裂纹奇异解析元，该类超级单元能够准确描述不同简化模型下的裂纹尖端场。

The approximate stationary probability density function for the response of multi-degree-of-freedom dissipated Hamiltonian systems to Poisson white noises are obtained by solving the four-order generalized Fokker-Planck-Kolmogorov equation using perturbation approach.

通过用摄动法求解四阶广义福克－普朗克方程，得到泊松白噪声激励的多自由度耗散的哈密顿系统的近似平稳响应概率密度函数。

Quasi Hamiltonian system; nonlinear stochastic optimal control; robustness; robust control; parametric uncertainty; uncertain disturbance; Bouc-Wen hysteretic system; Preisach hysteretic system; minimax optimal control; stochastic stabilization; stochastic averaging method; stochastic dynamical programming principle; stochastic differential game; maximal Lyapunov exponent

国家自然科学基金；拟Hamilton系统；非线性随机最优控制；鲁棒性；鲁棒控制；参数不确定性；不确定扰动； Bouc-Wen滞迟系统； Preisach滞迟系统；极小极大最优控制；随机稳定化；随机平均法；随机动态规划原理；随机微分对策；最大Lyapunov指数

A clear relationship between the Hamiltonian structure forthe soliton equations with sources and that for the constrained flows of solitonequation is also given.

文中还给出了带附加项的孤立子方程和孤立子方程的约束系统之间Hamilton结构的约化关系。

In thisarticle, we study a kind of sublinear second-order Hamiltonian systems with elastic impactionand obtain infinite subharmonic solutions.

本文讨论了一类带有碰撞的次线性哈密顿系统，得到了无穷多次调和解的存在性。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了