分歧参数具有对称性的等变分歧问题开折的无穷小稳定性(英文)

基于奇点理论中光滑映射芽的左右等价关系,讨论分歧参数带有对称性的等变分歧问题在左右等价群的一个子群作用下开折的无穷小稳定性,指出了这类分歧问题的通用开折必为无穷小稳定开折.     

参数具有对称性的等变分歧问题及其开折的稳定性(英文)

提出了参数具有对称性的等变分歧问题及其开折的稳定性 ,给出了参数具有对称性的等变分歧问题及其开折是稳定的充分必要条件     

关于等变分歧问题的通用开折的注记

本文给出了多参数等变分歧问题有通同开折的一个充分必要条件。     

等变分歧问题开折的（Γ,△）-等价不变性

分歧问题开折的研究是一个重要的内容,利用光滑映射芽奇点理论中的接触等价理论,定义了分歧参数带有对称性的等变分歧问题开折的（Γ,△）-等价,且允许分歧参数带有与状态变量可能不同的对称性,讨论开折在（Γ,△）-等价下的不变性,得到了开折的通用性是（Γ,△）-等价不变性.     

含两组状态变量的多参数等变分歧问题关于左右等价群的通用开折

在文献[7]的基础上，继续探讨舍两组状态变量的多参数等变分歧问题的通用开折的性质，其中包括万有开折的惟一性问题。     

无穷小性质与应用研究

对无穷小的性质与应用进行了探讨,得到了无穷小在判断级数敛散性、求一些未定型极限问题、运用无穷小的阶来判断广义积分的敛散性以及无穷小在计算含有变上限积分的极限等方面新的处理方法。     

等价无穷小代换求极限的方法推广

由于教学的需要,对利用等价无穷小代换求函数极限的方法作了进一步的推广,所得主要结论,在很容易验证的条件下,将无穷小代换的方法推广到多个复合函数无穷小代数和之比及幂指函数和含变上限积分函数的情况,扩大了等价无穷小代换使用的范围。     

罗素悖论与多元逻辑方程组无解问题的等价性

讨论了无穷序列及其极限的包含、相容、等价关系,主要有如下结论:1、无穷序列包含其极限为假命题;2、无穷序列及其极限相容,潜无穷与实无穷相容;3、无穷序列与其极限不等价;4、罗素悖论与多元逻辑方程组无解问题的等价;5、无穷小数的个数为可数无穷多个,不足以表示整个实数系。     

C_0半群关于参数的可微性及其应用(英文)

研究当无穷小生成元含有参数时,其生成的C0半群关于参数的可微性问题.证明了如果无穷小生成元关于参数广义连续且强可微,其生成的C0半群关于参数是可微的.还得到线性延迟微分方程的解关于延迟量的微分结果.     

极限式中等价无穷小代换的应用推广

等价无穷小代换方法是求极限过程中最常用的方法之一,正确使用等价无穷小代换可以大大简化极限的计算过程.一般的教材中提到的等价无穷小代换定理在极限运算中具有一定的局限性.本文将推广等价无穷小在极限运算中代换的范围,从极限式中含有加减关系、幂指结构、变上限积分结构及常见的多种类型展开探讨,在给出理论证明的同时,更增强了等价无穷小代换方法的应用价值.     

Local Bifurcation Analysis of Parameter-Excited Resonance of Pipes under Thermal Load

The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.     

具有摩擦支承边界矩形薄板的局部分岔

建立了具有摩擦支承边界的矩形薄板在面内载荷作用下的动力学方程 ,利用L S方法和奇异性理论对系统进行了局部分叉研究 ,讨论了非退化情况下Z2 分叉问题 .利用数值模拟给出了开折参数局部分叉集图和分叉响应曲线及物理参数平面上的分叉响应规律 ,其结果与解析和实验研究有很好的一致性 .     

Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures

In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.     

蛋白质分子能量与信息传输方程的局域普适开折与Hopf分支

考虑了蛋白质分子能量与信息传输方程的局域普适开折，在此基础上研究了方程的Hopf分支，普适开折的Hopf分支是通有的，这有利于生命体内蛋白质分子能量与信息传输的合理解释．     

工程结构中非线性动态失稳与分叉理论

In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories.The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.