数值稳定性

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

The vibro-impact systems are familiar with the non-smooth dynamic systems.The dynamics research of the vibro-impact systems not only is significant in theory but also has practical values in engineering.Firstly,using the Poincaré map method,we get an existent criterion of single impact period-n motion in a two-degree-of-freedom vibro-impact system with damper.It is shown that our conclusions are valid through the numerical simulations.Moreover,the satiability of periodic motions is studied and the correspon...

基于Poincaré映射的方法，通过解析的方法导出了一类具有阻尼的两自由度碰撞振动系统的单碰周期n次谐运动存在性判据，经过数值模拟验证了理论分析的正确性，并给出了分析其稳定性的判别公式，通过数值模拟，讨论系统的局部分岔与全局分岔，同时比较了系统参数变化对其周期运动的影响，发现在强阻尼、弱激励、小质量比、较大恢复系数下系统将会出现较多的有规律的周期碰撞。

In chapter 2, we firstly introduce the model of a discrete-time neural network with generalized input-output function. The model generalizes the input-output function in transiently chaotic neural network to a class of continuous, differentiable and monotone increasing functions. Secondly we study the uniformly asymptotical stability of equilibrium in the non-autonomous model. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories. In chapter 3, we firstly introduce a specific class of discrete-time neural network models with sinusoidal activation function.

在本文的第二章中，首先介绍了一类具有广义输入输出函数的非自治离散神经网络模型，该模型把瞬时混沌神经网络模型中的输入输出函数推广到了一般的单调递增且连续可微的函数；其次，利用Schauder不动点原理和利用Lyapunov函数逆定理依次证明了模型平衡点的存在性和该模型在时变权值下的一致渐近稳定性；最后，对几个具体的例子进行数值模拟，数值模拟的结果更好地说明了我们的结论。

The model generalizes the input-output function in transiently chaotic neural network to a class of continuous, differentiable and monotone increasing functions. Secondly we study the uniformly asymptotical stability of equilibrium in the non-autonomous model. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories. In chapter 3, we firstly introduce a specific class of discrete-time neural network models with sinusoidal activation function.

在本文的第二章中，首先介绍了一类具有广义输入输出函数的非自治离散神经网络模型，该模型把瞬时混沌神经网络模型中的输入输出函数推广到了一般的单调递增且连续可微的函数；其次，利用Schauder不动点原理和利用Lyapunov函数逆定理依次证明了模型平衡点的存在性和在时变权值下的一致渐近稳定性；最后，对几个具体的例子进行数值模拟，数值模拟的结果更好地说明了我们的结论。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

In this dissertation, periodic impact motions in vibro-impact systems are studied, and the existence and stability of superharmonic periodic impact motions are obtained. The critical bifurcation parameter intervals of superharmonic periodic impact motions are deduced, and numerical simulations are used to verify the results.

中文题名碰振或约束系统的全局分析及稳定性研究副题名外文题名 Studies on global analysis and stability in vibro-impact or constraint systems 论文作者张彦梅导师陆启韶教授学科专业一般力学与力学基础研究领域\研究方向学位级别博士学位授予单位北京航空航天大学学位授予日期2002 论文页码总数95页关键词碰振系统转子系统多体系统碰撞振动馆藏号BSLW /2003 /O322 /1 本论文讨论了碰撞振动系统的周期碰撞运动，得到了超谐周期碰撞运动的存在性和稳定性，推导出亚谐周期运动的临界分岔参数区间，并利用数值模拟进行验证。

A model for predicting aerodynamic stability of axial compressor in turbojet or turbofan engine is presented.

本文介绍一种模拟发动机压缩系统气动稳定性的数值模型和数值方法，并给出3个算例及其分析。

During the process of the fore mentioned analyses, some tentative works as follows were done.(1)On the basis of the fundamental of spatial analytic geometry, the basic method for displaceable block searching was put forward and the relevant program was written. With this program one can easily search out all the displaceable blocks and omitting of blocks, which is very common in searching blocks manually, can be avoided.(2)The coefficient of stability of blocks with failure mode II-2(that is, sliding on a single sliding surface, but confined by near intersecting line )was deduced.(3)The multi-cavern effect of Laxiwa underground caverns was studied on the assumption that all of the caverns were full face tunneled at the same time.(4)The stability classification scheme of rock mass surrounding large scale underground caverns was established. In addition to inherit the merits of the method of engineering geological

在完成上述工作的过程中，本论文主要在以下几个方面进行了一些探索：①基于空间解析几何原理，提出了块体搜索的基本思路并编制出相应的程序，基本实现了块体搜索的自动化，既大大缩短了块体搜索时间，又能防止因人工搜索引起的遗漏；②推导出Ⅱ-2型(单滑面滑动，但受侧限面约束)块体的稳定性系数计算公式；③以数值模拟方法论证了拉西瓦地下厂房洞室群全断面一次开挖时群洞效应的具体特点；④以岩体质量、开挖效应、群洞效应和次生灾害效应为评价指标，建立了&大型地下洞室群围岩稳定性分类&方案；该方案既继承了水电行业规范&围岩工程地质分类&法的优点，又综合考虑了大型地下洞室群的工程特点。

The numerical results show that our method is effective. For the noncharacteristic Cauchy problem for 2-D and 3-D heat equation, we give the explicit H\"{o}lder type stability estimates by using weighted energy method. Especially,H\"{o}lder type stability estimate for discrete solutions of the heat equation is obtained through a fully discrete method. The numerical results are presented.

对于二维和三维的热传导方程的非特征Cauchy 问题，我们利用权函数方法，给出了一个显式的H\&{o}lder 型的稳定性估计，特别的，对于二维的非特征Cauchy问题，我们利用充分离散的方法，对二维问题的离散形式同样给出了H\&{o}lder 型的稳定性估计，同时，我们也给出了数值例子来说明我们的估计。

It is shown that using PSE to study nonparallel stability, especially to study nonlinear stability of nonparallel flow is much more effective. The result, which is comparable with Direct Navier-Stokes Simulations , can be obtained, and the time needed is lessened greatly.

采用PSE方法对于研究非平行流稳定性问题，特别是非平行非线性的稳定性问题极为有效，可以获得与直接数值模拟(Direct Numerical Simulations，DNS)精度相当的结果，而所需计算时间则成数量级地减少。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。