非线性

Although the first thesis on Ferroresonance was published in 1920, FR is still not a fully understood phenomenon. This thesis focuses on single phase FR in Gas Insulated Switchgearwith inductive potential transformers, fed by the circuit breaker grading capacitance. In principle, FR is a forced oscillation in a non-linear series resonance circuit including a capacitance and non-linear inductance, which shows significantly distorted voltage and current waveforms.

中文摘要虽然第一篇有关铁磁共振（Ferroresonance，简称FR）的文献早在1920年即被发表，但是此一特殊的现象至今仍然未被完全了解，本论文将讨论电力系统中之气封绝缘开关设备（Gas Insulated Switchgear，简称GIS），由於断路器的极间电容和电感型比压器（Potential Transformer，简称PT）的非线性电感所构成的单相铁磁共振；理论上，铁磁共振是由电容和非线性电感所构成的非线性串联共振，造成电压和电流波形明显的畸变。

Furthermore,the stability behavior and accuracy characteristics of the algorithmare proven by a spectral decomposition method.

在前人工作的基础上，提出了一种新的用于解决结构动力分析问题的时间积分方法——Taylor级数方法；建立了求解线性问题和非线性项可以表示为多元多项式形式的非线性问题的Taylor级数方法的理论，并给出递归求解通式；阐述了该方法的程序实施过程，给出了计算流程图，并在非线性有限元分析平台NFAP中嵌入了Taylor级数方法的计算模块；利用谱分解的方法分析了该方法的稳定性和精度特性，以封闭的解析形式给出了描述积分法特性的周期延长率和振幅衰减率的表达式；通过对该方法的理论分析和特性研究，阐述了该方法的可行性和高效性。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑L-M方法求解。

A series of sulfanilamide group substituted derivatives were optimized on the basis of the semi-empirical quantum chemistry PM3 method.

以量子化学半经验PM3法对含磺胺基的一类有机化合物分子进行了几何构型优化，计算了分子的二阶非线性光学系数和电子转移，讨论了磺胺基在非线性光学材料设计中的特点和作用以及不同的取代基及取代位置对分子二阶非线性光学系数的影响

In this paper,by analyzing mathematically starting from physical concept,the relation between intensity of secondary nonlinear polarization and optico-electric field strength is presented under the condition of kleinman symmetrization,and the equation of amplitude coupling is deducted.

安徽大学物理系；四川激光，，编辑部邮箱 1983年 02期二次非线性；总电场；非线性极化率；极化场；振幅；耦合方程；极化强度；从物理概念出发，通过数学解析，在Kleinman对称性条件下，给出二次非线性极化强度与光电场强的关系，并推导出振幅耦合方程。

The hyperbolic-type nonlinear model and rigid and perfectly-plastic model are usually adopted to simulate the constitutive behavior in tangent direction of contact surface. in fact, however, the hyperbolic-type nonlinear model can not definitely display the plastic flow deformation after shear failure while rigid-perfectly-plastic model can not describe the nonlinear deformation before shear failure.

对于土与结构间接触面的切向本构关系，目前通常采用双曲线非线性弹性模型或刚塑性模型来描述，但是，传统的双曲线非线性模型不能明确地表达剪切破坏后的塑性流动变形特性；而刚塑性模型又无法描述剪切破坏之前的非线性弹性变形。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

In this paper, in order to prepare nonlinear optical polymer materials with high nonlinear optical activity and thermal stability, nonlinear optical thiazole chromophores with highβvalues were designed and synthesized, two kind of nonlinear optical polyurethane composite materials were prepared, and the structures and properties of them were researched.

本文以制备具有高非线性活性和热稳定性的非线性光学材料为目的，设计合成了新型具有高二阶极化率的噻唑生色分子，制备了两种新型非线性光学聚氨酯复合材料，并对它们的结构和性能进行了研究。

First of all, the paper carried out test study on four two-spanned model members of FSMRCWB, including three 1/2-scaled two-storeyed models and one 1/3-scaled three-storeyed model. The paper analyzed the test results, including analysis on mechanical property of the composite wall beam under vertical loads, and failure mode, deformation capacity, aseismic performance under horizontal loads and constant vertical loads. Secondly, the nonlinear property of concrete is studed and the nonlinear models of FSMRCSS is builded by ANSYS. Last, The paper studies the result of ANSYS, which mainly includes the loading-displace curve of FSMRCSS under horizontal loads and constant vertical loads, the mechanics of arch under vertical loads lonely and under horizontal loads and constant vertical loads respectively, and status of the distribution and changing of vertical stress and cross shear on the surface of the suporting beam, and the influence of span ratio and hole.All in all, the caculating results are in good agreement with the test results.

本文首先进行了三个1/2比例的两跨两层和一个1/3比例的两跨三层的框支密肋复合墙梁的模型试验，分析了框支密肋复合墙梁在竖向荷载作用下的受力性能，以及在竖向荷载与水平低周反复荷载共同作用下的受力性能、变形性能、滞回性能、耗能系数及破坏形态；其次，研究了混凝土的非线性特性，建立了框支密肋复合墙梁非线性有限元模型，并借助大型通用有限元软件ANSYS进行计算；再则，进行了非线性有限元结果分析，主要研究框支密肋复合墙梁在竖向荷载与水平地震力共同作用下的荷载位移曲线，分析在竖向荷载单独作用下和在竖向荷载与水平地震力共同作用下墙梁的拱作用，托梁顶面的竖向应力和横向剪应力分布及变化情况，并讨论跨度比、洞口对墙梁拱作用和托梁顶面的竖向应力的影响。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。