强函数

The common method, that all strong-correlation terms of the model are eliminated, can bring the loss in the engineering application, so the new method is proposed that the identified model reserves some correlation. The augmented matrix A is constructed by the outputΔW and the matrix S. The"determinating order based on ratio of determinant"is brought out to screen the strong-correlation terms in the structure identification. The latent root estimation is improved in screening the eigenvalues and eigenvectors. Thus the estimation precision is improved greatly.The consistence check of guidance instrument error coefficients of flight test and ground test is the purpose of flight experiment. The causes of inconsistency of the two models are analyzed. The hypothesis test of linear regression model based on F statistics is proposed to check the consistence.Finally, the instability of error coefficients is probably caused by the change of the flight environments, therefore, the relation between the error coefficients and flight environment is analyzed. The approach is presented to identify SINS guidance instrument error models and compensate the error in the segmented sections corresponding to the change of vertical acceleration of aircraft.

在结构辨识中，常用的方法由于将模型中的强相关项全部剔除而给工程应用带来损失，因此，本文提出了新的有益思想，即在保留一定相关性的基础上进行辨识：将输出向量ΔW与环境函数矩阵S构成增广矩阵A，然后采用"比定阶行列式"来剔除相关向量的方法，这样既可以尽可能多地保留了对落点影响大的强相关参数，又可以对落点影响小的强相关参数给予剔除；在参数估计中，改进了特征根估计中特征根和特征向量的筛选方法，提出"近零"准则，从而大大提高了参数估计的精度；再者，鉴于天地模型"一致性"检验是飞行试验和SINS制导工具误差系数分离的主要目的，因此，本文又深入分析了造成天地模型不一致的原因，提出了采用基于F统计的线性回归模型假设检验方法来进行捷联制导工具误差模型的天地"一致性"检验；最后，鉴于飞行环境剧烈变化可能会对惯性仪表误差系数稳定性带来一定的影响，因此本文深入地分析了SINS制导工具误差系数与外界环境的关系，提出了基于过载变化大小的分段辨识和分段实时补偿的算法。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

Under the assumptuion that the lower bound of the density of the observed nonlinear AR (1) time series is known, we prove that the nonlinear wavelet estimator of the conditional mean function g, which is similiar with the one introduced in Chapter 2, still has the same good adaptive properties for this kind of nonlinear AR (1) series on account of the moment inequalities and exponential type inequalities for strong mixing processes.

在假设观测序列的的密度函数的下界已知的条件下，我们利用关于强混合过程的矩不等式以及指数型不等式证明了类似于上一章的小波估计对于非线性AR（1）模型中条件均值函数的非参数函数估计仍然具有优良的自适应性质，并同样给出了数值模拟的结果分析。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

This method uses the strong non-linear mapping ability which the RBF network has and its short-time training merit to construct the network, substitutes the non-analytic function, make it to instate of the optimized question of the objective function, and iterates this objective function with the genetic algorithm to search the optimal solution.

该方法利用RBF网络所具有的非线性映射能力强，训练时间短的优点，构建网络，替代非解析函数，使之作为优化问题的目标函数，并用遗传算法搜索迭代出该目标函数的最优解。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

By iteratively combining these two procedures we achieve a way of training the configuration of RBFNN. In addition, the algorithm is very robust with respect to the noise level. Simulation experiments show that the proposed algorithms are sound. In chapter 3, which is the extension of chapter 2, the improvements of the architectures of RBFNNs and the solutions of their relating problems are discussed, Firstly, an new distance metric is advanced and a forward orthogonal least square selection procedure is applied to learning the parameters of classification function and selecting the important input nodes.

首先分析了目前存在的同时确定RBFNN结构和参数的方法的缺陷，在此基础上提出了用基于拉马克的进化学说的进化编程算法来改进算法，以克服某些缺陷；然后针对受到严重噪声污染的系统，如何提高RBFNN的泛化能力的问题，利用基于AIC的适应度函数的改进遗传算法学习结构和参数；最后介绍基于MDL原理的方法，将优化网络的结构和参数分为两个阶段：训练和进化，先自适应地改变RBFNN基函数的中心和宽度，同时训练输出线性权值，再用基于MDL原理的适应度函数的标准GA来优化隐层节点，通过交替使用这两过程达到训练RBFNN的结构和参数的目的，该算法具有较强的鲁棒性。

Some convergence results of the gradient projection method under milder conditions are obtained.

进一步给出了目标函数f是凸函数和拟凸函数时的更强的收敛性结果。

Strong pseudoconvex function is one of the important convex functions.

强伪凸函数是凸函数的重要推广函数之一。

The first-part of this paper evaluates the main stability theories concerned and concludes the conceptualization steps and essentials covering the various methods. Different disturbed-measure functions are studied in terms of their formulations and characteristics. Both Lyapunov functions and TEFs can be constructed only in a heuristic way of case-by-case. Ignoring changes in the disturbed-measure function's value after clearing the fault, Lyapunov functions and TEFs are applicable to neither nonautonomous one-machine infinite-bus systems nor any multimachine systems. Moreover, TEFs cannot guarantee the sign of errors because they don't satisfy the conditions for Lyapunov functions.

作为第1篇，文中归纳出这3种方法的共同分析步骤和要素，并比较各种受扰程度函数，指出：李雅普诺夫函数和TEF的建立都必须从具体模型出发并只能依靠启发的方式，它们没有考虑受扰程度函数的值在故障清除后的变化，因此既不适用于复杂模型的单机系统，也不适用于任何多机系统；又由于这2种方法都基于很强的假设，故分析的误差可能非常大，而TEF法更是由于不满足李雅普诺夫函数的条件而可能得到冒进的结果。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。