多函数

For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the wholenetworks to some sub-problems in some sub-areas.

对于单目标无功电压优化，根据实际电网分区情况，采用分解协调法复制各分区的边界节点，建立分解协调模型，采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题，然后采用辅助问题原理分解变量和增广拉格朗日函数，从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。

Another reason is that the degree of linear independence of the variable basis functions composed by sigmoid functions decreases as the hidden nodes increasing, and this lead up to the inferior matrix condition number during learning, which forces the learning step length to decrease and the convergence speed to slow down.

一是因为未知系统复杂时需要较多的隐节点，从而学习的参数过多减慢了学习速度；另一个原因是随着隐节点数增加，由Sigmoid函数构造的可变基函数线性无关程度减弱，从而导致学习过程中矩阵条件数变差，迫使学习步长减小，收敛速度不得不减慢。

The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence.

本文将函数序列的v－收敛性推广到向量值函数，在v－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件。

Copulas are functions that join multivariate distribution functions to their one-dimensional marginal distribution functions.

Copula函数是将多维随机变量的联合分布和其边缘分布连接起来的一种函数。

By a more precise estimation of maximum value of a B-spline basis function and utilizing of the local support property of B-spline basis function, the control points of a set of compatible B-spline curves are reduced, which makes the skinning algorithm more effective.

对B样条基函数的最大值进行了更为精确的估计，并且充分利用B样条基函数的局部支撑性，尽可能多地删除相容性处理后B样条曲线的控制点，使得蒙皮算法更加有效。

In chapter 4, the relation between Fatou components of a transcendental meromorphic function or a transcendental meromorphic solution of some differential equation and the set of singular values is discussed, the main considered question is the relation between wandering domains or Baker domains and the set of singular values.

第四章讨论了超越亚纯函数或微分方程超越亚纯解Fatou分支与奇值集的关系问题，主要是研究游荡域或Baker域与奇值集的关系，得到在一定条件下，某些超越亚纯函数的多连通游荡域以及某些微分方程超越亚纯解的Baker域必定含有奇值。

To overcome the difficulties, we use the method with three object functions which are the minimum Lp norm, the deviation between the calculated magnetic fields and the measured magnetic fields, and the number of the sources.

为了克服上述两种方法的困难，采用多目标函数最优化法。该方法的目标函数为，(1)未知源的Lp模，(2)由未知源计算出的磁场与测量的磁场之间的偏差，(3)源的数目。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

An improved Schur multistep method has been presented for controlling error severely cumulating and increasing computational accuracy.

为解决刚性问题中导函数项的"病态性"（导函数中同时含有较大参数和较小参数），本文提出了一种改进的Schur积多步法，数值实验表明，该方法能很好地抑制误差的急剧累积，与原方法相比，计算精度得到较大提高。

The speciality to let several coefficients of S-M algorithm are analyzed;(2) We first propose the nonlinear and adaptive prediction model based on several closest neighbors and extend the method to multistep prediction;(3) We first exploit Empirical Mode Decomposition technology to predict hopping frequency codes, it is namely that a complex time series is decomposed as several Intrinsic Mode Functions easy to prediction, then predict these IMF respectively, at last reconstruct estimated values of the time series;(4) We exploit the above prediction model validate effect while there are omitted data in observed time series and propose the corresponding resolve.

1具体分析了S-M算法中几个参数设置的特点；(2)首次提出了基于邻近点的非线性自适应预测模型，同时将这种算法推广到多步预测；(3)首次采用经验模态分解技术预测跳频码，即将一个复杂难以预测的时间序列分解为几个相对容易预测的本征函数，然后分别预测这些本征函数，最后重构出时间序列的估计值；(4)应用基于邻近点的非线性自适应预测模型验证了观测时间序列存在数据缺损时的预测效果，并提出了相应的解决办法。

And discuss some key point of integrated management system design, include hazard identification and risk assessment and risk control in the occupational health and safety management, the measure of satisfaction target of customer, the flawlessness of law system, the integration of the integrated management system and enterprise standardization system, unify lead institution and work orgnization, integreted internal audit and integrated management review.

同时，论述了一体化管理体系构建中的几个主要问题，包括职业健康安全管理中的危险源辨识、风险评价和风险控制、顾客满意度的科学监测、法律、法规体系的完善、一体化管理体系与企业标准化体系的有机结合、统一的领导机构和工作机构、一体化的内部审核和管理评审。

Deepwater Taranaki is investigated for its petroleum potential, using all available seismic data tied to shallow-water wells.

运用与浅水井相关的现有全部震波探测数据考察了深海区塔拉纳基盆地的油藏前景。