多函数

Several strong results on neural network approximation capability obtained in this dissertation are important in the approximation theory and applications of neural networks.

本文系统地研究了多层神经网络的非线性逼近能力，给出了多层网络可一致逼近有限维空间R〓紧集上的连续函数、无穷维函数空间紧集上的连续泛函和连续算子以及布尔函数的理论证明。

The example are also given to show that the two Expect Bayes estimation formula are both steady and the precision of Expect Bayes estimation of the reliability for geometric distribution under the entropy loss function is higher than that of the square loss function.

通过实例验证，在熵损失函数下计算出的几何分布可靠度的多层Bayes估计是稳健的，并进一步表明在熵损失函数下计算出的几何分布可靠度的多层Bayes估计值比其在平方损失函数下算出的结果精度更高。

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

In chapter 2, first of all,we characterize subspace V_0 of multiresultion analysis {V_j}_~ based on invariant subspace. Subsequently, we consider the equivalent conditions among orthogonal multiwavelet Ψ=(Ψ_1,Ψ_2,...Ψ_r)~T, subspace, basis and dimension of subspace, properties of filter function matrix P are dealt with.

第二章讨论了多尺度分析{V_j}_~中子空间V_0的性质，进而讨论了多尺度分析生成的多重正交小波Ψ=(ψ_1，ψ_2，…，ψ_r)~T和子空间V_0以及基和维数之间的等价关系，分析了滤子函数矩阵P的性质，最后给出了r阶矩阵函数P生成尺度函数Φ的充分条件。

Harmonic function generalizes the harmonic function, the following respects are discussed: the least energy, Liouville theorem with respect to harmonic function and the relation of harmonic function and subharmonic function.

如对次调和函数的平均值不等式的推导[3- 4 ] ，调和函数的存在性的证明等[5] 。2 0 0 0年，PeterLi提出了另外一种函数，即调和函数，这一类函数比调和函数的应用广泛得多，同时又具有和调和函数类似的性质。

This network's multidimensional wavelet basis function is built by substituting norm of the vector for that vector, not scalar product function of the vector, thus the cost of calculation of high dimensionalities is decreased nearly to the situation of one dimensionality.

此网直接用矢量的范数代替矢量来构造多维小波基函数，而不是采用通常的矢量的标量积函数的方法构造多维基函数，这样多维情况的运算量被降低到几乎和一维的情况基本相当的程度。

First we give the definition of semicontinuous and subharmonic functions and the propertities of the semicontinuous and subharmonic functions and then introduce the notion of plurisubharmonic functions and the propertities of psh functions, then we give the definition of closed positive currents and the relation between psh functi.

首先总结了半连续函数和次调和函数的定义及其性质，然后在此基础上介绍了多次调和函数的定义及其性质，引入了正闭流的定义，说明了正闭流与多次调和函数之间的联系。

Aiming at complicated computing and difficulty of being realized when extending single sensor PHD filtering to the multi-sensor case by means of probability generating function, a multi-sensor multi-target sequential particle-PHD tracking algorithm is proposed based on the thought of sequential filtering for a centralized fusion system. The algorithm chooses the importance density function with regard to every sensor, and updates sample particle of every sensor layer by layer.

当采用概率母函数将单传感器PHD滤波推广到多传感器情形时，针对计算繁琐，难于实现的问题，本文基于集中式融合系统的有序滤波思想，提出多传感器、多目标有序粒子PHD跟踪算法，该算法通过选取与各传感器相关的重要性密度函数，层层更新各传感器的采样粒子，达到多传感器多目标有序PHD跟踪。

By using testing functions to make comparative research on the precision of approximate models which were built by RBF under the condition of different sample amounts and different kernel function types, a conclusion was drawn: the model quality built by Reciprocal Multiquadric RBF as kernel function was highest when the sample amout was big, and the model quality built by Gaussian RBF as kernel function was highest when the sample amount was small.

运用测试函数对在不同样本数量与不同核函数形式下所建立的近似模型的精度进行对比研究，得出逆多二次函数与高斯函数作为核函数分别在大样本和小样本情况下精度最高的结论，并验证了径向基函数近似模型方法能够兼顾效率与精度。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

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起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。