函数

The new methodof defining spline function will generalize the concept to the more universal Hilbert space. Hence, we take into consideration the interpolation spline function, general linear differential operater in semi- open interval and the Green function defined accordingly, and the reproducing kernel to produce the Green function and prove the existence of the reproducing kernel.

采用了一种新的样条函数的定义方法，把样条函数的概念推广到更一般的Hilbert空间上，再考虑半开闭区间a，+∞上的插值样条函数，一般线性微分算子及其定义的Green函数和再生核，构造出Green函数并且证明了再生核的存在性。

The main results are as following: A A new demonstration to optical theorem is constructed B The scattering amplitude function for small particles, which is more accurate than that in classical RGB, is gained using electrostatics approximation, C Through a δ transform to the high frequent oscillation function, a concise deduction of the EG-type scattering amplitude function has been achieved.

主要结果如下： A给出了光学定理的一个新证法； B利用静场近似，得到了比经典RGB更精确的小粒子散射振幅函数； C通过一个高频振荡函数的δ变换，给出了一种EG散射振幅表达式的简明推导，并做了小角度散射简化，参照ADT，对EG近似又做了相位修正； D定义了一个新的函数—消光函数，并得到了组合散射体消光函数的平均定理。

We first introduce the positive real spectrum function and bounded spectrum function then establish the parametrization of the power spectrum by the Levinson polynomials associated with the autocorrelation matrix of the output and bounded spectrum function.

首先引入正实谱函数的和有界谱函数的概念，利用正实函数和有界实函数理论，通过和过程自相关矩阵相关联的Levinson多项式和有界谱函数，建立了功率谱参数化的表达式。

Also, if a complex analytic function is defined in an open ball around a point x 0, its power series expansion at x 0 is convergent in the whole ball. This is not true in general for real analytic functions.

复解析函数则不同：凡复解析函数必为全纯函数（即复可导，以实变量表示则是满足柯西-黎曼方程），反之亦然，因此全纯函数与解析函数在复分析中是同一类对象。

So using theory of power series to define and study function is an effective method of deal with question of function.

因此，用幂级数定义和研究函数是处理函数问题的一种有效的手段，并能给问题的解决带来一些方便，但是，幂级数只是函数的一种表示形式，只有与函数的其他表示形式相互协调和补充，才能真正简洁有效地处理函数问题。

Based on the Walsh functions, a new orthogonal system {T}(subscript n∈N) is presented, which is a sequence of piecewise linear functions that are of form triangle shape on subintervals of [0,1], named triangle orthogonal system.

基于Walsh函数，建立一个新的函数系{T}下标 n∈N(上标。它是一个分段线性函数序列，在[0，1]的子区间上其函数图像呈现三角形。并且证明了它是C[0，1]上一个完备的正交函数系。

First of all, we use approximate method of the super-symmetric quantum mechanics to calculate super-potential and eigenvalues of spheroidal functions in the first several terms. Further more , we derive the ground eigenfunction in the first order terms, which is very useful for applying of the spheroidal wave function probably

首先我们使用近似的超对称量子力学方法计算出前几阶超势和广义椭球函数的本征值；接着根据之前所求得的超势和本征值推导出广义椭球函数一阶基态波函数，该超对称量子力学方法的引入及一阶基态波函数形式将有利于广义椭球函数深入研究

In addition, the preferences are described by the common utility functions and S-shaped value functions in the system. A small number of experiments are conducted through a statistical hypothesis testing, and the latter are shown a better performance.

另外，我们首度将S型价值函数纳入协商双方的价值衡量，并运用统计检定方法，证实价值函数与一般普遍使用的效用函数在成交提案与最佳提案之差距具有显著差异，且价值函数结果优於效用函数。

The cost functions of the linear transversal and decision-feedback blind equalizers are proposed in this thesis, which are strictly convex function with respect to the complex tap-weight vector of the equalizer and the error probability. It is proved that their global convergence are guaranteed by using gradient algorithm.

本文提出了线性横向结构的盲均衡价值函数，DF结构的盲均衡价值函数，证明了这两种价值函数对均横器抽头矢量和系统误差概率，都是严格U函数；并且证明了用梯度算法，这两种价值函数保证收敛到全局极小点。

The nature of the acceleration unit-impulse response function of unbounded medium tending to vary linearly is proved by means of asymptotic analysis. Thus, the acceleration unit-impulse response function can be regarded as the summation of a linear function and a residual part which converges to zero. Based on this decomposition, two FE-SBFE coupling procedures are presented based on system realization and truncation integral technique respectively.

本文系统研究了相互作用力-运动关系的位移表达、速度表达和加速度表达，通过比较位移、速度和加速度单位脉冲响应函数的SBFE求解过程，确定采用相互作用力的加速度表达；通过渐近分析证明了无限地基加速度单位脉冲响应函数具有随时间延长而趋于线性变化的性质；利用这一性质将加速度单位脉冲响应函数分解为一个线性函数和一个衰减到零的残余函数的和，以此为起点发展出两种FE-SBFE时域耦合方法：基于系统实现的FE-SBFE时域耦合方法和基于截断卷积的FE-SBFE时域耦合方法。

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。