核函数

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

On the basis of the image correlation and the nonparametric kernel density estimation, kernel density functions of background and foreground were built., Bayesian theory was used to estimate the prior probabilities of the foreground and the background, so an estimative threshold was obtained and the classification of the background and the foreground was realized.

首先，在图像相关性的基础上，利用非参数核密度估计的方法，建立前景和背景的核密度函数，再利用贝叶斯理论，估计出背景和前景的先验概率，两者相结合得到一个估计的阈值，从而实现目标和背景的分类。

The direct method of solution for non-normal type of singular integral equation with Hubert kernel is discussed. Their solution have form of integral and the condition of solution have form of the system of equations.

给出了具有Hilbert核非正则型奇异积分方程的直接解法，对核密度函数k在附加某些条件下，得出了方程积分形式的解和方程组形式的可解条件。

Based on the theory of isomorphic mapping and singular value decomposition theorem, the maximum of the kernel Fisher discrimination criterion can be skillfully acquired by solving the minimum of its reciprocal in a small space, and the final solution is acquired without taking account of the null space and non-null space of the kernel within-class scatter matrices separately.

基于同构映射原理和奇异值分解定理，在一个更小的空间内将核Fisher描述准则函数的极大值问题转化为其倒数的极小值问题，使最终的解不需要分开考虑核类内散度矩阵的零空间和非零空间。

More than 30 kinds of meshfree methods are reviewed in this paper in the light of weighted residual method, and different meshfree methods can be viewed as different forms of weighted residual method and/or with different approximation functions. Various kinds of meshfree approximate schemes are presented in detail, including moving least square approximation, kernel and reproducing kernel approximation, partition of unity approximation, radial basis approximation, radial point interpolation and natural neighbor interpolation.

详尽介绍了各种无网格近似方案(包括移动最小二乘近似、核近似和重构核近似、单位分解近似、径向基函数近似、点插值近似、自然邻接点插值近似等)和无网格法中常用的各类加权余量法(伽辽金格式、配点格式、局部弱形式、加权最小二乘格式和边界积分格式等)，并讨论了数值积分方法和边界条件的处理等问题。

This paper presents the reproducing kernel wavelet functionrepresentation in frequency and time domain by residue principle for specificreproducing kernel space 〓.

对具体的再生核空间〓，用留数计算法则，巧妙地给出频域与时域上的再生核小波函数表达式。

With the continuous method, the displacement shape functions are constructed with the self-contained trigonometric function series, and then the formulae of normal stress and shear stress in the shear walls of the core tube subjected to a torque are brought forward.

根据结构连续化分析方法，采用完备的三角函数系形式表示正六边形核筒悬挂建筑结构中筒体在扭矩作用下的位移函数，并推导出核筒中的剪力墙的正应力和剪应力公式。

Optimization of liquid culture medium including maltose, glucose and tryptone for nucleotides production with Cordvceps sinensis CS-wx was carried out by response surface method.

采用响应面法对冬虫夏草茵CS-wx液态发酵生产核苷类物质的3种主要培养基成分——麦芽糖、葡萄糖和蛋白胨进行优化，采用多元二次回归方程拟合3种因素与核苷类物质含量为响应值之间的函数关系。

In this paper wecalculated the cross-section ratios of associate η_c +γ productionin the p-p and p-Au collisions and found that this process is connected closely with the nuclear gluon distribution function. Bystudying the associate η_c +γ production in high energy p-Aucollision, we can know more about the nuclear gluon distribution function.

我们计算了p-Au、p-p碰撞η_c与γ协同产生过程的微分截面dσ/dp_T的比值，发现η_c与γ协同产生过程与核内束缚核子的胶子分布函数关系密切，通过对高能质子与原子核碰撞η_c与γ协同产生过程的实验研究，可以加深我们对核内胶子分布的认识。

In order to overcome the limitations of kernel estimation and shortcomings of the method for determining inliers/outliers threshold in ErrorInVariables model, the projection based Mestimators was improved. First, a new mode search method named adaptive kernel density estimation was proposed. Then, a different strategy was given to determine the inliers.

针对EIV模型中基于投影的M估计方法存在的核密度估计和正常点与异常点阈值确定的局限性，提出一种改进的投影M估计算法：首先给出新的用于搜索极值点的自适应核密度估计函数，然后改进了正常点的确定方法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。