查询词典 reproducing kernel

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。

In this paper,the boundary singular kernel method in Reproducing Kernel Paicle Method has been applied to impose the essential boundary conditions in EFGM by revising the MLS shape function.The stress field and the displacement field are analysed by linear elastic theory.The contour integral method is used to calculate the J-integral,then the stress intensity factors of mixed-mode crack is acquired.The correctness and the validity of the method are validated.

本文将再生核质点方法中的边界奇异权方法引入EFGM中，通过对MLS形函数进行修正实现了本质边界条件在节点处的精确施加；运用线弹性断裂理论分析裂纹板的应力应变场，采用围线积分法计算J积分，给出了复合型裂纹板的应力强度因子的无网格伽辽金方法。

In the reproducing kernel hilbert space, It proved one-one mapping between positive regularization operator and kernel function.

本文在重构核希尔伯特空间中论述了正规化理论与核方法的一一对应关系。

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

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。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

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。

Reproducing Kernel Particle Method is one of the promising meshfreemethods with attractive features.

重构核质点法(Reproducing Kernel Particle Method，简称 RKPM)是一种有广泛发展前景的无网格方法，具有优良特性。

Then, we focus on the construction of a new type of kernels. It has been pointed out that the kernel function of SVM is equivalent to the reproducing kernel of a certain Reproducing Kernel Hilbert Space.

首先对线性核函数、Gaussian核函数等已经用于广泛实践的核函数的性能给出了简要评述，然后重点构造了一类新的核函数。

According to the fine structures of reproducing kernels, the characterization of the image space in the wavelets transform and the isometric identities formulas are given by the perfect theory of reproducing kernel space.

根据再生核的这种较好的结构，利用较完善的再生核空间理论给出了小波变换像空间的描述及等距恒等式。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐