核函数

In the single and double integral terms of Green function, the kernel function of wave-making resistance expression, Special function expansion method and Chebyshev polynomial approach method have been adopted respectively, which greatly increase the calculation speed.

对作为兴波阻力计算核函数的Green函数的单、双积分项分别采用特殊函数展开、切比雪夫多项式逼近的方法进行计算，提高了计算速度。

During the calculation the results got by quintic spline kernel was the best so it was chosen as the proper kernel for the SPH simulation. By comparison of the simulation results got by SPH and finite volume method, it was proved that the buffer cells method proposed in the SPH simulation to implement the Dirichlet boundary conditions was accurate, and this is of great importance for the simulation of flows pass a pipe. At last, the SPH method was improved to simulate the liquid-solid two phase flows and the results show that this method was appropriate for the simulation of flows containing viscous fluid and macroscopic solid components. Now the two methods are both able to predict the continuum flows and rarefied flows severally, but the hybrid program still has some aspects to be improved.

首先用标准算例验证了SPH方法的理论模型和计算程序的准确性；通过比较确定选用五次样条核作为计算低雷诺数下的粘性连续流动时的核函数；采用SPH方法和有限体积法分别对同一管道流动进行了对比计算，证明了本文提出的边界缓冲区方法在实现SPH方法中的流体边界条件时的有效性，解决了SPH方法模拟管道流动时的一个关键问题；巧妙地使用SPH方法对化工分离流动中常见的固液两相流及固液耦合作用进行了模拟尝试，获得了较好的结果；在跨尺度计算方面，目前两个子程序已经能够分别模拟连续的和稀薄的二维管流问题，二者的耦合计算程序还处于调试和优化阶段，各个参数对于计算精度和计算速度的影响规律仍在探索中。

Second, a framework of finding invariant kernel space for any single parameter group is developed based on the fixed point theory of contractive mapping.

最后，对尺度不变核函数的初始函数及参数选择进行了深入研究，提出了基于微分方程组的初始函数求解方法及类似Fisher准则的参数选择依据。

Application of fractional power polynomial kernel function to kernel direct discriminant analysis.

分数次幂多项式核函数在核直接判别式分析中的应用

Kernel principal component analysis can compute principal components in high-dimensional feature space by means of integral operators and nonlinear kernel functions.It can effectively capture the nonlinear relationship in the process variables.

核主元分析方法通过集成算子与非线性核函数计算高维特性空间的主元成分，有效捕捉过程变量中的非线性关系。

The first way is to ensure the kernel function to be positive definite by introducing space mapping transformation;the second way is using similar-SVR model to solve the unsolvable problem of SVR model with non-positive definite kernel function.

一是通过引入空间映射变换保证所得到的SVR的核函数是正定的；二是利用近似SVR模型解决具有非正定核的SVR模型的不可解问题。

A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from －∞to +∞.

欲取得一个函数的傅立叶变换，可以在－∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。

A function's Fourier transform is derive d by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from －∞to +∞.

欲取得一个函数的傅立叶变换，可以在－∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。

In the model, the non-sensitive loss function was replaced by quadratic loss function and the inequality constraints were replaced by equality constraints.

在该模型中，用二次损失函数取代支持向量机中的不敏感损失函数，将不等式约束条件变为等式约束，从而将二次规划问题转换为线性方程组的求解，并提出对核函数的盯参数进行动态选取。

Based on researching into the classification mechanisms of feedforward single-layer radial basis function and linear basis function networks,the author presents the viewpoints that the RBF centers and widths should be determined through a self-learning procedure,that some new kernels naturally come into being according to which class the labeled patterns are misclassified to.

研究了前向单层径基函数网络和前向单层线性基本函数网络的分类机理，提出了RBF的中心和宽度应通过学习自动确定，在学习过程中根据错分样本被错分入的类别自动生成新的核函数这一观点。

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。