查询词典 kernel of integral operator

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational functions.

不定积分概念，，不定积分性质，基本积分公式，不定积分证明方法，不定积分换元积分法，分部积分法，不定积分有理函数积分。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

The results show that mechanical heterogeneity has great influence on the J-integral of welded joint containing transverse crack. The J-integral on the path cross the interface between welded joint and base metal is higher than the J-integral on the paths in the weld metal for undermatched joint,while the J-integral on the path cross the interface between weld metal and base metal is lower than the J-integral on the paths in the weld metal for overmatched joint. Moreover,the difference of J-integral values increases with the increasing of the load and strength mismatching difference and the path-enclosed length of interface between weld metal and base metal.

计算结果表明：力学不均匀性对含横向裂纹焊接接头的J积分有重要影响，低匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值高于积分路径在焊缝内的J积分值，高匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值低于积分路径在焊缝内的J积分值；载荷越大，焊缝与母材的强度差别越大；积分路径中包含的焊缝与母材界面长度越大，J积分的差值越大。

We put forward some new ideas, such as: About the kernel word "tree", Whether "Mu" has the tendency to refer to the tall trees in terms of "Shu" and "Mu"; About the word "sun", we analyze the reason why "Taiyang" has been used until now, but "Daming" which has the same way of construction with "Taiyang" has disappeared for a long time;About the kernel word "swim", we think that "You" is not the same with "Youyong", and takes"swim" as an obvious kernel word which has dual characters in historic and etymologic significance; About the kernel word "sit", though refers to a posture that differes in ancient time and modern days, did not change the meaning of itself, but changes in semantic field.

4提出了一些我们新的想法，如关于"树"、"木"之间，"木"是否有指高大的树的倾向；在核心词"日"中，分析了"大明"、"太阳"构词方式一样，而"太阳"却一直沿用至今的原因；对核心词"游"的再认识，认为"游"是汉语核心词有着社会历史和语源上的双重证据；在核心词"坐"中，古今坐姿的变化，并未使"坐"本身的词义发生演变，而是导致了"坐"语义场的变化等。

Path analysis showed that N translocation rate of culm was higher for the high fresh ear yield varieties,while the N translocation rate of culm and tassel was higher for the high fresh kernel yield varieties,and the N translocation rate of leaf,bracteal leaf and ear axis was higher for the high kernel yield varieties.In addition,higher N translocation rate of leaf had a beneficial effect on N utilization efficiency as for fresh ear,fresh kernel or maturity kernel of the produce of waxy corn.

通径分析表明，鲜穗高产品种茎秆的氮素转移率较高，鲜子粒高产品种茎秆和雄穗的氮素转移率较高，成熟子粒高产品种叶片、苞叶及穗轴的氮素转移率均较高；叶片的氮素转移率高有利于品种鲜穗、鲜子粒及成熟子粒氮素利用效率的提高。

The main contributions of this thesis are as follows:(1)To address the problem of kernel parameterσselection and regulation of the decision boundary in SVDD algorithm,this thesis proposes a new kernel parameter optimization method based on the spheral distribution of samples in kernel space and regulation of the decision boundary method based on KPCA(Kernel Principal Component Analysis).

本论文主要以支持向量数据描述(Support Vector Data Description，SVDD)与随机森林(Random Forests，RF)模式识别工具为基础，对流程工业在线故障诊断的若干问题进行研究，其具体内容如下：(1)针对SVDD的核参数σ优化及其决策边界规整问题，提出了基于核样本球形分布的核参数优化方法与基于核主元分析(Kernel Principal ComponentAnalysis，KPCA)的SVDD决策边界规整方法。

Then we introduced transition probability kernel for the hidden state process and the confederated process. In the deep research, we found that some similar parameters of state transition probability, observation symbol probability and initial state probability were involved in the transition probability kernel of the confederated process. So we can complete the training of traditional HMM parameters by training the transition probability kernel of the confederated process. To our surprised, we got the consistency of transition probability kernel of the confederated process. Meanwhile, we proved the rationality and reliability of the parameters estimation equations under the classical B-W algorithm.

然后对联合过程的转移概率核展开研究，我们根据过程的取值空间的不同，引入了隐状态空间和联合过程空间上的转移概率核，研究中发现在联合空间上的转移概率核包含了在一般的隐马氏模型的参数估计中的所有类似的三组参数(转移概率，观测概率和初始概率)，因此对传统的隐马氏模型的参数训练我们可以通过联合过程的转移概率核的训练来完成，更令我们惊奇的是联合过程的转移概率核还具有一致性；同时对于Baum提出的经典的B-W算法给出的关于模型的参数重估计公式，证明了它的合理性和可靠性，即模型经过重估计后的参数能够满足给定的单观测序列在模型下发生的概率是单调递增的。

Researches on kernel clustering algorithms. After combining K-means clustering algorithm and the theory of kernel-based learning algorithms, we propose a fast kernel K-means clustering method which is based on CPD kernel. The experiment results indicate that the clustering effect of the algorithm is better than that of K-means algorithm, the clustering speed of the algorithm is also fast than that of K-means algorithm.

核聚类算法的研究：探讨了K-均值聚类算法，通过将核学习理论与K-均值聚类算法结合，提出了一种基于CPD核函数的快速核K-均值聚类算法，并将该算法与基于Mercer核的核聚类算法进行了比较，实验结果显示，我们的方法不仅比K-均值聚类算法的聚类效果好，而且聚类速度快。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。