核函数

Then the integral-differential equations were reduced to the form with degenerate core by expanding Green＇ s function as series of characteristic function.

再使用展开法求出格林函数，即将格林函数展开为特征函数的级数形式，积分微分方程就成为具有退化核的形式，从而容易得到关于时间的非线性常微分方程组。

Dorea advanced kernel estimation p of p ,which is a general density with respect to a σ-finite measure v on.ξ is a σ-field of subsets of ER. Some qualities have been gotten. And it has been proved that those results consist of theories of classical kernel estimation for continual density and further extended theories of disperse kernel estimation.

Y Dorea在2001年提出了关于上的σ-有限测度v的一般密度函数P的核估计几，其中ER，ξ是E的一个σ-域，得到了一些结果，并且验证了所得结论包含经典的连续密度核估计的结论，还进一步延伸了离散分布核估计的结论。

The main theorem of this paper is to, firstly, on the grounds of experience preliminarily estimate the parameter of the pavement nonlinear model, simulate the process with computer procedure, and check the result with the data collected in sit, then set the aim function and the superiority back-calculation method, if the function is not satisfied, it is to the method adjust the parameter and make the model impend the actuality, If the function is satisfied, it is to end the process, and record the stress, deformation, displacement and the parameter as the actual condition.

本文分析的主要原理：首先根据经验，初估路面结构层应力应变非线性参数，利用计算机程序模拟承载板试验测回弹弯沉的过程，通过现场实测的弯沉数据来检核该模拟过程的真实性，设定目标函数，选定适当的优化反算方法，当目标函数不满足时，即利用该优化反算方法调整本构模型参数，使得模型能够逐步向真实解逼近，当目标函数得到满足时，则认为此时反算得到的路面结构层的应力、应变、位移场为真实的应力、应变、位移场，所推算得到的非线性应力应变模型为真实的路面结构层应力应变模型。

Especially since Lindley and Smith (1972) addressed the thought of hierarchical prior distribution and Han (1997) provided the methods to construct hierarchical prior distribution, more achievements have been made on hierarchical Bayesian methods to be used for solving zero-failure data problem.

所谓λ的多层先验分布的构造方法——减函数法，主要是选取λ的减函数作为λ的第一层先验密度函数的核，第二层先验分布——第一层先验分布中超参数的先验分布取均匀分布。

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

In this paper, we study the problems of the kernel regression estimator with spherical data, the estimators of multivariate densit...

本文主要研究了球面数据回归函数核估计以及多维密度函数估计和多维回归函数估计问题。

The relationsare built among the Bergman kernel,the Riemann mapping function,the Szeg'o kerneland the Green function etc.,therefore,if we get the one of them,then it is easy toobtain the others from these relations.

五研究了Bergman核的理论，它具有再生性质，给出了Bergman核、Riemann映射、核以及Green函数之间的密切关系表达式。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

The result indicates that the critical accretion rate is affected not only by the hydrogen mass fraction and the core mass, but also by the metallicity, though the effect of the metallicity is smaller than that of the core mass.

研究结果表明，此临界吸积率不但是核质量的函数，同时还是金属丰富的函数，但金属丰度的影响比核质量的影响要小。

By means of the spin-dependent quark distributions in 6-quark clusters extended from a pQCD model, the polarized structure function of deuterons is investigated.

利用基于微扰QCD模型得到的 6夸克集团内部自旋夸克的分布函数，研究了氘核极化结构函数的核效应。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。