曲率

In section 4.2, we study the rescaled WLC model which is equivalent to Langer and Singer's theory of elastica because the Gauss curvature equals zero in three-dimensional Euclidean space.

我们首先讨论了Feoli 等人的结果，将之作为自由能仅为曲率的泛函的特例纳入普遍形式理论中来；并研究了Langer 和Singer 提出的关于弹性曲线的理论(即重新标度的WLC模型)，与当前理论符合得很好。

For generalizations of Gauss curvature to higher-dimensional

有高斯曲率在高维

The problem that the conformal Gauss curvature equation may have a solution for every nonegative Holder continuous function K is also an open problem.

当预定的函数K取正值时，共形高斯曲率方程解的存在性命题作为一个猜测至今未得到解决。

Gauss mipping is used to describe the bending of surface very visual,used to illustrate the geometric properties of Gauss curvature too.As the use of Gauss mipping image,we can discuss some surface's properties.

Gauss映射用来描述曲面的弯曲性非常直观，也用来说明高斯曲率的几何意义，利用高斯映射象的讨论可以探讨曲面的一些性质。

In Perona and Malik's anisotropic diffusion model, some small gradient information and noise will be diffused, but the small information point usually has zero gauss curvature. So this paper improves PM model by using the Gauss curvature.

在Perona和Malik的各项异性扩散方程的消噪模型中，一些小梯度的细节信息和噪声会被扩散掉，而在这些细节信息点往往具有零高斯曲率的特征，根据这一特点，对PM模型加以改进。

Then we give the linear expression of,by f,g.h:=-f;=ρ·g,here ρ is the Gauss curvature of the Riemann manifold,wealso give the geomety explaination and geometrical pattern of these expressions.

给出了与对于f，g，h线性分解的形式。＝-f；＝-ρg，这里ρ是曲面的高斯曲率。并给出了各自几何意义的解释与图示。

Thus, the -general structure topology optimization problem can be regarded as a material interface tracing problem.

其次在结构拓扑优化中还引入了黎曼测度下的平均曲率流正则化技术，以保证计算结果材料界面的光顺性，并有助于提高拓扑演化过程中的数值稳定性。

Firstly, the equivalency of case deletion model and mean-shift outlier model is investigated; and several diagnostic measures, such as Cook distance, generalized leverage, residuals, and likelihood ratio statistics et al., are obtained. Secondly, we investigate the local influence for the models, several commonly-used perturbed models are studied, and the close forms of influence matrices are obtained. At last, a real example illustrates that our method is available.

首先，证明了均值漂移模型与删除模型的等价性，并得到了残差、Cook距离，似然比统计量等诊断统计量；其次研究了该模型的局部影响分析，得到了局部影响分析的曲率度量；并分别对常见的扰动模型进行分析，得到了计算影响矩阵的简洁公式；然后，通过实例验证了方法的可行性。

The basic diagnostic statistics such as Cook distance, generalized leverage and residuals et al. are introduced, and the equivalency of case deletion model and mean-shift outlier model is investigated. Some specific problems, such as local influence analysis and the test for heteroscedasticity are discussed. Finally, numerical examples are given to illustrate our diagnostic methods.

首先，证明了均值漂移模型与数据点删除模型的等价性定理并定义了残差、Cook距离等诊断统计量；其次，研究了异常点的Score检验统计量；第三，研究了该模型的局部影响分析，得到了局部影响分析的曲率度量；第四，研究了该模型的异方差检验问题，得到了检验异方差的Score检验统计量和修正的Score检验统计量；最后，通过实例分析验证了这些诊断方法的有效性。

According to generating finite element model by meshing for special-shaped section columns, a computer program using the digital iteration method for full range analysis of special-shaped columns is complied. By the analytical results,"M-φ" related curves are obtained, at the same time, differences of ductile behavior, and bearing capacity are analyzed.

通过异形柱截面的有限元单元网格划分，用数值方法编制了计算机分析程序，通过计算，可以得到以上各种截面柱的弯矩—曲率关系曲线，分析它们在延性和承载力等性能方面的差异。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。