局部最小值

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Secondly, for the same hash function, the sample with the minimum hash value is selected as the global sample and the local samples are combined at the center node to filter out the biased effect of duplicated updates.

然后，对于相同散列函数产生的样本选取具有最小散列值的样本作为全局样本，完成局部样本集在中心节点的合并，滤除在分布节点上的重复更新对样本偏斜的影响。

This makes it possible to reduce vibration and noise on a certain frequency in application. By finite element method, frequency response and radiating noise of block's lateral surface under the impact are analyzed.

根据不同频率灵敏度最大值所对应的位置不同这一特点，可进行局部参数修改，而对其它频率响应的影响很小，使得实际中针对某一频率的减振降噪成为可能。

To register two partially-overlapping mesh surfaces, the least median of squares estimator is adopted to estimate the rigid body transformation, which is composed of two parts of"generation of hypothesis"and "verification of hypothesis".

为配准两个局部重叠的网格面，采用最小平方中值估算器来计算刚体变换，它由"假设的产生"和"假设的验证"等两个部分组成。

Fusion rules of maximum, local gradient and area energy based on wavelet transform are advanced.

为此在医学图像配准的基础上提出基于小波变换的最大值融合规则，局部平均梯度融合规则，区域能量融合规则等算法。

The adhesion region between two adjacent teeth on the 3D dental model is first detected by exploiting the minimum principal curvature information. Then, the adhesion region is cut off and the tooth profile opening caused by the removal of the adhesion region is filled with triangular patches adopting a local optimization scheme, it is then refined to form an intermediate restoration surface patch. The final restoration result is obtained by minimizing the surface energy to reflect the bio-characteristics of the single tooth.

根据三维牙颌模型的形态特征，采用基于曲面最小主曲率的方法对粘连区域进行准确的检测提取；对删除齿间粘连区域后生成的齿间开口利用局部最优化权值规则进行剖分并细分优化，生成"中间"恢复曲面；根据牙齿的生理医学特征，以齿间开口的边界信息为约束条件，采用基于最小化曲面能量函数的方法对"中间"恢复曲面进行变形调整，实现单颗牙齿缺失形状的准确恢复。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

Data pre-processing technologies such as singular points elimination, registration and radius compensation are studied. Base on chord high difference algorithm, a new one called chord high difference-ratio algorithm is proposed to improve veracity and robusticity of singular points elimination. Then, a registration algorithm based on local surface reconstruction is proposed, which avoids infaust influence coming from single reference point error.

在弦高差法的基础上，提出了全新的弦高差—比法，提高了异常点剔除的准确性和柔韧性；提出了一种基于局部图形重构的重定位方法，该方法通过对特征球的最小二乘拟合，消除了单一参考点的精度对重定位的影响；在此基础上对重定位的误差进行了详细的分析，给出了精确的误差值，从数学的角度保证了重定位的精度；在三角网格法的基础上提出了基于Delaunay三角剖分的半径补偿新方法，有效改善了补偿矢量的计算效率和准确性。

Results After 3 months of kidney radiation by 15 Gy of Cs137 γ-rays, the changes with kidney shrank, Bowman's capsules straitened or disappeared, glomerular swelled, some epithelia denaturalized or died were observed. Mitochondria tumefied and the cristae shortened, lessened and disordered. Urine β2-MP rose evidently. It was lowered significantly the renal 25-OH-D-1α-hydroxylase activity and its mRNA expression. The dry and ash weight, BMD of femur and lumbar were significantly reduced, volume and width of bone trabecula were distinctly decreased and the space increased in model group. The Pyd / Cr increased and ALP decreased as well.

结果 15Gy 137Cs-γ射线肾局部照射3个月后肾脏体积缩小，肾小球肿大，Bowman氏囊囊腔狭窄甚至消失，部分肾小管上皮细胞变性、坏死，线粒体肿胀，体积增大，线粒体嵴变短、减少、排列紊乱；尿β2-MP显著增加；肾1α羟化酶活性及1α羟化酶mRNA基因表达量明显下降；肾辐射组股骨干重、灰重、腰椎和股骨BMD明显降低；骨小梁体积和骨小梁宽度减少，骨小梁间距增加，MAR减小；腰椎压缩和股骨三点弯最大载荷明显降低，Pyd / Cr值明显增加，ALP显著降低。

The effects of frequency veering features on mode localization of the mistuned system were analyzed with L. It is shown that the distance between the frequency veering curves at nodal diameters is a key parameter, and it exists a minimum value for the parameter, around which blade modes are very sensitive to mistuning, and can result in dramatic fluctuation of the mode localization degree.

研究表明，频率转向曲线之间关于节径的最小间隙是反映频率转向特征的重要参数，并存在一个转向频率间隙的极小值点，在该极值点附近，频率转向区内的模态对叶片失谐非常敏感，并会导致模态局部化程度剧烈变化。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。