查询词典 partially differentiable function

Radial basis function coupled with a polynomial basis function was used as a trail function, and a Heaviside function was used as a test function of the weighted residual method.

这种无网格方法采用径向基函数耦合多项式基函数来近似试函数，采用Heaviside函数作为加权残值法中的权函数。

Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.

与具有光滑流函数的单个守恒律的初始值问题相比，具有弱间断流函数的单个守恒律初边值问题的整体弱熵解中包括下列新的相互作用类型：稀疏波碰到边界并被边界部分或全部吸收；稀疏波与边界相撞，边界反射出一个接触或非接触激波；接触或非接触激波碰到边界并被边界吸收；接触或非接触激波与边界相撞，边界同时或稍后反射出一个新的非接触激波。

Result Compared to concurrent control groups, neuromotor function are significantly improved in 1h and 6h experiment group. The indexes of neural cell apoptosis decreased significantly (P 0.01). But in 24h experiment group, the decrease of the index are not statistically significant. Conclusion Early application of rhEPO could lessen the lesion of neuromotor function. The protection is partially due to the reduction of neural cell apoptosis.

结果：与对照组相比，脊髓损伤后促红细胞生成素1小时，6小时实验组神经运动功能明显改善，脊髓神经细胞凋亡指数均明显下降(P 0.01)；而术后24小时组与对照组相比，脊髓神经细胞凋亡指数的下降无统计学意义结论：早期应用外源性EPO对脊髓不完全损伤后引起的神经运动功能损害具有保护作用，此种保护作用可能与EPO能够减少神经细胞凋亡有关。

Methods: Arthroscopic operation was performed in 37 patients with calcified supraspinatus tendinitis. Shoulder function of the patients was evaluated using the constant-Murley score, VAS, ASES and radiographs before and after operation. Results: The shoulder function of patients was improved, and the symptoms were disappeared or partially disappeared after operation.

采用关节镜下手术治疗37例钙化性冈上肌腱炎患者，评估其术前、术后的X光片表现，采用视觉模拟法疼痛评分，Constant-Murley评分和美国肩肘关节外科医师协会评分系统分析患者术后的改善情况。

First the associated Hamilton-Jacobi-Bellman equation is given, then its continuously differentiable solution is constructed.

首先给出了最优控制问题对应的Hamilton_Jacobi_Bellman方程，接着构造出了它的连续可微解。

Based on Cantor series expressions of real number,we constructa wide class of nowhere differentiable continuous functions.

其次，讨论了这类函数的几何特性，给出了它们几何对称的一个判别条件。

If is continuous on the closed interval and differentiable on the open interval, then there is at least one number in where

在闭区间上连续；(2)在开区间内可导

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

Improtant reasons are that fuzzy logic is not differentiable and the effective neural network needs differentiability.

其根本的原因是普通模糊逻辑是不可微的，而最有效的神经网络却要求可微性。

"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。