查询词典 differentiable manifold of class c

X, s. t. g≤0(i=1, 2,…, m), where x∈R and ? g: R→R are twice continuously differentiable convex function.

x，s.t.g≤0(i=1， 2，…， m)，其中，x∈R；f，g：R→R为二次连续可微凸函数。

Consider the convex programming problems min, s. t. g≤0(i=1, 2,…, m), where x∈R and g: R→R are twice continuously differentiable convex function.

对于凸规划问题min，s.t.g≤0(i=1， 2，…， m)，其中，x∈R；f，g：R→R为二次连续可微凸函数。

These results include several sufficient conditions for the global exponential stability of general neural networks with time-varying delays and without monotone, bounded, or continuously differentiable activation function.

不同于已有文献用Liapunov函数或泛函法研究稳定性问题时，将时滞项作为干扰处理的方法，给出了利用时滞项让系统稳定的结果。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

In this paper, we present a nonmonotone line search model algorithm for the nonsmooth composite minimization problems minhf(x, where each f: Rn→Rn is a locally Lipschitzian function, and h: Rn→R is a continuously differentiable convex function.

1引言考虑下面的复合极小化问题minF=hf(x，(1 。1)二〔丫其中f：R"一R"是局部Lipschitz函数，h：Rn一R是下有界的连续可微的凸函数。对于问题(l 。1)，QIL、袁亚湘和孙文瑜等z1一

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。

In order to correct it, a new model of differentiable nonsin gular strength envelope function is proposed.

通过工程实例计算证明，该计算模型是正确可行的。

Based on such function, a new differentiable merit function is constructed. A damped Newton-type algorithm is then present.

在此价值函数的基础上，本文给出了一个阻尼牛顿类算法。

We got alerted a couple of times while we were down south that HETs were on the way to bring us back up north because things were going to go hot again, but it was just rumors.

南下的途中我们不只一次得到警告说重型装备运输车将拉着我们重新北上，因为局势正在变得重新紧张起来，但这只是谣传。

It's the one where they find the ghost in the salt mine.

这一集是演他们在盐矿找到鬼