查询词典 totally differentiable function

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 our results, we do not require activation functions to be bounded,differentiable or strictly increasing.

同已有的结果相比，我们不要求函数有界，可微或严格增加等条件。

Theorem 3.2. Assume that is compact and that is continuously differentiable on a neighborhood of .

定理 3.2。假设紧密的并且f在的邻域中是连续可微的。

Why won't this woman just suck it up and right differentiable characters, with their own voices?

为什么吴尔芙不干脆吸收这个人的声音，然后利用不同的角色？

Every polynomial is differentiable, and so is every rational .

每个多项式都是可微的，而每个有理函数也是如此。

Theorem 1 If is differentiable at, and is a local extreme value of, then.

定理1 设函数在处可导，且在处取得极值，那么。

Let be defined on the open interval for some. If is differentiable at, and for any in

设函数在点的某邻域内有定义，并且在处可导，如果对任意的，有，那么。

In addition, the radial wavelet given in this example satisfies the following properties:ψ is infinitely differentiable.

按照I.Daubechies的理论，上述前两条性质对于一般的正交小波基是不能共存的。

For the head-teacher of the class said that I had seriously broken the school rules,which led me to a three-day suspend class.

为什么呢？因为我的班主任说我严重的违反了校规，于是让我停课三天。

Many of them believe that the conversion of thousands of working-class folk in England spared that nation from the mass carnage and the tyranny that came with the revolution in France.

他们之中有许多人相信，在英国数以千计的劳工阶级之悔改信主使英国免於遭受如法国大革命所造成的大屠杀和专制暴政。