查询词典 differentiable function

These constructional methods can be used to treat many problems, the numerical results show that the given interval extension has smaller excessive width relative to the range of the functions over a domain. For univariate differentiable functions, the definition of interval slope is extended from the first order to high order according to their differentiability, and iterative formula of high-order interval slope computation is also developed.

对多元函数，在不要求函数的可微性及有关Lipschitz常数的条件下，给出了分量函数区间展开的斜率算术运算规则；利用函数局部凸或凹的运算特点，通过递归计算建立了多元函数区间扩张的构造方法。

According to differentiable manifolds theory, the paper discusses tile Legendre transformation of the Pfaffian form, introdues the operator of the Legendre transformation, derives the relation between the Legendre transformation and the partial differentiation and proves three law s.

从微分流形理论出发，讨论了Pfaff形式的勒让德变换；引入了勒让德变换算子；给出了勒让德变换与偏微商的关系；证明了两个定理和一个引理。

In this paper,continuous differentiable conditios of output response functions of Hopfied neural networks in usual papers is reduced to Lipschitz condition.

因此，本文将通常论文中Hopfield神经网络的输出响应函数连续可微的假设削弱为满足L ipschitz条件。

In this paper continuous differentiable conditions of output response functions of bidirectional associate memory neural networks are reduced to Lipschitz condition.

因此，本文将双向联想记忆神经网络的输出响应函数连续可微的假设削弱为满足Lipschitz条件，通过引入Lyapunov函数，利用不等式的方法，证明了双向联想记忆神经网络全局指数稳定性的一个定理。

Let be twice differentiable on the open interval. Then

如果函数在上连续，在内具有一阶和二阶导数，那么

The principle of parallel coordinates are introduced firstly,then the differentiable curves' representation in parallel coordinate space is derived.

本文首先阐述了平行坐标的基本原理，并且推导了欧式空间的可微曲线在平行坐标空间的表达形式。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

A novel multidimensional radial wavelet is constructed based on the framework. It is inseparable, compactly supported and infinitely differentiable, which is different from tensor product wavelet and has been successfully applied to edge detection and adaptive filtering using wavelet networks.

Daubechies结论的一个崭新例子，也是前所未有的，而且这些具体的高维小波在快速边缘检测以及自适应小波网络滤噪方面的应用都获得了极大的成功，因此，在高维小波分析的应用方面可以填补空白。

Where , then is said to be differentiable at . is called the total differential of at, denoted by , i.e..

可表示为，其中，则称函数在点可微分，而称为函数在点的全微分，记作，即

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