查询词典 totally differentiable function

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

The objective of Chapter 2 is to give the weak convergence theorem of S ={T1 :t E G of asymptotically nonexpansive mappings in a uniformly convex Banach space without assuming that X has a Frechet differentiable norm.

本文第二章在G仅要求是一个定向网，X为不具有范数Frechet可微条件的一致凸Banach空间的情况下，给出了一族渐近非扩张映射的弱收敛定理。

We introduce the concepts of differential and integral of fuzzycomplex functions on the space〓,and get their properties.We provethe depictive theorem of differentiable fuzzy complex functions.

在模糊复数度量空间〓上重新引进模糊复函数的微分概念和积分概念，给出了其微积分的基本性质，证明了模糊复函数可微的刻划定理。

For most matrix of A,the linear diffrentiable equations with quasi-periodic finitely differentiable coefficients are reducible.

证明了对大多数的矩阵A，一类系数为有限次可微的拟周期线性常微分方程组是可约的。

Systems with hysteresis are nondifferentiable nonlinear systems. So they cannot be studied through control theories and methods used in differentiable nonlinear and linear systems.

具有回滞特性的系统是不可微分的非线性系统，所以不能采用可微分的非线性和线性系统的控制理论和方法来进行研究。

Finally, we mainly investigate the following three problems:(1) The problem of portfolio selection with transaction costs is formulated as a bi-objective programming model, but it is no-differentiable and difficult to solve. With a transformation, we can transform the nondifferentiable nonlinear programming problem to a linear program.

然后主要做了如下三个方面的工作：（1）针对带交易费的最优证券组合选择问题可以表示为一类不可微非线性规划模型，但其求解比较困难的特点，提出了一种新的化简方法，一次变换即可将该类不可微非线性规划模型转化为一个线性规划模型，不仅简化了求解过程，而且还减少了最终的线性规划问题的变量个数。

Nevertheless, induced bilevel programming models for the former category usually belong to a subject of nondifferentiable optimization problems, whereas that for the latter category becomes the continuously differentiable optimization problems.

此文首先从模型和算法的角度总结了有关这类问题已有的研究成果，接着介绍有关这方面的最新的研究进展，即如何把用户基于平衡原则下的交通网络优化问题的双层规划模型统一地转换为一个连续可微的单层最优化问题，并设计统一的算法。

This course should help students master definitions, basic peoperties and methods of differentiable and Riemannian manifolds, increase their ability from parts to a whole.

通过本课程的学习，希望学生能初步掌握微分流形的基本概念、方法和技巧，学习从局部到整体的数学技巧。

"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。