查询词典 differentiable manifold of class c

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。

Moreover,we consider the techniques in calculating the map\'s degree respectively in two cases that the functional responses function is monotone and differentiable or is nonmonotonic and undifferentiable.

本文深入到算子度的计算方法尤其是抽象算子同伦映射的构造，并为抽象算子同伦映射的构造提供了普遍适用的操作方法，即一步到位构造一个多项式函数作为抽象算子的同伦映射。

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。

Using normal distribution transform probability model to represent a laser range scan.Not need features corresponded,but transform the discrete scan date to the piecewise continuous and differentiable probability density function,and using Newton's algorithm to optimize scan matching,so can build the 2D global map.

利用正态分布转换概率模型来表示激光扫描，不需利用特征对应，而是通过将扫描得到的离散数据点转换成分段连续可微的概率密度函数，并利用牛顿优化算法来进行扫描匹配，从而建立2维全局地图。

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

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。

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