OK, so most of the functions we'll see are differentiable.
因此大多数我们会遇到的函数都是可微的。
That means you need your vector field to be continuous and differentiable everywhere on the surface s.
也就是，向量场是连续的，且在曲面s上处处可微。
The function is continuously differentiable.
函数是连续可微分的。
The results for differentiable homeomorphism are extended.
并推广了微分同胚的有关结果。
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。
In this paper, the star-kernel of a quasi-differentiable function in one-dimensional space is studied.
本文在一维情形下对拟可微函数的星核进行了讨论，证明了拟微分星-有界等价子类的存在性；
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。
In this paper an interval iterative method is given for seeking the global maximum of a second order differentiable function.
本文就二次可微函数类给出一类求大范围极值的区间迭代方法。
The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case.
可微非线性规划问题的线性化过程可以自然地推广到拟可微的情形。
Because the error transfer function of rough neural network is not differentiable, genetic algorithms are applied for training the network.
由于粗神经网络的误差传递函数不可微，所以采用遗传算法来训练粗神经网络。
By very elementary method, it is proved that every continuous differentiable function defined in a perfect set has differentiable extension.
本文完全用初等的方法证明了完全集上连续可微函数都有可微开拓。
It is also proved as application that any bounded variation function can be seen as a differentiable function beside a set of arbitrary small measure.
作为应用，证明了任意有界变差函数都与某可微函数在除过测度任意小的集合外重合。
For the learning process, a new kind of empirical risk function is proposed which is differentiable and can be minimized by gradient descent strategy.
对于参数的学习，提出了一种适用于分类器的可微经验风险函数，该函数能够有效地利用梯度下降法进行最小化。
Every Layer has a simple API: it transforms an input 3d volume to an output 3d volume with some differentiable function that may or may not have parameters.
每一层都有一个简单的API：用一些含或者不含参数的可导的函数，将输入的三维数据变换为三维的输出数据。
To solve a class of non-differentiable optimization problems, this paper proposed a new method called maximum-entropy particles swarm optimization algorithm.
针对一类不可微优化问题，本文提出了一个新的算法—极大熵微粒群混合算法。
A type of continuous and Non-differentiable Function is studied, its characteristics and essence are revealed, and its condition of construction is presented.
对一类连续但不可导函数进行研究，揭示其特点和本质，并给出其构造条件。
The value function turns out to be continuous in the whole plane, and is even continuously differentiable in the interiors of both right and left half planes.
说明了值函数在整个平面上是连续的，在左右两个半平面的内部还是连续可微的。
Minimax problem is a sort of non-differentiable optimization problem and the entropy function method provides a efficient approach to solve such kind of problems.
极大极小问题是一类不可微优化问题，熵函数法是求解这类问题的一种有效算法。
The approximation of differentiable functions by a kind of interpolatory rational functions is discussed, and the corresponding order of approximation is obtained.
讨论了一类插值有理函数对可微函数的逼近，得到了相应的逼近阶。
The economic dispatch problem of power systems is approximated and converted into a differentiable one by way of maximum entropy in accordance to its characteristics.
针对电力系统经济负荷分配问题的特点，应用极大熵理论将经济负荷分配问题转化为可微问题。
The traditional bi-level model formulation of these problems is transformed into a single-level continuously differentiable problem using a marginal function approach.
并提出了一种基于路段变量的连续可导的边际函数和距离函数，从而把两层规划转化成单层规划问题。
To meet these problems, an application of B-differentiable Equation method for the contact problem is presented and the contact flexibility matrix is no longer needed.
为此，本文利用接触条件的B-可微方程组形式，提出了一种不需形成柔度阵的求解方法。
A CAM of the CAM mechanism has a curvature course with points, in particular bends or jumps, which are not constantly differentiable within a movement region of the CAM.
该凸轮传动机构的凸轮具有曲率变化曲线，该曲率变化曲线在凸轮的运动范围之内具有不可连续微分的部位、特别是折点或者跃变。
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。
Because the optimization problem may be discontinuous and non-differentiable even has no objective function, the traditional optimization methods are unable to tackle with it.
由于优化问题可能是不连续的、不可微的甚或是没有函数解析式的，传统经典的无约束优化方法在应用时会受到限制。
Because the optimization problem may be discontinuous and non-differentiable even has no objective function, the traditional optimization methods are unable to tackle with it.
由于优化问题可能是不连续的、不可微的甚或是没有函数解析式的，传统经典的无约束优化方法在应用时会受到限制。
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