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递归神经网络微分流形方法。Differentiable manifolds methods in RNN.

你们会明白为什么的，它在R上有定义，且是可微的。You will see why. It is defined and differentiable in R.

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因此大多数我们会遇到的函数都是可微的。OK, so most of the functions we'll see are differentiable.

并推广了微分同胚的有关结果。The results for differentiable homeomorphism are extended.

每个多项式都是可微的，而每个有理函数也是如此。Every polynomial is differentiable , and so is every rational.

我们说一个函数是可微的,如果这些偏导数存在。And, we say that a function is differentiable if these things exist.

写下来吧，F应该是处处有定义的。Maybe I should write it F defines a differentiable everywhere on this.

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最后讨论了次可微函数上图的生存性问题。As a special case, the viability of epigraph of a sub- differentiable function is discussed.

对于非线性有界连续可导系统的观察器设计是观察器设计的难点之一。There is a nodus to design an observer for nonlinear bounded continuous differentiable system.

探讨一种求解非光滑优化特殊问题-分片光滑问题的算法。A new method is obtained for a special non differentiable problem-piecewise smooth optimization.

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

每一种由局域作用所产生的对称性都对应一守恒流。To every differentiable symmetry generated by local actions, there corresponds a conserved current.

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本文提出并采用微分流形理论证明智能机器人体系结构可分解性定理。In this paper, a decomposability theorem is presented and proved by differentiable manifolds theories.

也就是，向量场是连续的,且在曲面S上处处可微。That means you need your vector field to be continuous and differentiable everywhere on the surface S.

用间断分片可微的函数来近似未知位移场。The unknown displacement field is approximated by discontinuous , piecewisely differentiable functions.

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

共轭梯度方法是求解大规模优化问题的一种非常有效的方法。Conjugate gradient methods are efficient to minimize differentiable objective functions in large dimension spaces.

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我需要一个确定的向量场,而且它在，D，上是处处可微的，然后和平时一样的做法。I need to have a vector field that is defined and differentiable -- -- everywhere in D, so same instructions as usual.

对此，阐明了一些有效的建议，并给出了无处可微连续函数的图示结果。Some suggestions for executing this method are presented, graphical results of nowhere differentiable continuous function are shown.

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。The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case.