查询词典 monotone function

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

Suppose that f is a real-valued ω〓-lower semicontinuous function defined on a ω〓closed bounded subset A〓 of the dual E〓 of a locally convex space E, which is bounded below on A〓, and suppose every ω〓 closed convex subset of C〓≡ω〓-clcoA〓 is the ω〓closed convex hull of its w〓-β-exposed points.

假设X是一个局部凸空间，X〓是其对偶。A〓是X〓上的ω〓有界闭子集，f是A〓上的ω〓-下半连续实值函数且在A〓上下有界。

We prove that a bounded hyperconvex domain D is Bergman complete if the pluricoinplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

We prove that a bounded hyperconvex domain D isBergman complete if the pluricomplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

The property of bounded space Green's function in the neighbor domain of the singular point is studied.

研究了有界空间格林函数在奇异点邻域内的性质。

Where In is a bounded function.

其中In是一有界函数。

Assume is a decreasing function on with bounded supports.

假设 是在内的递减函数。

Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

定理 2 有界函数与无穷小的乘积是无穷小。

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

The main reason for using neural network in time series analysis and system identification is that a trained neural network has the capability to approximate a arbitrary bounded continuous function.

在时间序列分析和系统辨识中，利用神经网络的一个主要原因就是前向神经网络逼近任意连续有界函数的能力。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"