查询词典 abscissa of uniform convergence

Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space.

王娴 ，何震Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

The essence of design is to ensure trajectories of states ultimately entering into some neighborhood of the coordinate origin, and the convergence of states is evident later on.

设计的本质在于保证系统的状态最终进入坐标系原点的小邻域，而其后状态的收敛性是明显的。

This new method reduces the computational complexity by using the block tridiagonal structure of the input sample correlation matrix, and at the same time keeps the advantage of fast convergence.

在保持了该算法快速收敛优点的同时，利用相关矩阵块三对角的特殊结构，降低了该算法的计算复杂度。

In chapter 2, using the favorable characters of the function Q = ch{x - 1, we construct the hyperbolic cosine penalty function and algorithms and proved its convergence .

在第二章中，我们利用函数Q=ch-1良好的性质，提出一种用双曲余弦函数作罚项的双曲余弦罚函数及算法，证明了该罚函数和算法的合理性及迭代点列的收敛性。

In chapter 3, combining the traditional augmented Lagrange function and the hyperbolic cosine function, we construct a new hyperbolic penalty function multiplier method for the equality constrained optimization and deduced the iterative formulas, and proved the convergence under some conditions.

在第三章中，我们把传统的增广Lagrange函数和双曲余弦函数结合，构造了一类新的在等式约束下的双曲罚函数乘子法，推导出了双曲乘子迭代公式。

Then we use the local subbase to give the structure of topology τ induced by level convergence and prove that the space E〓,τ(l is a T〓 space satisfying the first countability axiom.

证明了空间E〓，τ(l是满足第一可数公理的T〓空间。

The author uses I-fuzzy quasi-coincident neighborhood system to introduce the concepts of I-fuzzy first countability and I-fuzzy second countability, and proves the degree to second countability in each of I-fuzzy topological space must be less than that to first countability, and gives the equivalent characterations about the continuity of function by convergence of sequences in first countable I-fuzzy topological spaces.

作者利用方进明在[4]中提出的I-fuzzy重域系引入了I-fuzzy拓扑空间的第一可数性和第二可数性的概念，证明了一个I-fuzzy拓扑空间空间是第二可数的I-fuzzy拓扑空间的程度一定小于它是第一可数的I-fuzzy拓扑空间的程度，并且在第一可数的I-fuzzy拓扑空间中对映射的连续性进行了等价刻画。

Furthermore, under the assumption that the covariant derivative of the sectionssatisfies the Lipschitz condition with L-average along the geodesic, the estimates of the radiiof convergence balls of Newton\'s method and uniqueness balls of singular points around thesingular points of sections on Riemannian manifolds are given.

当截面的协变导数满足沿着测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出关于截面的Newton法的收敛球半径的估计，及在奇异点附近的关于截面的奇异点的唯一性球的半径的估计。

Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

本章的主要内容包括以下两个方面：当截面的协变导数满足沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出了关于截面的Newton法收敛的统一判据，同时给出了在初始点附近的关于截面的奇异点的唯一性球的半径的估计。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？