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球覆盖
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  ball-covering
     Minimal Ball-covering of the Unit Spheres in R~n
     R~n空间中单位球面的极小球覆盖
短句来源
     This article first proves that there exists a specific ball-covering with the smallest radius in R~n if a set {x_i}~m_(i=1) satisfying some given term,then presents a minimal ball-covering with arbitrary given r≥32 as its radius.
     本文针对一特殊空间Rn,首先证明了在Rn中,若有一点集{xi}im=1满足一定条件,则可给出一特殊的球覆盖,且此覆盖的半径即为最小半径. 进一步本文还给出了在Rn中若任意给定r≥32,可找到一个以r为覆盖半径的球覆盖,且此覆盖的势为极小的.
短句来源
     We say A family B of closed balls in a Banach space X is a ball-covering of X if every ball in B does not contain the origin in its interior and whose union covers the unit sphere SX of X,and a ball-covering B is said to be minimal if the cardinal of B is less than or equal to the cardinal of every ball-covering of X.
     Banach空间X中的一个闭球族B是X的球覆盖,如果B中的任一元素不包含原点作为其内点,且B中元素之并覆盖了X的单位球面SX. 一个球覆盖B称为是极小的当且仅当B的势小于或等于X中所有球覆盖的势.
短句来源
  ball-coverings
     Ball-coverings Property of Banach Spaces
     Banach空间单位球面的球覆盖性质
短句来源
     By means of the projection method,adding a small disturbing function to the objective function, the penalty method, andthe gradient method, this dissertation proposes several neural networks for solvingsaddle point problems and minimum radius of ball-coverings problems, and investi-gates the stability of the proposed networks by the LaSalle invariance principle andthe Lyapunov method, so as to design neural networks which avoid getting stuck inthe local minimum. It is divided into five chapters.
     本文针对约束鞍点问题和球覆盖最小半径的计算问题,分别利用投影法、对目标函数加上很小“扰动函数”的逼近法、罚函数法和梯度法等建立神经网络模型进行求解,并基于LaSalle不变集原理和Lyapunov直接法等工具,对模型的动态特性进行研究,从而设计出避免陷入局部极小的优化计算神经网络模型.
短句来源
     Chapter 1 presents a survey of the study of optimization computing by neural net-works, including the stability analysis for recurrent neural networks, and neural net-works for solving saddle point problems and minimum radius of ball-coverings prob-lems.
     全文共分五章:第一章简要回顾了优化计算神经网络研究的发展概况,以及利用神经网络求解鞍点问题和球覆盖最小半径问题的研究现状.
短句来源
  “球覆盖”译为未确定词的双语例句
     m-weight is a new generalization of the classical Hamming weight and a new parameter of the linear codes over finite field. We generalize a classical exis-tence theorem, the Plotkin bound and the Sphere Packing bound on Hamming weight to m-weight.
     推广Hamming重量的三个经典结论,我们得到了具有特定m-重量的线性码的一个存在性定理,以及以m-重量为参数之一的码的参数所满足的相应的Plotkin界和球覆盖界。
短句来源
     This Paper Gives a decomposing approach for a distance net point set in E ̄n, that is themain element decomposing approach. It solves a key proboem, the implement of an n-dimensionalconnected decomposition with the equiball covering property,in the embedding of a distance net pointset into E ̄n by the divide-and-conquer approach.
     提出了E ̄n中距离网点集的一种分块方法──主元分块法,解决了距离网点集在E ̄n中分治嵌入的一个关键问题──具有等球覆盖性质的n-维连通分解的实施。
短句来源
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  ball-covering
Ball-covering property of Banach spaces that is not preserved under linear isomorphisms
      
By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X.
      
The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls.
      
(2) Let Λ be the set of all numbersr>amp;gt;0 satisfying: the unit sphere of every Banach spaceX admitting a ball-covering consisting of countably many balls not containing the origin with radii at mostr impliesX is separable.
      
(3) IfX is a Gateaux differentiability space or a locally uniformly convex space, then the unit sphere admits such a countable ball-covering if and only ifX* isw*-separable.
      


This Paper Gives a decomposing approach for a distance net point set in E ̄n, that is themain element decomposing approach.It solves a key proboem, the implement of an n-dimensionalconnected decomposition with the equiball covering property,in the embedding of a distance net pointset into E ̄n by the divide-and-conquer approach. The main element decomposing approach can be appliedtu the case of a bounded distance net point set in E ̄3 tu build a optimized decomposing algorithm for themacromolecular comformations...

This Paper Gives a decomposing approach for a distance net point set in E ̄n, that is themain element decomposing approach.It solves a key proboem, the implement of an n-dimensionalconnected decomposition with the equiball covering property,in the embedding of a distance net pointset into E ̄n by the divide-and-conquer approach. The main element decomposing approach can be appliedtu the case of a bounded distance net point set in E ̄3 tu build a optimized decomposing algorithm for themacromolecular comformations in E ̄3 with the Nuclear Magnetic Resonance data.

提出了E ̄n中距离网点集的一种分块方法──主元分块法,解决了距离网点集在E ̄n中分治嵌入的一个关键问题──具有等球覆盖性质的n-维连通分解的实施。此法应用到E ̄n中距离界网点集的情形为利用核磁共振测距技术,快速计算生物大分子三维溶液结构提出了一种具体的优化分块算法.

In this paper, the learning of binary neural network for Boolean function mapping is projected as representing sets of the learning patterns by neurons. For hidden layer, a concept of weighted Hamming distance sphere is introduced to further improve the learning efficiency and generalize the learning strategies as well. For output layer, some new results about representing combination of sets, which are devoted to simplify implementation of Boolean function, are proposed. Under the learning strategies the weights...

In this paper, the learning of binary neural network for Boolean function mapping is projected as representing sets of the learning patterns by neurons. For hidden layer, a concept of weighted Hamming distance sphere is introduced to further improve the learning efficiency and generalize the learning strategies as well. For output layer, some new results about representing combination of sets, which are devoted to simplify implementation of Boolean function, are proposed. Under the learning strategies the weights and thresholds are all integers, and the network is easy to be implemented by hardware.

把二进神经网络对布尔函数映射的学习归结为神经元对学习样本集合的表达.通过对神经元表达能力的分析研究,引入加权距离汉明球的概念,既提高了学习效率也简化了布尔函数实现结构,同时把汉明球及立方体集合覆盖思想等统一在加权汉明距离球覆盖的框架下.另外,还得到旨在提高输出层神经元表达能力的新结果.最后举例说明了此学习策略的可行性与特点.经学习得到的二进神经网络的权系数及阈值皆为整数,易于硬件实现

This paper constructs the Jame-Stein type confidence ellipsoid for the mean of multivariate normal distribution with a class of unknown non-spherical covariance matrix structure. The coverage probability of the usuall confidence ellipsoid is shown to be im proved asmptotically by centering at a Jame-Stein type estimator, and uniform order of the remainder term in the coverage probability expansion is also given.

本文构造了协方差阵具有非球型结构(未知)的多元正态分布均值的James-Stein 型置信椭球,它能渐近一致改进通常置信椭球的覆盖概率,并给出了改进余项的一致阶, 同时本质改进了文献中有关余项的一致阶。

 
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