不等式

We then apply the one-tailed version of Chebyshev's Inequality to estimate the percentage of light reaching a surface at depth t.

这样我们应用一个修改版的切尔雪夫不等式去估计光源到达深度t平面的百分比。

Aiming at the problems of over-fitting and generalization for neural networks, the locally most entropic colored Gaussian joint input-output probability density function estimate is studied, and a new method by means of Chebyshev inequality is proposed to self-revise respectively according to every cluster.

针对神经网络的过拟合和泛化能力差的问题，研究了样本数据的输入输出混合概率密度函数的局部最大熵密度估计，提出了运用Chebyshev不等式的样本参数按类分批自校正方法，以此估计拉伸样本集，得到新的随机扩充训练集。

We can thus choose any monotonic warp of the depth metric and still obtain an upper bound on the visibility using Chebyshev's Inequality as with standard VSMs.

我们可以选择一个单调的深度扭曲矩阵，但还是能够得到运用切尔雪夫不等式得到可见度的最高限。

Moreover, with its help people can also evaluate the fault-tolerant performance of ANN. In this paper, Chebyshev Inequality method, as a kind of evaluating thought, was firstly concerned in the faulttolerance analysis of ANN; 4. The variation of faulty behaviors of ANNs during the course of learning was studied by taking the discrete Hopfield neural network and Hebb learning algorithm as examples.

这种方法首次将切比雪夫不等式引入人工神经网络容错性分析当中，从而提出了对人工神经网络容错性分析采用估算的思想； 4 以离散型Hopfield神经网络和Hebb学习算法为例，着重研究了在学习过程中人工神经网络故障性能的变化。

Second, On the basis of analysis of density distribution of sequence points on the chaotic orbit of one-dimension chaotic mapping, a mutative interval chaotic optimization algorithm is presented in search for the solution optimums of the non-linear constrained problems with multi-variables and multi-peak values. With the objective function probability measurement approaching a limit 1, the convergence of the algorithm on the global optimal solution is proofed by aid of Chebyshev inequality.

二、基于一维混沌映射混沌点集的概率测度分析，提出了一种适于解决多变量多峰值非线性约束问题的新的混沌优化算法——变区间混沌优化算法，并应用切比雪夫不等式论证了算法依概率收敛于全局最优解。

By transforming the nonlinear saturation constraint into the special linear constraint, the problem of solving the feedback controller with saturated actuator is converted to the design of controller with linear constraint. The stochastic stability is ensured by using the intersection of ellipsoid invariant set of different modes existing in the attraction domain of the closed loop system. In this case, solving controllers can be equivalent to a solvability problem of linear matrix inequalities.

通过将非线性饱和约束转化为特殊的线性约束，使具有饱和执行器的控制器求解问题转化为线性约束控制器的求解问题，利用位于闭环系统吸引域内的不同模态下椭圆不变集的交集来保证系统的随机稳定性，此时控制器的求解可等效为线性矩阵不等式的可解性问题。

Moreover, we pointed out some errors in the litterature concerning the closure property of two families of ageing notions and gave a new proof; established probability inequalities for some common used discrete ageing notions, and obtained some comparison results of inspection paradox.

另外，我们指出文献中关于两类寿命分布类卷积封闭性证明的错误，并纠正其错误；建立了常见的离散型寿命分布类对应的概率不等式；给出了检查悖论中的一些随机比较结果。

And the closure property of inverseM-matrices under Hadamard product are analyzed, the properties of generalizedPerron complement of inverse M-matrices, inequality of Fan product of H-matricesand Perron root estimation of nonnegative matrix are studied.

本文研究了逆M-矩阵的性质和完成，并且讨论了有关逆M-矩阵Hadamard 积的封闭性，不可约逆M-矩阵的广义Perron补，H-矩阵的Fan积不等式以及非负矩阵的Perron根的估计。

On one hand, we analyse the virtues and disadvantages of existing algorithms based on inequality criterion and transform domain, then a fast codeword search algorithm based on ordered Hadamard transform is presented.

一方面，分析现有的基于不等式判据和基于变换域的各种算法的优缺点，提出了一种新的基于排序哈德玛变换的快速码字搜索算法。

The topics covered include the basic concepts of information theory--entropy, mutual information, channel capacity, information rate, Shannon's noiseless coding theorem and Shannon's fundamental coding theorem; modeling of information sources--zero-memory and Markov models; modeling of information channels--BSC and BEC channels, additivity of information and cascaded channels; construction of compact source codes--Kraft inequality, compact codes, Huffman and LZW compression codes; and analysis and design of error-control channel codes--Hamming distance, binary linear codes and the parity-check matrix, Hamming codes, checksum codes, cyclic codes and the generator polynomial and CRC codes.

课程的内容包括：信息论的基本概念（熵、交互信息、信道容量、信息率、 Shannon无噪声编码定理和Shannon基本编码定理）、信源模型（无记忆模型和Markov模型）、信息信道模型（BSC 和 BEC模型、信息的可加性和级联信道），紧致信源编码设计（Kraft不等式，紧致编码，Huffman 和LZW压缩编码）以及差错控制信道码的设计与分析（海明距离，二元线性码，奇偶校验矩阵，海明码，校验和，循环码，生成多项式和CRC码）。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。