不等式

Let a =∈〓. Then corresponding to 62 equivalence classes in χ for ～, we have 144polynomial elements in one variable in canonical basis, each of them also cor-responds to a region which consists of six independent inequalities.

定理。设a=∈〓。那么与χ关于～的62个等价类对应，在典范基中有144个单变量多项式元素，每个单变量多项式元素也对应一个由六个独立不等式构成的区域。

Our first main result is (see §9.1) 9.1. Theorem. Let a =∈〓.χ={i =｜〓=〓}, where 〓 is the unique longestelement in Weyl group of complex semi-simple Lie algebra for type 〓. Thencorresponding to 62 equivalence classes in χ for certain equivalent relation ～,we have 62 monomial elements in canonical basis, each of them correspondsto a region which consists of six independent inequalities.

我们的第一个主要结果是群的唯一最长元素，那么与χ的关于某种等价关系～的62个等价类对应，在典范基中有62个单项式元素，每个单项式元素对应一个由六个独立不等式构成的区域。

Generalized ridge estimation ; kantorovich inequality ; eigenvalue ; trace of matrix ; canonical correlation coefficient ; generalized correlation coefficient

广义岭估计； Kantorovich不等式；特征值；矩阵的迹；典型相关系数；广义相关系数

In this paper,taking Cauchy inequality for example,we discussed some problems on inequalities teaching in middle schools.

以经典的柯西不等式为例，从不等式的证明、推广以及它们的一些应用，对在中学数学教学中的一些问题进行讨论

In this paper, by virtue of some relevant results of Fourier Analysis and Cauchy Inequality, we begin with working on the necessary and sufficient condition for the existence of the periodic solution to a kind of compound-type linear periodical system with constant coefficients and periodical force term f.

高存臣 ，唐瑞娜，阎庆旭本文首先利用Fourier分析的有关结论和Cauchy不等式，对一类具有滞后与超前偏差变元的n阶常系数混合型线性周期系统周期解存在唯一性的充要条件进行了讨论。

First, we establish an energy inequality in the case that no boundary conditions are imposed, and obtain a uniqueness result in the Cauchy problem for the model.

首先，对没有任何边界条件的方程给出一个能量不等式，并且获得Koiter壳的一个Cauchy问题的唯一性结果。

Through above study, the theoretical analysis of the inherent fault tolerance of feed-forward neural networks has been extended from hard-limit activation functions to differentiable activation functions; 2. By using above method, fault tolerance of discrete Hopfield feedback neural networks have been also analyzed. It means that the above method can be applied not only for feed-forward neural networks but also for feedback neural networks; 3. For the feed-forward neural network with the Sigmoid activation function, Chebyshev Inequality method was presented.

这项研究将以前仅限于对硬限幅作用函数前向神经网络固有容错性能的理论分析推广到具有可微作用函数的前向神经网络； 2 针对离散型Hopfield反馈神经网络，利用上面提出的方法，对其同样进行了容错性分析，得出许多有用的结论和计算公式，说明上面提出的方法不仅适用于前向神经网络，同时也适用于反馈神经网络； 3 针对具有Sigmoid作用函数的前向神经网络提出了一种切比雪夫不等式法。

The famous Chebyshev's Inequality is usually used when estimating the boundary from above or below of probability .

在估计某些事件的概率的上下界时，常用到著名的切比雪夫不等式。

Chebyshev's Inequality and Law of Large Numbers are the foundational work on the limit theory of probability.

其创立的切贝舍夫不等式和切贝舍夫大数定律是概率论极限理论的基础，从而使概率论成为严密数学分支。

While Chebyshev's Inequality gives an upper bound on P, there is no guarantee that the upper bound is a good approximation.

因为切尔雪夫不等式给出的是每个象素灰度的上限，而又没法保证其上限是一个很好的估计。

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。