对偶的

The Maschke's Theorem of group algebras is well known, and [Mo2] gives us a version of Maschke's and Dual Maschke's Theorem of finite-dimensional Hopf algebras.

半格分次弱Hopf代数是弱Hopf代数的一类特殊情况，而且又是Hopf代数的一种推广，在第1.3节中，我们将会给出半格分次弱Hopf代数的Maschke和对偶Maschke定理的结论及其应用。

What I want to do is making it used in the elementary geometry, to prove the point of intersection in the same line and lines intersect at the same point .

由于Desargues定理及对偶定理是建立在仿射平面上的，而本文要讨论的是如何将其运用到以欧氏平面为基础的初等几何中，证明点共线和线共点的问题。

It is started with the Desargues theorems and dual theorems' formulation and proof of the elementary geometry, guaranteed the scientific of the method on the theoretical plane .

本文从Desargues定理及对偶定理的初等几何表述及证明入手，在理论上保证了此种方法的科学性，在证题的过程中可以看到此种方法是具有可行性的。

Both low memory size and small-scale computation are showed in the new algorithm, on the other hand, a new pivot rule, which is an exterior point method, also makes the new algorithm more efficient.

该算法以核心矩阵为运算单元，一方面呈现了存储空间小，计算量小的特点；另一方面，该算法采用了一种新的转轴规则的外点算法，在保持原始可行的基础上，不断改善对偶解使其可行。

Because the hardware and software may be implemented quickly if wechoose proper normal bases to represent finite fields. In this paper, we first introducesome basic definitions and facts on normal bases over finite fields, then extend theseresults to any Galois extension fields.

在这篇文章中，我们先介绍了有限域上的一些基本定义及关于正规基的相关结论，进而将域扩张到一般的伽罗瓦扩域中，得到了伽罗瓦扩域中正规基与其对偶基等价的充分必要条件，从而将有限域上正规基的等价条件推广到任意伽罗瓦扩域上。

To believe, this work will give some draw lessons to radar.

本文不但从介质的角度讨论了其对偶极子场的影响，而且从天线的特性方面也对其影响进行较深入的研究。

There exists a dual symmetry between the equations of motion and the Maurer-Cartan equations of the type IIB superstring on AdS〓 S〓. We generalize the finite dual transformation to the infinitesimal dual transformation by the twisted dual.

根据Euler-Lagrange运动方程与Maurer-Cartan方程的扭曲对偶变换，我们可得到AdS〓×S〓中IIB超弦的Lax平联络及其相应的可积的相容条件，由此可以说明体系是一个可积系统。

At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.

首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。

The maximum likelihood method for parameter estimation has an extensive application in the intelligence information processing.

本文从凸泛函的对偶表示的角度，深入探讨了具有隐变量的模型极大似然参数估计的变分学习方法。

The fermionic fields rotate oppositely according to κ symmetry. The symmetry of the twisted dual is the symmetry of the moduli space.

这种对偶变换的对称性不是超弦作用量的对称性，它是解的模空间的对称性。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。