对偶的

That is that information processing of neural networks is viewed as the composition of the two steps: field organization and field action, in which, field organization transformation converts input pattern into relevant structure representation, extracting the underlying architecture features and forms a architecture representation in action transformation space; The field action transformation converts the features representation into expected output. In strategies, we use the dual affine coordinates in dual flat manifold as way of representation of field organization system and field action system, which established a theoretical framework of analysis the coupling mechanism of information processing from the view of point of structure representation and model generation.

在具体人工神经网络结构描述的策略上，利用对偶流形空间上的对偶仿射坐标概念分别表示场组织变换系统和场反应变换系统，建立起从问题的结构表示和模型生成两种观点来分析信息处理的理论框架；分析了有监督和非监督学习人工神经网络模型在神经场变换机理下的形式化描述。

This dissertation is devoted to studying the ruin theory on the dual risk model with several dividend rates and on the bidimensional perturbed risk model with or without stochastic disturbance, which includes the discounted expected function about the dual risk model with three dividend rates and the ruin probability on the bidimensional perturbed risk model.

本文致力于研究分多段分红的对偶风险模型及二维风险模型的破产理论，主要研究了分三段分红的对偶风险模型的折现红利的期望函数，并对带有扰动项的二维风险模型的破产概率做了研究。

We prove that any irreduciblesymmetric self-dual Lie algebra 〓 whose Cartan subalgebra consists of semi-simpleelements is in one of the following classes:(1)〓 is simple;(2)〓 is 1-dimensional;(3)〓is solvable.

第五节讨论Cartan子代数由半单元构成的对称自对偶李代数的结构，证明了不可约对称自对偶李代数g如果它的Cartan子代数由半单元构成，那么它只能是下列情形之一：（1）g为单李代数；（2）g是1维的；（3）g是可解的。

By making a thorough study of WSGB curves, the author acquires two main results, i.e., the transformation formula from Bernstein basis to WSGB basis and the construction of the dual functionals for WSGB basis functions.

利用特殊多项式的分解与展开，推导出从Bernstein基函数到WSGB基函数的转换公式。 2。构造出WSGB基函数的对偶泛函，并应用WSGB基函数的对偶泛函，得到另一种方法实现WSGB曲线与Bézier曲线的互相转化。

It transforms the primal problem into an ordinary optimization problem with an explicit dual function and simple constraints, with smaller size than primal constraints. It is convenient for engineering application.

该方法不仅给出了原问题显式形式的对偶函数，而且对偶变量的数目仅等于原问题部分约束的个数，原来的线性0-1规划问题被转化为只有简单约束的普通优化问题，极大地方便了工程应用。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

With the development of the string theory, more and more attentions have been given to the study of the field theory with duality symmetry, especially the dual electromagnetic filed theory has caused great interests.

随着超弦理论的发展，人们愈来愈认识到了对偶场论的重要性，尤其是对电磁对偶理论的研究，引起了人们极大的兴趣。

Using the concept of regular elements,we obtain some results on the classificationof dipolarizations in general symmetric self-dual Lie algebras.

在第六节中，我们把半单李代数的特征元的概念推广到任意带有双极化的对称自对偶李代数上〓用正则元的概念，得到了一般对称自对偶李代数上双极化的一些分类结果。

Our results show that the duality of self-dual tetrahedral link is "trivial", and the duality of hexahedral and octahedral link as well as dodecahedral and icosahedral link are "nontrivial".

从构型角度考虑，四面体链环的自对偶是&平凡&的，六面体链环和八面体链环，十二面体和二十面体链环的对偶是&非平凡&的。

The main aims of this disseration are to extend the complex self-dual grav-itational theory-the Ashtekar theory in four dimensional spacetime and este-bhsh a parametric self-dual gravitational theory in order to solve the problemof reality conditions in the Ashtekar theory.

本文的主要目的是推广四维时空的复自对偶引力理论-阿西特卡理论，建立一个参数化的自对偶引力理论，进而解决阿西特卡理论中面临的至关重要的实性条件问题。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。