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This gives a new description of human recognition mechanism from the view of information geometrical and algebraic topological treatment, the results include Propose a structure representation and system identification approach for neural networks, based on the concept of simplical complexes and dual affine coordinates in the dual flat manifold.

主要的结果包括：提出用对偶平坦流形上的单、复形结构和对偶平坦流形的对偶仿射坐标作为神经网络内在结构表示的一种方法，具有广泛的意义。

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。

For any positive integer n, about the Smarandache LCM dual function SL*, the main purpose of the fifth Chapter is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL* and the mean value distribution property of SL*, obtain an exact calculating formula and a sharper asymptotic formula for it.

对于给定的自然数n，关于Smarandache LCM对偶函数SL~*，本文第五章利用初等方法研究了一个包含SL~*的Dirichlet级数计算问题及SL~*的均值性质，分别给出了精确计算公式和一个较强的渐近公式。

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。

The new foxL music system includes two Linear Magnetic Drive Twoofers (tuned to 100Hz) which features field-focused, back-to-back, dual Extreme-Energy neodymium magnets and bifilar, 1-inch dual voice coil.

新foxl音乐系统包括两个线性磁力传动twoofers （调整，以100 Hz ）哪些功能领域为重点，背对背，双极端能源钕磁铁和双线， 1英寸双音圈。

Concretely, starting from a short sequence primal masks possessing Hermite interpolation properties, a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established, then a dual masks with short support, symmetry and any preassigned order of sum rules is constructed, it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived. From which, a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with Hermite interpolation functions.

具体的，从具有Hermite插值性质的短序列尺度符号出发，首先建立它具有指定阶和规则的充要条件，然后构造出短支撑、对称的具有指定阶和规则的对偶尺度符号，从而得到一对对偶的尺度函数，再构造出相应的双正交多小波。

A differential equation is introduced to construct canonical dual function. The corresponding perfect duality theory is established to show the relationship between the KKT points of the primal problem and the canonical dual problem.

通过引入常微分方程和构造Canonical对偶函数的局部形式，引入了相应的对偶定理，勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系。

Dual citizenship, or dual nationality, is the most common type of multiple citizenship.

双重公民身份，或者说双重国籍，是多重国籍中最普遍的一种。

We will prove that the only compact dual Toeplitz operator is the zero operator, and that a densely defined dual Toeplitz operator with square integrable symbol is bounded if and only if its symbol is essentially bounded.

首先，我们证明了只有零算子是紧的对偶Toeplitz算子，同时给出了以平方可积函数为符号稠定义的对偶Toeplitz算子有界当且仅当它的符号函数是本性有界的。

The newly developed airborne Imaging Wind and Rain Airborne Profiler, built by the Microwave Remote Sensing Laboratory at University of Massachusetts, is a dual polarized dual frequency conically scanning Doppler profiling radar.

三维风雨微波成像仪是美国麻省大学微波遥感实验室研制的双频、全极化圆锥式扫描多普勒雷达，能够同时以四种不同的入射角（30， 35， 40， 50°），15-150m的径向分辨率测量海面和气－海边缘层降雨单元的微波后向散射强度和多普勒频移。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了