连续逼近

Main foundation is the approximation theorem of completely continuous operators and the Guo-Krasnosel' skii fixed point theorem of cone expansion-compression type.

主要工具是全连续算子的逼近定理和锥拉伸与锥压缩型的Guo-Krasnosel' skii不动点定理。

Proposed in the paper are the ordered monotony property of MFNNs when the transfer function is monotone, the continuous mapping theorem, and non approximation theorem to function.

给出了单调传递函数的 MFNNs按序单调特性、连续映射定理以及非函数一致逼近定理。

Methods The relationship of dynamic model′s input and output was analyzed and a basic structure of system identification model based on the principle of optimization in model reduction and the property of a function approximator to be composed of feed-forward networks was presented.

分析了控制系统动态模型的输入、输出关系，依据模型等效的最优化原理和神经网络任意逼近有限不连续函数的性质，提出神经网络辨识模型的基本结构。

The barycentric Lagrange interpolation collocation method for solving initial value problems of differential equation is introduced.

本文首先分析了重心Lagrange插值的基本性质，给出了采用重心Lagrange插值逼近任意连续函数的数值算法。

The main reason for using neural network in time series analysis and system identification is that a trained neural network has the capability to approximate a arbitrary bounded continuous function.

在时间序列分析和系统辨识中，利用神经网络的一个主要原因就是前向神经网络逼近任意连续有界函数的能力。

On defining the conditional threshold of discretized density evolution, a method for designing the time-invariant quantized decoder with finite levels, which can approach the optimal time-varying one and hence the continuous decoding, is proposed.

应用Shannon率失真理论以及密度进化理论，阐述了最佳量化译码的时变特性，建立了离散密度进化的条件阈值概念，提出了二元输入对称信道上逼近最佳时变量化译码、进而接近连续译码的时不变量化译码设计方法，推导了量化和积算法与最小和算法的等价条件，从误码率性能、错误平层和平均迭代次数等三个指标全面衡量量化译码性能； 5。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

Point to successive two days appear steep fall, shanghai points to drop for a time approach 5000 bits of col, two city do much power to continue to drop, those who drop from Zhou San occupy about 7 Chengshangsheng arrives to be controlled most probably; And two city clinch a deal 267.2 billion yuan, continue to the limit of one's capacity 7 percent, point to appear to drop urgently continuously of to the limit of one's capacity bad go situation, have 21 drop more than 8%, part a brunt capital is more apparent from field evidence.

股指连续两天出现暴跌，沪指一度下跌逼近5000点关口，两市做多动力继续减退，下跌的个股从周三的约占七成上升到八成左右；而两市成交2672亿元，继续放量7个百分点，股指呈现连续急跌放量的不妙走势，有21只个股跌幅超过8%，部分个股主力资金离场迹象比较明显。

Deduced the analytical structure of the Mamdani fuzzy system whose input sets were with generalized linear membership function and manifested that the output of the fuzzy systems were monotonical, decreasing, continuous and bounded.

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数，推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构，证明了典型模糊系统是单调、递减的有界连续函数；在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数，最后仿真实例证明了本设计的有效性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。