查询词典 weak approximation theorem

By the best approximation theory, it is first proved that the SISO (single-input single-output) linear Takagi-Sugeno fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain.

借助于最优逼近理论，证明了线性SISO TS模糊系统可以逼近任意一个多项式，然后以Weierstrass逼近定理为桥梁，证明了该模糊系统可以以任意精度逼近一个任意的连续函数，从而得到了该模糊系统万能逼近性的一个新的充分条件。

The properties of the λ-cut sets of the lower and upper approximation are discussed,and then the F-Union Decomposition theorem of the lower and upper approximation of rough fuzzy sets is given.

基于此，本文在逐一增加属性形式下的等价类F-分解的基础上，讨论了粗模糊集的F-分解形式，并给出了粗模糊上、下近似集合的F-分解定理及相关推论。

Since the structure self-organization and self-learning abilities of GFNN, it is different from the universal approximation theorem of FLS and BP theorem of NN.

由于GFNN的结构自组织和参数自学习能力，使得它与模糊逻辑系统中的万能逼近定理以及人工神经网络的BP逼近定理不同，GFNN不再只是一个存在性定理，它给出了GFNN的实现过程。

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。

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

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。

Chaos synchronization for integral order system is accomplished by employing both linear feedback control and adaptive control based on Lyapunov first approximation theorem and asymptotical stability theorem.

利用线性回馈控制与适应性控制，使得整数阶系统达成浑沌同步。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对"中间点"的渐近性进行了研究，得出了一系列"中间点"的渐近性的结果，概括了有关文献对微分中值公式的"中间点"的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

Based on this thought, in this thesis, the alternation theorem is first extended to the Chebyshev approximation problems with inequality constraints, and then two algorithms are devised for designing linear phase FIR filters with inequality constraints in Chebyshev sense according to the extended theorem.

L.J.Karam和McClellan在文献[20]中把交错点组定理扩展到复数域，并提出了求解复系数FIR滤波器的复Remez算法，但由于此扩展定理只是一个充分条件，所以此算法不能保证得到最优解。在文献[23]中，他们对复Remez算法进行了完善，使其收敛到最优解。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。