查询词典 extended mean value theorem

Wang-type fuzzy logic system and its functional approximation ability are researched deeply, A class of Gauss-type fuzzy logic system is presented and studied What it defers from Wang-type fuzzy logic system is its using Gauss fuzzifier The analytical expression of this fuzzy logic system is derived detailed Its universal approximation theorem for nonlinear functions is proved by StoneWeiestrass theorem.

通过对两类模糊系统作为非线性辨识器的仿真研究显示出高斯型模糊逻辑系统在抗数据干扰方面比Wang型模糊系统有优势。对非线性动态系统的辨识问题，借助递归神经网络的研究成果，提出一种基于递归网络结构的自适应模糊逻辑系统和参数学习算法。

Finaly, we introduce the Bernstein-Kantorovich quasi interpolant and study the approximation equivalent theorem with pointwise modulus (o≤λ≤1 ) in space L[0,1] and approximation equivalent theorem with Ditzian-Totik modulusin space L_[0,1](1 ≤p ≤ω).

最后，引入Bernstein-Kantorovich拟中插式，利用点态光滑模ω_~(2r)(0≤λ≤1)讨论了其在L_∞[0，1]空间的逼近等价定理和其在L_p[0，1](1≤p≤∞)空间关于模ω_ψ~(2r)的逼近等价定理。

In this paper we use pointwise modulus of smoothness to study approximation direct theorem and equivalent theorem for some linear operators and quasi-interpolant operators; Using pointwise modulus we discuss the strong converse inequality on K-functional; and using a modified weighted K-functional and weighted modulus of smoothness we study approximation with Jacobi weight on operator with non-zero first order moments.

本文利用点态光滑模ω_~(2r)来研究某些线性算子及逆中插式逼近正定理和等价定理；利用点态光滑模讨论其关于K-泛函的强逆不等式；同时利用一种改变的带权K-泛函和带权光滑模研究一阶矩不为零的算子的点态带Jacobi权逼近。

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

The others problems discussed are nested interval method, Cantor theorem, C del incompleteness theorem and Axiom of choice etc.

同时对区间套法，康托定理，哥德尔定理，选择公理等与之密切相关的一些问题，作了深入讨论并得出创新性结论。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

Theorem g is called binomial theorem.

定理g称为二项式定理。

The classical theorems of analytic function of one complex variable such as Morera theorem and Liouville theorem were generalized to the regular function, similarly to biregular function.

Clifford分析中，正则函数是单复分析中全纯函数在高维空间的推广，全纯函数的经典函数理论如Morera定理，刘维尔定理等都可推广到正则函数，同样也可推广到双正则函数。

By using the integral equation and the Schauder fixed point theorem, through considering the height of nonlinear term on some bounded set, a new existence theorem is established.

利用积分方程和Schauder不动点定理，通过考察非线性项在某些有界集合上的高度建立了一个新的存在定理。

Methods Clinical data of 3 cases of bile duct injury during laparoscopic cholecystectomy were analyzed retrospectively.

回顾总结3例LC术中胆管损伤的临床资料，分析3例胆管损伤的原因及对策。

These techniques are applied to the gobang.

本文将这些技术用于五子棋中。