利用同伦分析方法，得到了该模型的近似解。
Using the homotopy analysis method, the approximation solution is obtained.
论述了采用同伦法辨识armax模型的问题。
This paper deals with the problem of identifying ARMAX model using homotopy approach.
基于同伦映射的同伦算法，具有大范围收敛性。
The homotopy algorithm, basing on homotopy mapping, is convergent with wide range.
利用同伦映射理论，本文研究了一类非线性问题。
Using the homotopy mapping theory, a class of nonlinear problems were studied.
利用同伦分析方法，得到了该模型解的近似展开式。
Using the homotopy analysis method, the approximation of the solution for the model was obtained.
同胚映射和同伦等价是代数拓扑学中的两个重要概念。
Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology.
理论和数值实验都表明同伦方法是一种收敛稳定的方法。
Theory and numerical simulation show that the method presented is a convergence and stable method.
运用同伦方法的基本思想研究飞机非线性平衡状态的求解。
In this paper, the method of solving nonlinear equilibrium state of aircraft is studied according to homotopy concept.
利用组合极大熵同伦方法，研究一般的非凸非线性规划问题。
We utilized the combined maximum entropy homotopy method to solve the general nonconvex nonlinear programming problems.
结果推广了同胚映射、同伦等价和同伦正则态射的有关结果。
Results Generalizing some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism.
基于同伦映射的思想，改进了求解非线性反问题的梯度正则化算法。
Based on idea of homotopy mapping, an improved gradient regularization algorithm was developed.
该文基于非线性同伦内点法提出了检测无功优化不可行问题的新算法。
This paper presents new algorithm for detecting the solution infeasiblity in reactive power optimization calculation based on nonlinear homogeneous interior point method.
关于等变同伦满态和同伦单态的研究正是以上两种研究兴趣的交汇所在。
The research of equivariant epimorphisms and monomorphisms is just the intersection of the above two interests.
同伦是代数拓扑学中的概念，同伦算法已应用于一些工程实际问题的求解。
Homotopy is a concept of algebra topology, and homotopy algorithm has been applied to solving the practical problems.
本文给出了几个应用实例，以说明“同伦分析方法”的有效性及巨大的潜力。
Examples are given in this paper to show the validity of this method.
基于上述研究，论文还研制了均值变点检验、同伦延拓法及迭代法的计算软件。
The computational software is developed, which is based on the test of even change point, homotopy continuation algorithm and the iterative method.
同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法。
Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter.
我们给出同伦路径的存在性和收敛性证明，并通过数值实验验证新算法的有效性。
The existence and convergence of the homotopy path are proved, and efficiency of our method is illustrated by the numerical experimentations at last.
在网络方程同伦的概念的基础上，给出了一种求解非线性电阻性网络的有效算法。
Based on the homotopy idea of network equation, an efficient algorithm for solving nonlinear resistive network is given in the paper.
本文一篇综述类文章，综述了同伦摄动方法及它在非线性微积分方程中的某些应用。
The paper reviews Some applications of the homotopy perturbation method to nonlinear differential and integral equations.
证明了闭路函子和同纬函子保持同伦正则性，同时构造出了一系列同伦等价的空间。
It is showed that the loop space functor and the suspension functor preserve the properties of homotopy regular. And a series of homotopy equivalence Spaces are constructed.
结果表明，同伦分析法在求解高维非线性演化方程时，仍然是一种行之有效的方法。
The results indicate that the HAM is still valid for solving a class of higher dimensional evolution equations.
用同伦方法分析了可分解映射的零点存在性，并获得它对一类非线性特征值问题的应用。
Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.
地球物理反问题大部分是非线性问题，基于路径跟踪的同伦法是求解该类问题的有效方法。
Most of geophysical inversion are non-linear problems, the homotopy method based on path tracking is effective method for solving this kind of problems.
该文论述了拓扑空间(组)的同伦等价变换在有序介质状态和缺陷的拓扑分类中的应用问题。
In this paper the application of homotopy equivalence transformation of topological space sets to the topological classification of states and defects in ordered media is discussed.
为了寻求一种更有效的非线性最小二乘平差算法，根据同伦思想提出了一种改进的同伦算法。
Based on the homotopy idea, an improved homotopy algorithm was proposed in order to search a more efficient algorithm for nonlinear least squares adjustment.
为证明水平复形的正合性而构造的高阶欧拉算子、全内积公式和全同伦算子是本文最重要的结果；
The higher Euler operators, the total inner product and the total homotopy operator constructed for proving the exactness of the horizontal complex are the most important results of this thesis.
实例计算表明同伦函数法是一种对初值要求不高，对各种非理想物系分离计算效果较好的一种算法。
Case studies show that homotopy continuation method is an effective algorithm for the calculation of various nonideal systems separation with not high requirements for initial value.
实例计算表明同伦函数法是一种对初值要求不高，对各种非理想物系分离计算效果较好的一种算法。
Case studies show that homotopy continuation method is an effective algorithm for the calculation of various nonideal systems separation with not high requirements for initial value.
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