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.
当亚达薛西王年间，同我从巴比伦上来的人，他们的族长和他们的家谱记在下面。
These are now the chief of their fathers, and this is the genealogy of them that went up with me from Babylon, in the reign of Artaxerxes the king.
不过同卡梅伦和克莱格的较量或许可以弱化他冷淡形象的一面。
Yet taking on Mr Cameron and Mr Clegg might soften his aloof image.
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.
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.
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。
In this paper, we present a new interior point method-combined homotopy interior point method.
介绍了在数值试验中一些细节处理，包括如何进行一维搜索，在试验中一些初值的设定，以及同伦参数的调节问题。
Some details in numerical experiment are also presented, such as how to carry out one dimension search, how to set some initial values and how to adjust homotopy parameter.
本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目，以及推广若干经典定理。
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
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.
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.
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.
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.
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.
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.
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.
本文用某种同伦方法，借助于一些适当的变换，讨论了有序的局部凸拓扑线性空间中集值凝聚映象方程的正解问题。
Under several suitable transformations, the problem of positive solutions for set-valued condensing mapping equation in an ordered locally convex topological space is studied by some homotopy method.
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.
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.
第二章讨论同伦正则态射的应用。
In Chapter 2, we discussed the applications of homotopy regular morphism.
本文的研究结果丰富了介质波动理论和同伦方法的应用范围，对促进正、反演在工程中的应用具有一定的理论意义与实际价值。
The results in this thesis enrich the application range of media wave theory and the homotopy methods application in inversion problems, which are of great theoretical and practical significance.
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.
证明了同伦映射为正则映射的条件下，选取合适的同伦方程，用此同伦方法得到的K-K-T点一定是问题局部最优解。
We prove that when the homotopy map is a regular map, the K-K-T point obtained from this homotopy method must be a local optimal solution by choosing proper homotopy equation.
布伦南司法中心是一家同纽约大学法学院存在关联的的非营利性研究组织。
The Brennan Center for Justice is a non-profit research group with ties to New York University's Law School.
文章针对传统的声波阻抗反演方法的不足，将大范围收敛的同伦方法用于地震勘探声波阻抗的反演。
In consideration of the drawbacks in conventional acoustic impedance inversion method, the homotopy method with vast convergence was applied to the acoustic impedance inversion in seismic exploration.
为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性。
To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method, to train the weights of the network.
同时，在求解连杆曲线非线性方程组中引入同伦算法，使算法具有大范围收敛性，从而保证了优化过程的稳定收敛。
At the same time, homotopy algorithm is applied in the solution of non-linear equation of plane link curve, it enlarges the convergence range of optimization process steadily.
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.
其次给出一个不用约当曲线定理而仅用同伦曲线概念的更为简洁的证法。
Next, we give a briefer proof that USES the concept of homotopy of curves, In this course of the proof, we don't use the theorem of Jordan curves.
其次给出一个不用约当曲线定理而仅用同伦曲线概念的更为简洁的证法。
Next, we give a briefer proof that USES the concept of homotopy of curves, In this course of the proof, we don't use the theorem of Jordan curves.
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