1. Using the homotopy analysis method, the approximation of the solution for the model was obtained.

2. 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.

3. Using the homotopy mapping theory, class of nonlinear problems were studied.

4. Using the homotopy analysis method, the approximation solution is obtained.

5. Using the method of homotopy analysis, the approximation of the solution for the model was obtained.

6. Using the homotopy mapping theory, a class of nonlinear problems were studied.

7. Based on the approximate answer made by homotopy method, the discrete phenomenon of Newton iterative loop is greatly cut down in the course of solving the SHET equation group.

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8. Also , it introduces in detail the combined homotopy method and corresponding example are given.

9. 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.

10. We utilized the combined maximum entropy homotopy method to solve the general nonconvex nonlinear programming problems.

11. In this paper, a real number homotopy method is suggested on the basis of paper 1.

12. Moreover, a continuous method is employed to modify the homotopy parameter during iteration in order to ensure the ability of the iteration and the capability of the noise resistance.

13. The inverse matrix calculation is the key to solve harmonic elimination PWM model of inverter based on Homotopy algorithm.

14. The classification of the static magnetic domain wall structures of tube- and envelope-type is made in an unified way using the homotopy theory.

15. It was showed at first that the loop space functor and the suspension functor preserve the properties of homotopy regular.

16. Secondly, in order to favor utilizing this theorem, several propositions are given on the homotopy equivalence between two topological space sets.

17. 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.