1. The relative magnitudes of the coefficients of the power series vary with the sort of vibration.

2. By using power series expansion method, the integrand is expressed as the form of a series, and then the ellipse integral is expressed as a series through simple integration.

3. Abstract: The paper studies the random power series of general enough, and proves that the random power series of finite order do not have almost surely deficient function.

4. Within the restricted scope, the infinite power series is convergent and the formula is workable.

5. The product forms of level one power series of Lie type and level two power series of A type.

6. Based on the complex modal theory and power series expansion theorem, a modal acceleration method for calculating the frequency response fonction (Far) of viscous damped systems was derived.sentencedict .com

7. Based on leading matrix variable, the power series is extended.

8. When the power series is used as the basic functions in the finite strip method, the computation becomes simple and convenient.

9. The process of replacing polynomials by formal power series is an example of a general device known as completion.

10. The statistical distributions of surface elevation and wave height are derived with the expansion of their moments into power series of the square root of the spectrum width.

11. In this paper, we discuss how to use the geometric series to find the sums of power series and to represent functions by power series.

12. This paper presents the time domain analysis of three orders discrete system by power series, which can study not only the time invariant system[], but also the time variant system.

13. A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

14. It is found that the short-time propagators obtained by using the above two methods are nearly equal, but using power series expansion technique is much easier than Schwinger method.

15. In this article, a method of solving the summation of a special constant series is given with the power series.

16. This paper analyzes the load which causes the deformation of sucker rod string in a rod pumping well, and establishes the differential equation of bending and gives a power series solution.

17. The formula of finite summation of K Steps arithmetic progression is seeked out by using the summation function of power series.

18. Stress intensity factors at the craek tips are computed by complex variable functions and perturbation method and formulas are given in power series forms.

19. To terminate a computational process in accordance with some rule, e. g. , to end the evaluation of a power series at a specified term.

20. In this paper, we propose a reduced linear representation of such distribution based on the formal power series on free monoid which can be easily used to calculate the probability distribution.

21. Itis concluded that the synthesis of a multi-variate nonlinear power series network may be reduced to several linear direct product connections.

22. When Z is assigned the meaning of a complex variable, problem of "closed form" of formal power series emerges.

23. Power series, radius of convergence; function that can be expanded in a power series interval.

24. Power series, radius of convergence; function that can be expanded in a power series on an interval.

25. In this article, we discuss some exceptional sets in formal power series field.

26. A combined magnetic round lens and deflection system with a superimposed field has been studied, and the power series expressions for the magnetic field is given.

27. In this paper, an extended order method (EOM) is derived for solving the nonlinear problem which can be expanded in a power series.

28. In this paper, a general formula of sum of power series of natural number is given.

29. Is also a function of extreme value theory, and many other mathematical theory of power series basis.

30. The series solutions of the linear ordinary differential equation at singular point were studied via the infinite order matrix of the linear differential operator in power series basis.