In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian pol...

Abstract. Many tests for a changing mean in a time series require the estimation of a long run variance. Recent research of Crainiceanu and Vogelsang (2001) suggests that tests involving a long run variance estimate exhibit non-monotonic power. We propose an estimate of long run variances that allows for a time varying mean. In this way, we are able to avoid non-monotonic power while still reta...

—This paper proposes a method of real-time voltage stability assessment for load areas, in which the proximity to voltage collapse point at each bus can be accurately evaluated. Based on the non-iterative holomorphic embedding method (HEM), the voltage of each bus for different loading levels in the load area is quickly screened out by only performing one-time power flow calculation. A power se...

In the present study, vibration of cylindrical laminates with different layers and angles were studied. In order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. Laminates were assumed long enough so that plane strain state analysis in 2D can be used properly. In order to satisfy the boundary conditions, variables in terms of Fo...

THE FOURIER SPECTRAL ELEMENT METHOD FOR VIBRATION AND POWERFLOW ANALYSIS OF COMPLEX DYNAMIC SYSTEMS byHONGAN XUMay 2011Advisor: Dr. Wen LiMajor: Mechanical EngineeringDegree: Doctor of PhilosophyA general numerical method, the so-called Fourier-Space Element Method (FSEM), isproposed for the vibration and power flow analyses of complex built-up structures. In...

assessment of women's status entails calculating various indices from different fields including scientific, economic, social and political. calculating these factors and comparing them with that of male indicates a country's development and progress level thus determines their position in the world ranking as compared to other countries. although assessment of women's status in ...

In this paper, we compile the fractional power series method and Laplace transform to design a new algorithm for solving Volterra integro-differential equation. For that, assume (LPS) solution in terms of q=1m,m∈Z+, where derivative order α=qγ, which γ∈Z+. This assumption will help us write integral, kernel, nonhomogeneous as LPS with same power. The recurrence relations finding coefficients ca...