The Experts below are selected from a list of 65082 Experts worldwide ranked by ideXlab platform
Yongbo Peng - One of the best experts on this subject based on the ideXlab platform.
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a stochastic Harmonic Function representation for non stationary stochastic processes
Mechanical Systems and Signal Processing, 2017Co-Authors: Jianbing Chen, Fan Kong, Yongbo PengAbstract:Abstract The time-domain representation of non-stationary stochastic processes is of paramount importance, in particular for response analysis and reliability evaluation of nonlinear structures. In the present paper a stochastic Harmonic Function (SHF) representation originally developed for stationary processes is extended to evolutionary non-stationary processes. Utilizing the new scheme, the time-domain representation of non-stationary stochastic processes is expressed as the linear combination of a series of stochastic Harmonic components. Different from the classical spectral representation (SR), not only the phase angles but also the frequencies and their associated amplitudes, are treated as random variables. The proposed method could also be regarded as an extension of the classical spectral representation method. However, it is rigorously proved that the new scheme well accommodates the target evolutionary power spectral density Function. Compared to the classical spectral representation method, moreover, the new scheme needs much fewer terms to be retained. The first four moments and the distribution properties, e.g., the asymptotical Gaussianity, of the simulated stochastic process via SHF representation are studied. Numerical examples are addressed for illustrative purposes, showing the effectiveness of the proposed scheme.
Jianbing Chen - One of the best experts on this subject based on the ideXlab platform.
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a stochastic Harmonic Function representation for non stationary stochastic processes
Mechanical Systems and Signal Processing, 2017Co-Authors: Jianbing Chen, Fan Kong, Yongbo PengAbstract:Abstract The time-domain representation of non-stationary stochastic processes is of paramount importance, in particular for response analysis and reliability evaluation of nonlinear structures. In the present paper a stochastic Harmonic Function (SHF) representation originally developed for stationary processes is extended to evolutionary non-stationary processes. Utilizing the new scheme, the time-domain representation of non-stationary stochastic processes is expressed as the linear combination of a series of stochastic Harmonic components. Different from the classical spectral representation (SR), not only the phase angles but also the frequencies and their associated amplitudes, are treated as random variables. The proposed method could also be regarded as an extension of the classical spectral representation method. However, it is rigorously proved that the new scheme well accommodates the target evolutionary power spectral density Function. Compared to the classical spectral representation method, moreover, the new scheme needs much fewer terms to be retained. The first four moments and the distribution properties, e.g., the asymptotical Gaussianity, of the simulated stochastic process via SHF representation are studied. Numerical examples are addressed for illustrative purposes, showing the effectiveness of the proposed scheme.
Mei Liquan - One of the best experts on this subject based on the ideXlab platform.
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Spectral finite element method for a unsteady transport equation
Applied Mathematics-A Journal of Chinese Universities, 1999Co-Authors: Mei LiquanAbstract:In this paper, a new numerical method, the coupling method of spherical Harmonic Function spectral and finite elements, for a unsteady transport equation is discussed, and the error analysis of this scheme is proved.
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a spectral streamline diffusion finite element coupling method of unsteady transport equation in the field of neutron logging
Applied Mathematics and Mechanics-english Edition, 1999Co-Authors: Mei LiquanAbstract:In this paper, a new numerical method, the coupling method of spherical Harmonic Function spectral and streamline diffusion finite element for unsteady Boltzmann equation in the neutron logging field, is discussed. The convergence and error estimations of this scheme are proved. Its applications in the field of neutron logging show its effectiveness.
Wade Ramey - One of the best experts on this subject based on the ideXlab platform.
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Harmonic Function Theory
Graduate Texts in Mathematics, 2001Co-Authors: Sheldon Axler, Paul Bourdon, Wade RameyAbstract:This is a book about Harmonic Functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of Harmonic Functions, Poisson integrals, the Kelvin transform, spherical Harmonics, Harmonic Hardy spaces, Harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical Harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore Harmonic Function theory on a computer
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Harmonic Function theory
1992Co-Authors: Sheldon Axler, Paul S Bourdon, Wade RameyAbstract:* Basic Properties of Harmonic Functions * Bounded Harmonic Functions * Positive Harmonic Functions * The Kelvin Transform * Harmonic Polynomials * Harmonic Hardy Spaces * Harmonic Functions on Half-Spaces * Harmonic Bergman Spaces * The Decomposition Theorem * Annular Regions * The Dirichlet Problem and Boundary Behavior * Volume, Surface Area, and Integration on Spheres * Harmonic Function Theory and Mathematica * References * Symbol Index * Index
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Positive Harmonic Functions
Harmonic Function Theory, 1992Co-Authors: Sheldon Axler, Paul S Bourdon, Wade RameyAbstract:In Chapter 2 we proved that a bounded Harmonic Function on R n is constant. We now improve that result.
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Harmonic Functions on Half-Spaces
Harmonic Function Theory, 1992Co-Authors: Sheldon Axler, Paul S Bourdon, Wade RameyAbstract:In this chapter we study Harmonic Functions defined on the upper half-space H. Harmonic Function theory on H has a distinctly different flavor from that on B. One advantage of H over B is the dilation-invariance of H. We have already put this to good use in the section Limits Along Rays in Chapter 2. Some disadvantages: ∂H is not compact and Lebesgue measure on ∂H is not finite.
Fan Kong - One of the best experts on this subject based on the ideXlab platform.
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a stochastic Harmonic Function representation for non stationary stochastic processes
Mechanical Systems and Signal Processing, 2017Co-Authors: Jianbing Chen, Fan Kong, Yongbo PengAbstract:Abstract The time-domain representation of non-stationary stochastic processes is of paramount importance, in particular for response analysis and reliability evaluation of nonlinear structures. In the present paper a stochastic Harmonic Function (SHF) representation originally developed for stationary processes is extended to evolutionary non-stationary processes. Utilizing the new scheme, the time-domain representation of non-stationary stochastic processes is expressed as the linear combination of a series of stochastic Harmonic components. Different from the classical spectral representation (SR), not only the phase angles but also the frequencies and their associated amplitudes, are treated as random variables. The proposed method could also be regarded as an extension of the classical spectral representation method. However, it is rigorously proved that the new scheme well accommodates the target evolutionary power spectral density Function. Compared to the classical spectral representation method, moreover, the new scheme needs much fewer terms to be retained. The first four moments and the distribution properties, e.g., the asymptotical Gaussianity, of the simulated stochastic process via SHF representation are studied. Numerical examples are addressed for illustrative purposes, showing the effectiveness of the proposed scheme.
