The Experts below are selected from a list of 10032 Experts worldwide ranked by ideXlab platform

Xingyuan Wang - One of the best experts on this subject based on the ideXlab platform.

  • Julia sets of Newton’s method for a class of Complex-Exponential Function F(z)=P(z)eQ(z)
    Nonlinear Dynamics, 2010
    Co-Authors: Xingyuan Wang, Yuanyuan Sun, Jun-mei Song
    Abstract:

    In this paper, we analyze the theory of the Julia set (J set) of Newton’s method, construct the Julia sets of Newton’s method of Function $F(z)=ze^{z^{w}}$ (w∈ℂ) through iteration method, and analyze the attracting region of the two fixed points 0 and ∞ when w are different values. Consequently, we draw the following conclusions: (1) When the judge conditions for the iterative algorithm are changed to |N(z n )−z n |≤EOF, the properties of the figures in our experiments are contrary to the conclusions in (Wegner and Peterson, Fractal Creations, pp. 168–231, 1991); (2) The attracting regions of the fixed points 0 and ∞ for w=2n (n=0,±2,±4,…) are symmetrical about x-axis and y-axis; select the main argument to be in [−π,π), for arbitrary w=α (α∈ℂ), the attracting regions of the fixed points 0 and ∞ are symmetrical about the x-axis; (3) The attracting regions of the two fixed points 0 and ∞ of J set for w=±η have rotational symmetry of η times; (4) If w=−4.7, k=0.8, then the attracting regions of different magnifications display a startling similarity, J set holds infinite self-similar structures; (5) When w is a Complex number, because the selection of main argument θ z in the negative x-axis is not continuous, the fault and rupture of the attracting regions of the two fixed points 0 and ∞ appear only in the negative x-axis.

  • julia sets of newton s method for a class of Complex Exponential Function f z p z eq z
    Nonlinear Dynamics, 2010
    Co-Authors: Xingyuan Wang, Yuanyuan Sun, Jun-mei Song
    Abstract:

    In this paper, we analyze the theory of the Julia set (J set) of Newton’s method, construct the Julia sets of Newton’s method of Function $F(z)=ze^{z^{w}}$ (w∈ℂ) through iteration method, and analyze the attracting region of the two fixed points 0 and ∞ when w are different values. Consequently, we draw the following conclusions: (1) When the judge conditions for the iterative algorithm are changed to |N(z n )−z n |≤EOF, the properties of the figures in our experiments are contrary to the conclusions in (Wegner and Peterson, Fractal Creations, pp. 168–231, 1991); (2) The attracting regions of the fixed points 0 and ∞ for w=2n (n=0,±2,±4,…) are symmetrical about x-axis and y-axis; select the main argument to be in [−π,π), for arbitrary w=α (α∈ℂ), the attracting regions of the fixed points 0 and ∞ are symmetrical about the x-axis; (3) The attracting regions of the two fixed points 0 and ∞ of J set for w=±η have rotational symmetry of η times; (4) If w=−4.7, k=0.8, then the attracting regions of different magnifications display a startling similarity, J set holds infinite self-similar structures; (5) When w is a Complex number, because the selection of main argument θ z in the negative x-axis is not continuous, the fault and rupture of the attracting regions of the two fixed points 0 and ∞ appear only in the negative x-axis.

  • julia set of the newton transformation for solving some Complex Exponential equation
    Fractals, 2009
    Co-Authors: Xingyuan Wang, Xuejing Yu
    Abstract:

    We extend Kim's Complex Exponential Function, come up with theory about the Julia set of Newton's transformation for general Exponential equation, analyze the behavior of the roots of some Complex Exponential equation, and prove the symmetry, boundedness and embedding topology distribution structure of basins of attraction of the Julia set in theory.

  • JULIA SET OF THE NEWTON METHOD FOR SOLVING SOME Complex Exponential EQUATION
    International Journal of Image and Graphics, 2009
    Co-Authors: Xingyuan Wang, Wenjing Song, Lixian Zou
    Abstract:

    We extend Kim's Complex Exponential Function and come up with a theory about Julia sets of Newton method for general Exponential equation. We analyze the behavior of the roots of some Complex Exponential equation, and prove the Julia Set's symmetry, boundedness and embedding topology distribution structure of attraction regions in theory.

Muriel Medard - One of the best experts on this subject based on the ideXlab platform.

  • obfuscating poisson gaussian data using a rotation in the Complex plane
    Asilomar Conference on Signals Systems and Computers, 2016
    Co-Authors: Ruaridh R Macdonald, Muriel Medard
    Abstract:

    A novel method of data masking is presented which allows Poisson and some Gaussian data sets to be altered without changing the overall probability density Function. The method consists of multiplying each entry by a random Complex Exponential Function, i.e. a rotation in the Complex plane, and exchanging imaginary components between entries. The transformation preserves the properties of the data set, including all forms of entropy, while allowing correlations between individual members to be altered.

  • ACSSC - Obfuscating poisson & Gaussian data using a rotation in the Complex plane
    2016 50th Asilomar Conference on Signals Systems and Computers, 2016
    Co-Authors: Ruaridh R Macdonald, Muriel Medard
    Abstract:

    A novel method of data masking is presented which allows Poisson and some Gaussian data sets to be altered without changing the overall probability density Function. The method consists of multiplying each entry by a random Complex Exponential Function, i.e. a rotation in the Complex plane, and exchanging imaginary components between entries. The transformation preserves the properties of the data set, including all forms of entropy, while allowing correlations between individual members to be altered.

Jun-mei Song - One of the best experts on this subject based on the ideXlab platform.

  • Julia sets of Newton’s method for a class of Complex-Exponential Function F(z)=P(z)eQ(z)
    Nonlinear Dynamics, 2010
    Co-Authors: Xingyuan Wang, Yuanyuan Sun, Jun-mei Song
    Abstract:

    In this paper, we analyze the theory of the Julia set (J set) of Newton’s method, construct the Julia sets of Newton’s method of Function $F(z)=ze^{z^{w}}$ (w∈ℂ) through iteration method, and analyze the attracting region of the two fixed points 0 and ∞ when w are different values. Consequently, we draw the following conclusions: (1) When the judge conditions for the iterative algorithm are changed to |N(z n )−z n |≤EOF, the properties of the figures in our experiments are contrary to the conclusions in (Wegner and Peterson, Fractal Creations, pp. 168–231, 1991); (2) The attracting regions of the fixed points 0 and ∞ for w=2n (n=0,±2,±4,…) are symmetrical about x-axis and y-axis; select the main argument to be in [−π,π), for arbitrary w=α (α∈ℂ), the attracting regions of the fixed points 0 and ∞ are symmetrical about the x-axis; (3) The attracting regions of the two fixed points 0 and ∞ of J set for w=±η have rotational symmetry of η times; (4) If w=−4.7, k=0.8, then the attracting regions of different magnifications display a startling similarity, J set holds infinite self-similar structures; (5) When w is a Complex number, because the selection of main argument θ z in the negative x-axis is not continuous, the fault and rupture of the attracting regions of the two fixed points 0 and ∞ appear only in the negative x-axis.

  • julia sets of newton s method for a class of Complex Exponential Function f z p z eq z
    Nonlinear Dynamics, 2010
    Co-Authors: Xingyuan Wang, Yuanyuan Sun, Jun-mei Song
    Abstract:

    In this paper, we analyze the theory of the Julia set (J set) of Newton’s method, construct the Julia sets of Newton’s method of Function $F(z)=ze^{z^{w}}$ (w∈ℂ) through iteration method, and analyze the attracting region of the two fixed points 0 and ∞ when w are different values. Consequently, we draw the following conclusions: (1) When the judge conditions for the iterative algorithm are changed to |N(z n )−z n |≤EOF, the properties of the figures in our experiments are contrary to the conclusions in (Wegner and Peterson, Fractal Creations, pp. 168–231, 1991); (2) The attracting regions of the fixed points 0 and ∞ for w=2n (n=0,±2,±4,…) are symmetrical about x-axis and y-axis; select the main argument to be in [−π,π), for arbitrary w=α (α∈ℂ), the attracting regions of the fixed points 0 and ∞ are symmetrical about the x-axis; (3) The attracting regions of the two fixed points 0 and ∞ of J set for w=±η have rotational symmetry of η times; (4) If w=−4.7, k=0.8, then the attracting regions of different magnifications display a startling similarity, J set holds infinite self-similar structures; (5) When w is a Complex number, because the selection of main argument θ z in the negative x-axis is not continuous, the fault and rupture of the attracting regions of the two fixed points 0 and ∞ appear only in the negative x-axis.

Xuejing Yu - One of the best experts on this subject based on the ideXlab platform.

Ruaridh R Macdonald - One of the best experts on this subject based on the ideXlab platform.

  • obfuscating poisson gaussian data using a rotation in the Complex plane
    Asilomar Conference on Signals Systems and Computers, 2016
    Co-Authors: Ruaridh R Macdonald, Muriel Medard
    Abstract:

    A novel method of data masking is presented which allows Poisson and some Gaussian data sets to be altered without changing the overall probability density Function. The method consists of multiplying each entry by a random Complex Exponential Function, i.e. a rotation in the Complex plane, and exchanging imaginary components between entries. The transformation preserves the properties of the data set, including all forms of entropy, while allowing correlations between individual members to be altered.

  • ACSSC - Obfuscating poisson & Gaussian data using a rotation in the Complex plane
    2016 50th Asilomar Conference on Signals Systems and Computers, 2016
    Co-Authors: Ruaridh R Macdonald, Muriel Medard
    Abstract:

    A novel method of data masking is presented which allows Poisson and some Gaussian data sets to be altered without changing the overall probability density Function. The method consists of multiplying each entry by a random Complex Exponential Function, i.e. a rotation in the Complex plane, and exchanging imaginary components between entries. The transformation preserves the properties of the data set, including all forms of entropy, while allowing correlations between individual members to be altered.