• Title, Summary, Keyword: quadratic form

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Digital Watermarking using a Quadratic Equation Embedding Method in Wavelet Transform Domain (웨이블릿 변환영역에서 이차방정식 삽입 방법을 이용한 디지털 워터마킹)

  • 신용달
    • Journal of Korea Multimedia Society
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    • v.6 no.5
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    • pp.870-875
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    • 2003
  • We Present digital watermarking using a quadratic equation embedding method in wavelet transform domain in order to improve the invisibility. Generally, embedding watermark used a simple equation form, but we extended a quadratic equation form in this paper. We performed a computer simulation in order to compare proposed method to other methods using LENA, GOLDHILL, BARBARA, and MAN images By computer experiments, invisibility of the proposed method better than the conventional methods at 100 % normalized similarity.

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EXPLICIT ERROR BOUND FOR QUADRATIC SPLINE APPROXIMATION OF CUBIC SPLINE

  • Kim, Yeon-Soo;Ahn, Young-Joon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.4
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    • pp.257-265
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    • 2009
  • In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

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EVALUATIONS OF SOME QUADRATIC EULER SUMS

  • Si, Xin;Xu, Ce
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.489-508
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    • 2020
  • This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

DESIGN OF A DYNAMIC OUTPUT FEEDBACK CONTROLLER FOR POWER SUSTEM GENERATORS

  • Danjyo, Mitsuaki;Tanaka, Yukihiko;Kominato, Yoshihito;Sagara, Setsuo
    • 제어로봇시스템학회:학술대회논문집
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    • pp.871-876
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    • 1989
  • We propose a new algorithm to obtain the output feedback controller, which contains one dynamic element, for power system generators. The performance criterion of this controller is the integral of quadratic form of output differences between reference model and controlled system. with this criterion, we can easily compute the output feedback gains using Astrom's algorithm for the integral calculation of quadratic form.

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Design of an output-feedback controller for power system generator

  • Danjyo, Mitsuaki;Tanaka, Yukihiko;Sagara, Setsuo
    • 제어로봇시스템학회:학술대회논문집
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    • pp.837-842
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    • 1988
  • We propose a new algorithm to obtain the output feedback controller for power system generators. The performance criterion of this controller is the integral of quadratic form of output differences between reference model and controlled system. With this criterion, we can easily compute the output feedback gains using Astrom's algorithm for the integral calculation of quadratic form. Simulations on a one machine infinite bus system shows the effectiveness of this approach.

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The General Mornent of Non-central Wishart Distribution

  • Chul Kang;Kim, Byung-Chun
    • Journal of the Korean Statistical Society
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    • v.25 no.3
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    • pp.393-406
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    • 1996
  • We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

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MOMENTS OF VARIOGRAM ESTIMATOR FOR A GENERALIZED SKEW t DISTRIBUTION

  • KIM HYOUNG-MOON
    • Journal of the Korean Statistical Society
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    • v.34 no.2
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    • pp.109-123
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    • 2005
  • Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

Hull-form optimization of a container ship based on bell-shaped modification function

  • Choi, Hee Jong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.7 no.3
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    • pp.478-489
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    • 2015
  • In the present study, a hydrodynamic hull-form optimization algorithm for a container ship was presented in terms of the minimum wave-making resistance. Bell-shaped modification functions were developed to modify the original hull-form and a sequential quadratic programming algorithm was used as an optimizer. The wave-making resistance as an objective function was obtained by the Rankine source panel method in which non-linear free surface conditions and the trim and sinkage of the ship were fully taken into account. Numerical computation was performed to investigate the validity and effectiveness of the proposed hull-form modification algorithm for the container carrier. The computational results were validated by comparing them with the experimental data.

SOLUTIONS OF NONCONVEX QUADRATIC OPTIMIZATION PROBLEMS VIA DIAGONALIZATION

  • YU, MOONSOOK;KIM, SUNYOUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.2
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    • pp.137-147
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    • 2001
  • Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

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A LOWER BOUND FOR THE NUMBER OF SQUARES WHOSE SUM REPRESENTS INTEGRAL QUADRATIC FORMS

  • Kim, Myung-Hwan;Oh, Byeong-Kweon
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.651-655
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    • 1996
  • Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.

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