• Title/Summary/Keyword: singular approximation

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Optimization of Fermentation Processes with Singular Approximation and Minimum Principle (Singular Approximation과 Minimum Principle을 이용한 발효공정의 최적화)

  • 이중헌;정재철;박영훈
    • Microbiology and Biotechnology Letters
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    • v.27 no.3
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    • pp.223-229
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    • 1999
  • The two optimal control algorithms, singular approximation and minimum principle, were compared in this paper. The switching time with singular approximation was determined with mathematical derivation and the optimal control profile of specific growth rate was also calculated with minimum principle. The optimal control profiles were calculated by making simple model correlating the specific cell growth rate and specific product formation rate. The optimal control profiles calculated by singular approximation approach were similar to stepwise form of those calculatd by minimum principles. With the minimum principle, the product concentration was 8% more than that of singular approximation. This performance difference was due to a linearization of a nonlinear function with singular approximation. This optimal approaches were applicable to any system with different optimal cell growth and product formation.

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GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK

  • Anastassiou George A.;Gal Sorin G.
    • Journal of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.425-443
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    • 2006
  • The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.

A FINITE DIFFERENCE APPROXIMATION OF A SINGULAR BOUNDARY VALUE PROBLEM

  • Lee, H.Y.;Ohm, M.R.;Shin, J.Y.
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.473-484
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    • 1998
  • We consider a finite difference approximation to a singular boundary value problem arising in the study of a nonlinear circular membrane under normal pressure. It is proved that the rate of convergence is $O(h^2)$. To obtain the solution of the finite difference equation, an iterative scheme converging monotonically to the solution of the finite difference equation is introduced. And the numerical experiment of this method is given.

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THE DISCRETE SLOAN ITERATE FOR CAUCHY SINGULAR INTEGRAL EQUATIONS

  • KIM, SEKI
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.2 no.2
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    • pp.81-95
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    • 1998
  • The superconvergence of the Sloan iterate obtained from a Galerkin method for the approximate solution of the singular integral equation based on the use of two sets of orthogonal polynomials is investigated. The discrete Sloan iterate using Gaussian quadrature to evaluate the integrals in the equation becomes the Nystr$\ddot{o}$m approximation obtained by the same rules. Consequently, it is impossible to expect the faster convergence of the Sloan iterate than the discrete Galerkin approximation in practice.

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A study on the Hankel approximation of input delay systems (입력 시간지연 시스템의 한켈 근사화에 관한 연구)

  • Hwang, Lee-Cheol;Ha, Hui-Gwon;Lee, Man-Hyeong
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.3
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    • pp.308-314
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    • 1998
  • This paper studies the problem of computing the Hankel singular values and vectors in the input delay systems. It is shown that the Hankel singular values are solutions to a transcendental equation and the Hankel singular vectors are obtained from the kernel of the matrix. The computation is carried out in state space framework. Finally, Hankel approximation of a simple example shows the usefulness of this study.

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Hankel approximation of commensurate input delay systems (복수 입력 시간지연 시스템의 한켈 근사화)

  • 황이철;태전쾌인
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.1452-1455
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    • 1997
  • This paper studies the problem of approximating commensurate input delay sustems by finite dimensional systems based on the Hankel singular values. I is shown that the Gankel singular values are solutions a trancendental equation and the Hankel singular vectors are obtained form the kernel of the matrix. The computaioin is carried out in state spae framework. Once singular values and vectors are calcualted, finite dimensional approximated systems are constructed using stadnard linear system computational tools. An example is included.

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Rational Approximation of Multiple Input Delay Systems Using the Hankel Singular Values Vectors (한켈특이치와 특이벡터를 이용한 복수 입력 시간지연 시스템의 유리근사화)

  • 황이철
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.04a
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    • pp.299-304
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    • 1996
  • This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.

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Rational approximation of multiple input delay systems (복수입력 시간지연 시스템의 유리근사화)

  • HWANG, I Cheol;PARK, Kyoung Taik
    • Journal of the Korean Society for Precision Engineering
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    • v.14 no.1
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    • pp.194-204
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    • 1997
  • In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

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ESTIMATION OF THE SINGULAR COEFFICIENT IN THE STEADY STATE DIFFUSION EQUATION

  • Cho, Chung-Ki
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.309-323
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    • 2002
  • This paper studies the parameter estimation problem for a steady state flow in an inhomogeneous medium. Our approximation scheme could be used when the diffusion coefficient is singular. The function space parameter estimation convergence(FSPEC) is considered and numerical simulations are performed.

A REGULARIZED CORRECTION METHOD FOR ELLIPTIC PROBLEMS WITH A SINGULAR FORCE

  • Kim, Hyea-Hyun
    • Journal of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.927-945
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    • 2012
  • An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.