• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.127-132
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• 2003

The object of this paper is to extend and generalize the work of Brosowski ［Fixpunktsatze in der approximationstheorie. Mathematica Cluj 11 (1969), 195-200］, Hicks & Humphries ［A note on fixed point theorems. J. Approx. Theory 34 (1982), 221-225］, Khan & Khan ［An extension of Brosowski-Meinardus theorem on invariant approximation. Approx. Theory Appl. 11 (1995), 1-5］ and Singh ［An application of a fixed point theorem to approximation theory J. Approx. Theory 25 (1979), 89-90; Application of fixed point theorem in approximation theory. In: Applied nonlinear analysis (pp. 389-394). Academic Press, 1979］ in metric spaces having convex structure, and in metric linear spaces having strictly monotone metric.

• Journal of the Korean Chemical Society
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• v.11 no.2
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• pp.60-62
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• 1967

The statistical mechanical basis of the significant structure theory was compared and discussed with the improved Onno's approximation in the cell theory.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.191-196
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• 1991

LQG/LTR method have a theoretical constraint that it cannot applied to nonminimum phase plant. In this paper, we suggest two methods of approximation of minimum phase plant for a given nonminimum phase plant to solve this constraint. Error is described by additive form which can reduce its magnitude in broad frequency range. A optimal approximation method was suggesetd by using Hankel operator theory and Nehari theory. It is showen by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.10
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• pp.972-980
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• 1991

LQG/LTR method have a theoretical constraint that it cannot applied to nonminimum phase plant. In this paper we suggest two methods of approximation of minimum phase plant for a given nonminimum phase plant to solve this constraint. Error is described by additive form which can reduce its magnitude in broad frequency range. A optimal approximation method was suggested by using Hankel operator theory and Nehan theory it is shown by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.3
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• pp.21-30
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• 2013

Powell-Miller theory is a good method to express or treat incorrect information. But it has limitation that requires too much time to apply to actual situation because computational complexity increases in exponential and functional way. Accordingly, there have been several attempts to reduce computational complexity but side effect followed - certainty factor fell. This study suggested expanded Approximation Algorithm. Expanded Approximation Algorithm is a method to consider both smallest supersets and largest subsets to expand basic space into a space including inverse set and to reduce Approximation error. By using expanded Approximation Algorithm suggested in the study, basic probability assignment function value of subsets was alloted and added to basic probability assignment function value of sets related to the subsets. This made subsets newly created become Approximation more efficiently. As a result, it could be known that certain function value which is based on basic probability assignment function is closely near actual optimal result. And certainty in correctness can be obtained while computational complexity could be reduced. by using Algorithm suggested in the study, exact information necessary for a system can be obtained.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.367-374
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• 2014

Recently, interdisciplinary relation is emphasized on and various models are proposed. Since group theory is one of the important areas of modern mathematics, all the mathematics teachers for secondary school are familiar with it. Group theory, the theory of symmetries, are effectively applied to music or arts. In this paper, we understand the approximation model for gwaeyul of geomungo group theoretically to show the relation between mathematics and music(Korean music, in particular). This paper, in fact, proposes a group theoretic approximation model for gwaeyul of geomungo. The materials like this will be of help to teachers who try to integrate mathematics to other areas.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• The Mathematical Education
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• v.18 no.1
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• pp.21-23
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• 1980

In [3], an extension of B. Brosowski s T-invariant Point Theorem is given where the linearity of the function and the convexity of the set are relaxed. In this paper, our main purpose is to generalize S. P. Singh's T-invariant Point Theorem to Approximation Theory.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.423-434
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• 2003

We prove an approximation result, and we get a new proof of the main result in [7]. I hope that this new proof may be a step towards a generalization of the Poletsky theory of discs to the case of almost complex manifolds.

• The Journal of the Acoustical Society of Korea
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• v.28 no.3
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• pp.174-186
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• 2009

When we apply a propagation model to the ocean with boundaries, we can calculate reflected wave using reflection coefficient suggested by Rayleigh assuming the boundaries are flat. But boundaries in ocean such as sea surface and sea bottom have an irregular rough surface. To calculate the reflection loss for an irregular boundary, it is needed to compute the coherent reflection coefficient based on an experimental formula or scattering theory. In this article, we derive the coherent reflection coefficients for a fluid-fluid interface using perturbation theory, Kirchhoff approximation and small-slope approximation respectively. Based on each formula, we can calculate coherent reflection coefficients for a rough sea surface or sea bottom, and then compare them to the Rayleigh reflection coefficient to analyze the reflection loss for a random rough surface. In general, the coherent reflection coefficient based on small-slope approximation has a wide valid region. Comparing it with the coherent reflection coefficients derived from the Kirchhoff approximation and perturbation theory, we discuss a valid region of them.