• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1993.11a
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• pp.99-102
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• 1993

A consistent general order nodal method for solving the three-dimensional neutron diffusion equation in (x-y-z) geometry has been derived by using a weighted integral technique and expanding the spatial variable by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes fewer unknown variables in the schemes for iterative-convergence solution than other nodal methods listed in the literatures, and because the method utilizes the analytic solutions of the transverse-integrated one dimensional equations and a consistent approximation for a given spatial variable through all the solution procedures, which renders the use of an approximation for the transverse leakages no longer necessary, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1127-1139
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• 2023

We investigate an extension of Schauder's theorem by studying the relationship between various s-numbers of an operator T and its adjoint T^*. We have three main results. First, we present a new proof that the approximation number of T and T^* are equal for compact operators. Second, for non-compact, bounded linear operators from X to Y, we obtain a relationship between certain s-numbers of T and T^* under natural conditions on X and Y . Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of T with that of its adjoint T^*.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.387-396
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• 2003

This paper provides an approximation algorithm for STP-MSP(Steiner Tree Problem with minimum number of Steiner Points).Because it seems to be impossible to have a PTAS(Polynomial Time Approximation Schemes), which gives the near optimal solutions, for the problem, the algorithm of this paper is an alternative that has the approximation ratio 2 with $n^{O(1)}$ run time. The importance of this paper is the potential to solve other related unsolved problems. The idea of this paper is to distribute the error allowance over the problem instance so that we may reduce the run time to polynomial bound out of infinitely many cases. There are earlier works[1,2] that show the approximations that have practical run times with the ratio of bigger than 2, but this paper shows the existence of a poly time approximation algorithm with the ratio 2.

• East Asian mathematical journal
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• v.38 no.3
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• pp.365-377
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• 2022

In this paper, we present a new class of interpolatory Hermite subdivision schemes of order 2 reproducing polynomials. Each member in this class, denoted by H_n for n ≥ 1, preserves polynomials of degree up to 4n + 1 admitting the approximation order of 4n + 2. Furthermore, it has free parameters which provide flexibility in designing curves/surfaces. H₁, the simplest and the most attractive scheme in this class, achieves C⁴ smoothness with the parameters in certain ranges, and its performance is demonstrated with numerical examples.

• Journal of Korea Spatial Information System Society
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• v.7 no.2 s.14
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• pp.57-66
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• 2005

The Interconnecting Highways problem is an abstract of many practical Layout Design problems in the areas of VLSI design, the optical and wired network design, and the planning for the road constructions. For the road constructions, the shortest-length road layouts that interconnect existing positions will provide many more economic benefits than others. That is, finding new road layouts to interconnect existing roads and cities over a wide area is an important issue. This paper addresses an approximation scheme that finds near optimal road layouts for the Interconnecting Highways problem which is NP-hard. As long as computational resources are provided, the near optimality can be acquired asymptotically. This implies that the result of the scheme can be regarded as the optimal solution for the problem in practice. While other approximation schemes can be made for the problem, this proposed scheme provides a big merit that the algorithm designed by this scheme fits well to given problem instances.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.36-42
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• 2006

The existing numerical approximations of convection flux, especially the spatial higher-order difference schemes, in unstructured cell-centered finite volume methods are examined in detail with each other and evaluated with respect to the accuracy through their application to a 2-D benchmark problem. Six higher-order schemes are examined, which include two second-order upwind schemes, two central difference schemes and two hybrid schemes. It is found that the 2nd-order upwind scheme by Mathur and Murthy(1997) and the central difference scheme by Demirdzic and Muzaferija(1995) have more accurate prediction performance than the other higher-order schemes used in unstructured cell-centered finite volume methods.

• Proceedings of the IEEK Conference
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• 2000.11a
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• pp.501-504
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• 2000

The classical image reconstruction for stripmap SAR is the range-Doppler imaging. However, when the spotlight SAR system was envisioned, range-Bowler imaging fumed out to fail rapidly in this SAR imaging modality. What is referred to as polar format processing, which is based on the plane wave approximation, was introduced for imaging from spotlight SAR data. This paper has been studied for the raw data processing schemes in the spotlight-mode synthetic aperture radar. we apply the wavefront reconstruction scheme that does not utilize the approximation in spotlight-mode SAR imaging modelity, and compare the performance of target imaging with the polar format inversion scheme.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.1061-1063
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• 1998

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.5
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• pp.917-922
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• 2018

In the conventional interchannel interference self-cancellation (ICI-SC) schemes, the length of sampling window is the same as the symbol length of orthogonal frequency division multiplexing (OFDM). Thus, the number of complex operations to compute the interference coefficient of each subchannel is significantly increased. To solve this problem, we present an approximated mathematical model for the coefficients of ICI-SC schemes. Based on the proposed approximation, we analyze mean squared error (MSE) and computational complexity of the ICI-SC schemes with the length of sampling window. As a result, the presented approximation has an error of less than 0.01% on the MSE compared to the original equation. When the number of subchannels is 1024, the number of complex computations for the interference coefficients is reduced by 98% or more. Since the computational complexity can be remarkably reduced without sacrificing the self-cancellation capability, it is considered that the proposed approximation is very useful to develop an algorithm for the ICI-SC scheme.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.