• 충청수학회지
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• 제27권4호
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• pp.707-720
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• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• 대한수학회보
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• 제31권2호
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• pp.210-214
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• 1994

The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

• 한국음향학회지
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• 제21권1호
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• pp.42-46
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• 2002

본 논문에서는 스테레오 음향 반향 제거기의 성능을 향상시킬 수 있는 새로운 전처리 방법의 반향 제거기를 제안한다. 제안한 반향 제거기는 MINT (Multiple input/output INverse Theorem) 필터링에 의해 실내 전달함수의 잔향이 저감되어진 입력을 사용함으로써 필터계수의 추정오차를 감소시켜 성능을 향상시킬 수 있었다. 실제의 스테레오 음성과 실제 음장의 전달함수를 사용한 시뮬레이션 결과, 제안한 방법이 NLMS (Normalized Least Mean Square)와 Projection 등의 적응 알고리즘 종류에 관계없이 ERLE가 3∼5 dB 향상됨을 확인하였다.

• 대한수학회지
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• 제46권3호
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• pp.551-560
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• 2009

A theorem of Robert Blumenthal is used here in order to obtain a sufficient condition for a function between two Finsler manifolds to be a fibre bundle map. Our study is connected with two possible constructions: 1) a Finslerian generalization of usually Kaluza-Klein theories which use Riemannian metrics, the well-known particular case of Finsler metrics, 2) a Finslerian version of reduction process from geometric mechanics. Due to a condition in the Blumenthal's result the completeness of Euler-Lagrange vector fields of Finslerian type is discussed in detail and two situations yielding completeness are given: one concerning the energy and a second related to Finslerian fundamental function. The connection of our last framework, namely a regular Lagrangian having the energy as a proper (in topological sense) function, with the celebrated $Poincar{\acute{e}}$ Recurrence Theorem is pointed out.

• 한국해양공학회지
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• 제19권5호
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• pp.58-64
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• 2005

In this paper, a feedback linearizing anti-sway control law, using a 2-D model for container cranes, is investigated. The equations of motion are first derived from Lagrange's equation. Then, by substituting the sway dynamics into the trolley dynamics, a reduction of variables from three (trolley, hoist, sway) to two (trolley, hoist) is pursued. The anti-sway control law is designed based on the Lyapunov stability theorem. The proposed control law guarantees the uniform asymptotic stability of the closed-loop system. The simulation results of the derived control law, using MATLAB/Simulink, are compared with those of the sliding mode control law, noted in previous literature. Also, experimental results using a 3-D pilot crane are provided.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• 충청수학회지
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• 제12권1호
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• pp.147-155
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• 1999

Let {$C_t$} be a pencil of smooth quartics for $t{\neq}0$ degenerating to a plane quartic $C_0$ with an ordinary cusp of multiplicity 3. We compute the stable limit as $t{\rightarrow}0$ of {$C_t$} when the total surface of this family has a triple point at the singular point of $C_0$.

• 대한수학회지
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• 제60권5호
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• pp.1135-1136
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• 2023

In this erratum, we offer a correction to [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115-141]. We rectify Theorem 5.7 and Table 1 of the original paper.

• 산업경영시스템학회지
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• 제12권20호
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• pp.47-53
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• 1989

This paper presents an algorithm CAPFACT to evaluate the reliability of a capacitated two terminal network such as a communication network, a power distribution network, and a pipeline network. The network is good(working) if and only if it is possible to transmit successfully the required system capacity from one specified terminal to the other. This paper defines new Capacitated series-parallel reduction to be applied to a series-parallel structure of the network. New Capacitated factoring method is applied to a non-series-parallel structure. The method is based on the factoring theorem given by Agrawal and Barlow. According to the existing studies on the reliability evaluation of the network that the capacity is not considered, the factoring method using reduction is efficient. The CAPFACT is more efficient than Aggarwal algorithm which enumerated and combined the paths. The efficiency is proved by the result of testing the number of operations and cpu time on FORTRAN compiler of VAX-11/780 at Hanyang University.