• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1105-1117
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• 2009

In this paper a parameter identification problem for a damped sine-Gordon equation is studied from the theoretical and numerical perspectives. A spectral method is developed for the solution of the state and the adjoint equations. The Powell's minimization method is used for the numerical parameter identification. The necessary conditions for the optimization problem are shown to yield the bang-bang control law. Numerical results are discussed and the applicability of the necessary conditions is examined.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.125-130
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• 1996

최근 고리원자력 4호기 압력용기에 대한 제 3차 감시시험$^{(1)}$ 이 수행되었고 그 과정 중 측정된 시편에서의 반응률을 근거로 선량분석을 수행하였다. ENDF/B-VI를 근거로 만들어진BUGLE93$^{(2)}$ 라이브러리를 사용하여 각분할코드인 DORT version 2.7.3$^{(3)}$ 를 이용한 forward 및 adjoint 수송 계산 결과와 측정된 반응률을 결합하여 고리 4호기 원자로의 감시시편 X를 대상으로 1 MeV이상의 중성자속, 0.1 MeV 이상의 중성자속 및 dpa(displacement per atom)를 계산하여 측정치와 계산치를 비교하였다.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.623-644
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• 2019

We investigate the homotopy category ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ of N-complexes of injectives in a Grothendieck abelian category ${\mathfrak{A}}$ not necessarily locally noetherian, and prove that the inclusion ${\mathcal{K}}_N(Inj{\mathfrak{A}}){\rightarrow}{\mathcal{K}}({\mathfrak{A}})$ has a left adjoint and ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ is well generated. We also show that the homotopy category ${\mathcal{K}}_N(PrjR)$ of N-complexes of projectives is compactly generated whenever R is right coherent.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.511-518
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• 2021

In this paper, a relationship between the extended spectrum of the Aluthge transform and the extended spectrum of the operator T is proved. Other relationships between two different operators and other results are also given.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.271-291
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• 2021

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-Lie-Yamaguti color structure on T⊕V , where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2, 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.195-208
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• 2022

In this article, the matrix representation of commutative elliptic octonions and their properties are described. Firstly, definitions and theorems are given for the commutative elliptic octonion matrices using the elliptic quaternion matrices. Then the adjoint matrix, eigenvalue and eigenvector of the commutative elliptic octonions are investigated. Finally, α = -1 for the Gershgorin Theorem is proved using eigenvalue and eigenvector of the commutative elliptic octonion matrix.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.313-321
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• 2023

In this paper, we explore the additivity of the map Ω : 𝒜 → 𝒜 that satisfies Ω([ℒ, ℳ]_*)=[Ω (ℳ), ℒ]_* + [ℳ, Ω(ℒ)]_*, where [ℒ, ℳ]_*= ℒℳ^* - ℳ ℒ^*, for all ℒ, ℳ ∈ 𝒜, a prime *-algebra with unit ℐ. Additionally we show that if Ω (αℐ) is self-adjoint operator for α ∈ {1, i} then Ω = 0.