• 대한수학회지
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• 제56권3호
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• pp.723-738
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• 2019

A property of reduced rings is proved in relation with centers, and our argument in this article is spread out based on this. It is also proved that the Wedderburn radical coincides with the set of all nilpotents in symmetric-over-center rings, implying that the Jacobson radical, all nilradicals, and the set of all nilpotents are equal in polynomial rings over symmetric-over-center rings. It is shown that reduced rings are reversible-over-center, and that given reversible-over-center rings, various sorts of reversible-over-center rings can be constructed. The structure of radicals in reversible-over-center and symmetric-over-center rings is also investigated.

• 대한수학회보
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• 제60권5호
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• pp.1181-1199
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• 2023

For solving complex symmetric positive definite linear systems, we propose a single step real-valued (SSR) iterative method, which does not involve the complex arithmetic. The upper bound on the spectral radius of the iteration matrix of the SSR method is given and its convergence properties are analyzed. In addition, the quasi-optimal parameter which minimizes the upper bound for the spectral radius of the proposed method is computed. Finally, numerical experiments are given to demonstrate the effectiveness and robustness of the propose methods.

• Structural Engineering and Mechanics
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• 제7권2호
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

• 대한수학회보
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• 제45권1호
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• pp.95-99
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• 2008

It is known that each eigenvalue of a real symmetric, irreducible, tridiagonal matrix has multiplicity 1. The graph of such a matrix is a path. In this paper, we extend the result by classifying those trees for which each of the associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct.

• 대한수학회지
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• 제48권1호
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• pp.83-104
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• 2011

In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.32.4-32
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• 2002

We consider inertial navigation system (INS) sensor redundancy and propose a method which uses singular value decomposition to detect and isolate faults when even two sensors have faults simultaneously. When redundant sensor configuration is given, such as symmetric configuration in INS, the range space and null space of configuration matrix are determined. We use null space of configuration matrix and define 21 reference fault vectors which include 6 one-fault vectors and 15 two-fault vectors. Measurements are projected into null space of measurement matrix and compared with 21 normalized reference fault vectors, which determines fault detection and isolation.

• 대한수학회논문집
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• 제9권3호
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• pp.753-765
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• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• 대한수학회보
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• 제58권3호
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• pp.609-616
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• 2021

We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.

• 전산구조공학
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• 제4권2호
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• pp.103-110
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• 1991

컴퓨터의 제한된 코어메모리로 대형문제를 해결하기 위하여 디스크를 마치 메모리처럼 사용할 수 있는 가상 메모리 데이타베이스 기법을 개발하였다. 이 기법과 아울러 최대 가용코어메모리를 작동시키는 방식을 사용하여 유한요소 해석시 흔히 발생하는 스카이라인 형태로 저장된 대칭통산행예(Sparse Symmetric Matrix)에 대한 매우 효과적인 코어 내 및 코어 외 직립방정식의 해법을 개발하였다. 제안된 방법은 다른 코어 외 해법에 비해 알고리즘 및 코딩이 매우 간단하여 계산효율을 상당히 향상시켰다. 해석예에서는 제안된 방법을 사용하여 대규모 구조해석 문제를 메모리 용량이 작은 소형컴퓨터에서 대단히 효율적으로 해결하였음을 보여주었다.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.175-187
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• 2020

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.