• Structural Engineering and Mechanics
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• 제1권1호
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• pp.47-60
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• 1993

The eigen-equation of a wave traveling over repetitive structure is derived directly form the stiffness matrix formulation, in a form which can be used for the case of the cross stiffness submatrix $K_{ab}$ being singular. The weighted adjoint symplectic orthonormality relation is proved first. Then the general method of solution is derived, which can be used either to find all the eigensolutions, or to find the main eigensolutions for large scale problems.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.65-70
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• 2016

J. G. Stampfli proved that if a bounded linear operator T on a Hilbert space ${\mathfrak{H}}$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with ${\lambda}{\in}iso{\sigma}$(T) is self-adjoint and $P_{\lambda}{\mathfrak{H}}=(T-{\lambda})^{-1}(0)=(T^*-{\bar{\lambda}})^{-1}(0)$. In this note we show that Stampfli''s result is generalized to an nilpotent extension of an operator having ($G_1$) property.

• 대한수학회보
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• 제33권2호
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• pp.233-241
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• 1996

The study of non-self-adjoint operator algebras on Hilbert space was only beginned by W.B. Arveson[1] in 1974. Recently, such algebras have been found to be of use in physics, in electrical engineering, and in general systems theory. Of particular interest to mathematicians are reflexive algebras with commutative lattices of invariant subspaces.

• 대한수학회지
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• 제39권4호
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• pp.559-577
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• 2002

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

• 대한수학회지
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• 제45권3호
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 추계학술대회 학술발표 논문집 제14권 제2호
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• pp.351-354
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• 2004

Using the idea of generalized intuitionistic fuzzy set, we study the notion of generalized intuitionistic fuzzy matrices as a generalization of fuzzy matrices, We show that some properties of a square generalized intuitionistic fuzzy matrix such as reflexivity, transitivity and circularity are carried over to the adjoint generalized intuitionistic fuzzy matrix.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.49-60
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• 2000

We will characterize isomorphisms from the adjoint of a certain tridiag-onal algebra $AlgL_{2n}$ onto $AlgL_{2n}$. In this paper the following are proved: A map $\Phi{\;}:{\;}(AlgL_{2n})^{*}{\;}{\longrightarrow}{\;}AlgL_{2n}$ is an isomorphism if and only if there exists an operator S in $AlgL_{2n}$ with all diagonal entries are 1 and an invertible backward diagonal operator B such that ${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$.

• 대한기계학회논문집
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• 제9권1호
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• pp.119-126
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• 1985

형상은 3차원이지만 2차원 문제로 이상화하여 해석할 수 있는 탄성구조물의 최적설계를 내연기관 연결봉(Connecting Rod)을 예제로 사용하여 진행하였다. 연결봉은 각 부위에서의 두께는 다르나 평면응력상태에 있다고 가정하였다. 연결봉의 질량을 최소화하기 위해 두께의 분포 및 2차원 모델 경계의 모양을 설계변수로 채택하였고 설계변수 및 응력치에 대한 제한조건을 적용하였다. 설계감도계수 계산을 위해 Variational Formulation, Material Derivative, Adjoint Variable이론을 도입하였고 최적화 방법으로는 Gradient Projection Method를 사용하였다. 최적설계 결과 현재 사용중인 연결봉 무게의 20%를 줄일 수 있음이 밝혀졌다.

• 호남수학학술지
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• 제26권4호
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.479-484
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• 2000

The topology optimization of electromagnetic systems is investigated and the TOPEM (Topology Optimization for Electromagnetic Systems) is developed using the finite element method (FEM). The design sensitivity equation for topology optimization is derived using the adjoint variable method. The proposed method is validated by applying it to the topology optimizations of a C-core actuator and an optical pickup actuator.