• 대한수학회보
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• 제46권4호
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• pp.657-671
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• 2009

Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. In this paper we derive a class of the perfect ideals from a class of the complete matrices. From this we give a structure theorem for complete intersections of grade g > 3.

• 대한수학회지
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• 제34권2호
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• pp.285-291
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• 1997

In this paper, we obtain an abstract formulation of a fixed point theorem for nonexpansive mappings. Our theorem is a non-metric version of Kirk's original theorem.

• 대한수학회지
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• 제38권4호
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• pp.697-709
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• 2001

Generalized forms of the von neumann-Sion type minimax theorem, the Fan-Ma intersection theorem, the Fan-a type analytic alternative, and the Nash-Ma equilibrium theorem hold for generalized convex spaces without having any linear structure.

• 전기학회논문지
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• 제59권10호
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• pp.1908-1913
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• 2010

In this paper, a robust variable structure tracking controller is designed for the mixed tracking control of highly nonlinear rigid robot manipulators for the first time. The mixed control problem under consideration is extended from the basic tracking problem, with the different initial condition of both the planned trajectory and link of robots. This control problem in robotics is not addressed to until now. The tracking accuracy to the sliding trajectory after reaching is analyzed. The stability of the closed loop system is investigated in detail in Theorem 2. The results of Theorem 2 provide the stable condition for control gains. Combing the results of Theorem 1 and Theorem 2 gives rise to possibility of designing the improved variable structure tracking controller to guarantee the tracking error from the determined sliding trajectory within the prescribed accuracy after reaching. The usefulness of the algorithm has been demonstrated through simulation studies on the mixed tracking control of a two.link robot under parameter uncertainties and payload variations.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.531-539
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• 2009

In this paper we first present a structure theorem for an infinite locally finite 3-connected VAP-free planar graph, and in connection with this result we study a possible classification of infinite locally finite planar graphs by reducing modulo finiteness.

• 대한수학회보
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• 제27권2호
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• pp.183-188
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• 1990

The notion of a Dirichlet set has been studied for several decades. Such sets are named in honour of Dirichlet's Theorem [4, pp.235] which, in modern terminology, simply says that every finite set in R is a dirichlet set. In this paper, we present a structure theorem which characterizes all D-sets on the real line. We also use our structure theorem to give a new proof of a known criterion for proving that a set fails to be a D-set.

• 대한수학회논문집
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• 제13권1호
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• pp.21-27
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• 1998

In this paper we prove a structure theorem for p-hyponomal contractions and also give an example of a p-hyponormal operator which is not *-paranormal.

• Korean Journal of Mathematics
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• 제8권1호
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• pp.73-86
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• 2000

We study the Sobolev spaces to the generalized Sobolev spaces $H^s_{\mathcal{G}}$ of exponential type based on the Silva space $\mathcal{G}$ and investigate its properties such as imbedding theorem and structure theorem. In fact, the imbedding theorem says that for $s$ > 0 $u{\in}H^s_{\mathcal{G}}$ can be analytically continued to the set {$z{\in}\mathbb{C}^n{\mid}{\mid}Im\;z{\mid}$ < $s$}. Also, the structure theorem means that for $s$ > 0 $u{\in}H^{-s}_{\mathcal{G}}$ is of the form $$u={\sum_{\alpha}\frac{s^{{|\alpha|}}}{{\alpha}!}D^{\alpha}g{\alpha}$$ where $g{\alpha}$'s are square integrable functions for ${\alpha}{\in}\mathbb{N}^n_0$. Moreover, we introduce a classes of symbols of exponential type and its associated pseudo-differential operators of exponential type, which naturally act on the generalized Sobolev spaces of exponential type. Finally, a generalized Bessel potential is defined and its properties are investigated.

• 한국지진공학회논문집
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• 제7권4호
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• pp.81-87
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• 2003

본 논문에서는 Shannon의 샘플링 이론을 이용하여 제한된 수의 센서에서 얻은 모드형상으로 정확한 모드형상을 재생성하고, 이렇게 재생성한 모드형상을 이용하여 구조물에 발생한 손상을 탐지할 수 있는지의 가능성에 대해 조사하였다. 우선 시간 영역에서의 Shannon의 샘플링 이론을 검토하였고, 이를 공간영역으로 확대하였다. 공간영역으로 확대한 Shannon의 샘플링 이론은 그 효용성을 확인하기 위하여 단순보의 모드형상을 해석적으로 구한 후 최소한으로 제한된 수의 샘플 데이터로 모드형상을 재생하였고 이를 원래의 모드형상과 비교하였다. 이렇게 하여 얻은 결과를 바탕으로 구조물의 모드형상을 추출하는 동적실험에서 필요한 최적 가속도계의 위치를 구할 수 있는 간단한 관계식을 제안하였다. 제안된 관계식과 공간영역으로 확대한 Shannon의 샘플링 이론의 실용성은 연속 2스팬으로 구성된 실험실 빔 구조물의 손상 전과 후의 모드형상에 적용하여 손상을 탐지함으로써 입증하였다.

• 호남수학학술지
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• 제5권1호
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• pp.45-69
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• 1983

The hermitian structures on complex manifolds have been studied by several mathematicians ([1], [2], and [3]), and the Kähler structure on hermitian manifolds have been so much too ([6], [12], and [15]). There has been some gradual progress in studying the invariant forms on Grassmann manifolds ([17]). The purpose of this dissertation is to prove the Theorem 3.4 and the Theorem 4.7, with relation to the nature of complex Grassmann manifolds. In $\S$ 2. in order to prove the Theorem 4.7, which will be explicated further in $\S$ 4, the concepts of the hermitian structure, connection and curvature have been defined. and the characteristic nature about these were proved. (Proposition 2.3, 2.4, 2.9, 2.11, and 2.12) Two characteristics were proved in $\S$ 3. They are almost not proved before: particularly. we proved the Theorem 3.3 : $G_{k}(C^{n+k})=\frac{GL(n+k,C)}{GL(k,n,C)}=\frac{U(n+k)}{U(k){\times}U(n)}$ In $\S$ 4. we explained and proved the Theorem 4. 7 : i) Complex Grassmann manifolds are Kahlerian. ii) This Kähler form is $\pi$-fold of curvature form in hyperplane section bundle. Prior to this proof. some propositions and lemmas were proved at the same time. (Proposition 4.2, Lemma 4.3, Corollary 4.4 and Lemma 4.5).