• 대한수학회지
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• 제40권2호
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1117-1130
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• 2010

The main goal for this paper is consider the necessary conditions and sufficient conditions of wavelet frames in higher dimensions with an arbitrary expanding matrix dilation. At first, we give a necessary condition of wavelet frame in $L^2(R^n)$, which generalizes the univariate results of Shi from one dimension with an arbitrary real number a(a > 1) dilation to higher dimension with an arbitrary expansive matrix dilation. Secondly, we deduce a necessary condition for wavelet frames in $L^2(R^n)$ when the function $\psi$ satisfies some property of the decay. For the case n = 1, we obtain a corollary which has weaker condition comparing with existing result.

• 전기의세계
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• 제28권6호
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• pp.47-51
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• 1979

An optimal problem in which the dynamics is nonlinear and the cost functional includes a discontinuous integrand is investigated. By using Neustadt's abstract maximum principle, a necessary conditions in the form of Pontryagin's maximum principle is derived and it is further shown that this necessary condition is also a sufficient condition for normal problems with linear-in-the-state systems.

• 전기의세계
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• 제19권2호
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• pp.21-23
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• 1970

Necessary conditions of optimal distributed parameter control systems, Hamiltons coanonical equations, welerstress condition, transversality condition and boundary condition are obtained, when the control function is constrained and the performance index takes on the general form. Also it is concluded that the lumped parameter system is the special case of the distributed parameter system.

• 한국과학교육학회지
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• 제23권5호
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• pp.574-591
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• 2003

과학학습에서 인지갈등의 긍정적인 혹은 때때로 부정적인 영향에 관한 논의들이 아직까지 진행되고 있다. 그러나 분명한 것은 개념변화이론에 따르면 인지갈등이 개념변화에 중요한 역할을 한다는 것이다. 이 연구의 목적은 개념변화과정에서 인지갈등의 역할을 자세히 살펴보는 것이다. 구체적인 연구문제는 다음과 같다. 1) 불일치 상황은 인지갈등의 필요조건 혹은 충분조건인가? 2) 인지갈등은 개념변화의 필요조건 혹은 충분조건인가? 이 문제를 해결하기 위하여, 우리는 관련 문헌들 속의 이론과 결과들을 분석하였다. 마무리부분에서는 개념변화과정에서 인지갈등의 복잡한 역할과 앞으로의 연구과제에 대하여 논의 하였다.

• 대한수학회보
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• 제52권4호
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• 충청수학회지
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• 제16권1호
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• pp.61-71
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• 2003

We obtain a necessary condition for splitting T-space off a space in terms of cyclic maps, and also obtain a necessary condition for splitting co-T-spaces in terms of cocyclic maps.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2007년도 춘계학술대회 논문집
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• pp.1752-1759
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• 2007

In the new Seoul-Busan high speed railroad construction specially city center passage roadbed establishment is recommended the staibility for the existing subway tunnel segments of Busan subway line No. 1 and No.2. regarding the appearance condition, a quality condition and the durability of the objective facility site exact inspection, and it evaluates the numerical analysis which uses MIDAS GTS it leads and there is the objective of the place where the stability of the objective facility and this tunnel it investigates. To immediacy of the on-the-spot inspection result whole facility it is a condition where the reinforcement which is simple not to be hindrance is necessary, 2nd Line case it is a condition which transfer is good but the general defect and the damage which occur from the tunnel of NATM type were confirmed part. While roadbed establishment constructing that the continuous maintenance is necessary, it is judged. The result of 1st, 2nd Line maximum sinkage, unequal sinkage and the lining stress of numerical analysis are within permission and the damage degree is appearing with the fact that the degree it will can disregard it is slight. But it enforces necessary Pre-grouting in order to minimize an actual tunnel face conduct and when the tunnel is excavated it is judged with the fact that necessary to minimize the outflow possibility.

• 대한수학회보
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• 제39권2호
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• pp.269-276
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• 2002

Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.

• 한국수학교육학회지시리즈A:수학교육
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• 제48권2호
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• pp.141-148
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• 2009

The article discusses roles of analysis in problem solving, especially the problem posing. The author shows the procedure of analysis like the presentation of the hypothesis, the reasoning for the necessary conditions and the sufficient condition. Finally the author suggests that the analysis should be reviewed in the school mathematics.