• Journal of the Korean Mathematical Society
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• v.40 no.2
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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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• v.28 no.5_6
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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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• v.28 no.6
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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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• v.19 no.2
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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.

• Journal of The Korean Association For Science Education
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• v.23 no.5
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• pp.574-591
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• 2003

According to conceptual change theory, cognitive conflict is known as an important factor in conceptual change even though there are still questions about its positive and negative effects on science learning. The purpose of this study was to examine the role of cognitive conflict in the conceptual change process in detail. Specific research questions are as follows, 1) Is presenting of an anomalous situation necessary or sufficient condition for cognitive conflict? 2) Is cognitive conflict necessary or sufficient condition for conceptual change? To answer these questions, we analyzed the theories and research results in the related literature. At the end, we discussed the complex role of cognitive conflict in the conceptual change and future research.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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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.

• Proceedings of the KSR Conference
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• 2007.05a
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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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.

• The Mathematical Education
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• v.48 no.2
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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.