• 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.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.1167-1170
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• 1999

We consider a negative unity feedback control system in which a controller and a given minimum phase transfer function are in cascade. This paper present a sufficient condition for the existence of a constant gain controller under which the overall closed loop characteristic polynomial is stable. This sufficient condition is based on Lehnigk's lemmas.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.554-557
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• 2008

We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

• Research in Mathematical Education
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• v.15 no.4
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• pp.327-340
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• 2011

In this paper we propose an inquiry task on the subject of congruent triangles. The task deals with conditions that are sufficient for congruency, and conditions that are insufficient. The aim of the task is to find the minimal number of identical components in two triangles that is sufficient to ensure congruency.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.377-385
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• 2000

In this paper we find a sufficient condition to guarantee the existence of pure-strategy equilibria in matrix games. In the process of formulating our condition, the alternative theorem of Farkas is used. The formulated condition is necessary and sufficient to the existence of pure-strategy equilibria in undominated matrix games.

• 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.30 no.1
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• pp.29-34
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• 1993

J. Leray [7] proposed a sufficient condition ofr the solvability of the Cauchy problem on the initial hyperplane x$_{1}$=0 with Cauchy data which are holomorphic with respect to the variables parallel to some analytic subvariety S of the initial hyperplane. Limiting the problem to the case of operators with constant coefficients, A. Kaneko [2] proposed a new sharper sufficient condition. Later we generalized this condition and showed that it is necessary and sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data and the distribution Cauchy data which contain variables parallel to S as holomorphic parameters in [5, 6]. In this paper, we extend the results in [6] to the case of operators with variable coefficients and show that it is sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data. Our main theorem can be considered as an example of a deep theorem on micro-hyperbolic systems by Kashiwara-Schapira [4] and we give a direct proof based on an elementary sweeping out procedure developed in Kaneko [3].

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.223-233
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• 2008

In this paper we give sufficient conditions for a point to be a solution of an optimization problem in complex space.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.257-260
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• 1979

We show that the condition S of Sidon is sufficient for the integrability of the limit of Rees-$Stanojevi{\acute{c}$ cosine sums $g_n(x)={\frac{1}{2}}{\limits\sum^{n}_{k=0}}{\Delta}a_k+{\limits\sum^{n}_{k=1}}{\limits\sum^{n}_{j=k}}{\Delta}a_j\;cos\;kx$.