• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.239-244
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• 1993

The purpose of this paper is to determine conditions under which equicontinuity of the family of iterates {f$^{n}$ } of a continuous function that maps the circle S$^{1}$ into itself does occur. We shall see that equicontinuity of the family of iterates {f$^{n}$ } occurs only under special cases. Actually, we will show that this happens only for rotations when degree of the function is 1, and for involutions when degree of the function is -1.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.157-161
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• 2007

We show that there is an equivariant symplectic embedding of a two-torus with a nontrivial action into a symplectic manifold with a symplectic circle action if and only if the circle action on the manifold is non-Hamiltonian. This is a new equivalent condition for non-Hamiltonian action and gives us a new insight to solve the famous conjecture by Frankel and McDuff.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.107-113
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• 1996

For continuous maps f of the circle to itself, we show that (1) the set of ${\omega}$-limit points is contained in the set of nonwandering points of $f^n$ for all $n{\geq}1$. (2) if the set of turning points of f is finite, then the set of accumulation points of non wandering set is contained in the set of non wandering points of $f^n$ for all $n{\geq}1$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.707-716
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• 1999

In this pater we study the continuity of rotation numbers of liftings of circle maps with degree one. And apply our result to prove that a positively equicontinuous flow of homeomorphisms on the circle $S^1$ is topologically conjugate to a continuous flow of rotation maps.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.2
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• pp.36-45
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• 2005

This paper aims to investigate and analyze the process solving problems with activities of Quality Control Circle, carried out on a small scale, among various activities of industrial fields. Then this paper intends to provide and integrated model through integrating each process into one. In addition, this paper also aims to enhance the efficiency of the suggested model by realizing the model through support system.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.645-653
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• 1997

We study centrally symmetric orthogonal polynomials satisfying an admissible partial differential equation of the form $$ Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_x + Eu_y = \lambda_n y, $$ where $A, B, \cdots, E$ are polynomials independent of n and $\lambda_n$ is the eignevalue parameter depending on n. We show that they are either the product of Hermite polymials or the circle polynomials up to a complex linear change of variables. Also we give some properties of them.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.641-646
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• 2004

A convex combination of two products with same degree of finitely many finite geometric series with each having even degree does not always have all its zeros on the unit circle. However, in this paper, we show that a polynomial obtained by just adding a finite geometric series multiplied by a large constant to such a convex combination has all its zeros on the unit circle.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1115-1122
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• 1996

In study of the dynamics of a map f from a topological space X to itself, a central role is played by the various recursive properties of the points of X. One such property is periodicity. A weaker property is that of being nonwandering. Intermediate recursive properties include almost periodicity and recurrence.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.19-22
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• 2003

This paper proposes an algorithm for navigation of an autonomous mobile robot with vision sensor. For obstacle avoidance, we used a curvature trajectory method. Using this method, translational and rotational speeds are controlled independently and the mobile robot traces a smooth curvature trajectory that consists of circle trajectories to a target point. While trying to avoid obstacles, the robot fan be goal-directed using curvature trajectory.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.