• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.123-131
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• 2006

In this paper, a numerical programming for Liapunov index of differential equations with periodic coefficients depending on parameters is given. The associated equations are given at first, then existence of periodic solutions to the associated equations is proved in this paper. And we compute periodic solution u(t) of the associated equations. Finally, we give the error of approximate calculation.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1139-1144
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• 1990

In this paper, we consider linear periodic discrete-time control systems under periodic compensation. Such a closed-loop system generally represents a periodic time-varying system. We examine the problem of finding a compensator such that the closed-loop system is realized as LTI model (if possible) with the closed-loop stability being satisfied. We present a necessary and sufficient condition for solving such problem and also give the characterization of realizable LTI models.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.155-159
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• 2009

Using the Binet's formula, we show that the quotient related ratio $l_{1(x)}\;\neq\;0$ for the eventually periodic continued fraction x. Using this ratio, we also show that the derivative of the Minkowski question mark function at the simple periodic continued fraction is infinite or 0. In particular, $l_1({[\bar{1}]})$ = 2 log $\gamma$ where $\gamma$ is the golden mean $(1+\sqrt{5})/2$ and the derivative of the Minkowski question mark function at the simple periodic continued fraction $[\bar{1}]$ is infinite.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.263-271
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• 2006

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.265-277
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• 2004

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.227-232
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• 2006

We study some dynamical properties in the context of bitransformation groups, and show that if (H,X,T) is a bitransformation group such that (H,X) is almost periodic and (X/H,T) is pointwise almost periodic $T_2$ and $x{\in}X$, then $E_x=\{q{\in}E(H,X){\mid}qx{\in}{\overline{xT}\}$ is a compact $T_2$ topological group and $E_{qx}=E_x(q{\in}E(H,X))$ when H is abelian, where E(H,X) is the enveloping semigroup of the transformation group (H,X).

• The Journal of Korean Medicine
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• v.21 no.2
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• pp.87-94
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• 2000

Hypokalemic periodic paralysis(HypoPP) is characterized by an abrupt onset of flaccid paralysis with a clear mentality, but muscles of speech and swallowing are usually spared. We report on three patients who suffered attacks of acute paralysis. After exclusion of central nervous system involvement, the patients showing hypokalemia was diagnosed as hypokalemic periodic paralysis, which was completely reversible on parenteral potassium substitution.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.299-312
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• 2009

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.