• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.145-149
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• 1987

The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.335-345
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• 2014

In this paper, we investigate bounds for solutions of nonlinear perturbed functional differential systems.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.183-200
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• 2007

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.27.2-27
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• 2001

This paper proposes a receding horizon predictive control (RHPC) for nonlinear time-delay systems. The control law is obtained by minimizing finite horizon cost with a terminal weighting functional. An inequality condition on the terminal weighting functional is presented, under which the closed-loop stability of RHPC is guaranteed, A special class of nonlinear time-delay systems is introduced and a systematic method to find a terminal weighting functional satisfying the proposed inequality condition is given for these systems. Through a simulation example, it is demonstrated that the proposed RHPC has the guaranteed closed-loop stability for nonlinear time-delay systems.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1033-1038
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• 1997

A functional central limit theorem for a class of nonlinear stationary Markov processes which are geometrically Harris ergodic is derived.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.419-433
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• 2013

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

• East Asian mathematical journal
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• v.14 no.2
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• pp.299-309
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• 1998

• Journal of the Optical Society of Korea
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• v.16 no.2
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• pp.95-100
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• 2012

We show that the minimum EOP (eye-opening penalty) obtained by tunable dispersion compensation is a function of a figure of merit for a nonlinear process, $I_0L_{eff}$, where $I_0$ is the optical intensity and $L_{eff}$ is the effective length of the interaction region. Using this rule, we do not need to conduct nonlinear simulations in all the cases of signal power and transmission length to obtain the signal distortion in dispersion-managed optical transmission. Instead, we need to conduct a simulation in only one case of a signal power and find the functional relation, and then we can obtain the values of the signal distortion in other cases using the discovered functional relation. This technique can reduce the number of nonlinear simulations to less than 10%.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.687-697
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• 2015

This paper shows that the solutions to the perturbed nonlinear functional differential system