• 대한수학회논문집
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• 제29권1호
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• pp.205-212
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• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.553-563
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• 2013

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)

• 대한수학회지
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• 제37권6호
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.364-370
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• 2005

A stable walking pattern generation method for a biped robot is presented in this paper. In general, the ZMP (zero moment point) equations, which are expressed as differential equations, are solved to obtain a stable walking pattern. However, the number of differential equations is less than that of unknown coordinates in the ZMP equations. It is impossible to integrate the ZMP equations directly since one or more constraint equations are involved in the ZMP equations. To overcome this difficulty, DAE (differential and algebraic equation) solution method is employed. The proposed method has enough flexibility for various kinematic structures. Walking simulation for a virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method. The method can be applied to the biped robot for stable walking pattern generation.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.415-425
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• 2005

This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

• 대한기계학회논문집
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• 제9권5호
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• pp.621-626
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• 1985

본 논문에서는 정해를 구하기 어려운 이질의 세개의 층으로 된 비피압대수층 내에서의 물의 비정상유동에 대한 이론 및 실험에 대하여 연구하고자 한다.

• 대한수학회지
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• 제37권5호
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• pp.707-720
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• 2000

Conley index is used study bifurcation from equilibria of full bounded solutions to parameter dependent families of ordinary differential equations of the form {{{{ {dx} over {dt} }}}} =$\varepsilon$F(x, t, $\mu$). It is assumed that F(x, t,$\mu$) is uniformly almost periodic in t.

• 대한수학회지
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• 제42권4호
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.81-89
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• 2002

In this paper we prove the existence of solutions of fuzzy delay differential equations with nonlocal condition. The results are obtained by using the fixed point principles.