• Journal of the Korean Society of Industry Convergence
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• v.5 no.3
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• pp.219-224
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• 2002

We consider the problem y"=a(x,y)(y-b), y(0)=0, y'(1)=g(y(${\xi}$), y'(${\xi}$)), (0${\xi}$ fixed in(0,1)) as a model of steady-slate heat conduction in a rod when the heat flux at the end x = 1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness.

• Journal of Korean Society for Atmospheric Environment
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• v.14 no.4
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• pp.303-312
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• 1998

To obtain the solution to the time-dependent particle size distribution of an aerosol undergoing gravitational coagulation, the moment method was used which converts the non linear integro-differential equation to a set of ordinary differential equations. A semi-numerical solution was obtained using this method. Subsequently, an analytic solution was given by approximating the collision kernel into a form suitable for the analysis. The results show that during gravitational coagulation, the geometric standard deviation increases and the geometric mean radius decreases as time increases.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.516-521
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• 1993

In order to hold a underwater vehicle at a depth, we can modulate buoyancy that acts on the underwater vehicle. In this research, by using a ballon, we was able to generate buoyancy that could control depth in which vehicle was operate. And in order to control flux of air that was flowed in balloon, we used solenoid valve, relief valve and so on. We derived differential equations of volume of balloon, pressure of inside of balloon, dynamic of underwater vehicle, and air flux for the simulation and linearized these differential equation. So we designed LQG/LTR controller, and applied the controller to nonlinear system. Through the simulation, we compares the nonlinear system with the linear system and investigated the operation of solenoid valve.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.719-728
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• 2012

In this paper, we develop a numerical method to solving an optimal control problem, which is governed by a parabolic partial differential equations(PDEs). Our approach is to approximate the PDE problem to initial value problem(IVP) in $\mathbb{R}$. Then, the homogeneous part of IVP is solved using semigroup theory. In the next step, the convergence of this approach is verified by properties of one-parameter semigroup theory. In the rest of paper, the original optimal control problem is solved by utilizing the solution of homogeneous part. Finally one numerical example is given.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1989.10a
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• pp.45-50
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• 1989

The above theorm states that much larger classes of differential games have an equilibrium. The most severe assumption is the second one. It requires that state dynamic equations be linear on his own control variables. But, the dynamic programming approach applied in the above is hardly implementable for the purpose of computation. It is very difficult to solve (SP$_{it}$) directly. Notice, however, the problem can be transformed into a Hamiltonian maximization problem which is easy to solve if initial conditions are given. In this way, it is possible to design a solution algorithm to problems with nonlinear constraints. The above two theorems probide a basis for such an algorithm.m.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.995-1005
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• 2004

The aim of this paper is to prove the stability in the sense of Hyers-Ulam- Rassias of the Banach space valued differentialequation y' = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y' = λy, then there exists an exact solution of the equation near to f.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.2
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• pp.337-345
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• 1997

An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.167-182
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• 2007

The existence of solutions of the following multi-point boundary value problem $${x^{(n)}(t)=f(t,\;x(t),\;x'(t),{\cdots}, x^{(n-2)}(t))+r(t),\;0 is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.243-256
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• 2007

This paper deals with determining the sufficient conditions of minimum for the class of problems in which the necessary conditions of optimum are satisfied in the strengthened form Legendre-Clebsch. To this paper, we shall use the sweep method which analysis the conditions of existence of the conjugated points on the optimal trajectory. The study we have done evaluates the command variation on the neighboring optimal trajectory. The sufficient conditions of minimum are obtained by imposing the positivity of the second variation. The results that this method offers are applied to the problem o the orbital rendez-vous for the linear case of the equations of movement.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.215-228
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• 2007

By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange's characteristics method (a new approach) for solving non linear fractional partial differential equations. The key of this results is the fractional Taylor's series $f(x+h)=E_{\alpha}(h^{\alpha}D^{\alpha})f(x)$ where $E_{\alpha}(.)$ is the Mittag-Leffler function.