• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.931-950
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• 2006

We study the identification problems of constant parameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parameters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions [13].

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.6
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• pp.500-505
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• 2000

This paper deals with wafer temperature uniformity control essential in rapid thermal processing (RTP). One of the important control objectives of RTP is to keep the temperature over the wafer surface as uniformly as possible. For this, a discrete time state equation around the operating point is first identified by using the subspace fitting method, and a multivariable LQG(Linear Quadratic Gaussian) controller is designed based on the identified model. Simulation and experimental results show improvement in temperature uniformity over the conventional PID method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1149-1159
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• 2018

A quadratic polynomial ${\Phi}_{a,b,c}(x,y,z)=x(ax+1)+y(by+1)+z(cz+1)$ is called universal if the diophantine equation ${\Phi}_{a,b,c}(x,y,z)=n$ has an integer solution x, y, z for any nonnegative integer n. In this article, we show that if (a, b, c) = (2, 2, 6), (2, 3, 5) or (2, 3, 7), then ${\Phi}_{a,b,c}(x,y,z)$ is universal. These were conjectured by Sun in [8].

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.113-123
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• 1994

A method for computing the elastic buckling prestressing force of a post-tensioned composite steel-concrete tee-beam is presented. The method is based on a virtual work formulation, and incorporates the restraint provided by the concrete slab to the buckling displacements of the steel beam. The distortional buckling solutions are shown to be given by a quadratic equation. The application of the analysis to calculation buckling strengths is given, based on codified rules for beam-columns. Conclusions are then drawn on the importance of distortional buckling when a post-tensioned composite beam is stressed during jacking.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.473-476
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• 1989

Quadratic weighting matrices have an effect on the transition and steady state responses in a LQ tracking problem. They are usually decided on trial and error in order to get a good response. In this paper a method is presented which calculates a steady - state deviation without solving Riccati equation. By using this method, a new procedure for selecting the weighting matrices is proposed when a tolerance on the steady - state deviation is given.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.742-746
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• 1992

This paper proposes a new linear robust state feedback controller for the linear discrete time systems which have uncertainties in the state and input matrices. The uncertainties need not satisfy the matching conditions, but only their bounds are needed to be known. The proposed controller is derived from the linear quadratic game problem, which solution is obtained via the modified algebraic Riccati equation. The controller guarantees the robust performance bound. The bound of the solution and the condition of the uncertainties, which can stabilize the uncertain system are explored.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.521-537
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• 1994

We consider the Schrodinger equation of quantum mechanics $$ i\hbar\frac{\partial t}{\partial}\Gamma(t, \vec{\eta}) = -\frac{2m}{\hbar}\Delta(t, \vec{\eta}) + V(\vec{\eta}\Gamma(t, \vec{\eta}) (1.1) $$ $$ \Gamma(0, \vec{\eta}) = \psi(\vec{\eta}), \vec{\eta} \in R^n $$ where $\Delta$ is the Laplacian on $R^n$, $\hbar$ is Plank's constant and V is a suitable potential.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.313-326
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• 2015

In this paper, we present a fixed point method to prove generalized Hyers-Ulam stability of the systems of quadratic-cubic functional equations with constant coefficients in modular spaces.

• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.