• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.545-565
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• 2014

In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

• Proceedings of the KIEE Conference
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• 1993.11a
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• pp.320-322
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• 1993

In this paper, the decentralized adaptive control scheme is applied to the control of drum type boiler system. Because the scheme requires the stability of interconnections, static feedback is used to satisfy the requirement of the scheme. From a priori knowledge of the system, system parameter estimates are bounded to prevent parameter drifting. Computer simulation shows that the decentralized adaptive control is suitable for the control of drum type boiler system and robust in the presence of disturbance.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.971-974
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• 2002

Petri net is an effective modeling tool for concurrent systems. Liveness problem is one of analysis problems in Petri net theory verifying whether the system is free from any local deadlocks. It is well known that computational complexity of liveness problem of general Petri net is deterministic exponential space. Some subclasses, such as marked graph and free choice net, are suggested where liveness problem is verified in less complexity. This paper studies liveness of siphon containing circuit (SCC) net. Liveness condition based on algebraic inequalities is shown. Then polynomial time decidability of liveness of SCC net is derived, if the given net is known to be an SCC net a priori.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• 한국가시화정보학회:학술대회논문집
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• 2001.12a
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• pp.62-74
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• 2001

Present paper describes the principles of PIV measurement approaching from the analytical view, which enables to explain the general form of principles covering all the PIV measurement, and that gives theoretical basis for its higher measurement performances. The explanation of the measurement principles started from the definition of governing equation in differential form as same as the gradient method, and the integral along the particle path line was executed to show the principle of the correlation method with same basis. The integral processes clearly shows the analytical reason why the correlation peak gives the terminal point of path line, and how the effects of deformation and rotation of fluid appears in the correlation map. These results have no differences from our experiences and understandings of the conventional PIV measurement definition in final form. However, the analytical approach enable to understand those facts a priori, and it makes easy to achieve the innovative higher performances of measurement. Analytical explanation clearly shows the behavior of the residual errors caused by the fluid motion, and it enables to analyze the measurement uncertainty theoretically.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.69-72
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• 2001

Blind equalization of transmission channel is important in communication areas and signal processing applications because it does not need training sequence, nor does it require a priori channel information. Recently, Tong et al. proposed solutions for this problem exploit the diversity induced by antenna array or time oversampling, leading to the second order statistics techniques, fur example, subspace method, prediction error method, and so on. The linear prediction error method is perhaps the most attractive in practice due to the insensitive to blind equalizer length mismatch as well as for its simple adaptive filter implementation. Unfortunately, the previous one-step prediction error method is known to be limited in arbitrary delay. In this paper, we induce the optimal delay, and propose the adaptive blind equalizer with multi-step linear prediction using RLS-type algorithm. Simulation results are presented to demonstrate the proposed algorithm and to compare it with existing algorithms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.637-644
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• 1997

Sometimes, the first principal component may come logically from the established knowledge and premises. For example, for the high school students' test scores of Korean, English, Mathematics, Social Study, and Science, it is natural to define the first principal component as the average of all subject scores. In such cases, we need to respect both the background knowledge and the data exploration. The aim of this study is to find the remaining components in principal component analysis of multivariate data when the first principal component is defined a priori by the researcher. Moreover, we study related matrix decomposition and their application to the graphical display.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.226-231
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• 1998

This paper describes how a priori road geometry and its estimation may be used to detect road boundaries and lane markings in road scene images. We assume flat road and road boundaries and lane markings are all Bertrand curves which have common principal normal vectors. An active contour is used for the detection of road boundary, and we reconstruct its geometric property and make use of it to detect lane markings. Our approach to detect road boundary is based on minimizing energy function including edge related term and geometric constraint term. Lane position is estimated by pixel intensity statistics along the parallel curve shifted properly from boundary of the road. We will show the validity of our algorithm by processing real road images.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.7
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• pp.22-28
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• 1998

This paper includes AC servo motor speed control usig the predictive control strategy. Generally, AC servo motor control should have the fast response characteristics. For the issue, sliding mode control and PID control have been applied. However, the former has the speed ripple response due to the chattering and the latter requires the many trial efforts. Originally, the predictive control which has been used in process control area does not need the priori knowledge for the application system and it is easy to compute the optimal gain with the prediction. In this paper, the TMS320C31 DSP pocessor is used for AC motor control with fst dynamics and the tuning guid-line for the parameters of the predictive control algorithm is given in order to reduce the computation load. Also, the actuator saturationis implemented uisngthe QP(Quadratic Programming) method and the transient response is improved by the identified intertia coefficient when AC motor is drived at forward/reverse rotation.