• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.169-171
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• 1988

This paper deals with the robustness property of Kalman filters for linear systems with delay in output. The operator-type Riccati equation is transformed to algebraic equations, and the circle condition is derived. Based on the circle condition, it is shown that the same nondivergence margin, (1/2, .inf.) gain margin and +-60.deg. phase margin, is guaranteed as for ordinary systems.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.87-118
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• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.397-409
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• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.10
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• pp.972-980
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• 1991

LQG/LTR method have a theoretical constraint that it cannot applied to nonminimum phase plant. In this paper we suggest two methods of approximation of minimum phase plant for a given nonminimum phase plant to solve this constraint. Error is described by additive form which can reduce its magnitude in broad frequency range. A optimal approximation method was suggested by using Hankel operator theory and Nehan theory it is shown by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.791-797
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• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• East Asian mathematical journal
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• v.35 no.1
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• pp.99-108
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• 2019

In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

• East Asian mathematical journal
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• v.33 no.2
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• pp.199-216
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• 2017

A rational number as operator is eventually that it is considered a mapping. Depending on how selecting domain (the target of operation by rational number) and codomain (including the results of operations by rational number), it is possible to see the rational in two aspects. First, rational numbers can be deal with functions if we choose the target of operation by rational number as a number field containing rationals. On the other hand, if we choose the target of operation by rational number as integral domain $\mathbb{Z}$, then rational numbers can be regarded as partial functions on $\mathbb{Z}$. In this paper, we regard the rational numbers with a view of partial functions, we investigate the theoretical background of the relationship between the multiplication of rational numbers and the composition of rational numbers as operators.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.2
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• pp.344-354
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• 2009

Side scan sonar using acoustic wave plays a very important role in the underwater, sea floor, and shallow marine geologic survey. In this study, we have acquired side scan sonar data for the underwater man-made structures, artificial reefs and fishing grounds, installed and distributed in the survey area. We applied digital image processing techniques to side scan sonar data in order to improve and enhance an image quality. We carried out digital image processing with various kinds of filtering in spatial domain and frequency domain. We tested filtering parameters such as kernel size, differential operator, and statistical value. We could easily estimate the conditions, distribution and environment of artificial structures through the interpretation of side scan sonar.