• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.729-733
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• 1987

Stability of Co Semigroups perturbed via the steady state Riccati equation (SSRE) is studied. We consider an infinite dimensional system : .chi. over dot = A.chi. + Bu, in, (A), domain of A, where A is the infinitesimal generator of a Co semigroup [T(t), t.geq.0] in H. If the original Co semigroup [T(t), t.geq.0] has a lower bound : vertical bar T(t).chi. vertical bar .geq. k vertical bar .chi. vertical bar, for all .chi. in H. t.geq. 0 and k>0, then the perturbed Co semigroup via the SSRE, where the feedback operator B is compact, cannot be exponentially stable. Physical interpretation of this result is as follows : in real applications, a finite number of actuators are available, therefore the operator B is compact. When the original system is inherently unstable, that is, has an infinite number of unstable modes, the perturbed system via the SSRE cannot be stable with a uniform decay rate.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.423-438
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• 1994

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) ＋ $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f ＋ Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$ ⊂ $L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.65-70
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• 1993

In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.137-151
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• 2023

In this paper we prove the existence of nontrivial weak solutions to the boundary value problem -G₁u = u³ + f(x, y, u) in Ω, u ≥ 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝ³, G₁ is a Grushin type operator, and f(x, y, u) is a lower order perturbation of u³ with f(x, y, 0) = 0. The nonlinearity involved is of critical exponent, which differs from the existing results in [11, 12].

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.97-101
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• 1987

The edge, a discontinuity or abrupt change in the gray-level or color, is a fundamentally important primitive feature of an image necessary for the image analysis and classification. Two-dimensional 3x3 compass gradient operators (ex. Sobel, Prewitt, and Kirsch operators)are commonly used in the edge detection and usually detect 8 compass directional components. In this paper, we present a new interpretation of the relationships between the resulting 8 gradient magnitudes and the 8 intensity values of neighboring pixels which are covered by the two-dimensional 3x3 mask. It is expected that a new gradient edge operator may be designed by changing the eigenvalues in the transform domain and the fast optical edge operator may be implemented by using the optical system.

• Journal of the Korea Society of Computer and Information
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• v.25 no.12
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• pp.127-134
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• 2020

Recently, Harmful sites, including pornographic videos, drugs, personal information and hacking tool distribution sites, have caused serious social problems. However, due to the nature of the Internet environment where anyone can use it freely, it is difficult to control the user effectively. And the site operator operates by changing the domain to bypass the blockage. Therefore, even once identified sites have low persistence. In this paper, we propose multi-channel domain tracking technology, a technique that can effectively track changes in the domain addresses of harmful sites, including the same or similar content, by tracking changes in these harmful sites. Proposed technology is a technology that can continuously track information in a domain using OSINT technology. We tested and verified that the proposed technology was effective for domain tracking with a 90.4% trace rate (sensing 66 changes out of 73 domains).

• East Asian mathematical journal
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• v.27 no.1
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.191-196
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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 suggesetd by using Hankel operator theory and Nehari theory. It is showen by example that the methods suggested can resolve the frequency domain constraint arised in Stein and Athans approximation.