• 대한수학회보
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• 제38권1호
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• pp.93-100
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• 2001

Author proves weak type estimates of the maximal function associated with the Bochner-Riesz means while it is claimed p=2n/(n+1+$2\delta) and 0<\delta\leq(n-1)/2$ that the maximal function is bounded on L^p-{rad}$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2183-2187
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• 2005

In this paper we propose a new fault detection and isolation (FDI) method for those faults of parameter change type. First, we design a residual generator based on the ${\delta}$-operator model of the plant by using the stable pseudo inverse system. Second, the parameter change is estimated by using the property of the block Hankel operator. Third, reliability with respect to stability is quantified. Fourth, the limitations for the meaningful diagnosis in our method are given. The numerical examples demonstrate the effectiveness of the proposed method.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.912-916
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• 1992

In this paper we investigate the connection between the continuous-time FIR(finite impulse response) filter and the corresponding discrtet-time FIR filter with fast sampling. The interconnection is established by formulating the discrete-time case using delta operators which has superior numerical properties in discretizing prcedure. The aim of this paper is to present a unified FIR filter using the .delta.-operator and to show that, as sampling interval .DELYA. aperator to zero, the results of this filter converge to the corresponding continuous-time reuslts, which implies that the unified FIR filter unifies continous-time FIR filter and discrtet-time FIR filter.

• 대한수학회보
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• 제43권4호
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• pp.671-677
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• 2006

Let $A, B{\in}B(H)$ be Hilbert space contractions, and let ${\Delta}_{AB}$ be the elementary operator ${\Delta}_{AB}:X{\rightarrow}AXB-X$. A number of conditions which are equivalent to '${\Delta}_{AB}$ has closed range' are proved.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.34.5-34
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• 2001

This paper presents a reliable H$\infty$ controller design for singularly perturbed systems by the delta operator approach that guarantees stability with a known H$\infty$ norm bound in case of failures in some control channels. Prespecified are the control channels that may experience failures. Sensor outage is covered in this paper It is shown that the delta systems have improved finite wort length characteristics in the example.

• 한국정밀공학회지
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• 제17권11호
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• pp.151-157
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• 2000

The MRAC theory has proved to be one of the most popular algorithms in the field of adaptive control, particularly for practical application to devices such as an hydraulic servosystem of which parameters are unknown or varying during operation. For small sampling period, the discrete time system becomes a nonminimal phase system. The $\delta$-MRAC was introduced to obtain the control performance of nonminimal phase system, because the z-MRAC can not control the plant for small sampling period. In this paper, $\delta$-MRAC is applied to the control of an hydraulic servosystem which is composed of servovalve, hydraulic cylinder and inertia load.

• 한국지능시스템학회논문지
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• 제15권1호
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• pp.36-41
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• 2005

스마트 스페이스 환경은 유무선 네트워크기반과 다중 센서 기반이며 많은 제어기를 필요로 한다. 이러한 환경을 위해서 본 논문에서는 멀티레이트 디지털 분산 제어 제어기를 제안한다. 제안된 제어기 설계 방법은 디지털 재 설계 기법을 적용하는 것이다. 구체적으로 제안된 기법은 delta-operator와 멀티레이트를 기반으로 하며 선형 행렬 부등식형태로 나타난다. 제안된 기법의 우수성을 검증하기 위해서 스마트 스페이스에서 널리 사용되는 Heating, ventilating, and alt conditioning (HVAC) 시스템에 대해서 모의실험을 하였다.

• 대한수학회논문집
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• 제10권4호
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• pp.881-887
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• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• 대한수학회지
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• 제47권4호
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• pp.735-742
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• 2010

In this paper, we define and study the concept of $\wedge^s_{\delta}$-closure operator and the associated topology $\tau^{\wedge}^s_{\delta}$ on a topological space (X, $\tau$) in terms of g.$\wedge^s_{\delta}$-sets.