• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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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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• 2005.06a
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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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• v.16 no.4
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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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• 1992.10a
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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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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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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• 2001.10a
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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.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.1
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• pp.36-41
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• 2005

The smart space is composed of the wire and/or wireless network, multi-sensor-based environment, and many various controllers. For the smart space, this paper presents a new design method of multirate digital decentralized controller using the digital redesign technique. In specific, the proposed method is based on the delta-operator and the multirate sampling and takes the form of the LMIs. To shows the feasibility of the suggested method, the computer simulations for HVAC system are provided.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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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 $A_1$.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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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.