• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1003-1015
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• 2005

Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.707-720
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• 2000

Conley index is used study bifurcation from equilibria of full bounded solutions to parameter dependent families of ordinary differential equations of the form {{{{ {dx} over {dt} }}}} =$\varepsilon$F(x, t, $\mu$). It is assumed that F(x, t,$\mu$) is uniformly almost periodic in t.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.215-223
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• 2007

We in this note introduce the concept of NCI rings which is a generalization of NI rings. We study the basic structure of NCI rings, concentrating rings of bounded index of nilpotency and von Neumann regular rings. We also construct suitable examples to the situations raised naturally in the process.

• Smart Structures and Systems
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• v.19 no.1
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.19-37
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• 2013

The optimum design of base isolation system considering model parameter uncertainty is usually performed by using the unconditional response of structure obtained by the total probability theory, as the performance index. Though, the probabilistic approach is powerful, it cannot be applied when the maximum possible ranges of variations are known and can be only modelled as uncertain but bounded type. In such cases, the interval analysis method is a viable alternative. The present study focuses on the bounded optimization of base isolation system to mitigate the seismic vibration effect of structures characterized by bounded type system parameters. With this intention in view, the conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems correspond to a lower bound and upper bound optimum solutions. A lead rubber bearing isolating a multi-storeyed building frame is considered for numerical study to elucidate the proposed bounded optimization procedure and the optimum performance of the isolation system.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.959-965
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• 1996

In this paper we study the index stability theorem for a bounded linear operator with closed range and extend the Kato's decomposition theorem for an absence of the index.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.7
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• pp.1009-1017
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• 1993

The Robust Adaptive Servo Controller in this paper has an error-corrected and robust structure which guarantees asymptotic regulation and tracking in the presence of bounded parameter perturbations. The adaptive mechanism tunes the controller parameters such that a quadratic performance index is minimized. Through the speed and position control of the DC servo model with computer simulations, the minimum variance controller parameters are robust with respect to finite parameter perturbation and bounded disturbance.

• Journal of Biosystems Engineering
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• v.16 no.3
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• pp.272-280
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• 1991

The aims of this study were to investigate the feasivility of analyzing a few sorting factors such as size, coloration and defect of apples with a monochrome image processing system and to find apparent properties which could be effectively used for apple sorting. The results are summarized as follows. 1. A computer program was made to analyze the projection area, coloration and defect of an apple with a monochrome image processing system. 2. The algorithm developed to compute the projedtion area of an apple was between on the proportional relation between a given reference area and the corresponding number of pixels, and the computing time was 0.74 to 0.82 second depending on the size of apple. 3. The coloration of an apple was expressed as the ratio of the gray value of a reference color to that of a given bounded area of the stem end surface (defined as coloration index), and the computing time was about 3.0 seconds with this algorithm. 4. Defect of an apple could be isolated by lowpass filtering and image subtraction but it took about 20 seconds in computing time. 5. The coloration of the Fuji apple could be classified into 3 to 4 groups by the coloration index and also, it was found that the correlation coefficient between the indices and sugar contents was 0.74. 6. The coloration index obtained from a given bounded area of the stem end side of the Fuji apple could represent the coloration of total surface with a correlation coefficient of 0.922.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.897-921
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• 2018

Given bounded pseudoconvex domains in 2-dimensional complex Euclidean space, we derive analytical and geometric conditions which guarantee the Diederich-$Forn{\ae}ss$ index is 1. The analytical condition is independent of strongly pseudoconvex points and extends $Forn{\ae}ss$-Herbig's theorem in 2007. The geometric condition reveals the index reflects topological properties of boundary. The proof uses an idea including differential equations and geometric analysis to find the optimal defining function. We also give a precise domain of which the Diederich-$Forn{\ae}ss$ index is 1. The index of this domain can not be verified by formerly known theorems.

• Journal of Industrial Technology
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• v.10
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• pp.3-8
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• 1990

This paper presents a linear state feedback control approach to the stabilization of discrete-time uncertain systems with bounded uncertain parameters. The approach is based on the LQ(linear quadratic) regulator theory and Lyapunov's stability analysis. Asymptotically stable behavior is guaranteed in the presence of parameter uncertainties, and the upper bound of the performance index is determined.