• Bulletin of the Korean Chemical Society
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• v.18 no.3
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• pp.274-280
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• 1997

The rates and stoichiometry of the reaction of gallane-trimethylamine with selected organic compounds containing representative functional groups were examined in tetrahydrofuran solution under standardized conditions (THF, 0 ℃). And its reducing characteristics were compared with those of aluminum hydride-triethylamine(AHTEA). The rate of hydrogen evolution from active hydrogen compounds varied considerably with the nature of the functional group and the structure of the hydrocarbon moiety. Alcohols, phenol, amines, thiols evolved hydrogen rapidly and quantitatively. Aldehydes and ketones were reduced moderately to the corresponding alcohols. Cinnamaldehyde was reduced to cinnamyl alcohol, which means that the conjugated double bond was not attacked by gallane-trimethylamine. Carboxylic acids, esters, and lactones were stable to the reagent under standard conditions. Acid chlorides also were rapidly reduced to the corresponding alcohols. Epoxides and halides were inert to the reagent. Caproamide and nitrile were stable to the reagent, whereas benzamide was rapidly reduced to benzylamine. Nitropropane, nitrobenzene and azoxybenzene were stable to the reagent, whereas azobenzene was reduced to 1,2-diphenylhydrazine. Oximes and pyridine N-oxide were reduced rapidly. Di-n-butyl disulfide and dimethyl sulfoxide were reduced only slowly, but diphenyl disulfide was reduced rapidly. Finally, sulfones and sulfonic acids were inert to the reagent under the reaction.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.649-652
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• 2007

In this note we provide a generalization of the Schur-Cohn test. If $p_n$ be a polynomial of degree n then $p_n$ is a reduced-stable polynomial whose reduced degree is equal to r if and only if $D_n\;:=\;P_nQ_n^{-1}$ is a contraction such that rank ($I-D_nD_n^*$) = r.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.8
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• pp.584-593
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• 1987

A new combined approximation method using Routh stability array and mean-square error (MSE) method is proposed for deriving reduced-order z-transter functions for discrete time systems. The Routh stability array is used to obtain the reduced-order denominator polynomial, and the numerator polynomial is obtained by minimizing the mean-square error between the unit step responses of the original system and reduced model. The advantages of the new combined approximation method are that the reduced model is always stable provided the original model is stable and the initial and steady-state characteristics of the original model can be preserved in the reduced model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.2
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• pp.385-392
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• 1993

This paper presents a new stable composite control law for the flexible joint robot manipulators, which incorporate an additional stabilizing control law with the sliding property. The singularly perturbated models in this paper include inertia moments which are functions or the deformations of actuators as well as link positions. The values of renewedly defined fast controller variables are computer from the corrected reduced-order model without additional computational loads. Proposed schemes are compared with the conventional one. The simulations for 2 DOF flexible joint manipulator show that the proposed schemes are more stable than the conventional scheme, and especially effective for the manipulator with high joint-flexibilities.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.653-661
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• 2010

Let R be a ring, and let $\Psi$(R) be the ideal generated by the set {x $\in$R | 1 + sxt $\in$ R is unit-regular for all s, t $\in$ R}. We show that $\Psi$(R) has "radical-like" property. It is proven that $\Psi$(R) has stable range one. Thus, diagonal reduction of matrices over such ideal is reduced.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.266-271
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• 1992

This paper presents a new stable composite control law for the flexible joint robot manipulators, which incorporate the additional stabilizing control law with sliding property. The singularly perturbated models include inertia moments functions of the deformations of actuator. The newly defined fast controller variable is computed from the corrected reduced-order model without additional computational loads. The simulations for 2 DOF flexible joint manipulator show that the proposed schemes are more stable than conventional one, and especially effective for the manipulator with high joint-flexibilities.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.259-264
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• 1988

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.11
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• pp.2010-2016
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• 2007

PID control is windely used to control stable processes, However, its application to integrating processes is less common. In this paper, we proposed a stable PID controller tuning method for integrating processes with time delay using model reduction method. For proposed model reduction method, it disconnect an integrating factor from integrating processes and reduces separate process using reduction method. and it connect an integrating factor to reduced model. We can obtain stable integrating processes using P controller in inner feedback loop and PID tuning is then used to cancel the pole of the feedback loop. This guarantees both robustness and performance. Simulation examples are given to show the good performance of the proposed tuning method comparing with other methods.