• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.341-348
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• 1994

Some extensions of the law of the iterated logarithm via self-normalization are obtained for seuences of sign-invariant random variables.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.53-63
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• 1993

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Journal of the Korean Data and Information Science Society
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• 제2권
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• pp.41-44
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• 1991

Petrov (1968) gave two theorems on the law of the iterated logarithm without any assumptions about the existence of moments of independent random variables. In the present paper we show that the same holds true for sign-invariant random variables.

• 제어로봇시스템학회논문지
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• 제2권2호
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• pp.67-72
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• 1996

This paper presents a parameter adaptive control law that stabilizes and asymptotically regulates any single-input, linear time-invariant, controllable and observable, discrete-time system when only the upper bounds on the order of the system is given. The algorithm presented in this paper comprises basically a nonlinear state feedback law which is represented by functions of the state vector in the controllable subspace of the model, an adaptive identifier of plant parameters which uses inputs and outputs of a certain length, and an adaptive law for feedback gain adjustment. A new psedu-inverse algorithm is used for the adaptive feedback gain adjustment rather than a least-square algorithm. The proposed feedback law results in not only uniform boundedness of the state vector to zero. The superiority of the proposed algorithm over other algorithms is shown through some examples.

• 충청수학회지
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• 제24권4호
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• 충청수학회지
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• 제23권4호
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 심포지엄 논문집 정보 및 제어부문
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• pp.122-124
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• 2005

In this paper, we propose a switching control method for 2nd order nonlinear systems. The main idea behind the method is changing the control law before the trajectory of the solution arrives at the singularities imposed on the denominator of the control law. We show that the control system is asymptotically stable from the fact that the sector consisting of the singular hyperplanes is an invariant set. Illustrative examples are given.

• 대한전자공학회논문지
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• 제26권8호
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• pp.1167-1177
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• 1989

In this paper, a generalized adaptive law is proposed which uses a rational function type operator for parameter adjustment. To satisfy the passivity condition of the adaptation block, we introduce a constant feedback gain into the adaptation block. This adaptation scheme is applied to the model reference adaptive control of a continuous-time, linear time-invariant, minimum-phase system whose relative degree is 1. We prove the asymptotic stability of the output error of this adaptive system by hyperstability method. It is shown that by digital computer simulations this law can give a better output error transient response in some cases than the conventional gradient adaptive law. And the output error responses for the several types of the proposed adaptation law are examined in the presence of a kind of unmodeled dynamics.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.801-806
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• 1987

The receding horizon tracking control for the discrete time invariant systems is presented in this paper. This control law is derived with the receding horizon concept from the standard tracking problems. Stability properties of this control law are analyzed. It is shown that there exists a finite horizon index for which the closed loop systems are always asymptotically stable. The receding horizon tracking control is a kind of predictive control and will add a new clan to many existing predictive controls, with which some comparisons are made.