• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.209-225
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• 1998

In this paper we obtain sharp upper and lower bounds of small ball oprobabilities for Gaussian processes with stationary increments, whose results are essential to estabilish Chung type laws of iterated logarithm.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.649-657
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• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.37-44
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• 1980

우리는 먼저 Principal G-bundle와 성질을 살피고 representation of G over C를 irreducible CG-space의 direct sum으로 표시하여 Schur's Lemma를 이용하면 E가 임의의 CG-space, ${\sigma}E=Hom_c(E{\sigma},E)$라 할 때 ${\oplus}_{\sigma}(E_{\sigma}{\otimes}{\sigma}E){\rightarrow}E$ 가 G-ismorphism이 됨을 알아본다. 본 논문의 목적은 이러한 결과를 이용하여 K(X)와 $K_G(X)$의 관계를 구명하는데 있다.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.277-282
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• 1994

Convergence of the state error e to zero in adaptive systems is shown using the uniqueness of solutions and the existence of a Lyapunov function in which the adaptation laws are constructed. Results in the paper are general, and therefore applicable to any adaptive control of a linear/nonlinear, time-varying or distributed-parameter system. Since the approach taken in the paper does not require the boundedness of the derivative of the state error e for all t .geq. 0, it is particularly useful in the adaptive control of infinite dimensional systems.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.717-720
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• 1987

This paper presents a discrete-time model reference adaptive control technique for periodically time-varying plants. It is shown that the identification problem for periodic parameters can be reduced to that of constant unknown parameters case. The global stability of the resulting closed-loop system is established using the key technical lemma of Goodwin, Ramadge and Caines.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.44.3-44
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• 2002

Stability robustness of a linear time-varying system with time-varying structured state space uncertainties is considered by using extended-mean theorem and Bellman's lemma. The extended-mean theorem is a necessary and sufficient exponential stability criterion based on the recently developed PD-eigenvalue and PD-eigenvector for a linear time-varying system. Our new result required that the extended-mean of each nominal PD-eigenvalue should be negative real which is determined by a norm involving the structures of the uncertainty and the no...

• East Asian mathematical journal
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• v.32 no.3
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• pp.377-385
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• 2016

Global attractor is a basic concept to study the long-time behavior of solutions of the various equations. This paper is investigated with the existence of a global attractor for the beam equation $$u_{tt}+{\Delta}^2u-{\nabla}{\cdot}\{{\sigma}({\mid}{\nabla}u{\mid}^2){\nabla}u\}+f(u)+a(x)g(u_t)=h,$$ using multipliers technique and Nakao's Lemma.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.303-314
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• 2014

In this paper, a new lemma is established and several new inequalities for differentiable co-ordinated quasi-convex functions in two variables which are related to the left-hand side of Hermite-Hadamard type inequality for co-ordinated quasi-convex functions in two variables are obtained.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.103-117
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• 2011

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.515-531
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• 1997

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.