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임동만 청주대학교 학술연구소 2014 淸大學術論集 Vol.22 No.-
N. Nobusawa[7]가 환보다 더욱 일반적인 감마환의 개념을 처음 소개한 이후로 최근까지 W.E. Barnes[1], J. Luh, W.E. Coppage[2], S. Kyuno[5,6] 등 많은 저자들에 의하여 감마환의 구조가 연구되었고, 최근까지 환의 많은 이론을 감마환으로 일반화하는 연구들이 꾸준히 이어지고 있다. 본 논문에서는 감마환의 좌측, 우측 작용소환, 감마환위의 감마가군의 개념과 감마가군의 부분가군, 감마가군의 동반가군 등을 소개하고, 이와 관련된 몇가지 기본적인 성질들을 연구하여 이들 사이의 관계를 규명하고 감마환과 감마가군의 구조적특성을 조사하였다. The notion of a gamma ring was introduced by N. Nobusawa in [7]. Recently, W.E. Barnes[1], J. Luh, W.E. Coppage[2], S. Kyuno[5,6] studied the structure of gamma rings and obtained various generalization analogous of corresponding parts in ring theory. In this paper we have introduced the notion of gamma modules over the gamma ring, and the notion of associated module of a gamma modules and studied some properties of left(right) operator ring of a gamma ring, gamma module and associated module of a gamma module. With the help of this we examine in detail the reation between the submodules of a gamma module and the submodules of its associated module.
UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS
Im, Dong Man,Goo, Yoon Hoe The Kangwon-Kyungki Mathematical Society 2016 한국수학논문집 Vol.24 No.1
This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.
BOUNDEDNESS IN FUNCTIONAL PERTURBED DIFFERENTIAL SYSTEMS
Dong Man Im,Yoon Hoe Goo 충청수학회 2015 충청수학회지 Vol.28 No.4
This paper shows that the solutions to the perturbed differential system y 0 = f (t, y) +∫t t0g(s, y(s))ds + h(t, y(t), T y(t)) have bounded property. To show this property, we impose conditions on the perturbed part ∫t t0 g(s, y(s))ds, h(t, y(t), T y(t)), and on the fundamental matrix of the unperturbed system y 0 = f (t, y).
ASYMPTOTIC PROPERTY FOR NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS
Im, Dong Man,Goo, Yoon Hoe Chungcheong Mathematical Society 2016 충청수학회지 Vol.29 No.1
This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).
BOUNDEDNESS IN THE PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS
Dong Man Im,Sang Il Choi,Yoon Hoe Goo 충청수학회 2014 충청수학회지 Vol.27 No.3
In this paper, we investigate bounds for solutions of the the perturbed functional di??erential systems.
PERTURBATIONS OF FUNCTIONAL DIFFERENTIAL SYSTEMS
Im, Dong Man Chungcheong Mathematical Society 2019 충청수학회지 Vol.32 No.2
We show the boundedness and uniform Lipschitz stability for the solutions to the functional perturbed differential system $$y^{\prime}=f(t,y)+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^t}g(s,y(s),\;T_1y(s))ds+h(t,y(t),\;T_2y(t))$$, under perturbations. We impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s)$, $T_1y(s))ds$, $h(t,y(t)$, $T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.
BOUNDEDNESS FOR NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t ∞ -SIMILARITY
Dong Man Im 충청수학회 2016 충청수학회지 Vol.29 No.4
This paper shows that the solutions to the nonlinear perturbed differential system y 0 = f (t, y) + ∫t t0g(s, y(s), T 1 y(s))ds + h(t, y(t), T 2 y(t)), have bounded properties. To show these properties, we impose con-ditions on the perturbed part ∫ t t0 g(s, y(s), T 1 y(s))ds, h(t, y(t), T 2 y(t)), and on the fundamental matrix of the unperturbed system y 0 =f (t, y) using the notion of h-stability.