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FUNDAMENTAL MATRICES OF THE VARIATIONAL SYSTEMS FOR THE NONLINEAR SYSTEMS WITH A SMALL PARAMETER
Koo, Nam Jip,Ryu, Hyun Sook 충청수학회 1996 충청수학회지 Vol.9 No.1
We show that $\frac{{\partial}x}{{\partial}{\gamma}}(t,{\tau},{\gamma},{\lambda},{\varepsilon})$ is a fundamental matrix of the variational system $\dot{y}=fx(t,x(t,{\tau},{\gamma},{\lambda},{\varepsilon}),{\lambda},{\varepsilon})y$ corresponding to the solution $x(t,{\tau},{\gamma},{\lambda},{\varepsilon})$ of $\dot{x}=f(t,x,{\lambda},{\varepsilon})$.
FUNDAMENTAL MATRICES OF THE VARIATIONAL SYSTEMS FOR THE NONLINEAR SYSTEMS WITH A SMALL PARAMETER
NAM JIP KOO,HYUN SOOK RYU 충청수학회 1996 충청수학회지 Vol.9 No.1
We show that ∂χ/∂γ(t, τ, γ, λ, ε) is a fundamental matrix of the variational system y = fx (t, x(t, τ, γ, λ, ε), λ, ε)y corresponding to the solution x(t, τ, γ, λ, ε) of x = f(t, x, λ, ε).
OSCILLATION OF NEUTRAL DIFFERENCE EQUATIONS
NAM JIP KOO 충청수학회 1999 충청수학회지 Vol.12 No.1
We obtain some sufficient conditions for oscillation of the neutral difference equation with positive and negative coefficients
OSCILLATION OF NEUTRAL DIFFERENCE EQUATIONS
Koo, Nam Jip 충청수학회 1999 충청수학회지 Vol.12 No.1
We obtain some sufficient conditions for oscillation of the neutral difference equation with positive and negative coefficients $${\Delta}(x_n-cx_{n-m})+px_{n-k}-qx_{n-l}=0$$, where ${\Delta}$ denotes the forward difference operator, m, k, l, are nonnegative integers, and $c{\in}[0,1),p,q{\in}\mathbb{R}^+$.
私立大學生의 成長發育 및 營養狀態에 關한 硏究 : 中學校 入試有無過程을 通한 比較
朴淳永,具燾書,朴良元,金振浩,南炳執,朴昌植,朴喆斌 慶熙大學校 1980 論文集 Vol.10 No.-
In order to ascertain any possible changes in the physical and the nutritional status of Korean high school students before and after the abolishment of college entrance examination system, an intensive survey was conducted on the physical conditions of the incoming freshmen students (9532 males and 3428 females) of Kyung Hee University from 1972 to 1980. The finding are as below. 1. Physical growth conditions In each of the average physical dimensions of body height, body weight, chest girth and sitting height, a remarkable improvement was recorded for all age groups after the matriculation was abolished. 2. Physical and nutritional indices Relative body weight showed constant values of 35.0 in male and 32.0 in female. Relative chest girth showed the normal chest girth style in all age groups of both sexes. Relative sitting height showed a constant value of 54 for both sexes. The values of vervaeck index of th nutritional status were shown to be between 86-87 in male and 83-94 in female, Pelidisi index 91 and 92-93, Rohrer index of physical status 121-125 and 130-132, and Kaup index 206-211 and 202-210, respectively.
ON A GRONWALL-TYPE INEQUALITY ON TIME SCALES
Sung Kyu Choi,Nam jip Koo 충청수학회 2010 충청수학회지 Vol.23 No.1
In this paper we extend a di??erential inequality pre-sented in Theorem 2.2 [6] to a dynamic inequality on time scales.
STABILITY IN VARIATION FOR NONLINEAR VOLTERRA DIFFERENCE SYSTEMS
Choi, Sung-Kyu,Koo, Nam-Jip Korean Mathematical Society 2001 대한수학회보 Vol.38 No.1
We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.
ON ASYMPTOTIC PROPERTY FOR NONLINEAR DIFFERENCE SYSTEMS
CHOI, UNG-KYU,KOO, NAM-JIP,IM, DONG-MAN Korean Mathematical Society 2005 대한수학회논문집 Vol.20 No.2
We study asymptotic equivalence between nonlinear difference system $$\Delta\chi(n)=f(n,\chi(n))$$ and its variational system $${\Delta}v(n)=f_{\chi}(n,0)v(n)$$.
h-STABILITY FOR NONLINEAR PERTURBED DIFFERENCE SYSTEMS
Choi, Sung-Kyu,Koo, Nam-Jip,Song, Se-Mok Korean Mathematical Society 2004 대한수학회보 Vol.41 No.3
We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of $n_{\infty}$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.